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  return S;
1294 }
1295 
1296 // Get the limit of a recurrence such that incrementing by Step cannot cause
1297 // signed overflow as long as the value of the recurrence within the
1298 // loop does not exceed this limit before incrementing.
1299 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1300  ICmpInst::Predicate *Pred,
1301  ScalarEvolution *SE) {
1302  unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1303  if (SE->isKnownPositive(Step)) {
1304  *Pred = ICmpInst::ICMP_SLT;
1305  return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1306  SE->getSignedRangeMax(Step));
1307  }
1308  if (SE->isKnownNegative(Step)) {
1309  *Pred = ICmpInst::ICMP_SGT;
1310  return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1311  SE->getSignedRangeMin(Step));
1312  }
1313  return nullptr;
1314 }
1315 
1316 // Get the limit of a recurrence such that incrementing by Step cannot cause
1317 // unsigned overflow as long as the value of the recurrence within the loop does
1318 // not exceed this limit before incrementing.
1319 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1320  ICmpInst::Predicate *Pred,
1321  ScalarEvolution *SE) {
1322  unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1323  *Pred = ICmpInst::ICMP_ULT;
1324 
1325  return SE->getConstant(APInt::getMinValue(BitWidth) -
1326  SE->getUnsignedRangeMax(Step));
1327 }
1328 
1329 namespace {
1330 
1331 struct ExtendOpTraitsBase {
1332  typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
1333  unsigned);
1334 };
1335 
1336 // Used to make code generic over signed and unsigned overflow.
1337 template <typename ExtendOp> struct ExtendOpTraits {
1338  // Members present:
1339  //
1340  // static const SCEV::NoWrapFlags WrapType;
1341  //
1342  // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1343  //
1344  // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1345  // ICmpInst::Predicate *Pred,
1346  // ScalarEvolution *SE);
1347 };
1348 
1349 template <>
1350 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1351  static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1352 
1353  static const GetExtendExprTy GetExtendExpr;
1354 
1355  static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1356  ICmpInst::Predicate *Pred,
1357  ScalarEvolution *SE) {
1358  return getSignedOverflowLimitForStep(Step, Pred, SE);
1359  }
1360 };
1361 
1362 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1363  SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1364 
1365 template <>
1366 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1367  static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1368 
1369  static const GetExtendExprTy GetExtendExpr;
1370 
1371  static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1372  ICmpInst::Predicate *Pred,
1373  ScalarEvolution *SE) {
1374  return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1375  }
1376 };
1377 
1378 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1379  SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1380 
1381 } // end anonymous namespace
1382 
1383 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1384 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1385 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1386 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1387 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1388 // expression "Step + sext/zext(PreIncAR)" is congruent with
1389 // "sext/zext(PostIncAR)"
1390 template <typename ExtendOpTy>
1391 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1392  ScalarEvolution *SE, unsigned Depth) {
1393  auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1394  auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1395 
1396  const Loop *L = AR->getLoop();
1397  const SCEV *Start = AR->getStart();
1398  const SCEV *Step = AR->getStepRecurrence(*SE);
1399 
1400  // Check for a simple looking step prior to loop entry.
1401  const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1402  if (!SA)
1403  return nullptr;
1404 
1405  // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1406  // subtraction is expensive. For this purpose, perform a quick and dirty
1407  // difference, by checking for Step in the operand list.
1409  for (const SCEV *Op : SA->operands())
1410  if (Op != Step)
1411  DiffOps.push_back(Op);
1412 
1413  if (DiffOps.size() == SA->getNumOperands())
1414  return nullptr;
1415 
1416  // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1417  // `Step`:
1418 
1419  // 1. NSW/NUW flags on the step increment.
1420  auto PreStartFlags =
1422  const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1423  const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1424  SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1425 
1426  // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1427  // "S+X does not sign/unsign-overflow".
1428  //
1429 
1430  const SCEV *BECount = SE->getBackedgeTakenCount(L);
1431  if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1432  !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1433  return PreStart;
1434 
1435  // 2. Direct overflow check on the step operation's expression.
1436  unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1437  Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1438  const SCEV *OperandExtendedStart =
1439  SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
1440  (SE->*GetExtendExpr)(Step, WideTy, Depth));
1441  if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
1442  if (PreAR && AR->getNoWrapFlags(WrapType)) {
1443  // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1444  // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1445  // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1446  const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1447  }
1448  return PreStart;
1449  }
1450 
1451  // 3. Loop precondition.
1452  ICmpInst::Predicate Pred;
1453  const SCEV *OverflowLimit =
1454  ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1455 
1456  if (OverflowLimit &&
1457  SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1458  return PreStart;
1459 
1460  return nullptr;
1461 }
1462 
1463 // Get the normalized zero or sign extended expression for this AddRec's Start.
1464 template <typename ExtendOpTy>
1465 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1466  ScalarEvolution *SE,
1467  unsigned Depth) {
1468  auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1469 
1470  const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
1471  if (!PreStart)
1472  return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
1473 
1474  return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
1475  Depth),
1476  (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1477 }
1478 
1479 // Try to prove away overflow by looking at "nearby" add recurrences. A
1480 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1481 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1482 //
1483 // Formally:
1484 //
1485 // {S,+,X} == {S-T,+,X} + T
1486 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1487 //
1488 // If ({S-T,+,X} + T) does not overflow ... (1)
1489 //
1490 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1491 //
1492 // If {S-T,+,X} does not overflow ... (2)
1493 //
1494 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1495 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1496 //
1497 // If (S-T)+T does not overflow ... (3)
1498 //
1499 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1500 // == {Ext(S),+,Ext(X)} == LHS
1501 //
1502 // Thus, if (1), (2) and (3) are true for some T, then
1503 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1504 //
1505 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1506 // does not overflow" restricted to the 0th iteration. Therefore we only need
1507 // to check for (1) and (2).
1508 //
1509 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1510 // is `Delta` (defined below).
1511 template <typename ExtendOpTy>
1512 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1513  const SCEV *Step,
1514  const Loop *L) {
1515  auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1516 
1517  // We restrict `Start` to a constant to prevent SCEV from spending too much
1518  // time here. It is correct (but more expensive) to continue with a
1519  // non-constant `Start` and do a general SCEV subtraction to compute
1520  // `PreStart` below.
1521  const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1522  if (!StartC)
1523  return false;
1524 
1525  APInt StartAI = StartC->getAPInt();
1526 
1527  for (unsigned Delta : {-2, -1, 1, 2}) {
1528  const SCEV *PreStart = getConstant(StartAI - Delta);
1529 
1532  ID.AddPointer(PreStart);
1533  ID.AddPointer(Step);
1534  ID.AddPointer(L);
1535  void *IP = nullptr;
1536  const auto *PreAR =
1537  static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1538 
1539  // Give up if we don't already have the add recurrence we need because
1540  // actually constructing an add recurrence is relatively expensive.
1541  if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1542  const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1544  const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1545  DeltaS, &Pred, this);
1546  if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1547  return true;
1548  }
1549  }
1550 
1551  return false;
1552 }
1553 
1554 const SCEV *
1556  assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1557  "This is not an extending conversion!");
1558  assert(isSCEVable(Ty) &&
1559  "This is not a conversion to a SCEVable type!");
1560  Ty = getEffectiveSCEVType(Ty);
1561 
1562  // Fold if the operand is constant.
1563  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1564  return getConstant(
1565  cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1566 
1567  // zext(zext(x)) --> zext(x)
1568  if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1569  return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1570 
1571  // Before doing any expensive analysis, check to see if we've already
1572  // computed a SCEV for this Op and Ty.
1575  ID.AddPointer(Op);
1576  ID.AddPointer(Ty);
1577  void *IP = nullptr;
1578  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1579  if (Depth > MaxExtDepth) {
1580  SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1581  Op, Ty);
1582  UniqueSCEVs.InsertNode(S, IP);
1583  return S;
1584  }
1585 
1586  // zext(trunc(x)) --> zext(x) or x or trunc(x)
1587  if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1588  // It's possible the bits taken off by the truncate were all zero bits. If
1589  // so, we should be able to simplify this further.
1590  const SCEV *X = ST->getOperand();
1591  ConstantRange CR = getUnsignedRange(X);
1592  unsigned TruncBits = getTypeSizeInBits(ST->getType());
1593  unsigned NewBits = getTypeSizeInBits(Ty);
1594  if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1595  CR.zextOrTrunc(NewBits)))
1596  return getTruncateOrZeroExtend(X, Ty);
1597  }
1598 
1599  // If the input value is a chrec scev, and we can prove that the value
1600  // did not overflow the old, smaller, value, we can zero extend all of the
1601  // operands (often constants). This allows analysis of something like
1602  // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1603  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1604  if (AR->isAffine()) {
1605  const SCEV *Start = AR->getStart();
1606  const SCEV *Step = AR->getStepRecurrence(*this);
1607  unsigned BitWidth = getTypeSizeInBits(AR->getType());
1608  const Loop *L = AR->getLoop();
1609 
1610  if (!AR->hasNoUnsignedWrap()) {
1611  auto NewFlags = proveNoWrapViaConstantRanges(AR);
1612  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1613  }
1614 
1615  // If we have special knowledge that this addrec won't overflow,
1616  // we don't need to do any further analysis.
1617  if (AR->hasNoUnsignedWrap())
1618  return getAddRecExpr(
1619  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1620  getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1621 
1622  // Check whether the backedge-taken count is SCEVCouldNotCompute.
1623  // Note that this serves two purposes: It filters out loops that are
1624  // simply not analyzable, and it covers the case where this code is
1625  // being called from within backedge-taken count analysis, such that
1626  // attempting to ask for the backedge-taken count would likely result
1627  // in infinite recursion. In the later case, the analysis code will
1628  // cope with a conservative value, and it will take care to purge
1629  // that value once it has finished.
1630  const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1631  if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1632  // Manually compute the final value for AR, checking for
1633  // overflow.
1634 
1635  // Check whether the backedge-taken count can be losslessly casted to
1636  // the addrec's type. The count is always unsigned.
1637  const SCEV *CastedMaxBECount =
1638  getTruncateOrZeroExtend(MaxBECount, Start->getType());
1639  const SCEV *RecastedMaxBECount =
1640  getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1641  if (MaxBECount == RecastedMaxBECount) {
1642  Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1643  // Check whether Start+Step*MaxBECount has no unsigned overflow.
1644  const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
1645  SCEV::FlagAnyWrap, Depth + 1);
1646  const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
1648  Depth + 1),
1649  WideTy, Depth + 1);
1650  const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
1651  const SCEV *WideMaxBECount =
1652  getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1653  const SCEV *OperandExtendedAdd =
1654  getAddExpr(WideStart,
1655  getMulExpr(WideMaxBECount,
1656  getZeroExtendExpr(Step, WideTy, Depth + 1),
1657  SCEV::FlagAnyWrap, Depth + 1),
1658  SCEV::FlagAnyWrap, Depth + 1);
1659  if (ZAdd == OperandExtendedAdd) {
1660  // Cache knowledge of AR NUW, which is propagated to this AddRec.
1661  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1662  // Return the expression with the addrec on the outside.
1663  return getAddRecExpr(
1664  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1665  Depth + 1),
1666  getZeroExtendExpr(Step, Ty, Depth + 1), L,
1667  AR->getNoWrapFlags());
1668  }
1669  // Similar to above, only this time treat the step value as signed.
1670  // This covers loops that count down.
1671  OperandExtendedAdd =
1672  getAddExpr(WideStart,
1673  getMulExpr(WideMaxBECount,
1674  getSignExtendExpr(Step, WideTy, Depth + 1),
1675  SCEV::FlagAnyWrap, Depth + 1),
1676  SCEV::FlagAnyWrap, Depth + 1);
1677  if (ZAdd == OperandExtendedAdd) {
1678  // Cache knowledge of AR NW, which is propagated to this AddRec.
1679  // Negative step causes unsigned wrap, but it still can't self-wrap.
1680  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1681  // Return the expression with the addrec on the outside.
1682  return getAddRecExpr(
1683  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1684  Depth + 1),
1685  getSignExtendExpr(Step, Ty, Depth + 1), L,
1686  AR->getNoWrapFlags());
1687  }
1688  }
1689  }
1690 
1691  // Normally, in the cases we can prove no-overflow via a
1692  // backedge guarding condition, we can also compute a backedge
1693  // taken count for the loop. The exceptions are assumptions and
1694  // guards present in the loop -- SCEV is not great at exploiting
1695  // these to compute max backedge taken counts, but can still use
1696  // these to prove lack of overflow. Use this fact to avoid
1697  // doing extra work that may not pay off.
1698  if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1699  !AC.assumptions().empty()) {
1700  // If the backedge is guarded by a comparison with the pre-inc
1701  // value the addrec is safe. Also, if the entry is guarded by
1702  // a comparison with the start value and the backedge is
1703  // guarded by a comparison with the post-inc value, the addrec
1704  // is safe.
1705  if (isKnownPositive(Step)) {
1706  const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1707  getUnsignedRangeMax(Step));
1708  if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1709  (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1710  isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1711  AR->getPostIncExpr(*this), N))) {
1712  // Cache knowledge of AR NUW, which is propagated to this
1713  // AddRec.
1714  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1715  // Return the expression with the addrec on the outside.
1716  return getAddRecExpr(
1717  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1718  Depth + 1),
1719  getZeroExtendExpr(Step, Ty, Depth + 1), L,
1720  AR->getNoWrapFlags());
1721  }
1722  } else if (isKnownNegative(Step)) {
1723  const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1724  getSignedRangeMin(Step));
1725  if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1726  (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1727  isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1728  AR->getPostIncExpr(*this), N))) {
1729  // Cache knowledge of AR NW, which is propagated to this
1730  // AddRec. Negative step causes unsigned wrap, but it
1731  // still can't self-wrap.
1732  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1733  // Return the expression with the addrec on the outside.
1734  return getAddRecExpr(
1735  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1736  Depth + 1),
1737  getSignExtendExpr(Step, Ty, Depth + 1), L,
1738  AR->getNoWrapFlags());
1739  }
1740  }
1741  }
1742 
1743  if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1744  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1745  return getAddRecExpr(
1746  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1747  getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1748  }
1749  }
1750 
1751  if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1752  // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1753  if (SA->hasNoUnsignedWrap()) {
1754  // If the addition does not unsign overflow then we can, by definition,
1755  // commute the zero extension with the addition operation.
1757  for (const auto *Op : SA->operands())
1758  Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1759  return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
1760  }
1761  }
1762 
1763  // The cast wasn't folded; create an explicit cast node.
1764  // Recompute the insert position, as it may have been invalidated.
1765  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1766  SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1767  Op, Ty);
1768  UniqueSCEVs.InsertNode(S, IP);
1769  return S;
1770 }
1771 
1772 const SCEV *
1774  assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1775  "This is not an extending conversion!");
1776  assert(isSCEVable(Ty) &&
1777  "This is not a conversion to a SCEVable type!");
1778  Ty = getEffectiveSCEVType(Ty);
1779 
1780  // Fold if the operand is constant.
1781  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1782  return getConstant(
1783  cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1784 
1785  // sext(sext(x)) --> sext(x)
1786  if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1787  return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
1788 
1789  // sext(zext(x)) --> zext(x)
1790  if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1791  return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1792 
1793  // Before doing any expensive analysis, check to see if we've already
1794  // computed a SCEV for this Op and Ty.
1797  ID.AddPointer(Op);
1798  ID.AddPointer(Ty);
1799  void *IP = nullptr;
1800  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1801  // Limit recursion depth.
1802  if (Depth > MaxExtDepth) {
1803  SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1804  Op, Ty);
1805  UniqueSCEVs.InsertNode(S, IP);
1806  return S;
1807  }
1808 
1809  // sext(trunc(x)) --> sext(x) or x or trunc(x)
1810  if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1811  // It's possible the bits taken off by the truncate were all sign bits. If
1812  // so, we should be able to simplify this further.
1813  const SCEV *X = ST->getOperand();
1814  ConstantRange CR = getSignedRange(X);
1815  unsigned TruncBits = getTypeSizeInBits(ST->getType());
1816  unsigned NewBits = getTypeSizeInBits(Ty);
1817  if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1818  CR.sextOrTrunc(NewBits)))
1819  return getTruncateOrSignExtend(X, Ty);
1820  }
1821 
1822  // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1823  if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1824  if (SA->getNumOperands() == 2) {
1825  auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1826  auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1827  if (SMul && SC1) {
1828  if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1829  const APInt &C1 = SC1->getAPInt();
1830  const APInt &C2 = SC2->getAPInt();
1831  if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1832  C2.ugt(C1) && C2.isPowerOf2())
1833  return getAddExpr(getSignExtendExpr(SC1, Ty, Depth + 1),
1834  getSignExtendExpr(SMul, Ty, Depth + 1),
1835  SCEV::FlagAnyWrap, Depth + 1);
1836  }
1837  }
1838  }
1839 
1840  // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1841  if (SA->hasNoSignedWrap()) {
1842  // If the addition does not sign overflow then we can, by definition,
1843  // commute the sign extension with the addition operation.
