1//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// This file contains the implementation of the scalar evolution analysis
10// engine, which is used primarily to analyze expressions involving induction
11// variables in loops.
12//
13// There are several aspects to this library. First is the representation of
14// scalar expressions, which are represented as subclasses of the SCEV class.
15// These classes are used to represent certain types of subexpressions that we
16// can handle. We only create one SCEV of a particular shape, so
17// pointer-comparisons for equality are legal.
18//
19// One important aspect of the SCEV objects is that they are never cyclic, even
20// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
21// the PHI node is one of the idioms that we can represent (e.g., a polynomial
22// recurrence) then we represent it directly as a recurrence node, otherwise we
23// represent it as a SCEVUnknown node.
24//
25// In addition to being able to represent expressions of various types, we also
26// have folders that are used to build the *canonical* representation for a
27// particular expression. These folders are capable of using a variety of
28// rewrite rules to simplify the expressions.
29//
30// Once the folders are defined, we can implement the more interesting
31// higher-level code, such as the code that recognizes PHI nodes of various
32// types, computes the execution count of a loop, etc.
33//
34// TODO: We should use these routines and value representations to implement
35// dependence analysis!
36//
37//===----------------------------------------------------------------------===//
38//
39// There are several good references for the techniques used in this analysis.
40//
41// Chains of recurrences -- a method to expedite the evaluation
42// of closed-form functions
43// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
44//
45// On computational properties of chains of recurrences
46// Eugene V. Zima
47//
48// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
49// Robert A. van Engelen
50//
51// Efficient Symbolic Analysis for Optimizing Compilers
52// Robert A. van Engelen
53//
54// Using the chains of recurrences algebra for data dependence testing and
55// induction variable substitution
56// MS Thesis, Johnie Birch
57//
58//===----------------------------------------------------------------------===//
59
60#include "llvm/Analysis/ScalarEvolution.h"
61#include "llvm/ADT/APInt.h"
62#include "llvm/ADT/ArrayRef.h"
63#include "llvm/ADT/DenseMap.h"
64#include "llvm/ADT/DepthFirstIterator.h"
65#include "llvm/ADT/EquivalenceClasses.h"
66#include "llvm/ADT/FoldingSet.h"
67#include "llvm/ADT/STLExtras.h"
68#include "llvm/ADT/ScopeExit.h"
69#include "llvm/ADT/Sequence.h"
70#include "llvm/ADT/SmallPtrSet.h"
71#include "llvm/ADT/SmallSet.h"
72#include "llvm/ADT/SmallVector.h"
73#include "llvm/ADT/Statistic.h"
74#include "llvm/ADT/StringExtras.h"
75#include "llvm/ADT/StringRef.h"
76#include "llvm/Analysis/AssumptionCache.h"
77#include "llvm/Analysis/ConstantFolding.h"
78#include "llvm/Analysis/InstructionSimplify.h"
79#include "llvm/Analysis/LoopInfo.h"
80#include "llvm/Analysis/MemoryBuiltins.h"
81#include "llvm/Analysis/ScalarEvolutionExpressions.h"
82#include "llvm/Analysis/TargetLibraryInfo.h"
83#include "llvm/Analysis/ValueTracking.h"
84#include "llvm/Config/llvm-config.h"
85#include "llvm/IR/Argument.h"
86#include "llvm/IR/BasicBlock.h"
87#include "llvm/IR/CFG.h"
88#include "llvm/IR/Constant.h"
89#include "llvm/IR/ConstantRange.h"
90#include "llvm/IR/Constants.h"
91#include "llvm/IR/DataLayout.h"
92#include "llvm/IR/DerivedTypes.h"
93#include "llvm/IR/Dominators.h"
94#include "llvm/IR/Function.h"
95#include "llvm/IR/GlobalAlias.h"
96#include "llvm/IR/GlobalValue.h"
97#include "llvm/IR/InstIterator.h"
98#include "llvm/IR/InstrTypes.h"
99#include "llvm/IR/Instruction.h"
100#include "llvm/IR/Instructions.h"
101#include "llvm/IR/IntrinsicInst.h"
102#include "llvm/IR/Intrinsics.h"
103#include "llvm/IR/LLVMContext.h"
104#include "llvm/IR/Operator.h"
105#include "llvm/IR/PatternMatch.h"
106#include "llvm/IR/Type.h"
107#include "llvm/IR/Use.h"
108#include "llvm/IR/User.h"
109#include "llvm/IR/Value.h"
110#include "llvm/IR/Verifier.h"
111#include "llvm/InitializePasses.h"
112#include "llvm/Pass.h"
113#include "llvm/Support/Casting.h"
114#include "llvm/Support/CommandLine.h"
115#include "llvm/Support/Compiler.h"
116#include "llvm/Support/Debug.h"
117#include "llvm/Support/ErrorHandling.h"
118#include "llvm/Support/KnownBits.h"
119#include "llvm/Support/SaveAndRestore.h"
120#include "llvm/Support/raw_ostream.h"
121#include <algorithm>
122#include <cassert>
123#include <climits>
124#include <cstdint>
125#include <cstdlib>
126#include <map>
127#include <memory>
128#include <numeric>
129#include <optional>
130#include <tuple>
131#include <utility>
132#include <vector>
133
134using namespace llvm;
135using namespace PatternMatch;
136
137#define DEBUG_TYPE "scalar-evolution"
138
139STATISTIC(NumExitCountsComputed,
140 "Number of loop exits with predictable exit counts");
141STATISTIC(NumExitCountsNotComputed,
142 "Number of loop exits without predictable exit counts");
143STATISTIC(NumBruteForceTripCountsComputed,
144 "Number of loops with trip counts computed by force");
145
146#ifdef EXPENSIVE_CHECKS
147bool llvm::VerifySCEV = true;
148#else
149bool llvm::VerifySCEV = false;
150#endif
151
152static cl::opt<unsigned>
153 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
154 cl::desc("Maximum number of iterations SCEV will "
155 "symbolically execute a constant "
156 "derived loop"),
157 cl::init(Val: 100));
158
159static cl::opt<bool, true> VerifySCEVOpt(
160 "verify-scev", cl::Hidden, cl::location(L&: VerifySCEV),
161 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
162static cl::opt<bool> VerifySCEVStrict(
163 "verify-scev-strict", cl::Hidden,
164 cl::desc("Enable stricter verification with -verify-scev is passed"));
165
166static cl::opt<bool> VerifyIR(
167 "scev-verify-ir", cl::Hidden,
168 cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
169 cl::init(Val: false));
170
171static cl::opt<unsigned> MulOpsInlineThreshold(
172 "scev-mulops-inline-threshold", cl::Hidden,
173 cl::desc("Threshold for inlining multiplication operands into a SCEV"),
174 cl::init(Val: 32));
175
176static cl::opt<unsigned> AddOpsInlineThreshold(
177 "scev-addops-inline-threshold", cl::Hidden,
178 cl::desc("Threshold for inlining addition operands into a SCEV"),
179 cl::init(Val: 500));
180
181static cl::opt<unsigned> MaxSCEVCompareDepth(
182 "scalar-evolution-max-scev-compare-depth", cl::Hidden,
183 cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
184 cl::init(Val: 32));
185
186static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
187 "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
188 cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
189 cl::init(Val: 2));
190
191static cl::opt<unsigned> MaxValueCompareDepth(
192 "scalar-evolution-max-value-compare-depth", cl::Hidden,
193 cl::desc("Maximum depth of recursive value complexity comparisons"),
194 cl::init(Val: 2));
195
196static cl::opt<unsigned>
197 MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
198 cl::desc("Maximum depth of recursive arithmetics"),
199 cl::init(Val: 32));
200
201static cl::opt<unsigned> MaxConstantEvolvingDepth(
202 "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
203 cl::desc("Maximum depth of recursive constant evolving"), cl::init(Val: 32));
204
205static cl::opt<unsigned>
206 MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
207 cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
208 cl::init(Val: 8));
209
210static cl::opt<unsigned>
211 MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
212 cl::desc("Max coefficients in AddRec during evolving"),
213 cl::init(Val: 8));
214
215static cl::opt<unsigned>
216 HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
217 cl::desc("Size of the expression which is considered huge"),
218 cl::init(Val: 4096));
219
220static cl::opt<unsigned> RangeIterThreshold(
221 "scev-range-iter-threshold", cl::Hidden,
222 cl::desc("Threshold for switching to iteratively computing SCEV ranges"),
223 cl::init(Val: 32));
224
225static cl::opt<bool>
226ClassifyExpressions("scalar-evolution-classify-expressions",
227 cl::Hidden, cl::init(Val: true),
228 cl::desc("When printing analysis, include information on every instruction"));
229
230static cl::opt<bool> UseExpensiveRangeSharpening(
231 "scalar-evolution-use-expensive-range-sharpening", cl::Hidden,
232 cl::init(Val: false),
233 cl::desc("Use more powerful methods of sharpening expression ranges. May "
234 "be costly in terms of compile time"));
235
236static cl::opt<unsigned> MaxPhiSCCAnalysisSize(
237 "scalar-evolution-max-scc-analysis-depth", cl::Hidden,
238 cl::desc("Maximum amount of nodes to process while searching SCEVUnknown "
239 "Phi strongly connected components"),
240 cl::init(Val: 8));
241
242static cl::opt<bool>
243 EnableFiniteLoopControl("scalar-evolution-finite-loop", cl::Hidden,
244 cl::desc("Handle <= and >= in finite loops"),
245 cl::init(Val: true));
246
247static cl::opt<bool> UseContextForNoWrapFlagInference(
248 "scalar-evolution-use-context-for-no-wrap-flag-strenghening", cl::Hidden,
249 cl::desc("Infer nuw/nsw flags using context where suitable"),
250 cl::init(Val: true));
251
252//===----------------------------------------------------------------------===//
253// SCEV class definitions
254//===----------------------------------------------------------------------===//
255
256//===----------------------------------------------------------------------===//
257// Implementation of the SCEV class.
258//
259
260#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
261LLVM_DUMP_METHOD void SCEV::dump() const {
262 print(dbgs());
263 dbgs() << '\n';
264}
265#endif
266
267void SCEV::print(raw_ostream &OS) const {
268 switch (getSCEVType()) {
269 case scConstant:
270 cast<SCEVConstant>(Val: this)->getValue()->printAsOperand(O&: OS, PrintType: false);
271 return;
272 case scVScale:
273 OS << "vscale";
274 return;
275 case scPtrToInt: {
276 const SCEVPtrToIntExpr *PtrToInt = cast<SCEVPtrToIntExpr>(Val: this);
277 const SCEV *Op = PtrToInt->getOperand();
278 OS << "(ptrtoint " << *Op->getType() << " " << *Op << " to "
279 << *PtrToInt->getType() << ")";
280 return;
281 }
282 case scTruncate: {
283 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Val: this);
284 const SCEV *Op = Trunc->getOperand();
285 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
286 << *Trunc->getType() << ")";
287 return;
288 }
289 case scZeroExtend: {
290 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(Val: this);
291 const SCEV *Op = ZExt->getOperand();
292 OS << "(zext " << *Op->getType() << " " << *Op << " to "
293 << *ZExt->getType() << ")";
294 return;
295 }
296 case scSignExtend: {
297 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(Val: this);
298 const SCEV *Op = SExt->getOperand();
299 OS << "(sext " << *Op->getType() << " " << *Op << " to "
300 << *SExt->getType() << ")";
301 return;
302 }
303 case scAddRecExpr: {
304 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(Val: this);
305 OS << "{" << *AR->getOperand(i: 0);
306 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
307 OS << ",+," << *AR->getOperand(i);
308 OS << "}<";
309 if (AR->hasNoUnsignedWrap())
310 OS << "nuw><";
311 if (AR->hasNoSignedWrap())
312 OS << "nsw><";
313 if (AR->hasNoSelfWrap() &&
314 !AR->getNoWrapFlags(Mask: (NoWrapFlags)(FlagNUW | FlagNSW)))
315 OS << "nw><";
316 AR->getLoop()->getHeader()->printAsOperand(O&: OS, /*PrintType=*/false);
317 OS << ">";
318 return;
319 }
320 case scAddExpr:
321 case scMulExpr:
322 case scUMaxExpr:
323 case scSMaxExpr:
324 case scUMinExpr:
325 case scSMinExpr:
326 case scSequentialUMinExpr: {
327 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(Val: this);
328 const char *OpStr = nullptr;
329 switch (NAry->getSCEVType()) {
330 case scAddExpr: OpStr = " + "; break;
331 case scMulExpr: OpStr = " * "; break;
332 case scUMaxExpr: OpStr = " umax "; break;
333 case scSMaxExpr: OpStr = " smax "; break;
334 case scUMinExpr:
335 OpStr = " umin ";
336 break;
337 case scSMinExpr:
338 OpStr = " smin ";
339 break;
340 case scSequentialUMinExpr:
341 OpStr = " umin_seq ";
342 break;
343 default:
344 llvm_unreachable("There are no other nary expression types.");
345 }
346 OS << "(";
347 ListSeparator LS(OpStr);
348 for (const SCEV *Op : NAry->operands())
349 OS << LS << *Op;
350 OS << ")";
351 switch (NAry->getSCEVType()) {
352 case scAddExpr:
353 case scMulExpr:
354 if (NAry->hasNoUnsignedWrap())
355 OS << "<nuw>";
356 if (NAry->hasNoSignedWrap())
357 OS << "<nsw>";
358 break;
359 default:
360 // Nothing to print for other nary expressions.
361 break;
362 }
363 return;
364 }
365 case scUDivExpr: {
366 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(Val: this);
367 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
368 return;
369 }
370 case scUnknown:
371 cast<SCEVUnknown>(Val: this)->getValue()->printAsOperand(O&: OS, PrintType: false);
372 return;
373 case scCouldNotCompute:
374 OS << "***COULDNOTCOMPUTE***";
375 return;
376 }
377 llvm_unreachable("Unknown SCEV kind!");
378}
379
380Type *SCEV::getType() const {
381 switch (getSCEVType()) {
382 case scConstant:
383 return cast<SCEVConstant>(Val: this)->getType();
384 case scVScale:
385 return cast<SCEVVScale>(Val: this)->getType();
386 case scPtrToInt:
387 case scTruncate:
388 case scZeroExtend:
389 case scSignExtend:
390 return cast<SCEVCastExpr>(Val: this)->getType();
391 case scAddRecExpr:
392 return cast<SCEVAddRecExpr>(Val: this)->getType();
393 case scMulExpr:
394 return cast<SCEVMulExpr>(Val: this)->getType();
395 case scUMaxExpr:
396 case scSMaxExpr:
397 case scUMinExpr:
398 case scSMinExpr:
399 return cast<SCEVMinMaxExpr>(Val: this)->getType();
400 case scSequentialUMinExpr:
401 return cast<SCEVSequentialMinMaxExpr>(Val: this)->getType();
402 case scAddExpr:
403 return cast<SCEVAddExpr>(Val: this)->getType();
404 case scUDivExpr:
405 return cast<SCEVUDivExpr>(Val: this)->getType();
406 case scUnknown:
407 return cast<SCEVUnknown>(Val: this)->getType();
408 case scCouldNotCompute:
409 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
410 }
411 llvm_unreachable("Unknown SCEV kind!");
412}
413
414ArrayRef<const SCEV *> SCEV::operands() const {
415 switch (getSCEVType()) {
416 case scConstant:
417 case scVScale:
418 case scUnknown:
419 return {};
420 case scPtrToInt:
421 case scTruncate:
422 case scZeroExtend:
423 case scSignExtend:
424 return cast<SCEVCastExpr>(Val: this)->operands();
425 case scAddRecExpr:
426 case scAddExpr:
427 case scMulExpr:
428 case scUMaxExpr:
429 case scSMaxExpr:
430 case scUMinExpr:
431 case scSMinExpr:
432 case scSequentialUMinExpr:
433 return cast<SCEVNAryExpr>(Val: this)->operands();
434 case scUDivExpr:
435 return cast<SCEVUDivExpr>(Val: this)->operands();
436 case scCouldNotCompute:
437 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
438 }
439 llvm_unreachable("Unknown SCEV kind!");
440}
441
442bool SCEV::isZero() const {
443 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Val: this))
444 return SC->getValue()->isZero();
445 return false;
446}
447
448bool SCEV::isOne() const {
449 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Val: this))
450 return SC->getValue()->isOne();
451 return false;
452}
453
454bool SCEV::isAllOnesValue() const {
455 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Val: this))
456 return SC->getValue()->isMinusOne();
457 return false;
458}
459
460bool SCEV::isNonConstantNegative() const {
461 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Val: this);
462 if (!Mul) return false;
463
464 // If there is a constant factor, it will be first.
465 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Val: Mul->getOperand(i: 0));
466 if (!SC) return false;
467
468 // Return true if the value is negative, this matches things like (-42 * V).
469 return SC->getAPInt().isNegative();
470}
471
472SCEVCouldNotCompute::SCEVCouldNotCompute() :
473 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {}
474
475bool SCEVCouldNotCompute::classof(const SCEV *S) {
476 return S->getSCEVType() == scCouldNotCompute;
477}
478
479const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
480 FoldingSetNodeID ID;
481 ID.AddInteger(I: scConstant);
482 ID.AddPointer(Ptr: V);
483 void *IP = nullptr;
484 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP)) return S;
485 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(Allocator&: SCEVAllocator), V);
486 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
487 return S;
488}
489
490const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
491 return getConstant(V: ConstantInt::get(Context&: getContext(), V: Val));
492}
493
494const SCEV *
495ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
496 IntegerType *ITy = cast<IntegerType>(Val: getEffectiveSCEVType(Ty));
497 return getConstant(V: ConstantInt::get(Ty: ITy, V, IsSigned: isSigned));
498}
499
500const SCEV *ScalarEvolution::getVScale(Type *Ty) {
501 FoldingSetNodeID ID;
502 ID.AddInteger(I: scVScale);
503 ID.AddPointer(Ptr: Ty);
504 void *IP = nullptr;
505 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP))
506 return S;
507 SCEV *S = new (SCEVAllocator) SCEVVScale(ID.Intern(Allocator&: SCEVAllocator), Ty);
508 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
509 return S;
510}
511
512const SCEV *ScalarEvolution::getElementCount(Type *Ty, ElementCount EC) {
513 const SCEV *Res = getConstant(Ty, V: EC.getKnownMinValue());
514 if (EC.isScalable())
515 Res = getMulExpr(LHS: Res, RHS: getVScale(Ty));
516 return Res;
517}
518
519SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy,
520 const SCEV *op, Type *ty)
521 : SCEV(ID, SCEVTy, computeExpressionSize(Args: op)), Op(op), Ty(ty) {}
522
523SCEVPtrToIntExpr::SCEVPtrToIntExpr(const FoldingSetNodeIDRef ID, const SCEV *Op,
524 Type *ITy)
525 : SCEVCastExpr(ID, scPtrToInt, Op, ITy) {
526 assert(getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() &&
527 "Must be a non-bit-width-changing pointer-to-integer cast!");
528}
529
530SCEVIntegralCastExpr::SCEVIntegralCastExpr(const FoldingSetNodeIDRef ID,
531 SCEVTypes SCEVTy, const SCEV *op,
532 Type *ty)
533 : SCEVCastExpr(ID, SCEVTy, op, ty) {}
534
535SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, const SCEV *op,
536 Type *ty)
537 : SCEVIntegralCastExpr(ID, scTruncate, op, ty) {
538 assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
539 "Cannot truncate non-integer value!");
540}
541
542SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
543 const SCEV *op, Type *ty)
544 : SCEVIntegralCastExpr(ID, scZeroExtend, op, ty) {
545 assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
546 "Cannot zero extend non-integer value!");
547}
548
549SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
550 const SCEV *op, Type *ty)
551 : SCEVIntegralCastExpr(ID, scSignExtend, op, ty) {
552 assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
553 "Cannot sign extend non-integer value!");
554}
555
556void SCEVUnknown::deleted() {
557 // Clear this SCEVUnknown from various maps.
558 SE->forgetMemoizedResults(SCEVs: this);
559
560 // Remove this SCEVUnknown from the uniquing map.
561 SE->UniqueSCEVs.RemoveNode(N: this);
562
563 // Release the value.
564 setValPtr(nullptr);
565}
566
567void SCEVUnknown::allUsesReplacedWith(Value *New) {
568 // Clear this SCEVUnknown from various maps.
569 SE->forgetMemoizedResults(SCEVs: this);
570
571 // Remove this SCEVUnknown from the uniquing map.
572 SE->UniqueSCEVs.RemoveNode(N: this);
573
574 // Replace the value pointer in case someone is still using this SCEVUnknown.
575 setValPtr(New);
576}
577
578//===----------------------------------------------------------------------===//
579// SCEV Utilities
580//===----------------------------------------------------------------------===//
581
582/// Compare the two values \p LV and \p RV in terms of their "complexity" where
583/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
584/// operands in SCEV expressions. \p EqCache is a set of pairs of values that
585/// have been previously deemed to be "equally complex" by this routine. It is
586/// intended to avoid exponential time complexity in cases like:
587///
588/// %a = f(%x, %y)
589/// %b = f(%a, %a)
590/// %c = f(%b, %b)
591///
592/// %d = f(%x, %y)
593/// %e = f(%d, %d)
594/// %f = f(%e, %e)
595///
596/// CompareValueComplexity(%f, %c)
597///
598/// Since we do not continue running this routine on expression trees once we
599/// have seen unequal values, there is no need to track them in the cache.
600static int
601CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
602 const LoopInfo *const LI, Value *LV, Value *RV,
603 unsigned Depth) {
604 if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(V1: LV, V2: RV))
605 return 0;
606
607 // Order pointer values after integer values. This helps SCEVExpander form
608 // GEPs.
609 bool LIsPointer = LV->getType()->isPointerTy(),
610 RIsPointer = RV->getType()->isPointerTy();
611 if (LIsPointer != RIsPointer)
612 return (int)LIsPointer - (int)RIsPointer;
613
614 // Compare getValueID values.
615 unsigned LID = LV->getValueID(), RID = RV->getValueID();
616 if (LID != RID)
617 return (int)LID - (int)RID;
618
619 // Sort arguments by their position.
620 if (const auto *LA = dyn_cast<Argument>(Val: LV)) {
621 const auto *RA = cast<Argument>(Val: RV);
622 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
623 return (int)LArgNo - (int)RArgNo;
624 }
625
626 if (const auto *LGV = dyn_cast<GlobalValue>(Val: LV)) {
627 const auto *RGV = cast<GlobalValue>(Val: RV);
628
629 const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
630 auto LT = GV->getLinkage();
631 return !(GlobalValue::isPrivateLinkage(Linkage: LT) ||
632 GlobalValue::isInternalLinkage(Linkage: LT));
633 };
634
635 // Use the names to distinguish the two values, but only if the
636 // names are semantically important.
637 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
638 return LGV->getName().compare(RHS: RGV->getName());
639 }
640
641 // For instructions, compare their loop depth, and their operand count. This
642 // is pretty loose.
643 if (const auto *LInst = dyn_cast<Instruction>(Val: LV)) {
644 const auto *RInst = cast<Instruction>(Val: RV);
645
646 // Compare loop depths.
647 const BasicBlock *LParent = LInst->getParent(),
648 *RParent = RInst->getParent();
649 if (LParent != RParent) {
650 unsigned LDepth = LI->getLoopDepth(BB: LParent),
651 RDepth = LI->getLoopDepth(BB: RParent);
652 if (LDepth != RDepth)
653 return (int)LDepth - (int)RDepth;
654 }
655
656 // Compare the number of operands.
657 unsigned LNumOps = LInst->getNumOperands(),
658 RNumOps = RInst->getNumOperands();
659 if (LNumOps != RNumOps)
660 return (int)LNumOps - (int)RNumOps;
661
662 for (unsigned Idx : seq(Size: LNumOps)) {
663 int Result =
664 CompareValueComplexity(EqCacheValue, LI, LV: LInst->getOperand(i: Idx),
665 RV: RInst->getOperand(i: Idx), Depth: Depth + 1);
666 if (Result != 0)
667 return Result;
668 }
669 }
670
671 EqCacheValue.unionSets(V1: LV, V2: RV);
672 return 0;
673}
674
675// Return negative, zero, or positive, if LHS is less than, equal to, or greater
676// than RHS, respectively. A three-way result allows recursive comparisons to be
677// more efficient.
678// If the max analysis depth was reached, return std::nullopt, assuming we do
679// not know if they are equivalent for sure.
680static std::optional<int>
681CompareSCEVComplexity(EquivalenceClasses<const SCEV *> &EqCacheSCEV,
682 EquivalenceClasses<const Value *> &EqCacheValue,
683 const LoopInfo *const LI, const SCEV *LHS,
684 const SCEV *RHS, DominatorTree &DT, unsigned Depth = 0) {
685 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
686 if (LHS == RHS)
687 return 0;
688
689 // Primarily, sort the SCEVs by their getSCEVType().
690 SCEVTypes LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
691 if (LType != RType)
692 return (int)LType - (int)RType;
693
694 if (EqCacheSCEV.isEquivalent(V1: LHS, V2: RHS))
695 return 0;
696
697 if (Depth > MaxSCEVCompareDepth)
698 return std::nullopt;
699
700 // Aside from the getSCEVType() ordering, the particular ordering
701 // isn't very important except that it's beneficial to be consistent,
702 // so that (a + b) and (b + a) don't end up as different expressions.
703 switch (LType) {
704 case scUnknown: {
705 const SCEVUnknown *LU = cast<SCEVUnknown>(Val: LHS);
706 const SCEVUnknown *RU = cast<SCEVUnknown>(Val: RHS);
707
708 int X = CompareValueComplexity(EqCacheValue, LI, LV: LU->getValue(),
709 RV: RU->getValue(), Depth: Depth + 1);
710 if (X == 0)
711 EqCacheSCEV.unionSets(V1: LHS, V2: RHS);
712 return X;
713 }
714
715 case scConstant: {
716 const SCEVConstant *LC = cast<SCEVConstant>(Val: LHS);
717 const SCEVConstant *RC = cast<SCEVConstant>(Val: RHS);
718
719 // Compare constant values.