1845  for (const auto *Op : SA->operands())
1846  Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
1847  return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
1848  }
1849  }
1850  // If the input value is a chrec scev, and we can prove that the value
1851  // did not overflow the old, smaller, value, we can sign extend all of the
1852  // operands (often constants). This allows analysis of something like
1853  // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1854  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1855  if (AR->isAffine()) {
1856  const SCEV *Start = AR->getStart();
1857  const SCEV *Step = AR->getStepRecurrence(*this);
1858  unsigned BitWidth = getTypeSizeInBits(AR->getType());
1859  const Loop *L = AR->getLoop();
1860 
1861  if (!AR->hasNoSignedWrap()) {
1862  auto NewFlags = proveNoWrapViaConstantRanges(AR);
1863  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1864  }
1865 
1866  // If we have special knowledge that this addrec won't overflow,
1867  // we don't need to do any further analysis.
1868  if (AR->hasNoSignedWrap())
1869  return getAddRecExpr(
1870  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1871  getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
1872 
1873  // Check whether the backedge-taken count is SCEVCouldNotCompute.
1874  // Note that this serves two purposes: It filters out loops that are
1875  // simply not analyzable, and it covers the case where this code is
1876  // being called from within backedge-taken count analysis, such that
1877  // attempting to ask for the backedge-taken count would likely result
1878  // in infinite recursion. In the later case, the analysis code will
1879  // cope with a conservative value, and it will take care to purge
1880  // that value once it has finished.
1881  const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1882  if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1883  // Manually compute the final value for AR, checking for
1884  // overflow.
1885 
1886  // Check whether the backedge-taken count can be losslessly casted to
1887  // the addrec's type. The count is always unsigned.
1888  const SCEV *CastedMaxBECount =
1889  getTruncateOrZeroExtend(MaxBECount, Start->getType());
1890  const SCEV *RecastedMaxBECount =
1891  getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1892  if (MaxBECount == RecastedMaxBECount) {
1893  Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1894  // Check whether Start+Step*MaxBECount has no signed overflow.
1895  const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
1896  SCEV::FlagAnyWrap, Depth + 1);
1897  const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
1899  Depth + 1),
1900  WideTy, Depth + 1);
1901  const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
1902  const SCEV *WideMaxBECount =
1903  getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1904  const SCEV *OperandExtendedAdd =
1905  getAddExpr(WideStart,
1906  getMulExpr(WideMaxBECount,
1907  getSignExtendExpr(Step, WideTy, Depth + 1),
1908  SCEV::FlagAnyWrap, Depth + 1),
1909  SCEV::FlagAnyWrap, Depth + 1);
1910  if (SAdd == OperandExtendedAdd) {
1911  // Cache knowledge of AR NSW, which is propagated to this AddRec.
1912  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1913  // Return the expression with the addrec on the outside.
1914  return getAddRecExpr(
1915  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
1916  Depth + 1),
1917  getSignExtendExpr(Step, Ty, Depth + 1), L,
1918  AR->getNoWrapFlags());
1919  }
1920  // Similar to above, only this time treat the step value as unsigned.
1921  // This covers loops that count up with an unsigned step.
1922  OperandExtendedAdd =
1923  getAddExpr(WideStart,
1924  getMulExpr(WideMaxBECount,
1925  getZeroExtendExpr(Step, WideTy, Depth + 1),
1926  SCEV::FlagAnyWrap, Depth + 1),
1927  SCEV::FlagAnyWrap, Depth + 1);
1928  if (SAdd == OperandExtendedAdd) {
1929  // If AR wraps around then
1930  //
1931  // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1932  // => SAdd != OperandExtendedAdd
1933  //
1934  // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1935  // (SAdd == OperandExtendedAdd => AR is NW)
1936 
1937  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1938 
1939  // Return the expression with the addrec on the outside.
1940  return getAddRecExpr(
1941  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
1942  Depth + 1),
1943  getZeroExtendExpr(Step, Ty, Depth + 1), L,
1944  AR->getNoWrapFlags());
1945  }
1946  }
1947  }
1948 
1949  // Normally, in the cases we can prove no-overflow via a
1950  // backedge guarding condition, we can also compute a backedge
1951  // taken count for the loop. The exceptions are assumptions and
1952  // guards present in the loop -- SCEV is not great at exploiting
1953  // these to compute max backedge taken counts, but can still use
1954  // these to prove lack of overflow. Use this fact to avoid
1955  // doing extra work that may not pay off.
1956 
1957  if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1958  !AC.assumptions().empty()) {
1959  // If the backedge is guarded by a comparison with the pre-inc
1960  // value the addrec is safe. Also, if the entry is guarded by
1961  // a comparison with the start value and the backedge is
1962  // guarded by a comparison with the post-inc value, the addrec
1963  // is safe.
1964  ICmpInst::Predicate Pred;
1965  const SCEV *OverflowLimit =
1966  getSignedOverflowLimitForStep(Step, &Pred, this);
1967  if (OverflowLimit &&
1968  (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1969  (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1970  isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1971  OverflowLimit)))) {
1972  // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1973  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1974  return getAddRecExpr(
1975  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1976  getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1977  }
1978  }
1979 
1980  // If Start and Step are constants, check if we can apply this
1981  // transformation:
1982  // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1983  auto *SC1 = dyn_cast<SCEVConstant>(Start);
1984  auto *SC2 = dyn_cast<SCEVConstant>(Step);
1985  if (SC1 && SC2) {
1986  const APInt &C1 = SC1->getAPInt();
1987  const APInt &C2 = SC2->getAPInt();
1988  if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1989  C2.isPowerOf2()) {
1990  Start = getSignExtendExpr(Start, Ty, Depth + 1);
1991  const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1992  AR->getNoWrapFlags());
1993  return getAddExpr(Start, getSignExtendExpr(NewAR, Ty, Depth + 1),
1994  SCEV::FlagAnyWrap, Depth + 1);
1995  }
1996  }
1997 
1998  if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1999  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2000  return getAddRecExpr(
2001  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2002  getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2003  }
2004  }
2005 
2006  // If the input value is provably positive and we could not simplify
2007  // away the sext build a zext instead.
2008  if (isKnownNonNegative(Op))
2009  return getZeroExtendExpr(Op, Ty, Depth + 1);
2010 
2011  // The cast wasn't folded; create an explicit cast node.
2012  // Recompute the insert position, as it may have been invalidated.
2013  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2014  SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
2015  Op, Ty);
2016  UniqueSCEVs.InsertNode(S, IP);
2017  return S;
2018 }
2019 
2020 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
2021 /// unspecified bits out to the given type.
2023  Type *Ty) {
2024  assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
2025  "This is not an extending conversion!");
2026  assert(isSCEVable(Ty) &&
2027  "This is not a conversion to a SCEVable type!");
2028  Ty = getEffectiveSCEVType(Ty);
2029 
2030  // Sign-extend negative constants.
2031  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
2032  if (SC->getAPInt().isNegative())
2033  return getSignExtendExpr(Op, Ty);
2034 
2035  // Peel off a truncate cast.
2036  if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
2037  const SCEV *NewOp = T->getOperand();
2038  if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
2039  return getAnyExtendExpr(NewOp, Ty);
2040  return getTruncateOrNoop(NewOp, Ty);
2041  }
2042 
2043  // Next try a zext cast. If the cast is folded, use it.
2044  const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
2045  if (!isa<SCEVZeroExtendExpr>(ZExt))
2046  return ZExt;
2047 
2048  // Next try a sext cast. If the cast is folded, use it.
2049  const SCEV *SExt = getSignExtendExpr(Op, Ty);
2050  if (!isa<SCEVSignExtendExpr>(SExt))
2051  return SExt;
2052 
2053  // Force the cast to be folded into the operands of an addrec.
2054  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
2056  for (const SCEV *Op : AR->operands())
2057  Ops.push_back(getAnyExtendExpr(Op, Ty));
2058  return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
2059  }
2060 
2061  // If the expression is obviously signed, use the sext cast value.
2062  if (isa<SCEVSMaxExpr>(Op))
2063  return SExt;
2064 
2065  // Absent any other information, use the zext cast value.
2066  return ZExt;
2067 }
2068 
2069 /// Process the given Ops list, which is a list of operands to be added under
2070 /// the given scale, update the given map. This is a helper function for
2071 /// getAddRecExpr. As an example of what it does, given a sequence of operands
2072 /// that would form an add expression like this:
2073 ///
2074 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2075 ///
2076 /// where A and B are constants, update the map with these values:
2077 ///
2078 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2079 ///
2080 /// and add 13 + A*B*29 to AccumulatedConstant.
2081 /// This will allow getAddRecExpr to produce this:
2082 ///
2083 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2084 ///
2085 /// This form often exposes folding opportunities that are hidden in
2086 /// the original operand list.
2087 ///
2088 /// Return true iff it appears that any interesting folding opportunities
2089 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
2090 /// the common case where no interesting opportunities are present, and
2091 /// is also used as a check to avoid infinite recursion.
2092 static bool
2095  APInt &AccumulatedConstant,
2096  const SCEV *const *Ops, size_t NumOperands,
2097  const APInt &Scale,
2098  ScalarEvolution &SE) {
2099  bool Interesting = false;
2100 
2101  // Iterate over the add operands. They are sorted, with constants first.
2102  unsigned i = 0;
2103  while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2104  ++i;
2105  // Pull a buried constant out to the outside.
2106  if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
2107  Interesting = true;
2108  AccumulatedConstant += Scale * C->getAPInt();
2109  }
2110 
2111  // Next comes everything else. We're especially interested in multiplies
2112  // here, but they're in the middle, so just visit the rest with one loop.
2113  for (; i != NumOperands; ++i) {
2114  const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
2115  if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
2116  APInt NewScale =
2117  Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
2118  if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
2119  // A multiplication of a constant with another add; recurse.
2120  const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2121  Interesting |=
2122  CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2123  Add->op_begin(), Add->getNumOperands(),
2124  NewScale, SE);
2125  } else {
2126  // A multiplication of a constant with some other value. Update
2127  // the map.
2128  SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
2129  const SCEV *Key = SE.getMulExpr(MulOps);
2130  auto Pair = M.insert({Key, NewScale});
2131  if (Pair.second) {
2132  NewOps.push_back(Pair.first->first);
2133  } else {
2134  Pair.first->second += NewScale;
2135  // The map already had an entry for this value, which may indicate
2136  // a folding opportunity.
2137  Interesting = true;
2138  }
2139  }
2140  } else {
2141  // An ordinary operand. Update the map.
2142  std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2143  M.insert({Ops[i], Scale});
2144  if (Pair.second) {
2145  NewOps.push_back(Pair.first->first);
2146  } else {
2147  Pair.first->second += Scale;
2148  // The map already had an entry for this value, which may indicate
2149  // a folding opportunity.
2150  Interesting = true;
2151  }
2152  }
2153  }
2154 
2155  return Interesting;
2156 }
2157 
2158 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2159 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2160 // can't-overflow flags for the operation if possible.
2161 static SCEV::NoWrapFlags
2163  const SmallVectorImpl<const SCEV *> &Ops,
2165  using namespace std::placeholders;
2166 
2167  using OBO = OverflowingBinaryOperator;
2168 
2169  bool CanAnalyze =
2170  Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2171  (void)CanAnalyze;
2172  assert(CanAnalyze && "don't call from other places!");
2173 
2174  int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2175  SCEV::NoWrapFlags SignOrUnsignWrap =
2176  ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2177 
2178  // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2179  auto IsKnownNonNegative = [&](const SCEV *S) {
2180  return SE->isKnownNonNegative(S);
2181  };
2182 
2183  if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2184  Flags =
2185  ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2186 
2187  SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2188 
2189  if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
2190  Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
2191 
2192  // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
2193  // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
2194 
2195  const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2196  if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2198  Instruction::Add, C, OBO::NoSignedWrap);
2199  if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2200  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2201  }
2202  if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2204  Instruction::Add, C, OBO::NoUnsignedWrap);
2205  if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2206  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2207  }
2208  }
2209 
2210  return Flags;
2211 }
2212 
2214  if (!isLoopInvariant(S, L))
2215  return false;
2216  // If a value depends on a SCEVUnknown which is defined after the loop, we
2217  // conservatively assume that we cannot calculate it at the loop's entry.
2218  struct FindDominatedSCEVUnknown {
2219  bool Found = false;
2220  const Loop *L;
2221  DominatorTree &DT;
2222  LoopInfo &LI;
2223 
2224  FindDominatedSCEVUnknown(const Loop *L, DominatorTree &DT, LoopInfo &LI)
2225  : L(L), DT(DT), LI(LI) {}
2226 
2227  bool checkSCEVUnknown(const SCEVUnknown *SU) {
2228  if (auto *I = dyn_cast<Instruction>(SU->getValue())) {
2229  if (DT.dominates(L->getHeader(), I->getParent()))
2230  Found = true;
2231  else
2232  assert(DT.dominates(I->getParent(), L->getHeader()) &&
2233  "No dominance relationship between SCEV and loop?");
2234  }
2235  return false;
2236  }
2237 
2238  bool follow(const SCEV *S) {
2239  switch (static_cast<SCEVTypes>(S->getSCEVType())) {
2240  case scConstant:
2241  return false;
2242  case scAddRecExpr:
2243  case scTruncate:
2244  case scZeroExtend:
2245  case scSignExtend:
2246  case scAddExpr:
2247  case scMulExpr:
2248  case scUMaxExpr:
2249  case scSMaxExpr:
2250  case scUDivExpr:
2251  return true;
2252  case scUnknown:
2253  return checkSCEVUnknown(cast<SCEVUnknown>(S));
2254  case scCouldNotCompute:
2255  llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
2256  }
2257  return false;
2258  }
2259 
2260  bool isDone() { return Found; }
2261  };
2262 
2263  FindDominatedSCEVUnknown FSU(L, DT, LI);
2265  ST.visitAll(S);
2266  return !FSU.Found;
2267 }
2268 
2269 /// Get a canonical add expression, or something simpler if possible.
2272  unsigned Depth) {
2273  assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2274  "only nuw or nsw allowed");
2275  assert(!Ops.empty() && "Cannot get empty add!");
2276  if (Ops.size() == 1) return Ops[0];
2277 #ifndef NDEBUG
2278  Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2279  for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2280  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2281  "SCEVAddExpr operand types don't match!");
2282 #endif
2283 
2284  // Sort by complexity, this groups all similar expression types together.
2285  GroupByComplexity(Ops, &LI, DT);
2286 
2287  Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2288 
2289  // If there are any constants, fold them together.
2290  unsigned Idx = 0;
2291  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2292  ++Idx;
2293  assert(Idx < Ops.size());
2294  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2295  // We found two constants, fold them together!
2296  Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2297  if (Ops.size() == 2) return Ops[0];
2298  Ops.erase(Ops.begin()+1); // Erase the folded element
2299  LHSC = cast<SCEVConstant>(Ops[0]);
2300  }
2301 
2302  // If we are left with a constant zero being added, strip it off.
2303  if (LHSC->getValue()->isZero()) {
2304  Ops.erase(Ops.begin());
2305  --Idx;
2306  }
2307 
2308  if (Ops.size() == 1) return Ops[0];
2309  }
2310 
2311  // Limit recursion calls depth.
2312  if (Depth > MaxArithDepth)
2313  return getOrCreateAddExpr(Ops, Flags);
2314 
2315  // Okay, check to see if the same value occurs in the operand list more than
2316  // once. If so, merge them together into an multiply expression. Since we
2317  // sorted the list, these values are required to be adjacent.
2318  Type *Ty = Ops[0]->getType();
2319  bool FoundMatch = false;
2320  for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2321  if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2322  // Scan ahead to count how many equal operands there are.
2323  unsigned Count = 2;
2324  while (i+Count != e && Ops[i+Count] == Ops[i])
2325  ++Count;
2326  // Merge the values into a multiply.