720 const APInt &LA = LC->getAPInt();
721 const APInt &RA = RC->getAPInt();
722 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
723 if (LBitWidth != RBitWidth)
724 return (int)LBitWidth - (int)RBitWidth;
725 return LA.ult(RHS: RA) ? -1 : 1;
726 }
727
728 case scVScale: {
729 const auto *LTy = cast<IntegerType>(Val: cast<SCEVVScale>(Val: LHS)->getType());
730 const auto *RTy = cast<IntegerType>(Val: cast<SCEVVScale>(Val: RHS)->getType());
731 return LTy->getBitWidth() - RTy->getBitWidth();
732 }
733
734 case scAddRecExpr: {
735 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(Val: LHS);
736 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(Val: RHS);
737
738 // There is always a dominance between two recs that are used by one SCEV,
739 // so we can safely sort recs by loop header dominance. We require such
740 // order in getAddExpr.
741 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
742 if (LLoop != RLoop) {
743 const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
744 assert(LHead != RHead && "Two loops share the same header?");
745 if (DT.dominates(A: LHead, B: RHead))
746 return 1;
747 assert(DT.dominates(RHead, LHead) &&
748 "No dominance between recurrences used by one SCEV?");
749 return -1;
750 }
751
752 [[fallthrough]];
753 }
754
755 case scTruncate:
756 case scZeroExtend:
757 case scSignExtend:
758 case scPtrToInt:
759 case scAddExpr:
760 case scMulExpr:
761 case scUDivExpr:
762 case scSMaxExpr:
763 case scUMaxExpr:
764 case scSMinExpr:
765 case scUMinExpr:
766 case scSequentialUMinExpr: {
767 ArrayRef<const SCEV *> LOps = LHS->operands();
768 ArrayRef<const SCEV *> ROps = RHS->operands();
769
770 // Lexicographically compare n-ary-like expressions.
771 unsigned LNumOps = LOps.size(), RNumOps = ROps.size();
772 if (LNumOps != RNumOps)
773 return (int)LNumOps - (int)RNumOps;
774
775 for (unsigned i = 0; i != LNumOps; ++i) {
776 auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS: LOps[i],
777 RHS: ROps[i], DT, Depth: Depth + 1);
778 if (X != 0)
779 return X;
780 }
781 EqCacheSCEV.unionSets(V1: LHS, V2: RHS);
782 return 0;
783 }
784
785 case scCouldNotCompute:
786 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
787 }
788 llvm_unreachable("Unknown SCEV kind!");
789}
790
791/// Given a list of SCEV objects, order them by their complexity, and group
792/// objects of the same complexity together by value. When this routine is
793/// finished, we know that any duplicates in the vector are consecutive and that
794/// complexity is monotonically increasing.
795///
796/// Note that we go take special precautions to ensure that we get deterministic
797/// results from this routine. In other words, we don't want the results of
798/// this to depend on where the addresses of various SCEV objects happened to
799/// land in memory.
800static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
801 LoopInfo *LI, DominatorTree &DT) {
802 if (Ops.size() < 2) return; // Noop
803
804 EquivalenceClasses<const SCEV *> EqCacheSCEV;
805 EquivalenceClasses<const Value *> EqCacheValue;
806
807 // Whether LHS has provably less complexity than RHS.
808 auto IsLessComplex = [&](const SCEV *LHS, const SCEV *RHS) {
809 auto Complexity =
810 CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT);
811 return Complexity && *Complexity < 0;
812 };
813 if (Ops.size() == 2) {
814 // This is the common case, which also happens to be trivially simple.
815 // Special case it.
816 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
817 if (IsLessComplex(RHS, LHS))
818 std::swap(a&: LHS, b&: RHS);
819 return;
820 }
821
822 // Do the rough sort by complexity.
823 llvm::stable_sort(Range&: Ops, C: [&](const SCEV *LHS, const SCEV *RHS) {
824 return IsLessComplex(LHS, RHS);
825 });
826
827 // Now that we are sorted by complexity, group elements of the same
828 // complexity. Note that this is, at worst, N^2, but the vector is likely to
829 // be extremely short in practice. Note that we take this approach because we
830 // do not want to depend on the addresses of the objects we are grouping.
831 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
832 const SCEV *S = Ops[i];
833 unsigned Complexity = S->getSCEVType();
834
835 // If there are any objects of the same complexity and same value as this
836 // one, group them.
837 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
838 if (Ops[j] == S) { // Found a duplicate.
839 // Move it to immediately after i'th element.
840 std::swap(a&: Ops[i+1], b&: Ops[j]);
841 ++i; // no need to rescan it.
842 if (i == e-2) return; // Done!
843 }
844 }
845 }
846}
847
848/// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at
849/// least HugeExprThreshold nodes).
850static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) {
851 return any_of(Range&: Ops, P: [](const SCEV *S) {
852 return S->getExpressionSize() >= HugeExprThreshold;
853 });
854}
855
856//===----------------------------------------------------------------------===//
857// Simple SCEV method implementations
858//===----------------------------------------------------------------------===//
859
860/// Compute BC(It, K). The result has width W. Assume, K > 0.
861static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
862 ScalarEvolution &SE,
863 Type *ResultTy) {
864 // Handle the simplest case efficiently.
865 if (K == 1)
866 return SE.getTruncateOrZeroExtend(V: It, Ty: ResultTy);
867
868 // We are using the following formula for BC(It, K):
869 //
870 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
871 //
872 // Suppose, W is the bitwidth of the return value. We must be prepared for
873 // overflow. Hence, we must assure that the result of our computation is
874 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
875 // safe in modular arithmetic.
876 //
877 // However, this code doesn't use exactly that formula; the formula it uses
878 // is something like the following, where T is the number of factors of 2 in
879 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
880 // exponentiation:
881 //
882 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
883 //
884 // This formula is trivially equivalent to the previous formula. However,
885 // this formula can be implemented much more efficiently. The trick is that
886 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
887 // arithmetic. To do exact division in modular arithmetic, all we have
888 // to do is multiply by the inverse. Therefore, this step can be done at
889 // width W.
890 //
891 // The next issue is how to safely do the division by 2^T. The way this
892 // is done is by doing the multiplication step at a width of at least W + T
893 // bits. This way, the bottom W+T bits of the product are accurate. Then,
894 // when we perform the division by 2^T (which is equivalent to a right shift
895 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
896 // truncated out after the division by 2^T.
897 //
898 // In comparison to just directly using the first formula, this technique
899 // is much more efficient; using the first formula requires W * K bits,
900 // but this formula less than W + K bits. Also, the first formula requires
901 // a division step, whereas this formula only requires multiplies and shifts.
902 //
903 // It doesn't matter whether the subtraction step is done in the calculation
904 // width or the input iteration count's width; if the subtraction overflows,
905 // the result must be zero anyway. We prefer here to do it in the width of
906 // the induction variable because it helps a lot for certain cases; CodeGen
907 // isn't smart enough to ignore the overflow, which leads to much less
908 // efficient code if the width of the subtraction is wider than the native
909 // register width.
910 //
911 // (It's possible to not widen at all by pulling out factors of 2 before
912 // the multiplication; for example, K=2 can be calculated as
913 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
914 // extra arithmetic, so it's not an obvious win, and it gets
915 // much more complicated for K > 3.)
916
917 // Protection from insane SCEVs; this bound is conservative,
918 // but it probably doesn't matter.
919 if (K > 1000)
920 return SE.getCouldNotCompute();
921
922 unsigned W = SE.getTypeSizeInBits(Ty: ResultTy);
923
924 // Calculate K! / 2^T and T; we divide out the factors of two before
925 // multiplying for calculating K! / 2^T to avoid overflow.
926 // Other overflow doesn't matter because we only care about the bottom
927 // W bits of the result.
928 APInt OddFactorial(W, 1);
929 unsigned T = 1;
930 for (unsigned i = 3; i <= K; ++i) {
931 unsigned TwoFactors = countr_zero(Val: i);
932 T += TwoFactors;
933 OddFactorial *= (i >> TwoFactors);
934 }
935
936 // We need at least W + T bits for the multiplication step
937 unsigned CalculationBits = W + T;
938
939 // Calculate 2^T, at width T+W.
940 APInt DivFactor = APInt::getOneBitSet(numBits: CalculationBits, BitNo: T);
941
942 // Calculate the multiplicative inverse of K! / 2^T;
943 // this multiplication factor will perform the exact division by
944 // K! / 2^T.
945 APInt MultiplyFactor = OddFactorial.multiplicativeInverse();
946
947 // Calculate the product, at width T+W
948 IntegerType *CalculationTy = IntegerType::get(C&: SE.getContext(),
949 NumBits: CalculationBits);
950 const SCEV *Dividend = SE.getTruncateOrZeroExtend(V: It, Ty: CalculationTy);
951 for (unsigned i = 1; i != K; ++i) {
952 const SCEV *S = SE.getMinusSCEV(LHS: It, RHS: SE.getConstant(Ty: It->getType(), V: i));
953 Dividend = SE.getMulExpr(LHS: Dividend,
954 RHS: SE.getTruncateOrZeroExtend(V: S, Ty: CalculationTy));
955 }
956
957 // Divide by 2^T
958 const SCEV *DivResult = SE.getUDivExpr(LHS: Dividend, RHS: SE.getConstant(Val: DivFactor));
959
960 // Truncate the result, and divide by K! / 2^T.
961
962 return SE.getMulExpr(LHS: SE.getConstant(Val: MultiplyFactor),
963 RHS: SE.getTruncateOrZeroExtend(V: DivResult, Ty: ResultTy));
964}
965
966/// Return the value of this chain of recurrences at the specified iteration
967/// number. We can evaluate this recurrence by multiplying each element in the
968/// chain by the binomial coefficient corresponding to it. In other words, we
969/// can evaluate {A,+,B,+,C,+,D} as:
970///
971/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
972///
973/// where BC(It, k) stands for binomial coefficient.
974const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
975 ScalarEvolution &SE) const {
976 return evaluateAtIteration(Operands: operands(), It, SE);
977}
978
979const SCEV *
980SCEVAddRecExpr::evaluateAtIteration(ArrayRef<const SCEV *> Operands,
981 const SCEV *It, ScalarEvolution &SE) {
982 assert(Operands.size() > 0);
983 const SCEV *Result = Operands[0];
984 for (unsigned i = 1, e = Operands.size(); i != e; ++i) {
985 // The computation is correct in the face of overflow provided that the
986 // multiplication is performed _after_ the evaluation of the binomial
987 // coefficient.
988 const SCEV *Coeff = BinomialCoefficient(It, K: i, SE, ResultTy: Result->getType());
989 if (isa<SCEVCouldNotCompute>(Val: Coeff))
990 return Coeff;
991
992 Result = SE.getAddExpr(LHS: Result, RHS: SE.getMulExpr(LHS: Operands[i], RHS: Coeff));
993 }
994 return Result;
995}
996
997//===----------------------------------------------------------------------===//
998// SCEV Expression folder implementations
999//===----------------------------------------------------------------------===//
1000
1001const SCEV *ScalarEvolution::getLosslessPtrToIntExpr(const SCEV *Op,
1002 unsigned Depth) {
1003 assert(Depth <= 1 &&
1004 "getLosslessPtrToIntExpr() should self-recurse at most once.");
1005
1006 // We could be called with an integer-typed operands during SCEV rewrites.
1007 // Since the operand is an integer already, just perform zext/trunc/self cast.
1008 if (!Op->getType()->isPointerTy())
1009 return Op;
1010
1011 // What would be an ID for such a SCEV cast expression?
1012 FoldingSetNodeID ID;
1013 ID.AddInteger(I: scPtrToInt);
1014 ID.AddPointer(Ptr: Op);
1015
1016 void *IP = nullptr;
1017
1018 // Is there already an expression for such a cast?
1019 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP))
1020 return S;
1021
1022 // It isn't legal for optimizations to construct new ptrtoint expressions
1023 // for non-integral pointers.
1024 if (getDataLayout().isNonIntegralPointerType(Ty: Op->getType()))
1025 return getCouldNotCompute();
1026
1027 Type *IntPtrTy = getDataLayout().getIntPtrType(Op->getType());
1028
1029 // We can only trivially model ptrtoint if SCEV's effective (integer) type
1030 // is sufficiently wide to represent all possible pointer values.
1031 // We could theoretically teach SCEV to truncate wider pointers, but
1032 // that isn't implemented for now.
1033 if (getDataLayout().getTypeSizeInBits(Ty: getEffectiveSCEVType(Ty: Op->getType())) !=
1034 getDataLayout().getTypeSizeInBits(Ty: IntPtrTy))
1035 return getCouldNotCompute();
1036
1037 // If not, is this expression something we can't reduce any further?
1038 if (auto *U = dyn_cast<SCEVUnknown>(Val: Op)) {
1039 // Perform some basic constant folding. If the operand of the ptr2int cast
1040 // is a null pointer, don't create a ptr2int SCEV expression (that will be
1041 // left as-is), but produce a zero constant.
1042 // NOTE: We could handle a more general case, but lack motivational cases.
1043 if (isa<ConstantPointerNull>(Val: U->getValue()))
1044 return getZero(Ty: IntPtrTy);
1045
1046 // Create an explicit cast node.
1047 // We can reuse the existing insert position since if we get here,
1048 // we won't have made any changes which would invalidate it.
1049 SCEV *S = new (SCEVAllocator)
1050 SCEVPtrToIntExpr(ID.Intern(Allocator&: SCEVAllocator), Op, IntPtrTy);
1051 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
1052 registerUser(User: S, Ops: Op);
1053 return S;
1054 }
1055
1056 assert(Depth == 0 && "getLosslessPtrToIntExpr() should not self-recurse for "
1057 "non-SCEVUnknown's.");
1058
1059 // Otherwise, we've got some expression that is more complex than just a
1060 // single SCEVUnknown. But we don't want to have a SCEVPtrToIntExpr of an
1061 // arbitrary expression, we want to have SCEVPtrToIntExpr of an SCEVUnknown
1062 // only, and the expressions must otherwise be integer-typed.
1063 // So sink the cast down to the SCEVUnknown's.
1064
1065 /// The SCEVPtrToIntSinkingRewriter takes a scalar evolution expression,
1066 /// which computes a pointer-typed value, and rewrites the whole expression
1067 /// tree so that *all* the computations are done on integers, and the only
1068 /// pointer-typed operands in the expression are SCEVUnknown.
1069 class SCEVPtrToIntSinkingRewriter
1070 : public SCEVRewriteVisitor<SCEVPtrToIntSinkingRewriter> {
1071 using Base = SCEVRewriteVisitor<SCEVPtrToIntSinkingRewriter>;
1072
1073 public:
1074 SCEVPtrToIntSinkingRewriter(ScalarEvolution &SE) : SCEVRewriteVisitor(SE) {}
1075
1076 static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE) {
1077 SCEVPtrToIntSinkingRewriter Rewriter(SE);
1078 return Rewriter.visit(S: Scev);
1079 }
1080
1081 const SCEV *visit(const SCEV *S) {
1082 Type *STy = S->getType();
1083 // If the expression is not pointer-typed, just keep it as-is.
1084 if (!STy->isPointerTy())
1085 return S;
1086 // Else, recursively sink the cast down into it.
1087 return Base::visit(S);
1088 }
1089
1090 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
1091 SmallVector<const SCEV *, 2> Operands;
1092 bool Changed = false;
1093 for (const auto *Op : Expr->operands()) {
1094 Operands.push_back(Elt: visit(S: Op));
1095 Changed |= Op != Operands.back();
1096 }
1097 return !Changed ? Expr : SE.getAddExpr(Ops&: Operands, Flags: Expr->getNoWrapFlags());
1098 }
1099
1100 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
1101 SmallVector<const SCEV *, 2> Operands;
1102 bool Changed = false;
1103 for (const auto *Op : Expr->operands()) {
1104 Operands.push_back(Elt: visit(S: Op));
1105 Changed |= Op != Operands.back();
1106 }
1107 return !Changed ? Expr : SE.getMulExpr(Ops&: Operands, Flags: Expr->getNoWrapFlags());
1108 }
1109
1110 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
1111 assert(Expr->getType()->isPointerTy() &&
1112 "Should only reach pointer-typed SCEVUnknown's.");
1113 return SE.getLosslessPtrToIntExpr(Op: Expr, /*Depth=*/1);
1114 }
1115 };
1116
1117 // And actually perform the cast sinking.
1118 const SCEV *IntOp = SCEVPtrToIntSinkingRewriter::rewrite(Scev: Op, SE&: *this);
1119 assert(IntOp->getType()->isIntegerTy() &&
1120 "We must have succeeded in sinking the cast, "
1121 "and ending up with an integer-typed expression!");
1122 return IntOp;
1123}
1124
1125const SCEV *ScalarEvolution::getPtrToIntExpr(const SCEV *Op, Type *Ty) {
1126 assert(Ty->isIntegerTy() && "Target type must be an integer type!");
1127
1128 const SCEV *IntOp = getLosslessPtrToIntExpr(Op);
1129 if (isa<SCEVCouldNotCompute>(Val: IntOp))
1130 return IntOp;
1131
1132 return getTruncateOrZeroExtend(V: IntOp, Ty);
1133}
1134
1135const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
1136 unsigned Depth) {
1137 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1138 "This is not a truncating conversion!");
1139 assert(isSCEVable(Ty) &&
1140 "This is not a conversion to a SCEVable type!");
1141 assert(!Op->getType()->isPointerTy() && "Can't truncate pointer!");
1142 Ty = getEffectiveSCEVType(Ty);
1143
1144 FoldingSetNodeID ID;
1145 ID.AddInteger(I: scTruncate);
1146 ID.AddPointer(Ptr: Op);
1147 ID.AddPointer(Ptr: Ty);
1148 void *IP = nullptr;
1149 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP)) return S;
1150
1151 // Fold if the operand is constant.
1152 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Val: Op))
1153 return getConstant(
1154 V: cast<ConstantInt>(Val: ConstantExpr::getTrunc(C: SC->getValue(), Ty)));
1155
1156 // trunc(trunc(x)) --> trunc(x)
1157 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Val: Op))
1158 return getTruncateExpr(Op: ST->getOperand(), Ty, Depth: Depth + 1);
1159
1160 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1161 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Val: Op))
1162 return getTruncateOrSignExtend(V: SS->getOperand(), Ty, Depth: Depth + 1);
1163
1164 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1165 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Val: Op))
1166 return getTruncateOrZeroExtend(V: SZ->getOperand(), Ty, Depth: Depth + 1);
1167
1168 if (Depth > MaxCastDepth) {
1169 SCEV *S =
1170 new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(Allocator&: SCEVAllocator), Op, Ty);
1171 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
1172 registerUser(User: S, Ops: Op);
1173 return S;
1174 }
1175
1176 // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
1177 // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
1178 // if after transforming we have at most one truncate, not counting truncates
1179 // that replace other casts.
1180 if (isa<SCEVAddExpr>(Val: Op) || isa<SCEVMulExpr>(Val: Op)) {
1181 auto *CommOp = cast<SCEVCommutativeExpr>(Val: Op);
1182 SmallVector<const SCEV *, 4> Operands;
1183 unsigned numTruncs = 0;
1184 for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
1185 ++i) {
1186 const SCEV *S = getTruncateExpr(Op: CommOp->getOperand(i), Ty, Depth: Depth + 1);
1187 if (!isa<SCEVIntegralCastExpr>(Val: CommOp->getOperand(i)) &&
1188 isa<SCEVTruncateExpr>(Val: S))
1189 numTruncs++;
1190 Operands.push_back(Elt: S);
1191 }
1192 if (numTruncs < 2) {
1193 if (isa<SCEVAddExpr>(Val: Op))
1194 return getAddExpr(Ops&: Operands);
1195 if (isa<SCEVMulExpr>(Val: Op))
1196 return getMulExpr(Ops&: Operands);
1197 llvm_unreachable("Unexpected SCEV type for Op.");
1198 }
1199 // Although we checked in the beginning that ID is not in the cache, it is
1200 // possible that during recursion and different modification ID was inserted
1201 // into the cache. So if we find it, just return it.
1202 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP))
1203 return S;
1204 }
1205
1206 // If the input value is a chrec scev, truncate the chrec's operands.
1207 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Val: Op)) {
1208 SmallVector<const SCEV *, 4> Operands;
1209 for (const SCEV *Op : AddRec->operands())
1210 Operands.push_back(Elt: getTruncateExpr(Op, Ty, Depth: Depth + 1));
1211 return getAddRecExpr(Operands, L: AddRec->getLoop(), Flags: SCEV::FlagAnyWrap);
1212 }
1213
1214 // Return zero if truncating to known zeros.
1215 uint32_t MinTrailingZeros = getMinTrailingZeros(S: Op);
1216 if (MinTrailingZeros >= getTypeSizeInBits(Ty))
1217 return getZero(Ty);
1218
1219 // The cast wasn't folded; create an explicit cast node. We can reuse
1220 // the existing insert position since if we get here, we won't have
1221 // made any changes which would invalidate it.
1222 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(Allocator&: SCEVAllocator),
1223 Op, Ty);
1224 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
1225 registerUser(User: S, Ops: Op);
1226 return S;
1227}
1228
1229// Get the limit of a recurrence such that incrementing by Step cannot cause
1230// signed overflow as long as the value of the recurrence within the
1231// loop does not exceed this limit before incrementing.
1232static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1233 ICmpInst::Predicate *Pred,
1234 ScalarEvolution *SE) {
1235 unsigned BitWidth = SE->getTypeSizeInBits(Ty: Step->getType());
1236 if (SE->isKnownPositive(S: Step)) {
1237 *Pred = ICmpInst::ICMP_SLT;
1238 return SE->getConstant(Val: APInt::getSignedMinValue(numBits: BitWidth) -
1239 SE->getSignedRangeMax(S: Step));
1240 }
1241 if (SE->isKnownNegative(S: Step)) {
1242 *Pred = ICmpInst::ICMP_SGT;
1243 return SE->getConstant(Val: APInt::getSignedMaxValue(numBits: BitWidth) -
1244 SE->getSignedRangeMin(S: Step));
1245 }
1246 return nullptr;
1247}
1248
1249// Get the limit of a recurrence such that incrementing by Step cannot cause
1250// unsigned overflow as long as the value of the recurrence within the loop does
1251// not exceed this limit before incrementing.
1252static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1253 ICmpInst::Predicate *Pred,
1254 ScalarEvolution *SE) {
1255 unsigned BitWidth = SE->getTypeSizeInBits(Ty: Step->getType());
1256 *Pred = ICmpInst::ICMP_ULT;
1257
1258 return SE->getConstant(Val: APInt::getMinValue(numBits: BitWidth) -
1259 SE->getUnsignedRangeMax(S: Step));
1260}
1261
1262namespace {
1263
1264struct ExtendOpTraitsBase {
1265 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
1266 unsigned);
1267};
1268
1269// Used to make code generic over signed and unsigned overflow.
1270template <typename ExtendOp> struct ExtendOpTraits {
1271 // Members present:
1272 //
1273 // static const SCEV::NoWrapFlags WrapType;
1274 //
1275 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1276 //
1277 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1278 // ICmpInst::Predicate *Pred,
1279 // ScalarEvolution *SE);
1280};
1281
1282template <>
1283struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1284 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1285
1286 static const GetExtendExprTy GetExtendExpr;
1287
1288 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1289 ICmpInst::Predicate *Pred,
1290 ScalarEvolution *SE) {
1291 return getSignedOverflowLimitForStep(Step, Pred, SE);
1292 }
1293};
1294
1295const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1296 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1297
1298template <>
1299struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1300 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1301
1302 static const GetExtendExprTy GetExtendExpr;
1303
1304 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1305 ICmpInst::Predicate *Pred,
1306 ScalarEvolution *SE) {
1307 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1308 }
1309};
1310
1311const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1312 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1313
1314} // end anonymous namespace
1315
1316// The recurrence AR has been shown to have no signed/unsigned wrap or something
1317// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1318// easily prove NSW/NUW for its preincrement or postincrement sibling. This
1319// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1320// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1321// expression "Step + sext/zext(PreIncAR)" is congruent with
1322// "sext/zext(PostIncAR)"
1323template <typename ExtendOpTy>
1324static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1325 ScalarEvolution *SE, unsigned Depth) {
1326 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1327 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1328
1329 const Loop *L = AR->getLoop();
1330 const SCEV *Start = AR->getStart();
1331 const SCEV *Step = AR->getStepRecurrence(SE&: *SE);
1332
1333 // Check for a simple looking step prior to loop entry.
1334 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Val: Start);
1335 if (!SA)
1336 return nullptr;
1337
1338 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1339 // subtraction is expensive. For this purpose, perform a quick and dirty
1340 // difference, by checking for Step in the operand list. Note, that
1341 // SA might have repeated ops, like %a + %a + ..., so only remove one.
1342 SmallVector<const SCEV *, 4> DiffOps(SA->operands());
1343 for (auto It = DiffOps.begin(); It != DiffOps.end(); ++It)
1344 if (*It == Step) {
1345 DiffOps.erase(CI: It);
1346 break;
1347 }
1348
1349 if (DiffOps.size() == SA->getNumOperands())
1350 return nullptr;
1351
1352 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1353 // `Step`:
1354
1355 // 1. NSW/NUW flags on the step increment.
1356 auto PreStartFlags =
1357 ScalarEvolution::maskFlags(Flags: SA->getNoWrapFlags(), Mask: SCEV::FlagNUW);
1358 const SCEV *PreStart = SE->getAddExpr(Ops&: DiffOps, Flags: PreStartFlags);
1359 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1360 Val: SE->getAddRecExpr(Start: PreStart, Step, L, Flags: SCEV::FlagAnyWrap));
1361
1362 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1363 // "S+X does not sign/unsign-overflow".