2327  const SCEV *Scale = getConstant(Ty, Count);
2328  const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
2329  if (Ops.size() == Count)
2330  return Mul;
2331  Ops[i] = Mul;
2332  Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2333  --i; e -= Count - 1;
2334  FoundMatch = true;
2335  }
2336  if (FoundMatch)
2337  return getAddExpr(Ops, Flags);
2338 
2339  // Check for truncates. If all the operands are truncated from the same
2340  // type, see if factoring out the truncate would permit the result to be
2341  // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
2342  // if the contents of the resulting outer trunc fold to something simple.
2343  auto FindTruncSrcType = [&]() -> Type * {
2344  // We're ultimately looking to fold an addrec of truncs and muls of only
2345  // constants and truncs, so if we find any other types of SCEV
2346  // as operands of the addrec then we bail and return nullptr here.
2347  // Otherwise, we return the type of the operand of a trunc that we find.
2348  if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
2349  return T->getOperand()->getType();
2350  if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2351  const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
2352  if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
2353  return T->getOperand()->getType();
2354  }
2355  return nullptr;
2356  };
2357  if (auto *SrcType = FindTruncSrcType()) {
2359  bool Ok = true;
2360  // Check all the operands to see if they can be represented in the
2361  // source type of the truncate.
2362  for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2363  if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2364  if (T->getOperand()->getType() != SrcType) {
2365  Ok = false;
2366  break;
2367  }
2368  LargeOps.push_back(T->getOperand());
2369  } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2370  LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2371  } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2372  SmallVector<const SCEV *, 8> LargeMulOps;
2373  for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2374  if (const SCEVTruncateExpr *T =
2375  dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2376  if (T->getOperand()->getType() != SrcType) {
2377  Ok = false;
2378  break;
2379  }
2380  LargeMulOps.push_back(T->getOperand());
2381  } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2382  LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2383  } else {
2384  Ok = false;
2385  break;
2386  }
2387  }
2388  if (Ok)
2389  LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
2390  } else {
2391  Ok = false;
2392  break;
2393  }
2394  }
2395  if (Ok) {
2396  // Evaluate the expression in the larger type.
2397  const SCEV *Fold = getAddExpr(LargeOps, Flags, Depth + 1);
2398  // If it folds to something simple, use it. Otherwise, don't.
2399  if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2400  return getTruncateExpr(Fold, Ty);
2401  }
2402  }
2403 
2404  // Skip past any other cast SCEVs.
2405  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2406  ++Idx;
2407 
2408  // If there are add operands they would be next.
2409  if (Idx < Ops.size()) {
2410  bool DeletedAdd = false;
2411  while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2412  if (Ops.size() > AddOpsInlineThreshold ||
2413  Add->getNumOperands() > AddOpsInlineThreshold)
2414  break;
2415  // If we have an add, expand the add operands onto the end of the operands
2416  // list.
2417  Ops.erase(Ops.begin()+Idx);
2418  Ops.append(Add->op_begin(), Add->op_end());
2419  DeletedAdd = true;
2420  }
2421 
2422  // If we deleted at least one add, we added operands to the end of the list,
2423  // and they are not necessarily sorted. Recurse to resort and resimplify
2424  // any operands we just acquired.
2425  if (DeletedAdd)
2426  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2427  }
2428 
2429  // Skip over the add expression until we get to a multiply.
2430  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2431  ++Idx;
2432 
2433  // Check to see if there are any folding opportunities present with
2434  // operands multiplied by constant values.
2435  if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2436  uint64_t BitWidth = getTypeSizeInBits(Ty);
2439  APInt AccumulatedConstant(BitWidth, 0);
2440  if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2441  Ops.data(), Ops.size(),
2442  APInt(BitWidth, 1), *this)) {
2443  struct APIntCompare {
2444  bool operator()(const APInt &LHS, const APInt &RHS) const {
2445  return LHS.ult(RHS);
2446  }
2447  };
2448 
2449  // Some interesting folding opportunity is present, so its worthwhile to
2450  // re-generate the operands list. Group the operands by constant scale,
2451  // to avoid multiplying by the same constant scale multiple times.
2452  std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2453  for (const SCEV *NewOp : NewOps)
2454  MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2455  // Re-generate the operands list.
2456  Ops.clear();
2457  if (AccumulatedConstant != 0)
2458  Ops.push_back(getConstant(AccumulatedConstant));
2459  for (auto &MulOp : MulOpLists)
2460  if (MulOp.first != 0)
2461  Ops.push_back(getMulExpr(
2462  getConstant(MulOp.first),
2463  getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
2464  SCEV::FlagAnyWrap, Depth + 1));
2465  if (Ops.empty())
2466  return getZero(Ty);
2467  if (Ops.size() == 1)
2468  return Ops[0];
2469  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2470  }
2471  }
2472 
2473  // If we are adding something to a multiply expression, make sure the
2474  // something is not already an operand of the multiply. If so, merge it into
2475  // the multiply.
2476  for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2477  const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2478  for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2479  const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2480  if (isa<SCEVConstant>(MulOpSCEV))
2481  continue;
2482  for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2483  if (MulOpSCEV == Ops[AddOp]) {
2484  // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2485  const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2486  if (Mul->getNumOperands() != 2) {
2487  // If the multiply has more than two operands, we must get the
2488  // Y*Z term.
2489  SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2490  Mul->op_begin()+MulOp);
2491  MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2492  InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2493  }
2494  SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
2495  const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2496  const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
2497  SCEV::FlagAnyWrap, Depth + 1);
2498  if (Ops.size() == 2) return OuterMul;
2499  if (AddOp < Idx) {
2500  Ops.erase(Ops.begin()+AddOp);
2501  Ops.erase(Ops.begin()+Idx-1);
2502  } else {
2503  Ops.erase(Ops.begin()+Idx);
2504  Ops.erase(Ops.begin()+AddOp-1);
2505  }
2506  Ops.push_back(OuterMul);
2507  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2508  }
2509 
2510  // Check this multiply against other multiplies being added together.
2511  for (unsigned OtherMulIdx = Idx+1;
2512  OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2513  ++OtherMulIdx) {
2514  const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2515  // If MulOp occurs in OtherMul, we can fold the two multiplies
2516  // together.
2517  for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2518  OMulOp != e; ++OMulOp)
2519  if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2520  // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2521  const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2522  if (Mul->getNumOperands() != 2) {
2523  SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2524  Mul->op_begin()+MulOp);
2525  MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2526  InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2527  }
2528  const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2529  if (OtherMul->getNumOperands() != 2) {
2530  SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2531  OtherMul->op_begin()+OMulOp);
2532  MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2533  InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2534  }
2535  SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
2536  const SCEV *InnerMulSum =
2537  getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2538  const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
2539  SCEV::FlagAnyWrap, Depth + 1);
2540  if (Ops.size() == 2) return OuterMul;
2541  Ops.erase(Ops.begin()+Idx);
2542  Ops.erase(Ops.begin()+OtherMulIdx-1);
2543  Ops.push_back(OuterMul);
2544  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2545  }
2546  }
2547  }
2548  }
2549 
2550  // If there are any add recurrences in the operands list, see if any other
2551  // added values are loop invariant. If so, we can fold them into the
2552  // recurrence.
2553  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2554  ++Idx;
2555 
2556  // Scan over all recurrences, trying to fold loop invariants into them.
2557  for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2558  // Scan all of the other operands to this add and add them to the vector if
2559  // they are loop invariant w.r.t. the recurrence.
2561  const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2562  const Loop *AddRecLoop = AddRec->getLoop();
2563  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2564  if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2565  LIOps.push_back(Ops[i]);
2566  Ops.erase(Ops.begin()+i);
2567  --i; --e;
2568  }
2569 
2570  // If we found some loop invariants, fold them into the recurrence.
2571  if (!LIOps.empty()) {
2572  // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2573  LIOps.push_back(AddRec->getStart());
2574 
2575  SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2576  AddRec->op_end());
2577  // This follows from the fact that the no-wrap flags on the outer add
2578  // expression are applicable on the 0th iteration, when the add recurrence
2579  // will be equal to its start value.
2580  AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
2581 
2582  // Build the new addrec. Propagate the NUW and NSW flags if both the
2583  // outer add and the inner addrec are guaranteed to have no overflow.
2584  // Always propagate NW.
2585  Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2586  const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2587 
2588  // If all of the other operands were loop invariant, we are done.
2589  if (Ops.size() == 1) return NewRec;
2590 
2591  // Otherwise, add the folded AddRec by the non-invariant parts.
2592  for (unsigned i = 0;; ++i)
2593  if (Ops[i] == AddRec) {
2594  Ops[i] = NewRec;
2595  break;
2596  }
2597  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2598  }
2599 
2600  // Okay, if there weren't any loop invariants to be folded, check to see if
2601  // there are multiple AddRec's with the same loop induction variable being
2602  // added together. If so, we can fold them.
2603  for (unsigned OtherIdx = Idx+1;
2604  OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2605  ++OtherIdx) {
2606  // We expect the AddRecExpr's to be sorted in reverse dominance order,
2607  // so that the 1st found AddRecExpr is dominated by all others.
2608  assert(DT.dominates(
2609  cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
2610  AddRec->getLoop()->getHeader()) &&
2611  "AddRecExprs are not sorted in reverse dominance order?");
2612  if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2613  // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2614  SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2615  AddRec->op_end());
2616  for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2617  ++OtherIdx) {
2618  const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2619  if (OtherAddRec->getLoop() == AddRecLoop) {
2620  for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2621  i != e; ++i) {
2622  if (i >= AddRecOps.size()) {
2623  AddRecOps.append(OtherAddRec->op_begin()+i,
2624  OtherAddRec->op_end());
2625  break;
2626  }
2627  SmallVector<const SCEV *, 2> TwoOps = {
2628  AddRecOps[i], OtherAddRec->getOperand(i)};
2629  AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2630  }
2631  Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2632  }
2633  }
2634  // Step size has changed, so we cannot guarantee no self-wraparound.
2635  Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2636  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2637  }
2638  }
2639 
2640  // Otherwise couldn't fold anything into this recurrence. Move onto the
2641  // next one.
2642  }
2643 
2644  // Okay, it looks like we really DO need an add expr. Check to see if we
2645  // already have one, otherwise create a new one.
2646  return getOrCreateAddExpr(Ops, Flags);
2647 }
2648 
2649 const SCEV *
2650 ScalarEvolution::getOrCreateAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2653  ID.AddInteger(scAddExpr);
2654  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2655  ID.AddPointer(Ops[i]);
2656  void *IP = nullptr;
2657  SCEVAddExpr *S =
2658  static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2659  if (!S) {
2660  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2661  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2662  S = new (SCEVAllocator)
2663  SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
2664  UniqueSCEVs.InsertNode(S, IP);
2665  }
2666  S->setNoWrapFlags(Flags);
2667  return S;
2668 }
2669 
2670 const SCEV *
2671 ScalarEvolution::getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2672  SCEV::NoWrapFlags Flags) {
2674  ID.AddInteger(scMulExpr);
2675  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2676  ID.AddPointer(Ops[i]);
2677  void *IP = nullptr;
2678  SCEVMulExpr *S =
2679  static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2680  if (!S) {
2681  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2682  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2683  S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2684  O, Ops.size());
2685  UniqueSCEVs.InsertNode(S, IP);
2686  }
2687  S->setNoWrapFlags(Flags);
2688  return S;
2689 }
2690 
2691 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2692  uint64_t k = i*j;
2693  if (j > 1 && k / j != i) Overflow = true;
2694  return k;
2695 }
2696 
2697 /// Compute the result of "n choose k", the binomial coefficient. If an
2698 /// intermediate computation overflows, Overflow will be set and the return will
2699 /// be garbage. Overflow is not cleared on absence of overflow.
2700 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2701  // We use the multiplicative formula:
2702  // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2703  // At each iteration, we take the n-th term of the numeral and divide by the
2704  // (k-n)th term of the denominator. This division will always produce an
2705  // integral result, and helps reduce the chance of overflow in the
2706  // intermediate computations. However, we can still overflow even when the
2707  // final result would fit.
2708 
2709  if (n == 0 || n == k) return 1;
2710  if (k > n) return 0;
2711 
2712  if (k > n/2)
2713  k = n-k;
2714 
2715  uint64_t r = 1;
2716  for (uint64_t i = 1; i <= k; ++i) {
2717  r = umul_ov(r, n-(i-1), Overflow);
2718  r /= i;
2719  }
2720  return r;
2721 }
2722 
2723 /// Determine if any of the operands in this SCEV are a constant or if
2724 /// any of the add or multiply expressions in this SCEV contain a constant.
2725 static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
2726  struct FindConstantInAddMulChain {
2727  bool FoundConstant = false;
2728 
2729  bool follow(const SCEV *S) {
2730  FoundConstant |= isa<SCEVConstant>(S);
2731  return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
2732  }
2733 
2734  bool isDone() const {
2735  return FoundConstant;
2736  }
2737  };
2738 
2739  FindConstantInAddMulChain F;
2741  ST.visitAll(StartExpr);
2742  return F.FoundConstant;
2743 }
2744 
2745 /// Get a canonical multiply expression, or something simpler if possible.
2747  SCEV::NoWrapFlags Flags,
2748  unsigned Depth) {
2749  assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2750  "only nuw or nsw allowed");
2751  assert(!Ops.empty() && "Cannot get empty mul!");
2752  if (Ops.size() == 1) return Ops[0];
2753 #ifndef NDEBUG
2754  Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2755  for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2756  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2757  "SCEVMulExpr operand types don't match!");
2758 #endif
2759 
2760  // Sort by complexity, this groups all similar expression types together.
2761  GroupByComplexity(Ops, &LI, DT);
2762 
2763  Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2764 
2765  // Limit recursion calls depth.
2766  if (Depth > MaxArithDepth)
2767  return getOrCreateMulExpr(Ops, Flags);
2768 
2769  // If there are any constants, fold them together.
2770  unsigned Idx = 0;
2771  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2772 
2773  // C1*(C2+V) -> C1*C2 + C1*V
2774  if (Ops.size() == 2)
2775  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2776  // If any of Add's ops are Adds or Muls with a constant,
2777  // apply this transformation as well.
2778  if (Add->getNumOperands() == 2)
2779  // TODO: There are some cases where this transformation is not
2780  // profitable, for example:
2781  // Add = (C0 + X) * Y + Z.
2782  // Maybe the scope of this transformation should be narrowed down.
2784  return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
2785  SCEV::FlagAnyWrap, Depth + 1),
2786  getMulExpr(LHSC, Add->getOperand(1),
2787  SCEV::FlagAnyWrap, Depth + 1),
2788  SCEV::FlagAnyWrap, Depth + 1);
2789 
2790  ++Idx;
2791  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2792  // We found two constants, fold them together!
2793  ConstantInt *Fold =
2794  ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2795  Ops[0] = getConstant(Fold);
2796  Ops.erase(Ops.begin()+1); // Erase the folded element
2797  if (Ops.size() == 1) return Ops[0];
2798  LHSC = cast<SCEVConstant>(Ops[0]);
2799  }
2800 
2801  // If we are left with a constant one being multiplied, strip it off.
2802  if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
2803  Ops.erase(Ops.begin());
2804  --Idx;
2805  } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2806  // If we have a multiply of zero, it will always be zero.
2807  return Ops[0];
2808  } else if (Ops[0]->isAllOnesValue()) {
2809  // If we have a mul by -1 of an add, try distributing the -1 among the
2810  // add operands.
2811  if (Ops.size() == 2) {
2812  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2814  bool AnyFolded = false;
2815  for (const SCEV *AddOp : Add->operands()) {
2816  const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
2817  Depth + 1);
2818  if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2819  NewOps.push_back(Mul);
2820  }
2821  if (AnyFolded)
2822  return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
2823  } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2824  // Negation preserves a recurrence's no self-wrap property.
2826  for (const SCEV *AddRecOp : AddRec->operands())
2827  Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
2828  Depth + 1));
2829 
2830  return getAddRecExpr(Operands, AddRec->getLoop(),
2831  AddRec->getNoWrapFlags(SCEV::FlagNW));
2832  }
2833  }
2834  }
2835 
2836  if (Ops.size() == 1)
2837  return Ops[0];
2838  }
2839 
2840  // Skip over the add expression until we get to a multiply.
2841  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2842  ++Idx;
2843 
2844  // If there are mul operands inline them all into this expression.
2845  if (Idx < Ops.size()) {
2846  bool DeletedMul = false;
2847  while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2848  if (Ops.size() > MulOpsInlineThreshold)
2849  break;
2850  // If we have an mul, expand the mul operands onto the end of the
2851  // operands list.