1364 //
1365
1366 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1367 if (PreAR && PreAR->getNoWrapFlags(Mask: WrapType) &&
1368 !isa<SCEVCouldNotCompute>(Val: BECount) && SE->isKnownPositive(S: BECount))
1369 return PreStart;
1370
1371 // 2. Direct overflow check on the step operation's expression.
1372 unsigned BitWidth = SE->getTypeSizeInBits(Ty: AR->getType());
1373 Type *WideTy = IntegerType::get(C&: SE->getContext(), NumBits: BitWidth * 2);
1374 const SCEV *OperandExtendedStart =
1375 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
1376 (SE->*GetExtendExpr)(Step, WideTy, Depth));
1377 if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
1378 if (PreAR && AR->getNoWrapFlags(Mask: WrapType)) {
1379 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1380 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1381 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1382 SE->setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(PreAR), Flags: WrapType);
1383 }
1384 return PreStart;
1385 }
1386
1387 // 3. Loop precondition.
1388 ICmpInst::Predicate Pred;
1389 const SCEV *OverflowLimit =
1390 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1391
1392 if (OverflowLimit &&
1393 SE->isLoopEntryGuardedByCond(L, Pred, LHS: PreStart, RHS: OverflowLimit))
1394 return PreStart;
1395
1396 return nullptr;
1397}
1398
1399// Get the normalized zero or sign extended expression for this AddRec's Start.
1400template <typename ExtendOpTy>
1401static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1402 ScalarEvolution *SE,
1403 unsigned Depth) {
1404 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1405
1406 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
1407 if (!PreStart)
1408 return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
1409
1410 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(SE&: *SE), Ty,
1411 Depth),
1412 (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1413}
1414
1415// Try to prove away overflow by looking at "nearby" add recurrences. A
1416// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1417// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1418//
1419// Formally:
1420//
1421// {S,+,X} == {S-T,+,X} + T
1422// => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1423//
1424// If ({S-T,+,X} + T) does not overflow ... (1)
1425//
1426// RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1427//
1428// If {S-T,+,X} does not overflow ... (2)
1429//
1430// RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1431// == {Ext(S-T)+Ext(T),+,Ext(X)}
1432//
1433// If (S-T)+T does not overflow ... (3)
1434//
1435// RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1436// == {Ext(S),+,Ext(X)} == LHS
1437//
1438// Thus, if (1), (2) and (3) are true for some T, then
1439// Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1440//
1441// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1442// does not overflow" restricted to the 0th iteration. Therefore we only need
1443// to check for (1) and (2).
1444//
1445// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1446// is `Delta` (defined below).
1447template <typename ExtendOpTy>
1448bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1449 const SCEV *Step,
1450 const Loop *L) {
1451 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1452
1453 // We restrict `Start` to a constant to prevent SCEV from spending too much
1454 // time here. It is correct (but more expensive) to continue with a
1455 // non-constant `Start` and do a general SCEV subtraction to compute
1456 // `PreStart` below.
1457 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Val: Start);
1458 if (!StartC)
1459 return false;
1460
1461 APInt StartAI = StartC->getAPInt();
1462
1463 for (unsigned Delta : {-2, -1, 1, 2}) {
1464 const SCEV *PreStart = getConstant(Val: StartAI - Delta);
1465
1466 FoldingSetNodeID ID;
1467 ID.AddInteger(I: scAddRecExpr);
1468 ID.AddPointer(Ptr: PreStart);
1469 ID.AddPointer(Ptr: Step);
1470 ID.AddPointer(Ptr: L);
1471 void *IP = nullptr;
1472 const auto *PreAR =
1473 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP));
1474
1475 // Give up if we don't already have the add recurrence we need because
1476 // actually constructing an add recurrence is relatively expensive.
1477 if (PreAR && PreAR->getNoWrapFlags(Mask: WrapType)) { // proves (2)
1478 const SCEV *DeltaS = getConstant(Ty: StartC->getType(), V: Delta);
1479 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1480 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1481 DeltaS, &Pred, this);
1482 if (Limit && isKnownPredicate(Pred, LHS: PreAR, RHS: Limit)) // proves (1)
1483 return true;
1484 }
1485 }
1486
1487 return false;
1488}
1489
1490// Finds an integer D for an expression (C + x + y + ...) such that the top
1491// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
1492// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
1493// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
1494// the (C + x + y + ...) expression is \p WholeAddExpr.
1495static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1496 const SCEVConstant *ConstantTerm,
1497 const SCEVAddExpr *WholeAddExpr) {
1498 const APInt &C = ConstantTerm->getAPInt();
1499 const unsigned BitWidth = C.getBitWidth();
1500 // Find number of trailing zeros of (x + y + ...) w/o the C first:
1501 uint32_t TZ = BitWidth;
1502 for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
1503 TZ = std::min(a: TZ, b: SE.getMinTrailingZeros(S: WholeAddExpr->getOperand(i: I)));
1504 if (TZ) {
1505 // Set D to be as many least significant bits of C as possible while still
1506 // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
1507 return TZ < BitWidth ? C.trunc(width: TZ).zext(width: BitWidth) : C;
1508 }
1509 return APInt(BitWidth, 0);
1510}
1511
1512// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
1513// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
1514// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
1515// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
1516static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1517 const APInt &ConstantStart,
1518 const SCEV *Step) {
1519 const unsigned BitWidth = ConstantStart.getBitWidth();
1520 const uint32_t TZ = SE.getMinTrailingZeros(S: Step);
1521 if (TZ)
1522 return TZ < BitWidth ? ConstantStart.trunc(width: TZ).zext(width: BitWidth)
1523 : ConstantStart;
1524 return APInt(BitWidth, 0);
1525}
1526
1527static void insertFoldCacheEntry(
1528 const ScalarEvolution::FoldID &ID, const SCEV *S,
1529 DenseMap<ScalarEvolution::FoldID, const SCEV *> &FoldCache,
1530 DenseMap<const SCEV *, SmallVector<ScalarEvolution::FoldID, 2>>
1531 &FoldCacheUser) {
1532 auto I = FoldCache.insert(KV: {ID, S});
1533 if (!I.second) {
1534 // Remove FoldCacheUser entry for ID when replacing an existing FoldCache
1535 // entry.
1536 auto &UserIDs = FoldCacheUser[I.first->second];
1537 assert(count(UserIDs, ID) == 1 && "unexpected duplicates in UserIDs");
1538 for (unsigned I = 0; I != UserIDs.size(); ++I)
1539 if (UserIDs[I] == ID) {
1540 std::swap(a&: UserIDs[I], b&: UserIDs.back());
1541 break;
1542 }
1543 UserIDs.pop_back();
1544 I.first->second = S;
1545 }
1546 auto R = FoldCacheUser.insert(KV: {S, {}});
1547 R.first->second.push_back(Elt: ID);
1548}
1549
1550const SCEV *
1551ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1552 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1553 "This is not an extending conversion!");
1554 assert(isSCEVable(Ty) &&
1555 "This is not a conversion to a SCEVable type!");
1556 assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
1557 Ty = getEffectiveSCEVType(Ty);
1558
1559 FoldID ID(scZeroExtend, Op, Ty);
1560 auto Iter = FoldCache.find(Val: ID);
1561 if (Iter != FoldCache.end())
1562 return Iter->second;
1563
1564 const SCEV *S = getZeroExtendExprImpl(Op, Ty, Depth);
1565 if (!isa<SCEVZeroExtendExpr>(Val: S))
1566 insertFoldCacheEntry(ID, S, FoldCache, FoldCacheUser);
1567 return S;
1568}
1569
1570const SCEV *ScalarEvolution::getZeroExtendExprImpl(const SCEV *Op, Type *Ty,
1571 unsigned Depth) {
1572 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1573 "This is not an extending conversion!");
1574 assert(isSCEVable(Ty) && "This is not a conversion to a SCEVable type!");
1575 assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
1576
1577 // Fold if the operand is constant.
1578 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Val: Op))
1579 return getConstant(Val: SC->getAPInt().zext(width: getTypeSizeInBits(Ty)));
1580
1581 // zext(zext(x)) --> zext(x)
1582 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Val: Op))
1583 return getZeroExtendExpr(Op: SZ->getOperand(), Ty, Depth: Depth + 1);
1584
1585 // Before doing any expensive analysis, check to see if we've already
1586 // computed a SCEV for this Op and Ty.
1587 FoldingSetNodeID ID;
1588 ID.AddInteger(I: scZeroExtend);
1589 ID.AddPointer(Ptr: Op);
1590 ID.AddPointer(Ptr: Ty);
1591 void *IP = nullptr;
1592 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP)) return S;
1593 if (Depth > MaxCastDepth) {
1594 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(Allocator&: SCEVAllocator),
1595 Op, Ty);
1596 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
1597 registerUser(User: S, Ops: Op);
1598 return S;
1599 }
1600
1601 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1602 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Val: Op)) {
1603 // It's possible the bits taken off by the truncate were all zero bits. If
1604 // so, we should be able to simplify this further.
1605 const SCEV *X = ST->getOperand();
1606 ConstantRange CR = getUnsignedRange(S: X);
1607 unsigned TruncBits = getTypeSizeInBits(Ty: ST->getType());
1608 unsigned NewBits = getTypeSizeInBits(Ty);
1609 if (CR.truncate(BitWidth: TruncBits).zeroExtend(BitWidth: NewBits).contains(
1610 CR: CR.zextOrTrunc(BitWidth: NewBits)))
1611 return getTruncateOrZeroExtend(V: X, Ty, Depth);
1612 }
1613
1614 // If the input value is a chrec scev, and we can prove that the value
1615 // did not overflow the old, smaller, value, we can zero extend all of the
1616 // operands (often constants). This allows analysis of something like
1617 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1618 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Val: Op))
1619 if (AR->isAffine()) {
1620 const SCEV *Start = AR->getStart();
1621 const SCEV *Step = AR->getStepRecurrence(SE&: *this);
1622 unsigned BitWidth = getTypeSizeInBits(Ty: AR->getType());
1623 const Loop *L = AR->getLoop();
1624
1625 // If we have special knowledge that this addrec won't overflow,
1626 // we don't need to do any further analysis.
1627 if (AR->hasNoUnsignedWrap()) {
1628 Start =
1629 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, SE: this, Depth: Depth + 1);
1630 Step = getZeroExtendExpr(Op: Step, Ty, Depth: Depth + 1);
1631 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
1632 }
1633
1634 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1635 // Note that this serves two purposes: It filters out loops that are
1636 // simply not analyzable, and it covers the case where this code is
1637 // being called from within backedge-taken count analysis, such that
1638 // attempting to ask for the backedge-taken count would likely result
1639 // in infinite recursion. In the later case, the analysis code will
1640 // cope with a conservative value, and it will take care to purge
1641 // that value once it has finished.
1642 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
1643 if (!isa<SCEVCouldNotCompute>(Val: MaxBECount)) {
1644 // Manually compute the final value for AR, checking for overflow.
1645
1646 // Check whether the backedge-taken count can be losslessly casted to
1647 // the addrec's type. The count is always unsigned.
1648 const SCEV *CastedMaxBECount =
1649 getTruncateOrZeroExtend(V: MaxBECount, Ty: Start->getType(), Depth);
1650 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
1651 V: CastedMaxBECount, Ty: MaxBECount->getType(), Depth);
1652 if (MaxBECount == RecastedMaxBECount) {
1653 Type *WideTy = IntegerType::get(C&: getContext(), NumBits: BitWidth * 2);
1654 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1655 const SCEV *ZMul = getMulExpr(LHS: CastedMaxBECount, RHS: Step,
1656 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
1657 const SCEV *ZAdd = getZeroExtendExpr(Op: getAddExpr(LHS: Start, RHS: ZMul,
1658 Flags: SCEV::FlagAnyWrap,
1659 Depth: Depth + 1),
1660 Ty: WideTy, Depth: Depth + 1);
1661 const SCEV *WideStart = getZeroExtendExpr(Op: Start, Ty: WideTy, Depth: Depth + 1);
1662 const SCEV *WideMaxBECount =
1663 getZeroExtendExpr(Op: CastedMaxBECount, Ty: WideTy, Depth: Depth + 1);
1664 const SCEV *OperandExtendedAdd =
1665 getAddExpr(LHS: WideStart,
1666 RHS: getMulExpr(LHS: WideMaxBECount,
1667 RHS: getZeroExtendExpr(Op: Step, Ty: WideTy, Depth: Depth + 1),
1668 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1),
1669 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
1670 if (ZAdd == OperandExtendedAdd) {
1671 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1672 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags: SCEV::FlagNUW);
1673 // Return the expression with the addrec on the outside.
1674 Start = getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, SE: this,
1675 Depth: Depth + 1);
1676 Step = getZeroExtendExpr(Op: Step, Ty, Depth: Depth + 1);
1677 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
1678 }
1679 // Similar to above, only this time treat the step value as signed.
1680 // This covers loops that count down.