2852  Ops.erase(Ops.begin()+Idx);
2853  Ops.append(Mul->op_begin(), Mul->op_end());
2854  DeletedMul = true;
2855  }
2856 
2857  // If we deleted at least one mul, we added operands to the end of the
2858  // list, and they are not necessarily sorted. Recurse to resort and
2859  // resimplify any operands we just acquired.
2860  if (DeletedMul)
2861  return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2862  }
2863 
2864  // If there are any add recurrences in the operands list, see if any other
2865  // added values are loop invariant. If so, we can fold them into the
2866  // recurrence.
2867  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2868  ++Idx;
2869 
2870  // Scan over all recurrences, trying to fold loop invariants into them.
2871  for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2872  // Scan all of the other operands to this mul and add them to the vector
2873  // if they are loop invariant w.r.t. the recurrence.
2875  const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2876  const Loop *AddRecLoop = AddRec->getLoop();
2877  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2878  if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2879  LIOps.push_back(Ops[i]);
2880  Ops.erase(Ops.begin()+i);
2881  --i; --e;
2882  }
2883 
2884  // If we found some loop invariants, fold them into the recurrence.
2885  if (!LIOps.empty()) {
2886  // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2888  NewOps.reserve(AddRec->getNumOperands());
2889  const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
2890  for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2891  NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
2892  SCEV::FlagAnyWrap, Depth + 1));
2893 
2894  // Build the new addrec. Propagate the NUW and NSW flags if both the
2895  // outer mul and the inner addrec are guaranteed to have no overflow.
2896  //
2897  // No self-wrap cannot be guaranteed after changing the step size, but
2898  // will be inferred if either NUW or NSW is true.
2899  Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2900  const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2901 
2902  // If all of the other operands were loop invariant, we are done.
2903  if (Ops.size() == 1) return NewRec;
2904 
2905  // Otherwise, multiply the folded AddRec by the non-invariant parts.
2906  for (unsigned i = 0;; ++i)
2907  if (Ops[i] == AddRec) {
2908  Ops[i] = NewRec;
2909  break;
2910  }
2911  return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2912  }
2913 
2914  // Okay, if there weren't any loop invariants to be folded, check to see
2915  // if there are multiple AddRec's with the same loop induction variable
2916  // being multiplied together. If so, we can fold them.
2917 
2918  // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2919  // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2920  // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2921  // ]]],+,...up to x=2n}.
2922  // Note that the arguments to choose() are always integers with values
2923  // known at compile time, never SCEV objects.
2924  //
2925  // The implementation avoids pointless extra computations when the two
2926  // addrec's are of different length (mathematically, it's equivalent to
2927  // an infinite stream of zeros on the right).
2928  bool OpsModified = false;
2929  for (unsigned OtherIdx = Idx+1;
2930  OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2931  ++OtherIdx) {
2932  const SCEVAddRecExpr *OtherAddRec =
2933  dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2934  if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2935  continue;
2936 
2937  // Limit max number of arguments to avoid creation of unreasonably big
2938  // SCEVAddRecs with very complex operands.
2939  if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
2940  MaxAddRecSize)
2941  continue;
2942 
2943  bool Overflow = false;
2944  Type *Ty = AddRec->getType();
2945  bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2946  SmallVector<const SCEV*, 7> AddRecOps;
2947  for (int x = 0, xe = AddRec->getNumOperands() +
2948  OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2949  const SCEV *Term = getZero(Ty);
2950  for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2951  uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2952  for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2953  ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2954  z < ze && !Overflow; ++z) {
2955  uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2956  uint64_t Coeff;
2957  if (LargerThan64Bits)
2958  Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2959  else
2960  Coeff = Coeff1*Coeff2;
2961  const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2962  const SCEV *Term1 = AddRec->getOperand(y-z);
2963  const SCEV *Term2 = OtherAddRec->getOperand(z);
2964  Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1, Term2,
2965  SCEV::FlagAnyWrap, Depth + 1),
2966  SCEV::FlagAnyWrap, Depth + 1);
2967  }
2968  }
2969  AddRecOps.push_back(Term);
2970  }
2971  if (!Overflow) {
2972  const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2974  if (Ops.size() == 2) return NewAddRec;
2975  Ops[Idx] = NewAddRec;
2976  Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2977  OpsModified = true;
2978  AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2979  if (!AddRec)
2980  break;
2981  }
2982  }
2983  if (OpsModified)
2984  return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2985 
2986  // Otherwise couldn't fold anything into this recurrence. Move onto the
2987  // next one.
2988  }
2989 
2990  // Okay, it looks like we really DO need an mul expr. Check to see if we
2991  // already have one, otherwise create a new one.
2992  return getOrCreateMulExpr(Ops, Flags);
2993 }
2994 
2995 /// Represents an unsigned remainder expression based on unsigned division.
2997  const SCEV *RHS) {
2998  assert(getEffectiveSCEVType(LHS->getType()) ==
2999  getEffectiveSCEVType(RHS->getType()) &&
3000  "SCEVURemExpr operand types don't match!");
3001 
3002  // Short-circuit easy cases
3003  if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3004  // If constant is one, the result is trivial
3005  if (RHSC->getValue()->isOne())
3006  return getZero(LHS->getType()); // X urem 1 --> 0
3007 
3008  // If constant is a power of two, fold into a zext(trunc(LHS)).
3009  if (RHSC->getAPInt().isPowerOf2()) {
3010  Type *FullTy = LHS->getType();
3011  Type *TruncTy =
3012  IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
3013  return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
3014  }
3015  }
3016 
3017  // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
3018  const SCEV *UDiv = getUDivExpr(LHS, RHS);
3019  const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
3020  return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
3021 }
3022 
3023 /// Get a canonical unsigned division expression, or something simpler if
3024 /// possible.
3026  const SCEV *RHS) {
3027  assert(getEffectiveSCEVType(LHS->getType()) ==
3028  getEffectiveSCEVType(RHS->getType()) &&
3029  "SCEVUDivExpr operand types don't match!");
3030 
3031  if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3032  if (RHSC->getValue()->isOne())
3033  return LHS; // X udiv 1 --> x
3034  // If the denominator is zero, the result of the udiv is undefined. Don't
3035  // try to analyze it, because the resolution chosen here may differ from
3036  // the resolution chosen in other parts of the compiler.
3037  if (!RHSC->getValue()->isZero()) {
3038  // Determine if the division can be folded into the operands of
3039  // its operands.
3040  // TODO: Generalize this to non-constants by using known-bits information.
3041  Type *Ty = LHS->getType();
3042  unsigned LZ = RHSC->getAPInt().countLeadingZeros();
3043  unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
3044  // For non-power-of-two values, effectively round the value up to the
3045  // nearest power of two.
3046  if (!RHSC->getAPInt().isPowerOf2())
3047  ++MaxShiftAmt;
3048  IntegerType *ExtTy =
3049  IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
3050  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
3051  if (const SCEVConstant *Step =
3052  dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
3053  // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
3054  const APInt &StepInt = Step->getAPInt();
3055  const APInt &DivInt = RHSC->getAPInt();
3056  if (!StepInt.urem(DivInt) &&
3057  getZeroExtendExpr(AR, ExtTy) ==
3058  getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3059  getZeroExtendExpr(Step, ExtTy),
3060  AR->getLoop(), SCEV::FlagAnyWrap)) {
3062  for (const SCEV *Op : AR->operands())
3063  Operands.push_back(getUDivExpr(Op, RHS));
3064  return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
3065  }
3066  /// Get a canonical UDivExpr for a recurrence.
3067  /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
3068  // We can currently only fold X%N if X is constant.
3069  const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
3070  if (StartC && !DivInt.urem(StepInt) &&
3071  getZeroExtendExpr(AR, ExtTy) ==
3072  getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3073  getZeroExtendExpr(Step, ExtTy),
3074  AR->getLoop(), SCEV::FlagAnyWrap)) {
3075  const APInt &StartInt = StartC->getAPInt();
3076  const APInt &StartRem = StartInt.urem(StepInt);
3077  if (StartRem != 0)
3078  LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
3079  AR->getLoop(), SCEV::FlagNW);
3080  }
3081  }
3082  // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
3083  if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
3085  for (const SCEV *Op : M->operands())
3086  Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3087  if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
3088  // Find an operand that's safely divisible.
3089  for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
3090  const SCEV *Op = M->getOperand(i);
3091  const SCEV *Div = getUDivExpr(Op, RHSC);
3092  if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
3093  Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
3094  M->op_end());
3095  Operands[i] = Div;
3096  return getMulExpr(Operands);
3097  }
3098  }
3099  }
3100  // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
3101  if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
3103  for (const SCEV *Op : A->operands())
3104  Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3105  if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
3106  Operands.clear();
3107  for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
3108  const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
3109  if (isa<SCEVUDivExpr>(Op) ||
3110  getMulExpr(Op, RHS) != A->getOperand(i))
3111  break;
3112  Operands.push_back(Op);
3113  }
3114  if (Operands.size() == A->getNumOperands())
3115  return getAddExpr(Operands);
3116  }
3117  }
3118 
3119  // Fold if both operands are constant.
3120  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
3121  Constant *LHSCV = LHSC->getValue();
3122  Constant *RHSCV = RHSC->getValue();
3123  return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
3124  RHSCV)));
3125  }
3126  }
3127  }
3128 
3130  ID.AddInteger(scUDivExpr);
3131  ID.AddPointer(LHS);
3132  ID.AddPointer(RHS);
3133  void *IP = nullptr;
3134  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3135  SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
3136  LHS, RHS);
3137  UniqueSCEVs.InsertNode(S, IP);
3138  return S;
3139 }
3140 
3141 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
3142  APInt A = C1->getAPInt().abs();
3143  APInt B = C2->getAPInt().abs();
3144  uint32_t ABW = A.getBitWidth();
3145  uint32_t BBW = B.getBitWidth();
3146 
3147  if (ABW > BBW)
3148  B = B.zext(ABW);
3149  else if (ABW < BBW)
3150  A = A.zext(BBW);
3151 
3152  return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
3153 }
3154 
3155 /// Get a canonical unsigned division expression, or something simpler if
3156 /// possible. There is no representation for an exact udiv in SCEV IR, but we
3157 /// can attempt to remove factors from the LHS and RHS. We can't do this when
3158 /// it's not exact because the udiv may be clearing bits.
3160  const SCEV *RHS) {
3161  // TODO: we could try to find factors in all sorts of things, but for now we
3162  // just deal with u/exact (multiply, constant). See SCEVDivision towards the
3163  // end of this file for inspiration.
3164 
3165  const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
3166  if (!Mul || !Mul->hasNoUnsignedWrap())
3167  return getUDivExpr(LHS, RHS);
3168 
3169  if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
3170  // If the mulexpr multiplies by a constant, then that constant must be the
3171  // first element of the mulexpr.
3172  if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
3173  if (LHSCst == RHSCst) {
3175  Operands.append(Mul->op_begin() + 1, Mul->op_end());
3176  return getMulExpr(Operands);
3177  }
3178 
3179  // We can't just assume that LHSCst divides RHSCst cleanly, it could be
3180  // that there's a factor provided by one of the other terms. We need to
3181  // check.
3182  APInt Factor = gcd(LHSCst, RHSCst);
3183  if (!Factor.isIntN(1)) {
3184  LHSCst =
3185  cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
3186  RHSCst =
3187  cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
3189  Operands.push_back(LHSCst);
3190  Operands.append(Mul->op_begin() + 1, Mul->op_end());
3191  LHS = getMulExpr(Operands);
3192  RHS = RHSCst;
3193  Mul = dyn_cast<SCEVMulExpr>(LHS);
3194  if (!Mul)
3195  return getUDivExactExpr(LHS, RHS);
3196  }
3197  }
3198  }
3199 
3200  for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
3201  if (Mul->getOperand(i) == RHS) {
3203  Operands.append(Mul->op_begin(), Mul->op_begin() + i);
3204  Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
3205  return getMulExpr(Operands);
3206  }
3207  }
3208 
3209  return getUDivExpr(LHS, RHS);
3210 }
3211 
3212 /// Get an add recurrence expression for the specified loop. Simplify the
3213 /// expression as much as possible.
3214 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
3215  const Loop *L,
3216  SCEV::NoWrapFlags Flags) {
3218  Operands.push_back(Start);
3219  if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
3220  if (StepChrec->getLoop() == L) {
3221  Operands.append(StepChrec->op_begin(), StepChrec->op_end());
3222  return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
3223  }
3224 
3225  Operands.push_back(Step);
3226  return getAddRecExpr(Operands, L, Flags);
3227 }
3228 
3229 /// Get an add recurrence expression for the specified loop. Simplify the
3230 /// expression as much as possible.
3231 const SCEV *
3233  const Loop *L, SCEV::NoWrapFlags Flags) {
3234  if (Operands.size() == 1) return Operands[0];
3235 #ifndef NDEBUG
3236  Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
3237  for (unsigned i = 1, e = Operands.size(); i != e; ++i)
3238  assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
3239  "SCEVAddRecExpr operand types don't match!");
3240  for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3241  assert(isLoopInvariant(Operands[i], L) &&
3242  "SCEVAddRecExpr operand is not loop-invariant!");
3243 #endif
3244 
3245  if (Operands.back()->isZero()) {
3246  Operands.pop_back();
3247  return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
3248  }
3249 
3250  // It's tempting to want to call getMaxBackedgeTakenCount count here and
3251  // use that information to infer NUW and NSW flags. However, computing a
3252  // BE count requires calling getAddRecExpr, so we may not yet have a
3253  // meaningful BE count at this point (and if we don't, we'd be stuck
3254  // with a SCEVCouldNotCompute as the cached BE count).
3255 
3256  Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
3257 
3258  // Canonicalize nested AddRecs in by nesting them in order of loop depth.
3259  if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
3260  const Loop *NestedLoop = NestedAR->getLoop();
3261  if (L->contains(NestedLoop)
3262  ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
3263  : (!NestedLoop->contains(L) &&
3264  DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
3265  SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
3266  NestedAR->op_end());
3267  Operands[0] = NestedAR->getStart();
3268  // AddRecs require their operands be loop-invariant with respect to their
3269  // loops. Don't perform this transformation if it would break this
3270  // requirement.
3271  bool AllInvariant = all_of(
3272  Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
3273 
3274  if (AllInvariant) {
3275  // Create a recurrence for the outer loop with the same step size.
3276  //
3277  // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3278  // inner recurrence has the same property.
3279  SCEV::NoWrapFlags OuterFlags =
3280  maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3281 
3282  NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3283  AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3284  return isLoopInvariant(Op, NestedLoop);
3285  });
3286 
3287  if (AllInvariant) {
3288  // Ok, both add recurrences are valid after the transformation.
3289  //
3290  // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3291  // the outer recurrence has the same property.
3292  SCEV::NoWrapFlags InnerFlags =
3293  maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3294  return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3295  }
3296  }
3297  // Reset Operands to its original state.
3298  Operands[0] = NestedAR;
3299  }
3300  }
3301 
3302  // Okay, it looks like we really DO need an addrec expr. Check to see if we
3303  // already have one, otherwise create a new one.
3306  for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3307  ID.AddPointer(Operands[i]);
3308  ID.AddPointer(L);
3309  void *IP = nullptr;
3310  SCEVAddRecExpr *S =
3311  static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
3312  if (!S) {
3313  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
3314  std::uninitialized_copy(Operands.begin(), Operands.end(), O);
3315  S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
3316  O, Operands.size(), L);
3317  UniqueSCEVs.InsertNode(S, IP);
3318  }
3319  S->setNoWrapFlags(Flags);
3320  return S;
3321 }
3322 
3323 const SCEV *
3325  const SmallVectorImpl<const SCEV *> &IndexExprs) {
3326  const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3327  // getSCEV(Base)->getType() has the same address space as Base->getType()
3328  // because SCEV::getType() preserves the address space.
3329  Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
3330  // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3331  // instruction to its SCEV, because the Instruction may be guarded by control
3332  // flow and the no-overflow bits may not be valid for the expression in any
3333  // context. This can be fixed similarly to how these flags are handled for
3334  // adds.
3337 
3338  const SCEV *TotalOffset = getZero(IntPtrTy);
3339  // The array size is unimportant. The first thing we do on CurTy is getting
3340  // its element type.
3341  Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
3342  for (const SCEV *IndexExpr : IndexExprs) {
3343  // Compute the (potentially symbolic) offset in bytes for this index.
3344  if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3345  // For a struct, add the member offset.
3346  ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3347  unsigned FieldNo = Index->getZExtValue();
3348  const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3349 
3350  // Add the field offset to the running total offset.
3351  TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3352 
3353  // Update CurTy to the type of the field at Index.