1681 OperandExtendedAdd =
1682 getAddExpr(LHS: WideStart,
1683 RHS: getMulExpr(LHS: WideMaxBECount,
1684 RHS: getSignExtendExpr(Op: Step, Ty: WideTy, Depth: Depth + 1),
1685 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1),
1686 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
1687 if (ZAdd == OperandExtendedAdd) {
1688 // Cache knowledge of AR NW, which is propagated to this AddRec.
1689 // Negative step causes unsigned wrap, but it still can't self-wrap.
1690 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags: SCEV::FlagNW);
1691 // Return the expression with the addrec on the outside.
1692 Start = getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, SE: this,
1693 Depth: Depth + 1);
1694 Step = getSignExtendExpr(Op: Step, Ty, Depth: Depth + 1);
1695 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
1696 }
1697 }
1698 }
1699
1700 // Normally, in the cases we can prove no-overflow via a
1701 // backedge guarding condition, we can also compute a backedge
1702 // taken count for the loop. The exceptions are assumptions and
1703 // guards present in the loop -- SCEV is not great at exploiting
1704 // these to compute max backedge taken counts, but can still use
1705 // these to prove lack of overflow. Use this fact to avoid
1706 // doing extra work that may not pay off.
1707 if (!isa<SCEVCouldNotCompute>(Val: MaxBECount) || HasGuards ||
1708 !AC.assumptions().empty()) {
1709
1710 auto NewFlags = proveNoUnsignedWrapViaInduction(AR);
1711 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags: NewFlags);
1712 if (AR->hasNoUnsignedWrap()) {
1713 // Same as nuw case above - duplicated here to avoid a compile time
1714 // issue. It's not clear that the order of checks does matter, but
1715 // it's one of two issue possible causes for a change which was
1716 // reverted. Be conservative for the moment.
1717 Start =
1718 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, SE: this, Depth: Depth + 1);
1719 Step = getZeroExtendExpr(Op: Step, Ty, Depth: Depth + 1);
1720 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
1721 }
1722
1723 // For a negative step, we can extend the operands iff doing so only
1724 // traverses values in the range zext([0,UINT_MAX]).
1725 if (isKnownNegative(S: Step)) {
1726 const SCEV *N = getConstant(Val: APInt::getMaxValue(numBits: BitWidth) -
1727 getSignedRangeMin(S: Step));
1728 if (isLoopBackedgeGuardedByCond(L, Pred: ICmpInst::ICMP_UGT, LHS: AR, RHS: N) ||
1729 isKnownOnEveryIteration(Pred: ICmpInst::ICMP_UGT, LHS: AR, RHS: N)) {
1730 // Cache knowledge of AR NW, which is propagated to this
1731 // AddRec. Negative step causes unsigned wrap, but it
1732 // still can't self-wrap.
1733 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags: SCEV::FlagNW);
1734 // Return the expression with the addrec on the outside.
1735 Start = getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, SE: this,
1736 Depth: Depth + 1);
1737 Step = getSignExtendExpr(Op: Step, Ty, Depth: Depth + 1);
1738 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
1739 }
1740 }
1741 }
1742
1743 // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
1744 // if D + (C - D + Step * n) could be proven to not unsigned wrap
1745 // where D maximizes the number of trailing zeros of (C - D + Step * n)
1746 if (const auto *SC = dyn_cast<SCEVConstant>(Val: Start)) {
1747 const APInt &C = SC->getAPInt();
1748 const APInt &D = extractConstantWithoutWrapping(SE&: *this, ConstantStart: C, Step);
1749 if (D != 0) {
1750 const SCEV *SZExtD = getZeroExtendExpr(Op: getConstant(Val: D), Ty, Depth);
1751 const SCEV *SResidual =
1752 getAddRecExpr(Start: getConstant(Val: C - D), Step, L, Flags: AR->getNoWrapFlags());
1753 const SCEV *SZExtR = getZeroExtendExpr(Op: SResidual, Ty, Depth: Depth + 1);
1754 return getAddExpr(LHS: SZExtD, RHS: SZExtR,
1755 Flags: (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1756 Depth: Depth + 1);
1757 }
1758 }
1759
1760 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1761 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags: SCEV::FlagNUW);
1762 Start =
1763 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, SE: this, Depth: Depth + 1);
1764 Step = getZeroExtendExpr(Op: Step, Ty, Depth: Depth + 1);
1765 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
1766 }
1767 }
1768
1769 // zext(A % B) --> zext(A) % zext(B)
1770 {
1771 const SCEV *LHS;
1772 const SCEV *RHS;
1773 if (matchURem(Expr: Op, LHS, RHS))
1774 return getURemExpr(LHS: getZeroExtendExpr(Op: LHS, Ty, Depth: Depth + 1),
1775 RHS: getZeroExtendExpr(Op: RHS, Ty, Depth: Depth + 1));
1776 }
1777
1778 // zext(A / B) --> zext(A) / zext(B).
1779 if (auto *Div = dyn_cast<SCEVUDivExpr>(Val: Op))
1780 return getUDivExpr(LHS: getZeroExtendExpr(Op: Div->getLHS(), Ty, Depth: Depth + 1),
1781 RHS: getZeroExtendExpr(Op: Div->getRHS(), Ty, Depth: Depth + 1));
1782
1783 if (auto *SA = dyn_cast<SCEVAddExpr>(Val: Op)) {
1784 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1785 if (SA->hasNoUnsignedWrap()) {
1786 // If the addition does not unsign overflow then we can, by definition,
1787 // commute the zero extension with the addition operation.
1788 SmallVector<const SCEV *, 4> Ops;
1789 for (const auto *Op : SA->operands())
1790 Ops.push_back(Elt: getZeroExtendExpr(Op, Ty, Depth: Depth + 1));
1791 return getAddExpr(Ops, Flags: SCEV::FlagNUW, Depth: Depth + 1);
1792 }
1793
1794 // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
1795 // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
1796 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1797 //
1798 // Often address arithmetics contain expressions like
1799 // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
1800 // This transformation is useful while proving that such expressions are
1801 // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
1802 if (const auto *SC = dyn_cast<SCEVConstant>(Val: SA->getOperand(i: 0))) {
1803 const APInt &D = extractConstantWithoutWrapping(SE&: *this, ConstantTerm: SC, WholeAddExpr: SA);
1804 if (D != 0) {
1805 const SCEV *SZExtD = getZeroExtendExpr(Op: getConstant(Val: D), Ty, Depth);
1806 const SCEV *SResidual =
1807 getAddExpr(LHS: getConstant(Val: -D), RHS: SA, Flags: SCEV::FlagAnyWrap, Depth);
1808 const SCEV *SZExtR = getZeroExtendExpr(Op: SResidual, Ty, Depth: Depth + 1);
1809 return getAddExpr(LHS: SZExtD, RHS: SZExtR,
1810 Flags: (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1811 Depth: Depth + 1);
1812 }
1813 }
1814 }
1815
1816 if (auto *SM = dyn_cast<SCEVMulExpr>(Val: Op)) {
1817 // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
1818 if (SM->hasNoUnsignedWrap()) {
1819 // If the multiply does not unsign overflow then we can, by definition,
1820 // commute the zero extension with the multiply operation.
1821 SmallVector<const SCEV *, 4> Ops;
1822 for (const auto *Op : SM->operands())
1823 Ops.push_back(Elt: getZeroExtendExpr(Op, Ty, Depth: Depth + 1));
1824 return getMulExpr(Ops, Flags: SCEV::FlagNUW, Depth: Depth + 1);
1825 }
1826
1827 // zext(2^K * (trunc X to iN)) to iM ->
1828 // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
1829 //
1830 // Proof:
1831 //
1832 // zext(2^K * (trunc X to iN)) to iM
1833 // = zext((trunc X to iN) << K) to iM
1834 // = zext((trunc X to i{N-K}) << K)<nuw> to iM
1835 // (because shl removes the top K bits)
1836 // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
1837 // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
1838 //
1839 if (SM->getNumOperands() == 2)
1840 if (auto *MulLHS = dyn_cast<SCEVConstant>(Val: SM->getOperand(i: 0)))
1841 if (MulLHS->getAPInt().isPowerOf2())
1842 if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(Val: SM->getOperand(i: 1))) {
1843 int NewTruncBits = getTypeSizeInBits(Ty: TruncRHS->getType()) -
1844 MulLHS->getAPInt().logBase2();
1845 Type *NewTruncTy = IntegerType::get(C&: getContext(), NumBits: NewTruncBits);
1846 return getMulExpr(
1847 LHS: getZeroExtendExpr(Op: MulLHS, Ty),
1848 RHS: getZeroExtendExpr(
1849 Op: getTruncateExpr(Op: TruncRHS->getOperand(), Ty: NewTruncTy), Ty),
1850 Flags: SCEV::FlagNUW, Depth: Depth + 1);
1851 }
1852 }
1853
1854 // zext(umin(x, y)) -> umin(zext(x), zext(y))
1855 // zext(umax(x, y)) -> umax(zext(x), zext(y))
1856 if (isa<SCEVUMinExpr>(Val: Op) || isa<SCEVUMaxExpr>(Val: Op)) {
1857 auto *MinMax = cast<SCEVMinMaxExpr>(Val: Op);
1858 SmallVector<const SCEV *, 4> Operands;
1859 for (auto *Operand : MinMax->operands())
1860 Operands.push_back(Elt: getZeroExtendExpr(Op: Operand, Ty));
1861 if (isa<SCEVUMinExpr>(Val: MinMax))
1862 return getUMinExpr(Operands);
1863 return getUMaxExpr(Operands);
1864 }
1865
1866 // zext(umin_seq(x, y)) -> umin_seq(zext(x), zext(y))
1867 if (auto *MinMax = dyn_cast<SCEVSequentialMinMaxExpr>(Val: Op)) {
1868 assert(isa<SCEVSequentialUMinExpr>(MinMax) && "Not supported!");
1869 SmallVector<const SCEV *, 4> Operands;
1870 for (auto *Operand : MinMax->operands())
1871 Operands.push_back(Elt: getZeroExtendExpr(Op: Operand, Ty));
1872 return getUMinExpr(Operands, /*Sequential*/ true);
1873 }
1874
1875 // The cast wasn't folded; create an explicit cast node.
1876 // Recompute the insert position, as it may have been invalidated.
1877 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP)) return S;
1878 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(Allocator&: SCEVAllocator),
1879 Op, Ty);
1880 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
1881 registerUser(User: S, Ops: Op);
1882 return S;
1883}
1884
1885const SCEV *
1886ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1887 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1888 "This is not an extending conversion!");
1889 assert(isSCEVable(Ty) &&
1890 "This is not a conversion to a SCEVable type!");
1891 assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
1892 Ty = getEffectiveSCEVType(Ty);
1893
1894 FoldID ID(scSignExtend, Op, Ty);
1895 auto Iter = FoldCache.find(Val: ID);
1896 if (Iter != FoldCache.end())
1897 return Iter->second;
1898
1899 const SCEV *S = getSignExtendExprImpl(Op, Ty, Depth);
1900 if (!isa<SCEVSignExtendExpr>(Val: S))
1901 insertFoldCacheEntry(ID, S, FoldCache, FoldCacheUser);
1902 return S;
1903}
1904
1905const SCEV *ScalarEvolution::getSignExtendExprImpl(const SCEV *Op, Type *Ty,
1906 unsigned Depth) {
1907 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1908 "This is not an extending conversion!");
1909 assert(isSCEVable(Ty) && "This is not a conversion to a SCEVable type!");
1910 assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
1911 Ty = getEffectiveSCEVType(Ty);
1912
1913 // Fold if the operand is constant.
1914 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Val: Op))
1915 return getConstant(Val: SC->getAPInt().sext(width: getTypeSizeInBits(Ty)));
1916
1917 // sext(sext(x)) --> sext(x)
1918 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Val: Op))
1919 return getSignExtendExpr(Op: SS->getOperand(), Ty, Depth: Depth + 1);
1920
1921 // sext(zext(x)) --> zext(x)
1922 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Val: Op))
1923 return getZeroExtendExpr(Op: SZ->getOperand(), Ty, Depth: Depth + 1);
1924
1925 // Before doing any expensive analysis, check to see if we've already
1926 // computed a SCEV for this Op and Ty.
1927 FoldingSetNodeID ID;
1928 ID.AddInteger(I: scSignExtend);
1929 ID.AddPointer(Ptr: Op);
1930 ID.AddPointer(Ptr: Ty);
1931 void *IP = nullptr;
1932 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP)) return S;
1933 // Limit recursion depth.
1934 if (Depth > MaxCastDepth) {
1935 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(Allocator&: SCEVAllocator),
1936 Op, Ty);
1937 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
1938 registerUser(User: S, Ops: Op);
1939 return S;
1940 }
1941
1942 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1943 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Val: Op)) {
1944 // It's possible the bits taken off by the truncate were all sign bits. If
1945 // so, we should be able to simplify this further.