3354  CurTy = STy->getTypeAtIndex(Index);
3355  } else {
3356  // Update CurTy to its element type.
3357  CurTy = cast<SequentialType>(CurTy)->getElementType();
3358  // For an array, add the element offset, explicitly scaled.
3359  const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3360  // Getelementptr indices are signed.
3361  IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3362 
3363  // Multiply the index by the element size to compute the element offset.
3364  const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3365 
3366  // Add the element offset to the running total offset.
3367  TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3368  }
3369  }
3370 
3371  // Add the total offset from all the GEP indices to the base.
3372  return getAddExpr(BaseExpr, TotalOffset, Wrap);
3373 }
3374 
3376  const SCEV *RHS) {
3377  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3378  return getSMaxExpr(Ops);
3379 }
3380 
3381 const SCEV *
3383  assert(!Ops.empty() && "Cannot get empty smax!");
3384  if (Ops.size() == 1) return Ops[0];
3385 #ifndef NDEBUG
3386  Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3387  for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3388  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3389  "SCEVSMaxExpr operand types don't match!");
3390 #endif
3391 
3392  // Sort by complexity, this groups all similar expression types together.
3393  GroupByComplexity(Ops, &LI, DT);
3394 
3395  // If there are any constants, fold them together.
3396  unsigned Idx = 0;
3397  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3398  ++Idx;
3399  assert(Idx < Ops.size());
3400  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3401  // We found two constants, fold them together!
3402  ConstantInt *Fold = ConstantInt::get(
3403  getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3404  Ops[0] = getConstant(Fold);
3405  Ops.erase(Ops.begin()+1); // Erase the folded element
3406  if (Ops.size() == 1) return Ops[0];
3407  LHSC = cast<SCEVConstant>(Ops[0]);
3408  }
3409 
3410  // If we are left with a constant minimum-int, strip it off.
3411  if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3412  Ops.erase(Ops.begin());
3413  --Idx;
3414  } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3415  // If we have an smax with a constant maximum-int, it will always be
3416  // maximum-int.
3417  return Ops[0];
3418  }
3419 
3420  if (Ops.size() == 1) return Ops[0];
3421  }
3422 
3423  // Find the first SMax
3424  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3425  ++Idx;
3426 
3427  // Check to see if one of the operands is an SMax. If so, expand its operands
3428  // onto our operand list, and recurse to simplify.
3429  if (Idx < Ops.size()) {
3430  bool DeletedSMax = false;
3431  while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3432  Ops.erase(Ops.begin()+Idx);
3433  Ops.append(SMax->op_begin(), SMax->op_end());
3434  DeletedSMax = true;
3435  }
3436 
3437  if (DeletedSMax)
3438  return getSMaxExpr(Ops);
3439  }
3440 
3441  // Okay, check to see if the same value occurs in the operand list twice. If
3442  // so, delete one. Since we sorted the list, these values are required to
3443  // be adjacent.
3444  for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3445  // X smax Y smax Y --> X smax Y
3446  // X smax Y --> X, if X is always greater than Y
3447  if (Ops[i] == Ops[i+1] ||
3448  isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3449  Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3450  --i; --e;
3451  } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3452  Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3453  --i; --e;
3454  }
3455 
3456  if (Ops.size() == 1) return Ops[0];
3457 
3458  assert(!Ops.empty() && "Reduced smax down to nothing!");
3459 
3460  // Okay, it looks like we really DO need an smax expr. Check to see if we
3461  // already have one, otherwise create a new one.
3463  ID.AddInteger(scSMaxExpr);
3464  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3465  ID.AddPointer(Ops[i]);
3466  void *IP = nullptr;
3467  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3468  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3469  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3470  SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3471  O, Ops.size());
3472  UniqueSCEVs.InsertNode(S, IP);
3473  return S;
3474 }
3475 
3477  const SCEV *RHS) {
3478  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3479  return getUMaxExpr(Ops);
3480 }
3481 
3482 const SCEV *
3484  assert(!Ops.empty() && "Cannot get empty umax!");
3485  if (Ops.size() == 1) return Ops[0];
3486 #ifndef NDEBUG
3487  Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3488  for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3489  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3490  "SCEVUMaxExpr operand types don't match!");
3491 #endif
3492 
3493  // Sort by complexity, this groups all similar expression types together.
3494  GroupByComplexity(Ops, &LI, DT);
3495 
3496  // If there are any constants, fold them together.
3497  unsigned Idx = 0;
3498  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3499  ++Idx;
3500  assert(Idx < Ops.size());
3501  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3502  // We found two constants, fold them together!
3503  ConstantInt *Fold = ConstantInt::get(
3504  getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3505  Ops[0] = getConstant(Fold);
3506  Ops.erase(Ops.begin()+1); // Erase the folded element
3507  if (Ops.size() == 1) return Ops[0];
3508  LHSC = cast<SCEVConstant>(Ops[0]);
3509  }
3510 
3511  // If we are left with a constant minimum-int, strip it off.
3512  if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3513  Ops.erase(Ops.begin());
3514  --Idx;
3515  } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3516  // If we have an umax with a constant maximum-int, it will always be
3517  // maximum-int.
3518  return Ops[0];
3519  }
3520 
3521  if (Ops.size() == 1) return Ops[0];
3522  }
3523 
3524  // Find the first UMax
3525  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3526  ++Idx;
3527 
3528  // Check to see if one of the operands is a UMax. If so, expand its operands
3529  // onto our operand list, and recurse to simplify.
3530  if (Idx < Ops.size()) {
3531  bool DeletedUMax = false;
3532  while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3533  Ops.erase(Ops.begin()+Idx);
3534  Ops.append(UMax->op_begin(), UMax->op_end());
3535  DeletedUMax = true;
3536  }
3537 
3538  if (DeletedUMax)
3539  return getUMaxExpr(Ops);
3540  }
3541 
3542  // Okay, check to see if the same value occurs in the operand list twice. If
3543  // so, delete one. Since we sorted the list, these values are required to
3544  // be adjacent.
3545  for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3546  // X umax Y umax Y --> X umax Y
3547  // X umax Y --> X, if X is always greater than Y
3548  if (Ops[i] == Ops[i+1] ||
3549  isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3550  Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3551  --i; --e;
3552  } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3553  Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3554  --i; --e;
3555  }
3556 
3557  if (Ops.size() == 1) return Ops[0];
3558 
3559  assert(!Ops.empty() && "Reduced umax down to nothing!");
3560 
3561  // Okay, it looks like we really DO need a umax expr. Check to see if we
3562  // already have one, otherwise create a new one.
3564  ID.AddInteger(scUMaxExpr);
3565  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3566  ID.AddPointer(Ops[i]);
3567  void *IP = nullptr;
3568  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3569  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3570  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3571  SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3572  O, Ops.size());
3573  UniqueSCEVs.InsertNode(S, IP);
3574  return S;
3575 }
3576 
3578  const SCEV *RHS) {
3579  // ~smax(~x, ~y) == smin(x, y).
3580  return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3581 }
3582 
3584  const SCEV *RHS) {
3585  // ~umax(~x, ~y) == umin(x, y)
3586  return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3587 }
3588 
3589 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3590  // We can bypass creating a target-independent
3591  // constant expression and then folding it back into a ConstantInt.
3592  // This is just a compile-time optimization.
3593  return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3594 }
3595 
3597  StructType *STy,
3598  unsigned FieldNo) {
3599  // We can bypass creating a target-independent
3600  // constant expression and then folding it back into a ConstantInt.
3601  // This is just a compile-time optimization.
3602  return getConstant(
3603  IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3604 }
3605 
3607  // Don't attempt to do anything other than create a SCEVUnknown object
3608  // here. createSCEV only calls getUnknown after checking for all other
3609  // interesting possibilities, and any other code that calls getUnknown
3610  // is doing so in order to hide a value from SCEV canonicalization.
3611 
3613  ID.AddInteger(scUnknown);
3614  ID.AddPointer(V);
3615  void *IP = nullptr;
3616  if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3617  assert(cast<SCEVUnknown>(S)->getValue() == V &&
3618  "Stale SCEVUnknown in uniquing map!");
3619  return S;
3620  }
3621  SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3622  FirstUnknown);
3623  FirstUnknown = cast<SCEVUnknown>(S);
3624  UniqueSCEVs.InsertNode(S, IP);
3625  return S;
3626 }
3627 
3628 //===----------------------------------------------------------------------===//
3629 // Basic SCEV Analysis and PHI Idiom Recognition Code
3630 //
3631 
3632 /// Test if values of the given type are analyzable within the SCEV
3633 /// framework. This primarily includes integer types, and it can optionally
3634 /// include pointer types if the ScalarEvolution class has access to
3635 /// target-specific information.
3637  // Integers and pointers are always SCEVable.
3638  return Ty->isIntegerTy() || Ty->isPointerTy();
3639 }
3640 
3641 /// Return the size in bits of the specified type, for which isSCEVable must
3642 /// return true.
3644  assert(isSCEVable(Ty) && "Type is not SCEVable!");
3645  return getDataLayout().getTypeSizeInBits(Ty);
3646 }
3647 
3648 /// Return a type with the same bitwidth as the given type and which represents
3649 /// how SCEV will treat the given type, for which isSCEVable must return
3650 /// true. For pointer types, this is the pointer-sized integer type.
3652  assert(isSCEVable(Ty) && "Type is not SCEVable!");
3653 
3654  if (Ty->isIntegerTy())
3655  return Ty;
3656 
3657  // The only other support type is pointer.
3658  assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3659  return getDataLayout().getIntPtrType(Ty);
3660 }
3661 
3663  return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
3664 }
3665 
3667  return CouldNotCompute.get();
3668 }
3669 
3670 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3671  bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3672  auto *SU = dyn_cast<SCEVUnknown>(S);
3673  return SU && SU->getValue() == nullptr;
3674  });
3675 
3676  return !ContainsNulls;
3677 }
3678 
3680  HasRecMapType::iterator I = HasRecMap.find(S);
3681  if (I != HasRecMap.end())
3682  return I->second;
3683 
3684  bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
3685  HasRecMap.insert({S, FoundAddRec});
3686  return FoundAddRec;
3687 }
3688 
3689 /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3690 /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3691 /// offset I, then return {S', I}, else return {\p S, nullptr}.
3692 static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3693  const auto *Add = dyn_cast<SCEVAddExpr>(S);
3694  if (!Add)
3695  return {S, nullptr};
3696 
3697  if (Add->getNumOperands() != 2)
3698  return {S, nullptr};
3699 
3700  auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3701  if (!ConstOp)
3702  return {S, nullptr};
3703 
3704  return {Add->getOperand(1), ConstOp->getValue()};
3705 }
3706 
3707 /// Return the ValueOffsetPair set for \p S. \p S can be represented
3708 /// by the value and offset from any ValueOffsetPair in the set.
3710 ScalarEvolution::getSCEVValues(const SCEV *S) {
3711  ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3712  if (SI == ExprValueMap.end())
3713  return nullptr;
3714 #ifndef NDEBUG
3715  if (VerifySCEVMap) {
3716  // Check there is no dangling Value in the set returned.
3717  for (const auto &VE : SI->second)
3718  assert(ValueExprMap.count(VE.first));
3719  }
3720 #endif
3721  return &SI->second;
3722 }
3723 
3724 /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3725 /// cannot be used separately. eraseValueFromMap should be used to remove
3726 /// V from ValueExprMap and ExprValueMap at the same time.
3728  ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3729  if (I != ValueExprMap.end()) {
3730  const SCEV *S = I->second;
3731  // Remove {V, 0} from the set of ExprValueMap[S]
3732  if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
3733  SV->remove({V, nullptr});
3734 
3735  // Remove {V, Offset} from the set of ExprValueMap[Stripped]
3736  const SCEV *Stripped;
3738  std::tie(Stripped, Offset) = splitAddExpr(S);
3739  if (Offset != nullptr) {
3740  if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
3741  SV->remove({V, Offset});
3742  }
3743  ValueExprMap.erase(V);
3744  }
3745 }
3746 
3747 /// Return an existing SCEV if it exists, otherwise analyze the expression and
3748 /// create a new one.
3750  assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3751 
3752  const SCEV *S = getExistingSCEV(V);
3753  if (S == nullptr) {
3754  S = createSCEV(V);
3755  // During PHI resolution, it is possible to create two SCEVs for the same
3756  // V, so it is needed to double check whether V->S is inserted into
3757  // ValueExprMap before insert S->{V, 0} into ExprValueMap.
3758  std::pair<ValueExprMapType::iterator, bool> Pair =
3759  ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3760  if (Pair.second) {
3761  ExprValueMap[S].insert({V, nullptr});
3762 
3763  // If S == Stripped + Offset, add Stripped -> {V, Offset} into
3764  // ExprValueMap.
3765  const SCEV *Stripped = S;
3766  ConstantInt *Offset = nullptr;
3767  std::tie(Stripped, Offset) = splitAddExpr(S);
3768  // If stripped is SCEVUnknown, don't bother to save
3769  // Stripped -> {V, offset}. It doesn't simplify and sometimes even
3770  // increase the complexity of the expansion code.
3771  // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
3772  // because it may generate add/sub instead of GEP in SCEV expansion.
3773  if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
3774  !isa<GetElementPtrInst>(V))
3775  ExprValueMap[Stripped].insert({V, Offset});
3776  }
3777  }
3778  return S;
3779 }
3780 
3781 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3782  assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3783 
3784  ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3785  if (I != ValueExprMap.end()) {
3786  const SCEV *S = I->second;
3787  if (checkValidity(S))
3788  return S;
3789  eraseValueFromMap(V);
3790  forgetMemoizedResults(S);
3791  }
3792  return nullptr;
3793 }
3794 
3795 /// Return a SCEV corresponding to -V = -1*V
3797  SCEV::NoWrapFlags Flags) {
3798  if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3799  return getConstant(
3800  cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3801 
3802  Type *Ty = V->getType();
3803  Ty = getEffectiveSCEVType(Ty);
3804  return getMulExpr(
3805  V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3806 }
3807 
3808 /// Return a SCEV corresponding to ~V = -1-V
3810  if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3811  return getConstant(
3812  cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3813 
3814  Type *Ty = V->getType();
3815  Ty = getEffectiveSCEVType(Ty);
3816  const SCEV *AllOnes =
3817  getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3818  return getMinusSCEV(AllOnes, V);
3819 }
3820 
3821 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3822  SCEV::NoWrapFlags Flags,
3823  unsigned Depth) {
3824  // Fast path: X - X --> 0.
3825  if (LHS == RHS)
3826  return getZero(LHS->getType());
3827 
3828  // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3829  // makes it so that we cannot make much use of NUW.
3830  auto AddFlags = SCEV::FlagAnyWrap;
3831  const bool RHSIsNotMinSigned =
3832  !getSignedRangeMin(RHS).isMinSignedValue();
3833  if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3834  // Let M be the minimum representable signed value. Then (-1)*RHS
3835  // signed-wraps if and only if RHS is M. That can happen even for
3836  // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3837  // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3838  // (-1)*RHS, we need to prove that RHS != M.
3839  //
3840  // If LHS is non-negative and we know that LHS - RHS does not
3841  // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3842  // either by proving that RHS > M or that LHS >= 0.
3843  if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3844  AddFlags = SCEV::FlagNSW;
3845  }
3846  }
3847 
3848  // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3849  // RHS is NSW and LHS >= 0.
3850  //
3851  // The difficulty here is that the NSW flag may have been proven
3852  // relative to a loop that is to be found in a recurrence in LHS and
3853  // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3854  // larger scope than intended.
3855  auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3856 
3857  return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
3858 }
3859 
3860 const SCEV *
3862  Type *SrcTy = V->getType();
3863  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3864  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3865  "Cannot truncate or zero extend with non-integer arguments!");
3866  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3867  return V; // No conversion
3868  if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3869  return getTruncateExpr(V, Ty);
3870  return getZeroExtendExpr(V, Ty);
3871 }
3872 
3873 const SCEV *
3875  Type *Ty) {
3876  Type *SrcTy = V->getType();
3877  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3878  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3879  "Cannot truncate or zero extend with non-integer arguments!");
3880  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3881  return V; // No conversion
3882  if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3883  return getTruncateExpr(V, Ty);
3884  return getSignExtendExpr(V, Ty);
3885 }
3886 
3887 const SCEV *
3889  Type *SrcTy = V->getType();
3890  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3891  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3892  "Cannot noop or zero extend with non-integer arguments!");
3893  assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3894  "getNoopOrZeroExtend cannot truncate!");
3895  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3896  return V; // No conversion
3897  return getZeroExtendExpr(V, Ty);
3898 }
3899 
3900 const SCEV *
3902  Type *SrcTy = V->getType();
3903  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3904  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3905  "Cannot noop or sign extend with non-integer arguments!");
3906  assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3907  "getNoopOrSignExtend cannot truncate!");
3908  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3909  return V; // No conversion
3910  return getSignExtendExpr(V, Ty);
3911 }
3912 
3913 const SCEV *
3915  Type *SrcTy = V->getType();
3916  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3917  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3918  "Cannot noop or any extend with non-integer arguments!");
3919  assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3920  "getNoopOrAnyExtend cannot truncate!");
3921  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3922  return V; // No conversion
3923  return getAnyExtendExpr(V, Ty);
3924 }
3925 
3926 const SCEV *
3928  Type *SrcTy = V->getType();
3929  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3930  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3931  "Cannot truncate or noop with non-integer arguments!");
3932  assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3933  "getTruncateOrNoop cannot extend!");
3934  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3935  return V; // No conversion
3936  return getTruncateExpr(V, Ty);
3937 }
3938 
3940  const SCEV *RHS) {
3941  const SCEV *PromotedLHS = LHS;
3942  const SCEV *PromotedRHS = RHS;
3943 
3944  if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3945  PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3946  else
3947  PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3948 
3949  return getUMaxExpr(PromotedLHS, PromotedRHS);
3950 }
3951 
3953  const SCEV *RHS) {
3954  const SCEV *PromotedLHS = LHS;
3955  const SCEV *PromotedRHS = RHS;
3956 
3957  if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3958  PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3959  else
3960  PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3961 
3962  return getUMinExpr(PromotedLHS, PromotedRHS);
3963 }
3964 
3966  // A pointer operand may evaluate to a nonpointer expression, such as null.
3967  if (!V->getType()->isPointerTy())
3968  return V;
3969 
3970  if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3971  return getPointerBase(Cast->getOperand());
3972  } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3973  const SCEV *PtrOp = nullptr;
3974  for (const SCEV *NAryOp : NAry->operands()) {
3975  if (NAryOp->getType()->isPointerTy()) {
3976  // Cannot find the base of an expression with multiple pointer operands.
3977  if (PtrOp)
3978  return V;
3979  PtrOp = NAryOp;
3980  }
3981  }
3982  if (!PtrOp)
3983  return V;
3984  return getPointerBase(PtrOp);
3985  }
3986  return V;
3987 }
3988 
3989 /// Push users of the given Instruction onto the given Worklist.
3990 static void
3992  SmallVectorImpl<Instruction *> &Worklist) {
3993  // Push the def-use children onto the Worklist stack.
3994  for (User *U : I->users())
3995  Worklist.push_back(cast<Instruction>(U));
3996 }
3997 
3998 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
4000  PushDefUseChildren(PN, Worklist);
4001 
4003  Visited.insert(PN);
4004  while (!Worklist.empty()) {
4005  Instruction *I = Worklist.pop_back_val();
4006  if (!Visited.insert(I).second)
4007  continue;
4008 
4009  auto It = ValueExprMap.find_as(static_cast<Value *>(I));
4010  if (It != ValueExprMap.end()) {
4011  const SCEV *Old = It->second;
4012 
4013  // Short-circuit the def-use traversal if the symbolic name
4014  // ceases to appear in expressions.
4015  if (Old != SymName && !hasOperand(Old, SymName))
4016  continue;
4017 
4018  // SCEVUnknown for a PHI either means that it has an unrecognized
4019  // structure, it's a PHI that's in the progress of being computed
4020  // by createNodeForPHI, or it's a single-value PHI. In the first case,
4021  // additional loop trip count information isn't going to change anything.
4022  // In the second case, createNodeForPHI will perform the necessary
4023  // updates on its own when it gets to that point. In the third, we do
4024  // want to forget the SCEVUnknown.
4025  if (!isa<PHINode>(I) ||
4026  !isa<SCEVUnknown>(Old) ||
4027  (I != PN && Old == SymName)) {
4028  eraseValueFromMap(It->first);
4029  forgetMemoizedResults(Old);
4030  }
4031  }
4032 
4033  PushDefUseChildren(I, Worklist);
4034  }
4035 }
4036 
4037 namespace {
4038 
4039 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4040 public:
4041  SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
4042  : SCEVRewriteVisitor(SE), L(L) {}
4043 
4044  static const SCEV *rewrite(const SCEV *S, const Loop *L,
4045  ScalarEvolution &SE) {
4046  SCEVInitRewriter Rewriter(L, SE);
4047  const SCEV *Result = Rewriter.visit(S);
4048  return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4049  }
4050 
4051  const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4052  if (!SE.isLoopInvariant(Expr, L))
4053  Valid = false;
4054  return Expr;
4055  }
4056 
4057  const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4058  // Only allow AddRecExprs for this loop.
4059  if (Expr->getLoop() == L)
4060  return Expr->getStart();
4061  Valid = false;
4062  return Expr;
4063  }
4064 
4065  bool isValid() { return Valid; }
4066 
4067 private:
4068  const Loop *L;
4069  bool Valid = true;
4070 };
4071 
4072 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4073 public:
4074  SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
4075  : SCEVRewriteVisitor(SE), L(L) {}
4076 
4077  static const SCEV *rewrite(const SCEV *S, const Loop *L,
4078  ScalarEvolution &SE) {
4079  SCEVShiftRewriter Rewriter(L, SE);
4080  const SCEV *Result = Rewriter.visit(S);
4081  return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4082  }
4083 
4084  const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4085  // Only allow AddRecExprs for this loop.
4086  if (!SE.isLoopInvariant(Expr, L))
4087  Valid = false;
4088  return Expr;
4089  }
4090 
4091  const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4092  if (Expr->getLoop() == L && Expr->isAffine())
4093  return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
4094  Valid = false;
4095  return Expr;
4096  }
4097 
4098  bool isValid() { return Valid; }
4099 
4100 private:
4101  const Loop *L;
4102  bool Valid = true;
4103 };
4104 
4105 } // end anonymous namespace
4106 
4108 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
4109  if (!AR->isAffine())
4110  return SCEV::FlagAnyWrap;
4111 
4112  using OBO = OverflowingBinaryOperator;
4113 
4115 
4116  if (!AR->hasNoSignedWrap()) {
4117  ConstantRange AddRecRange = getSignedRange(AR);
4118  ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
4119 
4121  Instruction::Add, IncRange, OBO::NoSignedWrap);
4122  if (NSWRegion.contains(AddRecRange))
4123  Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
4124  }
4125 
4126  if (!AR->hasNoUnsignedWrap()) {
4127  ConstantRange AddRecRange = getUnsignedRange(AR);
4128  ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
4129 
4131  Instruction::Add, IncRange, OBO::NoUnsignedWrap);
4132  if (NUWRegion.contains(AddRecRange))
4133  Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
4134  }
4135 
4136  return Result;
4137 }
4138 
4139 namespace {
4140 
4141 /// Represents an abstract binary operation. This may exist as a
4142 /// normal instruction or constant expression, or may have been
4143 /// derived from an expression tree.
4144 struct BinaryOp {
4145  unsigned Opcode;
4146  Value *LHS;
4147  Value *RHS;
4148  bool IsNSW = false;
4149  bool IsNUW = false;
4150 
4151  /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
4152  /// constant expression.
4153  Operator *Op = nullptr;
4154 
4155  explicit BinaryOp(Operator *Op)
4156  : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
4157  Op(Op) {
4158  if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
4159  IsNSW = OBO->hasNoSignedWrap();
4160  IsNUW = OBO->hasNoUnsignedWrap();
4161  }
4162  }
4163 
4164  explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
4165  bool IsNUW = false)
4166  : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
4167 };
4168 
4169 } // end anonymous namespace
4170 
4171 /// Try to map \p V into a BinaryOp, and return \c None on failure.
4173  auto *Op = dyn_cast<Operator>(V);
4174  if (!Op)
4175  return None;
4176 
4177  // Implementation detail: all the cleverness here should happen without
4178  // creating new SCEV expressions -- our caller knowns tricks to avoid creating
4179  // SCEV expressions when possible, and we should not break that.
4180 
4181  switch (Op->getOpcode()) {
4182  case Instruction::Add:
4183  case Instruction::Sub:
4184  case Instruction::Mul:
4185  case Instruction::UDiv:
4186  case Instruction::URem:
4187  case Instruction::And:
4188  case Instruction::Or:
4189  case Instruction::AShr:
4190  case Instruction::Shl:
4191  return BinaryOp(Op);
4192 
4193  case Instruction::Xor:
4194  if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
4195  // If the RHS of the xor is a signmask, then this is just an add.
4196  // Instcombine turns add of signmask into xor as a strength reduction step.
4197  if (RHSC->getValue().isSignMask())
4198  return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
4199  return BinaryOp(Op);
4200 
4201  case Instruction::LShr:
4202  // Turn logical shift right of a constant into a unsigned divide.
4203  if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
4204  uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
4205 
4206  // If the shift count is not less than the bitwidth, the result of
4207  // the shift is undefined. Don't try to analyze it, because the
4208  // resolution chosen here may differ from the resolution chosen in
4209  // other parts of the compiler.
4210  if (SA->getValue().ult(BitWidth)) {
4211  Constant *X =
4212  ConstantInt::get(SA->getContext(),
4213  APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4214  return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
4215  }
4216  }
4217  return BinaryOp(Op);
4218 
4219  case Instruction::ExtractValue: {
4220  auto *EVI = cast<ExtractValueInst>(Op);
4221  if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
4222  break;
4223 
4224  auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
4225  if (!CI)
4226  break;
4227 
4228  if (auto *F = CI->getCalledFunction())
4229  switch (F->getIntrinsicID()) {
4230  case Intrinsic::sadd_with_overflow:
4231  case Intrinsic::uadd_with_overflow:
4232  if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
4233  return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4234  CI->getArgOperand(1));
4235 
4236  // Now that we know that all uses of the arithmetic-result component of
4237  // CI are guarded by the overflow check, we can go ahead and pretend
4238  // that the arithmetic is non-overflowing.
4239  if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
4240  return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4241  CI->getArgOperand(1), /* IsNSW = */ true,
4242  /* IsNUW = */ false);
4243  else
4244  return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4245  CI->getArgOperand(1), /* IsNSW = */ false,
4246  /* IsNUW*/ true);
4247  case Intrinsic::ssub_with_overflow:
4248  case Intrinsic::usub_with_overflow:
4249  if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
4250  return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4251  CI->getArgOperand(1));
4252 
4253  // The same reasoning as sadd/uadd above.
4254  if (F->getIntrinsicID() == Intrinsic::ssub_with_overflow)
4255  return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4256  CI->getArgOperand(1), /* IsNSW = */ true,
4257  /* IsNUW = */ false);
4258  else
4259  return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4260  CI->getArgOperand(1), /* IsNSW = */ false,
4261  /* IsNUW = */ true);
4262  case Intrinsic::smul_with_overflow:
4263  case Intrinsic::umul_with_overflow:
4264  return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
4265  CI->getArgOperand(1));
4266  default:
4267  break;
4268  }
4269  }
4270 
4271  default:
4272  break;
4273  }
4274 
4275  return None;
4276 }
4277 
4278 /// Helper function to createAddRecFromPHIWithCasts. We have a phi
4279 /// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
4280 /// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
4281 /// way. This function checks if \p Op, an operand of this SCEVAddExpr,
4282 /// follows one of the following patterns:
4283 /// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4284 /// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4285 /// If the SCEV expression of \p Op conforms with one of the expected patterns
4286 /// we return the type of the truncation operation, and indicate whether the
4287 /// truncated type should be treated as signed/unsigned by setting
4288 /// \p Signed to true/false, respectively.
4289 static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
4290  bool &Signed, ScalarEvolution &SE) {
4291  // The case where Op == SymbolicPHI (that is, with no type conversions on
4292  // the way) is handled by the regular add recurrence creating logic and
4293  // would have already been triggered in createAddRecForPHI. Reaching it here
4294  // means that createAddRecFromPHI had failed for this PHI before (e.g.,
4295  // because one of the other operands of the SCEVAddExpr updating this PHI is
4296  // not invariant).
4297  //
4298  // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
4299  // this case predicates that allow us to prove that Op == SymbolicPHI will
4300  // be added.
4301  if (Op == SymbolicPHI)
4302  return nullptr;
4303 
4304  unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
4305  unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
4306  if (SourceBits != NewBits)
4307  return nullptr;
4308 
4311  if (!SExt && !ZExt)
4312  return nullptr;
4313  const SCEVTruncateExpr *Trunc =
4314  SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
4315  : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
4316  if (!Trunc)
4317  return nullptr;
4318  const SCEV *X = Trunc->getOperand();
4319  if (X != SymbolicPHI)
4320  return nullptr;
4321  Signed = SExt != nullptr;
4322  return Trunc->getType();
4323 }
4324 
4325 static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
4326  if (!PN->getType()->isIntegerTy())
4327  return nullptr;
4328  const Loop *L = LI.getLoopFor(PN->getParent());
4329  if (!L || L->getHeader() != PN->getParent())
4330  return nullptr;
4331  return L;
4332 }
4333 
4334 // Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
4335 // computation that updates the phi follows the following pattern:
4336 // (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
4337 // which correspond to a phi->trunc->sext/zext->add->phi update chain.
4338 // If so, try to see if it can be rewritten as an AddRecExpr under some
4339 // Predicates. If successful, return them as a pair. Also cache the results
4340 // of the analysis.
4341 //
4342 // Example usage scenario:
4343 // Say the Rewriter is called for the following SCEV:
4344 // 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4345 // where:
4346 // %X = phi i64 (%Start, %BEValue)
4347 // It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
4348 // and call this function with %SymbolicPHI = %X.
4349 //
4350 // The analysis will find that the value coming around the backedge has
4351 // the following SCEV:
4352 // BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4353 // Upon concluding that this matches the desired pattern, the function
4354 // will return the pair {NewAddRec, SmallPredsVec} where:
4355 // NewAddRec = {%Start,+,%Step}
4356 // SmallPredsVec = {P1, P2, P3} as follows:
4357 // P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
4358 // P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
4359 // P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
4360 // The returned pair means that SymbolicPHI can be rewritten into NewAddRec
4361 // under the predicates {P1,P2,P3}.
4362 // This predicated rewrite will be cached in PredicatedSCEVRewrites:
4363 // PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
4364 //
4365 // TODO's:
4366 //
4367 // 1) Extend the Induction descriptor to also support inductions that involve
4368 // casts: When needed (namely, when we are called in the context of the
4369 // vectorizer induction analysis), a Set of cast instructions will be
4370 // populated by this method, and provided back to isInductionPHI. This is
4371 // needed to allow the vectorizer to properly record them to be ignored by
4372 // the cost model and to avoid vectorizing them (otherwise these casts,
4373 // which are redundant under the runtime overflow checks, will be
4374 // vectorized, which can be costly).
4375 //
4376 // 2) Support additional induction/PHISCEV patterns: We also want to support
4377 // inductions where the sext-trunc / zext-trunc operations (partly) occur
4378 // after the induction update operation (the induction increment):
4379 //
4380 // (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
4381 // which correspond to a phi->add->trunc->sext/zext->phi update chain.
4382 //
4383 // (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
4384 // which correspond to a phi->trunc->add->sext/zext->phi update chain.
4385 //
4386 // 3) Outline common code with createAddRecFromPHI to avoid duplication.
4388 ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
4390 
4391  // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
4392  // return an AddRec expression under some predicate.
4393 
4394  auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4395  const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4396  assert(L && "Expecting an integer loop header phi");
4397 
4398  // The loop may have multiple entrances or multiple exits; we can analyze
4399  // this phi as an addrec if it has a unique entry value and a unique
4400  // backedge value.
4401  Value *BEValueV = nullptr, *StartValueV = nullptr;
4402  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4403  Value *V = PN->getIncomingValue(i);
4404  if (L->contains(PN->getIncomingBlock(i))) {
4405  if (!BEValueV) {
4406  BEValueV = V;
4407  } else if (BEValueV != V) {
4408  BEValueV = nullptr;
4409  break;
4410  }
4411  } else if (!StartValueV) {
4412  StartValueV = V;
4413  } else if (StartValueV != V) {
4414  StartValueV = nullptr;
4415  break;
4416  }
4417  }
4418  if (!BEValueV || !StartValueV)
4419  return None;
4420 
4421  const SCEV *BEValue = getSCEV(BEValueV);
4422 
4423  // If the value coming around the backedge is an add with the symbolic
4424  // value we just inserted, possibly with casts that we can ignore under
4425  // an appropriate runtime guard, then we found a simple induction variable!