1946 const SCEV *X = ST->getOperand();
1947 ConstantRange CR = getSignedRange(S: X);
1948 unsigned TruncBits = getTypeSizeInBits(Ty: ST->getType());
1949 unsigned NewBits = getTypeSizeInBits(Ty);
1950 if (CR.truncate(BitWidth: TruncBits).signExtend(BitWidth: NewBits).contains(
1951 CR: CR.sextOrTrunc(BitWidth: NewBits)))
1952 return getTruncateOrSignExtend(V: X, Ty, Depth);
1953 }
1954
1955 if (auto *SA = dyn_cast<SCEVAddExpr>(Val: Op)) {
1956 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1957 if (SA->hasNoSignedWrap()) {
1958 // If the addition does not sign overflow then we can, by definition,
1959 // commute the sign extension with the addition operation.
1960 SmallVector<const SCEV *, 4> Ops;
1961 for (const auto *Op : SA->operands())
1962 Ops.push_back(Elt: getSignExtendExpr(Op, Ty, Depth: Depth + 1));
1963 return getAddExpr(Ops, Flags: SCEV::FlagNSW, Depth: Depth + 1);
1964 }
1965
1966 // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
1967 // if D + (C - D + x + y + ...) could be proven to not signed wrap
1968 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1969 //
1970 // For instance, this will bring two seemingly different expressions:
1971 // 1 + sext(5 + 20 * %x + 24 * %y) and
1972 // sext(6 + 20 * %x + 24 * %y)
1973 // to the same form:
1974 // 2 + sext(4 + 20 * %x + 24 * %y)
1975 if (const auto *SC = dyn_cast<SCEVConstant>(Val: SA->getOperand(i: 0))) {
1976 const APInt &D = extractConstantWithoutWrapping(SE&: *this, ConstantTerm: SC, WholeAddExpr: SA);
1977 if (D != 0) {
1978 const SCEV *SSExtD = getSignExtendExpr(Op: getConstant(Val: D), Ty, Depth);
1979 const SCEV *SResidual =
1980 getAddExpr(LHS: getConstant(Val: -D), RHS: SA, Flags: SCEV::FlagAnyWrap, Depth);
1981 const SCEV *SSExtR = getSignExtendExpr(Op: SResidual, Ty, Depth: Depth + 1);
1982 return getAddExpr(LHS: SSExtD, RHS: SSExtR,
1983 Flags: (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1984 Depth: Depth + 1);
1985 }
1986 }
1987 }
1988 // If the input value is a chrec scev, and we can prove that the value
1989 // did not overflow the old, smaller, value, we can sign extend all of the
1990 // operands (often constants). This allows analysis of something like
1991 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1992 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Val: Op))
1993 if (AR->isAffine()) {
1994 const SCEV *Start = AR->getStart();
1995 const SCEV *Step = AR->getStepRecurrence(SE&: *this);
1996 unsigned BitWidth = getTypeSizeInBits(Ty: AR->getType());
1997 const Loop *L = AR->getLoop();
1998
1999 // If we have special knowledge that this addrec won't overflow,
2000 // we don't need to do any further analysis.
2001 if (AR->hasNoSignedWrap()) {
2002 Start =
2003 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, SE: this, Depth: Depth + 1);
2004 Step = getSignExtendExpr(Op: Step, Ty, Depth: Depth + 1);
2005 return getAddRecExpr(Start, Step, L, Flags: SCEV::FlagNSW);
2006 }
2007
2008 // Check whether the backedge-taken count is SCEVCouldNotCompute.
2009 // Note that this serves two purposes: It filters out loops that are
2010 // simply not analyzable, and it covers the case where this code is
2011 // being called from within backedge-taken count analysis, such that
2012 // attempting to ask for the backedge-taken count would likely result
2013 // in infinite recursion. In the later case, the analysis code will
2014 // cope with a conservative value, and it will take care to purge
2015 // that value once it has finished.
2016 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
2017 if (!isa<SCEVCouldNotCompute>(Val: MaxBECount)) {
2018 // Manually compute the final value for AR, checking for
2019 // overflow.
2020
2021 // Check whether the backedge-taken count can be losslessly casted to
2022 // the addrec's type. The count is always unsigned.
2023 const SCEV *CastedMaxBECount =
2024 getTruncateOrZeroExtend(V: MaxBECount, Ty: Start->getType(), Depth);
2025 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
2026 V: CastedMaxBECount, Ty: MaxBECount->getType(), Depth);
2027 if (MaxBECount == RecastedMaxBECount) {
2028 Type *WideTy = IntegerType::get(C&: getContext(), NumBits: BitWidth * 2);
2029 // Check whether Start+Step*MaxBECount has no signed overflow.
2030 const SCEV *SMul = getMulExpr(LHS: CastedMaxBECount, RHS: Step,
2031 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2032 const SCEV *SAdd = getSignExtendExpr(Op: getAddExpr(LHS: Start, RHS: SMul,
2033 Flags: SCEV::FlagAnyWrap,
2034 Depth: Depth + 1),
2035 Ty: WideTy, Depth: Depth + 1);
2036 const SCEV *WideStart = getSignExtendExpr(Op: Start, Ty: WideTy, Depth: Depth + 1);
2037 const SCEV *WideMaxBECount =
2038 getZeroExtendExpr(Op: CastedMaxBECount, Ty: WideTy, Depth: Depth + 1);
2039 const SCEV *OperandExtendedAdd =
2040 getAddExpr(LHS: WideStart,
2041 RHS: getMulExpr(LHS: WideMaxBECount,
2042 RHS: getSignExtendExpr(Op: Step, Ty: WideTy, Depth: Depth + 1),
2043 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1),
2044 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2045 if (SAdd == OperandExtendedAdd) {
2046 // Cache knowledge of AR NSW, which is propagated to this AddRec.
2047 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags: SCEV::FlagNSW);
2048 // Return the expression with the addrec on the outside.
2049 Start = getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, SE: this,
2050 Depth: Depth + 1);
2051 Step = getSignExtendExpr(Op: Step, Ty, Depth: Depth + 1);
2052 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
2053 }
2054 // Similar to above, only this time treat the step value as unsigned.
2055 // This covers loops that count up with an unsigned step.
2056 OperandExtendedAdd =
2057 getAddExpr(LHS: WideStart,
2058 RHS: getMulExpr(LHS: WideMaxBECount,
2059 RHS: getZeroExtendExpr(Op: Step, Ty: WideTy, Depth: Depth + 1),
2060 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1),
2061 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2062 if (SAdd == OperandExtendedAdd) {
2063 // If AR wraps around then
2064 //
2065 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
2066 // => SAdd != OperandExtendedAdd
2067 //
2068 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
2069 // (SAdd == OperandExtendedAdd => AR is NW)
2070
2071 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags: SCEV::FlagNW);
2072
2073 // Return the expression with the addrec on the outside.
2074 Start = getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, SE: this,
2075 Depth: Depth + 1);
2076 Step = getZeroExtendExpr(Op: Step, Ty, Depth: Depth + 1);
2077 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
2078 }
2079 }
2080 }
2081
2082 auto NewFlags = proveNoSignedWrapViaInduction(AR);
2083 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags: NewFlags);
2084 if (AR->hasNoSignedWrap()) {
2085 // Same as nsw case above - duplicated here to avoid a compile time
2086 // issue. It's not clear that the order of checks does matter, but
2087 // it's one of two issue possible causes for a change which was
2088 // reverted. Be conservative for the moment.
2089 Start =
2090 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, SE: this, Depth: Depth + 1);
2091 Step = getSignExtendExpr(Op: Step, Ty, Depth: Depth + 1);
2092 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
2093 }
2094
2095 // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
2096 // if D + (C - D + Step * n) could be proven to not signed wrap
2097 // where D maximizes the number of trailing zeros of (C - D + Step * n)
2098 if (const auto *SC = dyn_cast<SCEVConstant>(Val: Start)) {
2099 const APInt &C = SC->getAPInt();
2100 const APInt &D = extractConstantWithoutWrapping(SE&: *this, ConstantStart: C, Step);
2101 if (D != 0) {
2102 const SCEV *SSExtD = getSignExtendExpr(Op: getConstant(Val: D), Ty, Depth);
2103 const SCEV *SResidual =
2104 getAddRecExpr(Start: getConstant(Val: C - D), Step, L, Flags: AR->getNoWrapFlags());
2105 const SCEV *SSExtR = getSignExtendExpr(Op: SResidual, Ty, Depth: Depth + 1);
2106 return getAddExpr(LHS: SSExtD, RHS: SSExtR,
2107 Flags: (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
2108 Depth: Depth + 1);
2109 }
2110 }
2111
2112 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
2113 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags: SCEV::FlagNSW);
2114 Start =
2115 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, SE: this, Depth: Depth + 1);
2116 Step = getSignExtendExpr(Op: Step, Ty, Depth: Depth + 1);
2117 return getAddRecExpr(Start, Step, L, Flags: AR->getNoWrapFlags());
2118 }
2119 }
2120
2121 // If the input value is provably positive and we could not simplify
2122 // away the sext build a zext instead.
2123 if (isKnownNonNegative(S: Op))
2124 return getZeroExtendExpr(Op, Ty, Depth: Depth + 1);
2125
2126 // sext(smin(x, y)) -> smin(sext(x), sext(y))
2127 // sext(smax(x, y)) -> smax(sext(x), sext(y))
2128 if (isa<SCEVSMinExpr>(Val: Op) || isa<SCEVSMaxExpr>(Val: Op)) {
2129 auto *MinMax = cast<SCEVMinMaxExpr>(Val: Op);
2130 SmallVector<const SCEV *, 4> Operands;
2131 for (auto *Operand : MinMax->operands())
2132 Operands.push_back(Elt: getSignExtendExpr(Op: Operand, Ty));
2133 if (isa<SCEVSMinExpr>(Val: MinMax))
2134 return getSMinExpr(Operands);
2135 return getSMaxExpr(Operands);
2136 }
2137
2138 // The cast wasn't folded; create an explicit cast node.
2139 // Recompute the insert position, as it may have been invalidated.
2140 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP)) return S;
2141 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(Allocator&: SCEVAllocator),
2142 Op, Ty);
2143 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
2144 registerUser(User: S, Ops: { Op });
2145 return S;
2146}
2147
2148const SCEV *ScalarEvolution::getCastExpr(SCEVTypes Kind, const SCEV *Op,
2149 Type *Ty) {
2150 switch (Kind) {
2151 case scTruncate:
2152 return getTruncateExpr(Op, Ty);
2153 case scZeroExtend:
2154 return getZeroExtendExpr(Op, Ty);
2155 case scSignExtend:
2156 return getSignExtendExpr(Op, Ty);
2157 case scPtrToInt:
2158 return getPtrToIntExpr(Op, Ty);
2159 default:
2160 llvm_unreachable("Not a SCEV cast expression!");
2161 }
2162}
2163
2164/// getAnyExtendExpr - Return a SCEV for the given operand extended with
2165/// unspecified bits out to the given type.
2166const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
2167 Type *Ty) {
2168 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
2169 "This is not an extending conversion!");
2170 assert(isSCEVable(Ty) &&
2171 "This is not a conversion to a SCEVable type!");
2172 Ty = getEffectiveSCEVType(Ty);
2173
2174 // Sign-extend negative constants.
2175 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Val: Op))
2176 if (SC->getAPInt().isNegative())
2177 return getSignExtendExpr(Op, Ty);
2178
2179 // Peel off a truncate cast.
2180 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Val: Op)) {
2181 const SCEV *NewOp = T->getOperand();
2182 if (getTypeSizeInBits(Ty: NewOp->getType()) < getTypeSizeInBits(Ty))
2183 return getAnyExtendExpr(Op: NewOp, Ty);
2184 return getTruncateOrNoop(V: NewOp, Ty);
2185 }
2186
2187 // Next try a zext cast. If the cast is folded, use it.
2188 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
2189 if (!isa<SCEVZeroExtendExpr>(Val: ZExt))
2190 return ZExt;
2191
2192 // Next try a sext cast. If the cast is folded, use it.
2193 const SCEV *SExt = getSignExtendExpr(Op, Ty);
2194 if (!isa<SCEVSignExtendExpr>(Val: SExt))
2195 return SExt;
2196
2197 // Force the cast to be folded into the operands of an addrec.
2198 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Val: Op)) {
2199 SmallVector<const SCEV *, 4> Ops;
2200 for (const SCEV *Op : AR->operands())
2201 Ops.push_back(Elt: getAnyExtendExpr(Op, Ty));
2202 return getAddRecExpr(Operands&: Ops, L: AR->getLoop(), Flags: SCEV::FlagNW);
2203 }
2204
2205 // If the expression is obviously signed, use the sext cast value.
2206 if (isa<SCEVSMaxExpr>(Val: Op))
2207 return SExt;
2208
2209 // Absent any other information, use the zext cast value.
2210 return ZExt;
2211}
2212
2213/// Process the given Ops list, which is a list of operands to be added under
2214/// the given scale, update the given map. This is a helper function for
2215/// getAddRecExpr. As an example of what it does, given a sequence of operands
2216/// that would form an add expression like this:
2217///
2218/// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2219///
2220/// where A and B are constants, update the map with these values:
2221///
2222/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2223///
2224/// and add 13 + A*B*29 to AccumulatedConstant.