4426  const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
4427  if (!Add)
4428  return None;
4429 
4430  // If there is a single occurrence of the symbolic value, possibly
4431  // casted, replace it with a recurrence.
4432  unsigned FoundIndex = Add->getNumOperands();
4433  Type *TruncTy = nullptr;
4434  bool Signed;
4435  for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4436  if ((TruncTy =
4437  isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
4438  if (FoundIndex == e) {
4439  FoundIndex = i;
4440  break;
4441  }
4442 
4443  if (FoundIndex == Add->getNumOperands())
4444  return None;
4445 
4446  // Create an add with everything but the specified operand.
4448  for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4449  if (i != FoundIndex)
4450  Ops.push_back(Add->getOperand(i));
4451  const SCEV *Accum = getAddExpr(Ops);
4452 
4453  // The runtime checks will not be valid if the step amount is
4454  // varying inside the loop.
4455  if (!isLoopInvariant(Accum, L))
4456  return None;
4457 
4458  // *** Part2: Create the predicates
4459 
4460  // Analysis was successful: we have a phi-with-cast pattern for which we
4461  // can return an AddRec expression under the following predicates:
4462  //
4463  // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
4464  // fits within the truncated type (does not overflow) for i = 0 to n-1.
4465  // P2: An Equal predicate that guarantees that
4466  // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
4467  // P3: An Equal predicate that guarantees that
4468  // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
4469  //
4470  // As we next prove, the above predicates guarantee that:
4471  // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
4472  //
4473  //
4474  // More formally, we want to prove that:
4475  // Expr(i+1) = Start + (i+1) * Accum
4476  // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4477  //
4478  // Given that:
4479  // 1) Expr(0) = Start
4480  // 2) Expr(1) = Start + Accum
4481  // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
4482  // 3) Induction hypothesis (step i):
4483  // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
4484  //
4485  // Proof:
4486  // Expr(i+1) =
4487  // = Start + (i+1)*Accum
4488  // = (Start + i*Accum) + Accum
4489  // = Expr(i) + Accum
4490  // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
4491  // :: from step i
4492  //
4493  // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
4494  //
4495  // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
4496  // + (Ext ix (Trunc iy (Accum) to ix) to iy)
4497  // + Accum :: from P3
4498  //
4499  // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
4500  // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
4501  //
4502  // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
4503  // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4504  //
4505  // By induction, the same applies to all iterations 1<=i<n:
4506  //
4507 
4508  // Create a truncated addrec for which we will add a no overflow check (P1).
4509  const SCEV *StartVal = getSCEV(StartValueV);
4510  const SCEV *PHISCEV =
4511  getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
4512  getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
4513 
4514  // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
4515  // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
4516  // will be constant.
4517  //
4518  // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
4519  // add P1.
4520  if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
4524  const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
4525  Predicates.push_back(AddRecPred);
4526  } else
4527  assert(isa<SCEVConstant>(PHISCEV) && "Expected constant SCEV");
4528 
4529  // Create the Equal Predicates P2,P3:
4530 
4531  // It is possible that the predicates P2 and/or P3 are computable at
4532  // compile time due to StartVal and/or Accum being constants.
4533  // If either one is, then we can check that now and escape if either P2
4534  // or P3 is false.
4535 
4536  // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
4537  // for each of StartVal and Accum
4538  auto GetExtendedExpr = [&](const SCEV *Expr) -> const SCEV * {
4539  assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
4540  const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
4541  const SCEV *ExtendedExpr =
4542  Signed ? getSignExtendExpr(TruncatedExpr, Expr->getType())
4543  : getZeroExtendExpr(TruncatedExpr, Expr->getType());
4544  return ExtendedExpr;
4545  };
4546 
4547  // Given:
4548  // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
4549  // = GetExtendedExpr(Expr)
4550  // Determine whether the predicate P: Expr == ExtendedExpr
4551  // is known to be false at compile time
4552  auto PredIsKnownFalse = [&](const SCEV *Expr,
4553  const SCEV *ExtendedExpr) -> bool {
4554  return Expr != ExtendedExpr &&
4555  isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
4556  };
4557 
4558  const SCEV *StartExtended = GetExtendedExpr(StartVal);
4559  if (PredIsKnownFalse(StartVal, StartExtended)) {
4560  DEBUG(dbgs() << "P2 is compile-time false\n";);
4561  return None;
4562  }
4563 
4564  const SCEV *AccumExtended = GetExtendedExpr(Accum);
4565  if (PredIsKnownFalse(Accum, AccumExtended)) {
4566  DEBUG(dbgs() << "P3 is compile-time false\n";);
4567  return None;
4568  }
4569 
4570  auto AppendPredicate = [&](const SCEV *Expr,
4571  const SCEV *ExtendedExpr) -> void {
4572  if (Expr != ExtendedExpr &&
4573  !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
4574  const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
4575  DEBUG (dbgs() << "Added Predicate: " << *Pred);
4576  Predicates.push_back(Pred);
4577  }
4578  };
4579 
4580  AppendPredicate(StartVal, StartExtended);
4581  AppendPredicate(Accum, AccumExtended);
4582 
4583  // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
4584  // which the casts had been folded away. The caller can rewrite SymbolicPHI
4585  // into NewAR if it will also add the runtime overflow checks specified in
4586  // Predicates.
4587  auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
4588 
4589  std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
4590  std::make_pair(NewAR, Predicates);
4591  // Remember the result of the analysis for this SCEV at this locayyytion.
4592  PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
4593  return PredRewrite;
4594 }
4595 
4598  auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4599  const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4600  if (!L)
4601  return None;
4602 
4603  // Check to see if we already analyzed this PHI.
4604  auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
4605  if (I != PredicatedSCEVRewrites.end()) {
4606  std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
4607  I->second;
4608  // Analysis was done before and failed to create an AddRec:
4609  if (Rewrite.first == SymbolicPHI)
4610  return None;
4611  // Analysis was done before and succeeded to create an AddRec under
4612  // a predicate:
4613  assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
4614  assert(!(Rewrite.second).empty() && "Expected to find Predicates");
4615  return Rewrite;
4616  }
4617 
4619  Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
4620 
4621  // Record in the cache that the analysis failed
4622  if (!Rewrite) {
4624  PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
4625  return None;
4626  }
4627 
4628  return Rewrite;
4629 }
4630 
4631 /// A helper function for createAddRecFromPHI to handle simple cases.
4632 ///
4633 /// This function tries to find an AddRec expression for the simplest (yet most
4634 /// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
4635 /// If it fails, createAddRecFromPHI will use a more general, but slow,
4636 /// technique for finding the AddRec expression.
4637 const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
4638  Value *BEValueV,
4639  Value *StartValueV) {
4640  const Loop *L = LI.getLoopFor(PN->getParent());
4641  assert(L && L->getHeader() == PN->getParent());
4642  assert(BEValueV && StartValueV);
4643 
4644  auto BO = MatchBinaryOp(BEValueV, DT);
4645  if (!BO)
4646  return nullptr;
4647 
4648  if (BO->Opcode != Instruction::Add)
4649  return nullptr;
4650 
4651  const SCEV *Accum = nullptr;
4652  if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
4653  Accum = getSCEV(BO->RHS);
4654  else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
4655  Accum = getSCEV(BO->LHS);
4656 
4657  if (!Accum)
4658  return nullptr;
4659 
4661  if (BO->IsNUW)
4662  Flags = setFlags(Flags, SCEV::FlagNUW);
4663  if (BO->IsNSW)
4664  Flags = setFlags(Flags, SCEV::FlagNSW);
4665 
4666  const SCEV *StartVal = getSCEV(StartValueV);
4667  const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4668 
4669  ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4670 
4671  // We can add Flags to the post-inc expression only if we
4672  // know that it is *undefined behavior* for BEValueV to
4673  // overflow.
4674  if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4675  if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4676  (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4677 
4678  return PHISCEV;
4679 }
4680 
4681 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
4682  const Loop *L = LI.getLoopFor(PN->getParent());
4683  if (!L || L->getHeader() != PN->getParent())
4684  return nullptr;
4685 
4686  // The loop may have multiple entrances or multiple exits; we can analyze
4687  // this phi as an addrec if it has a unique entry value and a unique
4688  // backedge value.
4689  Value *BEValueV = nullptr, *StartValueV = nullptr;
4690  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4691  Value *V = PN->getIncomingValue(i);
4692  if (L->contains(PN->getIncomingBlock(i))) {
4693  if (!BEValueV) {
4694  BEValueV = V;
4695  } else if (BEValueV != V) {
4696  BEValueV = nullptr;
4697  break;
4698  }
4699  } else if (!StartValueV) {
4700  StartValueV = V;
4701  } else if (StartValueV != V) {
4702  StartValueV = nullptr;
4703  break;
4704  }
4705  }
4706  if (!BEValueV || !StartValueV)
4707  return nullptr;
4708 
4709  assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
4710  "PHI node already processed?");
4711 
4712  // First, try to find AddRec expression without creating a fictituos symbolic
4713  // value for PN.
4714  if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
4715  return S;
4716 
4717  // Handle PHI node value symbolically.
4718  const SCEV *SymbolicName = getUnknown(PN);
4719  ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
4720 
4721  // Using this symbolic name for the PHI, analyze the value coming around
4722  // the back-edge.
4723  const SCEV *BEValue = getSCEV(BEValueV);
4724 
4725  // NOTE: If BEValue is loop invariant, we know that the PHI node just
4726  // has a special value for the first iteration of the loop.
4727 
4728  // If the value coming around the backedge is an add with the symbolic
4729  // value we just inserted, then we found a simple induction variable!
4730  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
4731  // If there is a single occurrence of the symbolic value, replace it
4732  // with a recurrence.
4733  unsigned FoundIndex = Add->getNumOperands();
4734  for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4735  if (Add->getOperand(i) == SymbolicName)
4736  if (FoundIndex == e) {
4737  FoundIndex = i;
4738  break;
4739  }
4740 
4741  if (FoundIndex != Add->getNumOperands()) {
4742  // Create an add with everything but the specified operand.
4744  for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4745  if (i != FoundIndex)
4746  Ops.push_back(Add->getOperand(i));
4747  const SCEV *Accum = getAddExpr(Ops);
4748 
4749  // This is not a valid addrec if the step amount is varying each
4750  // loop iteration, but is not itself an addrec in this loop.
4751  if (isLoopInvariant(Accum, L) ||
4752  (isa<SCEVAddRecExpr>(Accum) &&
4753  cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
4755 
4756  if (auto BO = MatchBinaryOp(BEValueV, DT)) {
4757  if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
4758  if (BO->IsNUW)
4759  Flags = setFlags(Flags, SCEV::FlagNUW);
4760  if (BO->IsNSW)
4761  Flags = setFlags(Flags, SCEV::FlagNSW);
4762  }
4763  } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
4764  // If the increment is an inbounds GEP, then we know the address
4765  // space cannot be wrapped around. We cannot make any guarantee
4766  // about signed or unsigned overflow because pointers are
4767  // unsigned but we may have a negative index from the base
4768  // pointer. We can guarantee that no unsigned wrap occurs if the
4769  // indices form a positive value.
4770  if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
4771  Flags = setFlags(Flags, SCEV::FlagNW);
4772 
4773  const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
4774  if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
4775  Flags = setFlags(Flags, SCEV::FlagNUW);
4776  }
4777 
4778  // We cannot transfer nuw and nsw flags from subtraction
4779  // operations -- sub nuw X, Y is not the same as add nuw X, -Y
4780  // for instance.
4781  }
4782 
4783  const SCEV *StartVal = getSCEV(StartValueV);
4784  const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4785 
4786  // Okay, for the entire analysis of this edge we assumed the PHI
4787  // to be symbolic. We now need to go back and purge all of the
4788  // entries for the scalars that use the symbolic expression.
4789  forgetSymbolicName(PN, SymbolicName);
4790  ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4791 
4792  // We can add Flags to the post-inc expression only if we
4793  // know that it is *undefined behavior* for BEValueV to
4794  // overflow.
4795  if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4796  if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4797  (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4798 
4799  return PHISCEV;
4800  }
4801  }
4802  } else {
4803  // Otherwise, this could be a loop like this:
4804  // i = 0; for (j = 1; ..; ++j) { .... i = j; }
4805  // In this case, j = {1,+,1} and BEValue is j.
4806  // Because the other in-value of i (0) fits the evolution of BEValue
4807  // i really is an addrec evolution.
4808  //
4809  // We can generalize this saying that i is the shifted value of BEValue
4810  // by one iteration:
4811  // PHI(f(0), f({1,+,1})) --> f({0,+,1})
4812  const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
4813  const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
4814  if (Shifted != getCouldNotCompute() &&
4815  Start != getCouldNotCompute()) {
4816  const SCEV *StartVal = getSCEV(StartValueV);
4817  if (Start == StartVal) {
4818  // Okay, for the entire analysis of this edge we assumed the PHI
4819  // to be symbolic. We now need to go back and purge all of the
4820  // entries for the scalars that use the symbolic expression.
4821  forgetSymbolicName(PN, SymbolicName);
4822  ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
4823  return Shifted;
4824  }
4825  }
4826  }
4827 
4828  // Remove the temporary PHI node SCEV that has been inserted while intending
4829  // to create an AddRecExpr for this PHI node. We can not keep this temporary
4830  // as it will prevent later (possibly simpler) SCEV expressions to be added
4831  // to the ValueExprMap.
4832  eraseValueFromMap(PN);
4833 
4834  return nullptr;
4835 }
4836 
4837 // Checks if the SCEV S is available at BB. S is considered available at BB
4838 // if S can be materialized at BB without introducing a fault.
4839 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
4840  BasicBlock *BB) {
4841  struct CheckAvailable {
4842  bool TraversalDone = false;
4843  bool Available = true;
4844 
4845  const Loop *L = nullptr; // The loop BB is in (can be nullptr)
4846  BasicBlock *BB = nullptr;
4847  DominatorTree &DT;
4848 
4849  CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
4850  : L(L), BB(BB), DT(DT) {}
4851 
4852  bool setUnavailable() {
4853  TraversalDone = true;
4854  Available = false;
4855  return false;
4856  }
4857 
4858  bool follow(const SCEV *S) {
4859  switch (S->getSCEVType()) {
4860  case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
4861  case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
4862  // These expressions are available if their operand(s) is/are.
4863  return true;
4864 
4865  case scAddRecExpr: {
4866  // We allow add recurrences that are on the loop BB is in, or some
4867  // outer loop. This guarantees availability because the value of the
4868  // add recurrence at BB is simply the "current" value of the induction
4869  // variable. We can relax this in the future; for instance an add
4870  // recurrence on a sibling dominating loop is also available at BB.
4871  const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
4872  if (L && (ARLoop == L || ARLoop->contains(L)))
4873  return true;
4874 
4875  return setUnavailable();
4876  }
4877 
4878  case scUnknown: {
4879  // For SCEVUnknown, we check for simple dominance.
4880  const auto *SU = cast<SCEVUnknown>(S);
4881  Value *V = SU->getValue();
4882 
4883  if (isa<Argument>(V))
4884  return false;
4885 
4886  if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
4887  return false;
4888 
4889  return setUnavailable();
4890  }
4891 
4892  case scUDivExpr:
4893  case scCouldNotCompute:
4894  // We do not try to smart about these at all.
4895  return setUnavailable();
4896  }
4897  llvm_unreachable("switch should be fully covered!");
4898  }
4899 
4900  bool isDone() { return TraversalDone; }
4901  };
4902 
4903  CheckAvailable CA(L, BB, DT);
4905 
4906  ST.visitAll(S);
4907  return CA.Available;
4908 }
4909 
4910 // Try to match a control flow sequence that branches out at BI and merges back
4911 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
4912 // match.
4914  Value *&C, Value *&LHS, Value *&RHS) {
4915  C = BI->getCondition();
4916 
4917  BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
4918  BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
4919 
4920  if (!LeftEdge.isSingleEdge())
4921  return false;
4922 
4923  assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
4924 
4925  Use &LeftUse = Merge->getOperandUse(0);
4926  Use &RightUse = Merge->getOperandUse(1);
4927 
4928  if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
4929  LHS = LeftUse;
4930  RHS = RightUse;
4931  return true;
4932  }
4933 
4934  if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
4935  LHS = RightUse;
4936  RHS = LeftUse;
4937  return true;
4938  }
4939 
4940  return false;
4941 }
4942 
4943 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
4944  auto IsReachable =
4945  [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
4946  if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
4947  const Loop *L = LI.getLoopFor(PN->getParent());
4948 
4949  // We don't want to break LCSSA, even in a SCEV expression tree.
4950  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
4951  if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
4952  return nullptr;
4953 
4954  // Try to match
4955  //
4956  // br %cond, label %left, label %right
4957  // left:
4958  // br label %merge
4959  // right:
4960  // br label %merge
4961  // merge:
4962  // V = phi [ %x, %left ], [ %y, %right ]
4963  //
4964  // as "select %cond, %x, %y"
4965 
4966  BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
4967  assert(IDom && "At least the entry block should dominate PN");
4968 
4969  auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
4970  Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
4971 
4972  if (BI && BI->isConditional() &&
4973  BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
4974  IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
4975  IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
4976  return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
4977  }
4978 
4979  return nullptr;
4980 }
4981 
4982 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
4983  if (const SCEV *S = createAddRecFromPHI(PN))
4984  return S;
4985 
4986  if (const SCEV *S = createNodeFromSelectLikePHI(PN))
4987  return S;
4988 
4989  // If the PHI has a single incoming value, follow that value, unless the
4990  // PHI's incoming blocks are in a different loop, in which case doing so
4991  // risks breaking LCSSA form. Instcombine would normally zap these, but
4992  // it doesn't have DominatorTree information, so it may miss cases.
4993  if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
4994  if (LI.replacementPreservesLCSSAForm(PN, V))
4995  return getSCEV(V);
4996 
4997  // If it's not a loop phi, we can't handle it yet.
4998  return getUnknown(PN);
4999 }
5000 
5001 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
5002  Value *Cond,
5003  Value *TrueVal,
5004  Value *FalseVal) {
5005  // Handle "constant" branch or select. This can occur for instance when a
5006  // loop pass transforms an inner loop and moves on to process the outer loop.
5007  if (auto *CI = dyn_cast<ConstantInt>(Cond))
5008  return getSCEV(CI->isOne() ? TrueVal : FalseVal);
5009 
5010  // Try to match some simple smax or umax patterns.
5011  auto *ICI = dyn_cast<ICmpInst>(Cond);
5012  if (!ICI)
5013  return getUnknown(I);
5014 
5015  Value *LHS = ICI->getOperand(0);
5016  Value *RHS = ICI->getOperand(1);
5017 
5018  switch (ICI->getPredicate()) {
5019  case ICmpInst::ICMP_SLT:
5020  case ICmpInst::ICMP_SLE:
5021  std::swap(LHS, RHS);
5023  case ICmpInst::ICMP_SGT:
5024  case ICmpInst::ICMP_SGE:
5025  // a >s b ? a+x : b+x -> smax(a, b)+x
5026  // a >s b ? b+x : a+x -> smin(a, b)+x
5027  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5028  const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
5029  const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
5030  const SCEV *LA = getSCEV(TrueVal);
5031  const SCEV *RA = getSCEV(FalseVal);
5032  const SCEV *LDiff = getMinusSCEV(LA, LS);
5033  const SCEV *RDiff = getMinusSCEV(RA, RS);
5034  if (LDiff == RDiff)
5035  return getAddExpr(getSMaxExpr(LS, RS), LDiff);
5036  LDiff = getMinusSCEV(LA, RS);
5037  RDiff = getMinusSCEV(RA, LS);
5038  if (LDiff == RDiff)
5039  return getAddExpr(getSMinExpr(LS, RS), LDiff);
5040  }
5041  break;
5042  case ICmpInst::ICMP_ULT:
5043  case ICmpInst::ICMP_ULE:
5044  std::swap(LHS, RHS);
5046  case ICmpInst::ICMP_UGT:
5047  case ICmpInst::ICMP_UGE:
5048  // a >u b ? a+x : b+x -> umax(a, b)+x
5049  // a >u b ? b+x : a+x -> umin(a, b)+x
5050  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5051  const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5052  const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
5053  const SCEV *LA = getSCEV(TrueVal);
5054  const SCEV *RA = getSCEV(FalseVal);
5055  const SCEV *LDiff = getMinusSCEV(LA, LS);
5056  const SCEV *RDiff = getMinusSCEV(RA, RS);
5057  if (LDiff == RDiff)
5058  return getAddExpr(getUMaxExpr(LS, RS), LDiff);
5059  LDiff = getMinusSCEV(LA, RS);
5060  RDiff = getMinusSCEV(RA, LS);
5061  if (LDiff == RDiff)
5062  return getAddExpr(getUMinExpr(LS, RS), LDiff);
5063  }
5064  break;
5065  case ICmpInst::ICMP_NE:
5066  // n != 0 ? n+x : 1+x -> umax(n, 1)+x
5067  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5068  isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5069  const SCEV *One = getOne(I->getType());
5070  const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5071  const SCEV *LA = getSCEV(TrueVal);
5072  const SCEV *RA = getSCEV(FalseVal);
5073  const SCEV *LDiff = getMinusSCEV(LA, LS);
5074  const SCEV *RDiff = getMinusSCEV(RA, One);
5075  if (LDiff == RDiff)
5076  return getAddExpr(getUMaxExpr(One, LS), LDiff);
5077  }
5078  break;
5079  case ICmpInst::ICMP_EQ:
5080  // n == 0 ? 1+x : n+x -> umax(n, 1)+x
5081  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5082  isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5083  const SCEV *One = getOne(I->getType());
5084  const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5085  const SCEV *LA = getSCEV(TrueVal);
5086  const SCEV *RA = getSCEV(FalseVal);
5087  const SCEV *LDiff = getMinusSCEV(LA, One);
5088  const SCEV *RDiff = getMinusSCEV(RA, LS);
5089  if (LDiff == RDiff)
5090  return getAddExpr(getUMaxExpr(One, LS), LDiff);
5091  }
5092  break;
5093  default:
5094  break;
5095  }
5096 
5097  return getUnknown(I);
5098 }
5099 
5100 /// Expand GEP instructions into add and multiply operations. This allows them
5101 /// to be analyzed by regular SCEV code.
5102 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
5103  // Don't attempt to analyze GEPs over unsized objects.
5104  if (!GEP->getSourceElementType()->isSized())
5105  return getUnknown(GEP);
5106 
5107  SmallVector<const SCEV *, 4> IndexExprs;
5108  for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
5109  IndexExprs.push_back(getSCEV(*Index));
5110  return getGEPExpr(GEP, IndexExprs);
5111 }
5112 
5113 uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
5114  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5115  return C->getAPInt().countTrailingZeros();
5116 
5117  if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
5118  return std::min(GetMinTrailingZeros(T->getOperand()),
5119  (uint32_t)getTypeSizeInBits(T->getType()));
5120 
5121  if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
5122  uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5123  return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5124  ? getTypeSizeInBits(E->getType())
5125  : OpRes;
5126  }
5127 
5128  if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
5129  uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5130  return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5131  ? getTypeSizeInBits(E->getType())
5132  : OpRes;
5133  }
5134 
5135  if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
5136  // The result is the min of all operands results.
5137  uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5138  for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5139  MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5140  return MinOpRes;
5141  }
5142 
5143  if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
5144  // The result is the sum of all operands results.
5145  uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
5146  uint32_t BitWidth = getTypeSizeInBits(M->getType());
5147  for (unsigned i = 1, e = M->getNumOperands();
5148  SumOpRes != BitWidth && i != e; ++i)
5149  SumOpRes =
5150  std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
5151  return SumOpRes;
5152  }
5153 
5154  if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
5155  // The result is the min of all operands results.
5156  uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5157  for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5158  MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5159  return MinOpRes;
5160  }
5161 
5162  if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
5163  // The result is the min of all operands results.
5164  uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5165  for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5166  MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5167  return MinOpRes;
5168  }
5169 
5170  if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
5171  // The result is the min of all operands results.
5172  uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5173  for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5174  MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5175  return MinOpRes;
5176  }
5177 
5178  if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5179  // For a SCEVUnknown, ask ValueTracking.
5180  KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
5181  return Known.countMinTrailingZeros();
5182  }
5183 
5184  // SCEVUDivExpr
5185  return 0;
5186 }
5187 
5189  auto I = MinTrailingZerosCache.find(S);
5190  if (I != MinTrailingZerosCache.end())
5191  return I->second;
5192 
5193  uint32_t Result = GetMinTrailingZerosImpl(S);
5194  auto InsertPair = MinTrailingZerosCache.insert({S, Result});
5195  assert(InsertPair.second && "Should insert a new key");
5196  return InsertPair.first->second;
5197 }
5198 
5199 /// Helper method to assign a range to V from metadata present in the IR.
5201  if (Instruction *I = dyn_cast<Instruction>(V))
5203  return getConstantRangeFromMetadata(*MD);
5204 
5205  return None;
5206 }
5207 
5208 /// Determine the range for a particular SCEV. If SignHint is
5209 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
5210 /// with a "cleaner" unsigned (resp. signed) representation.
5211 const ConstantRange &
5212 ScalarEvolution::getRangeRef(const SCEV *S,
5213  ScalarEvolution::RangeSignHint SignHint) {
5215  SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
5216  : SignedRanges;
5217 
5218  // See if we've computed this range already.
5220  if (I != Cache.end())
5221  return I->second;
5222 
5223  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5224  return setRange(C, SignHint, ConstantRange(C->getAPInt()));
5225 
5226  unsigned BitWidth = getTypeSizeInBits(S->getType());
5227  ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
5228 
5229  // If the value has known zeros, the maximum value will have those known zeros
5230  // as well.
5231  uint32_t TZ = GetMinTrailingZeros(S);
5232  if (TZ != 0) {
5233  if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
5234  ConservativeResult =
5236  APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
5237  else
5238  ConservativeResult = ConstantRange(
5239  APInt::getSignedMinValue(BitWidth),
5240  APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
5241  }
5242 
5243  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
5244  ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
5245  for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
5246  X = X.add(getRangeRef(Add->getOperand(i), SignHint));
5247  return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
5248  }
5249 
5250  if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
5251  ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
5252  for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
5253  X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
5254  return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
5255  }
5256 
5257  if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
5258  ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
5259  for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
5260  X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
5261  return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
5262  }
5263 
5264  if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
5265  ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
5266  for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
5267  X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
5268  return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
5269  }
5270 
5271  if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
5272  ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
5273  ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
5274  return setRange(UDiv, SignHint,
5275  ConservativeResult.intersectWith(X.udiv(Y)));
5276  }
5277 
5278  if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
5279  ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
5280  return setRange(ZExt, SignHint,
5281  ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
5282  }
5283 
5284  if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
5285  ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
5286  return setRange(SExt, SignHint,
5287  ConservativeResult.intersectWith(X.signExtend(BitWidth)));
5288  }
5289 
5290  if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
5291  ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
5292  return setRange(Trunc, SignHint,
5293  ConservativeResult.intersectWith(X.truncate(BitWidth)));
5294  }
5295 
5296  if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
5297  // If there's no unsigned wrap, the value will never be less than its
5298  // initial value.
5299  if (AddRec->hasNoUnsignedWrap())
5300  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
5301  if (!C->getValue()->isZero())
5302  ConservativeResult = ConservativeResult.intersectWith(
5303  ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
5304 
5305  // If there's no signed wrap, and all the operands have the same sign or
5306  // zero, the value won't ever change sign.
5307  if (AddRec->hasNoSignedWrap()) {
5308  bool AllNonNeg = true;
5309  bool AllNonPos = true;
5310  for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5311  if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
5312  if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
5313  }
5314  if (AllNonNeg)
5315  ConservativeResult = ConservativeResult.intersectWith(
5316  ConstantRange(APInt(BitWidth, 0),
5317  APInt::getSignedMinValue(BitWidth)));
5318  else if (AllNonPos)
5319  ConservativeResult = ConservativeResult.intersectWith(
5321  APInt(BitWidth, 1)));
5322  }
5323 
5324  // TODO: non-affine addrec
5325  if (AddRec->isAffine()) {
5326  const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
5327  if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
5328  getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
5329  auto RangeFromAffine = getRangeForAffineAR(
5330  AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5331  BitWidth);
5332  if (!RangeFromAffine.isFullSet())
5333  ConservativeResult =
5334  ConservativeResult.intersectWith(RangeFromAffine);
5335 
5336  auto RangeFromFactoring = getRangeViaFactoring(
5337  AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5338  BitWidth);
5339  if (!RangeFromFactoring.isFullSet())
5340  ConservativeResult =
5341  ConservativeResult.intersectWith(RangeFromFactoring);
5342  }
5343  }
5344 
5345  return setRange(AddRec, SignHint, std::move(ConservativeResult));
5346  }
5347 
5348  if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5349  // Check if the IR explicitly contains !range metadata.
5350  Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
5351  if (MDRange.hasValue())
5352  ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
5353 
5354  // Split here to avoid paying the compile-time cost of calling both
5355  // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
5356  // if needed.
5357  const DataLayout &DL = getDataLayout();
5358  if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
5359  // For a SCEVUnknown, ask ValueTracking.
5360  KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5361  if (Known.One != ~Known.Zero + 1)
5362  ConservativeResult =
5363  ConservativeResult.intersectWith(ConstantRange(Known.One,
5364  ~Known.Zero + 1));
5365  } else {
5366  assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
5367  "generalize as needed!");
5368  unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5369  if (NS > 1)
5370  ConservativeResult = ConservativeResult.intersectWith(
5371  ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
5372  APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
5373  }
5374 
5375  return setRange(U, SignHint, std::move(ConservativeResult));
5376  }
5377 
5378  return setRange(S, SignHint, std::move(ConservativeResult));
5379 }
5380 
5381 // Given a StartRange, Step and MaxBECount for an expression compute a range of
5382 // values that the expression can take. Initially, the expression has a value
5383 // from StartRange and then is changed by Step up to MaxBECount times. Signed
5384 // argument defines if we treat Step as signed or unsigned.
5386  const ConstantRange &StartRange,
5387  const APInt &MaxBECount,
5388  unsigned BitWidth, bool Signed) {
5389  // If either Step or MaxBECount is 0, then the expression won't change, and we
5390  // just need to return the initial range.
5391  if (Step == 0 || MaxBECount == 0)
5392  return StartRange;
5393 
5394  // If we don't know anything about the initial value (i.e. StartRange is
5395  // FullRange), then we don't know anything about the final range either.
5396  // Return FullRange.
5397  if (StartRange.isFullSet())
5398  return ConstantRange(BitWidth, /* isFullSet = */ true);
5399 
5400  // If Step is signed and negative, then we use its absolute value, but we also
5401  // note that we're moving in the opposite direction.
5402  bool Descending = Signed && Step.isNegative();
5403 
5404  if (Signed)
5405  // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
5406  // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
5407  // This equations hold true due to the well-defined wrap-around behavior of
5408  // APInt.
5409  Step = Step.abs();
5410 
5411  // Check if Offset is more than full span of BitWidth. If it is, the
5412  // expression is guaranteed to overflow.
5413  if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
5414  return ConstantRange(BitWidth, /* isFullSet = */ true);
5415 
5416  // Offset is by how much the expression can change. Checks above guarantee no
5417  // overflow here.
5418  APInt Offset = Step * MaxBECount;
5419 
5420  // Minimum value of the final range will match the minimal value of StartRange
5421  // if the expression is increasing and will be decreased by Offset otherwise.
5422  // Maximum value of the final range will match the maximal value of StartRange
5423  // if the expression is decreasing and will be increased by Offset otherwise.
5424  APInt StartLower = StartRange.getLower();
5425  APInt StartUpper = StartRange.getUpper() - 1;
5426  APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
5427  : (StartUpper + std::move(Offset));
5428 
5429  // It's possible that the new minimum/maximum value will fall into the initial
5430  // range (due to wrap around). This means that the expression can take any
5431  // value in this bitwidth, and we have to return full range.
5432  if (StartRange.contains(MovedBoundary))
5433  return ConstantRange(BitWidth, /* isFullSet = */ true);
5434 
5435  APInt NewLower =
5436  Descending ? std::move(MovedBoundary) : std::move(StartLower);
5437  APInt NewUpper =
5438  Descending ? std::move(StartUpper) : std::move(MovedBoundary);
5439  NewUpper += 1;
5440 
5441  // If we end up with full range, return a proper full range.
5442  if (NewLower == NewUpper)
5443  return ConstantRange(BitWidth, /* isFullSet = */ true);
5444 
5445  // No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
5446  return ConstantRange(std::move(NewLower), std::move(NewUpper));
5447 }
5448 
5449 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
5450  const SCEV *Step,
5451  const SCEV *MaxBECount,
5452  unsigned BitWidth) {
5453  assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
5454  getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&