2225/// This will allow getAddRecExpr to produce this:
2226///
2227/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2228///
2229/// This form often exposes folding opportunities that are hidden in
2230/// the original operand list.
2231///
2232/// Return true iff it appears that any interesting folding opportunities
2233/// may be exposed. This helps getAddRecExpr short-circuit extra work in
2234/// the common case where no interesting opportunities are present, and
2235/// is also used as a check to avoid infinite recursion.
2236static bool
2237CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
2238 SmallVectorImpl<const SCEV *> &NewOps,
2239 APInt &AccumulatedConstant,
2240 ArrayRef<const SCEV *> Ops, const APInt &Scale,
2241 ScalarEvolution &SE) {
2242 bool Interesting = false;
2243
2244 // Iterate over the add operands. They are sorted, with constants first.
2245 unsigned i = 0;
2246 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Val: Ops[i])) {
2247 ++i;
2248 // Pull a buried constant out to the outside.
2249 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
2250 Interesting = true;
2251 AccumulatedConstant += Scale * C->getAPInt();
2252 }
2253
2254 // Next comes everything else. We're especially interested in multiplies
2255 // here, but they're in the middle, so just visit the rest with one loop.
2256 for (; i != Ops.size(); ++i) {
2257 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Val: Ops[i]);
2258 if (Mul && isa<SCEVConstant>(Val: Mul->getOperand(i: 0))) {
2259 APInt NewScale =
2260 Scale * cast<SCEVConstant>(Val: Mul->getOperand(i: 0))->getAPInt();
2261 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Val: Mul->getOperand(i: 1))) {
2262 // A multiplication of a constant with another add; recurse.
2263 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Val: Mul->getOperand(i: 1));
2264 Interesting |=
2265 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2266 Ops: Add->operands(), Scale: NewScale, SE);
2267 } else {
2268 // A multiplication of a constant with some other value. Update
2269 // the map.
2270 SmallVector<const SCEV *, 4> MulOps(drop_begin(RangeOrContainer: Mul->operands()));
2271 const SCEV *Key = SE.getMulExpr(Ops&: MulOps);
2272 auto Pair = M.insert(KV: {Key, NewScale});
2273 if (Pair.second) {
2274 NewOps.push_back(Elt: Pair.first->first);
2275 } else {
2276 Pair.first->second += NewScale;
2277 // The map already had an entry for this value, which may indicate
2278 // a folding opportunity.
2279 Interesting = true;
2280 }
2281 }
2282 } else {
2283 // An ordinary operand. Update the map.
2284 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2285 M.insert(KV: {Ops[i], Scale});
2286 if (Pair.second) {
2287 NewOps.push_back(Elt: Pair.first->first);
2288 } else {
2289 Pair.first->second += Scale;
2290 // The map already had an entry for this value, which may indicate
2291 // a folding opportunity.
2292 Interesting = true;
2293 }
2294 }
2295 }
2296
2297 return Interesting;
2298}
2299
2300bool ScalarEvolution::willNotOverflow(Instruction::BinaryOps BinOp, bool Signed,
2301 const SCEV *LHS, const SCEV *RHS,
2302 const Instruction *CtxI) {
2303 const SCEV *(ScalarEvolution::*Operation)(const SCEV *, const SCEV *,
2304 SCEV::NoWrapFlags, unsigned);
2305 switch (BinOp) {
2306 default:
2307 llvm_unreachable("Unsupported binary op");
2308 case Instruction::Add:
2309 Operation = &ScalarEvolution::getAddExpr;
2310 break;
2311 case Instruction::Sub:
2312 Operation = &ScalarEvolution::getMinusSCEV;
2313 break;
2314 case Instruction::Mul:
2315 Operation = &ScalarEvolution::getMulExpr;
2316 break;
2317 }
2318
2319 const SCEV *(ScalarEvolution::*Extension)(const SCEV *, Type *, unsigned) =
2320 Signed ? &ScalarEvolution::getSignExtendExpr
2321 : &ScalarEvolution::getZeroExtendExpr;
2322
2323 // Check ext(LHS op RHS) == ext(LHS) op ext(RHS)
2324 auto *NarrowTy = cast<IntegerType>(Val: LHS->getType());
2325 auto *WideTy =
2326 IntegerType::get(C&: NarrowTy->getContext(), NumBits: NarrowTy->getBitWidth() * 2);
2327
2328 const SCEV *A = (this->*Extension)(
2329 (this->*Operation)(LHS, RHS, SCEV::FlagAnyWrap, 0), WideTy, 0);
2330 const SCEV *LHSB = (this->*Extension)(LHS, WideTy, 0);
2331 const SCEV *RHSB = (this->*Extension)(RHS, WideTy, 0);
2332 const SCEV *B = (this->*Operation)(LHSB, RHSB, SCEV::FlagAnyWrap, 0);
2333 if (A == B)
2334 return true;
2335 // Can we use context to prove the fact we need?
2336 if (!CtxI)
2337 return false;
2338 // TODO: Support mul.
2339 if (BinOp == Instruction::Mul)
2340 return false;
2341 auto *RHSC = dyn_cast<SCEVConstant>(Val: RHS);
2342 // TODO: Lift this limitation.
2343 if (!RHSC)
2344 return false;
2345 APInt C = RHSC->getAPInt();
2346 unsigned NumBits = C.getBitWidth();
2347 bool IsSub = (BinOp == Instruction::Sub);
2348 bool IsNegativeConst = (Signed && C.isNegative());
2349 // Compute the direction and magnitude by which we need to check overflow.
2350 bool OverflowDown = IsSub ^ IsNegativeConst;
2351 APInt Magnitude = C;
2352 if (IsNegativeConst) {
2353 if (C == APInt::getSignedMinValue(numBits: NumBits))
2354 // TODO: SINT_MIN on inversion gives the same negative value, we don't
2355 // want to deal with that.
2356 return false;
2357 Magnitude = -C;
2358 }
2359
2360 ICmpInst::Predicate Pred = Signed ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
2361 if (OverflowDown) {
2362 // To avoid overflow down, we need to make sure that MIN + Magnitude <= LHS.
2363 APInt Min = Signed ? APInt::getSignedMinValue(numBits: NumBits)
2364 : APInt::getMinValue(numBits: NumBits);
2365 APInt Limit = Min + Magnitude;
2366 return isKnownPredicateAt(Pred, LHS: getConstant(Val: Limit), RHS: LHS, CtxI);
2367 } else {
2368 // To avoid overflow up, we need to make sure that LHS <= MAX - Magnitude.
2369 APInt Max = Signed ? APInt::getSignedMaxValue(numBits: NumBits)
2370 : APInt::getMaxValue(numBits: NumBits);
2371 APInt Limit = Max - Magnitude;
2372 return isKnownPredicateAt(Pred, LHS, RHS: getConstant(Val: Limit), CtxI);
2373 }
2374}
2375
2376std::optional<SCEV::NoWrapFlags>
2377ScalarEvolution::getStrengthenedNoWrapFlagsFromBinOp(
2378 const OverflowingBinaryOperator *OBO) {
2379 // It cannot be done any better.
2380 if (OBO->hasNoUnsignedWrap() && OBO->hasNoSignedWrap())
2381 return std::nullopt;
2382
2383 SCEV::NoWrapFlags Flags = SCEV::NoWrapFlags::FlagAnyWrap;
2384
2385 if (OBO->hasNoUnsignedWrap())
2386 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNUW);
2387 if (OBO->hasNoSignedWrap())
2388 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNSW);
2389
2390 bool Deduced = false;
2391
2392 if (OBO->getOpcode() != Instruction::Add &&
2393 OBO->getOpcode() != Instruction::Sub &&
2394 OBO->getOpcode() != Instruction::Mul)
2395 return std::nullopt;
2396
2397 const SCEV *LHS = getSCEV(V: OBO->getOperand(i_nocapture: 0));
2398 const SCEV *RHS = getSCEV(V: OBO->getOperand(i_nocapture: 1));
2399
2400 const Instruction *CtxI =
2401 UseContextForNoWrapFlagInference ? dyn_cast<Instruction>(Val: OBO) : nullptr;
2402 if (!OBO->hasNoUnsignedWrap() &&
2403 willNotOverflow(BinOp: (Instruction::BinaryOps)OBO->getOpcode(),
2404 /* Signed */ false, LHS, RHS, CtxI)) {
2405 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNUW);
2406 Deduced = true;
2407 }
2408
2409 if (!OBO->hasNoSignedWrap() &&
2410 willNotOverflow(BinOp: (Instruction::BinaryOps)OBO->getOpcode(),
2411 /* Signed */ true, LHS, RHS, CtxI)) {
2412 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNSW);
2413 Deduced = true;
2414 }
2415
2416 if (Deduced)
2417 return Flags;
2418 return std::nullopt;
2419}
2420
2421// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2422// `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2423// can't-overflow flags for the operation if possible.
2424static SCEV::NoWrapFlags
2425StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
2426 const ArrayRef<const SCEV *> Ops,
2427 SCEV::NoWrapFlags Flags) {
2428 using namespace std::placeholders;
2429
2430 using OBO = OverflowingBinaryOperator;
2431
2432 bool CanAnalyze =
2433 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2434 (void)CanAnalyze;
2435 assert(CanAnalyze && "don't call from other places!");
2436
2437 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2438 SCEV::NoWrapFlags SignOrUnsignWrap =
2439 ScalarEvolution::maskFlags(Flags, Mask: SignOrUnsignMask);
2440
2441 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2442 auto IsKnownNonNegative = [&](const SCEV *S) {
2443 return SE->isKnownNonNegative(S);
2444 };
2445
2446 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Range: Ops, P: IsKnownNonNegative))
2447 Flags =
2448 ScalarEvolution::setFlags(Flags, OnFlags: (SCEV::NoWrapFlags)SignOrUnsignMask);
2449
2450 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, Mask: SignOrUnsignMask);
2451
2452 if (SignOrUnsignWrap != SignOrUnsignMask &&
2453 (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
2454 isa<SCEVConstant>(Val: Ops[0])) {
2455
2456 auto Opcode = [&] {
2457 switch (Type) {
2458 case scAddExpr:
2459 return Instruction::Add;
2460 case scMulExpr:
2461 return Instruction::Mul;
2462 default:
2463 llvm_unreachable("Unexpected SCEV op.");
2464 }
2465 }();
2466
2467 const APInt &C = cast<SCEVConstant>(Val: Ops[0])->getAPInt();
2468
2469 // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
2470 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2471 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2472 BinOp: Opcode, Other: C, NoWrapKind: OBO::NoSignedWrap);
2473 if (NSWRegion.contains(CR: SE->getSignedRange(S: Ops[1])))
2474 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNSW);
2475 }
2476
2477 // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
2478 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2479 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2480 BinOp: Opcode, Other: C, NoWrapKind: OBO::NoUnsignedWrap);
2481 if (NUWRegion.contains(CR: SE->getUnsignedRange(S: Ops[1])))
2482 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNUW);
2483 }
2484 }
2485
2486 // <0,+,nonnegative><nw> is also nuw
2487 // TODO: Add corresponding nsw case
2488 if (Type == scAddRecExpr && ScalarEvolution::hasFlags(Flags, TestFlags: SCEV::FlagNW) &&
2489 !ScalarEvolution::hasFlags(Flags, TestFlags: SCEV::FlagNUW) && Ops.size() == 2 &&
2490 Ops[0]->isZero() && IsKnownNonNegative(Ops[1]))
2491 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNUW);
2492
2493 // both (udiv X, Y) * Y and Y * (udiv X, Y) are always NUW
2494 if (Type == scMulExpr && !ScalarEvolution::hasFlags(Flags, TestFlags: SCEV::FlagNUW) &&
2495 Ops.size() == 2) {
2496 if (auto *UDiv = dyn_cast<SCEVUDivExpr>(Val: Ops[0]))
2497 if (UDiv->getOperand(i: 1) == Ops[1])
2498 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNUW);
2499 if (auto *UDiv = dyn_cast<SCEVUDivExpr>(Val: Ops[1]))
2500 if (UDiv->getOperand(i: 1) == Ops[0])
2501 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNUW);
2502 }
2503
2504 return Flags;
2505}
2506
2507bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
2508 return isLoopInvariant(S, L) && properlyDominates(S, BB: L->getHeader());
2509}
2510
2511/// Get a canonical add expression, or something simpler if possible.
2512const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2513 SCEV::NoWrapFlags OrigFlags,
2514 unsigned Depth) {
2515 assert(!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2516 "only nuw or nsw allowed");
2517 assert(!Ops.empty() && "Cannot get empty add!");
2518 if (Ops.size() == 1) return Ops[0];
2519#ifndef NDEBUG
2520 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2521 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2522 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2523 "SCEVAddExpr operand types don't match!");
2524 unsigned NumPtrs = count_if(
2525 Ops, [](const SCEV *Op) { return Op->getType()->isPointerTy(); });
2526 assert(NumPtrs <= 1 && "add has at most one pointer operand");
2527#endif
2528
2529 // Sort by complexity, this groups all similar expression types together.
2530 GroupByComplexity(Ops, LI: &LI, DT);
2531
2532 // If there are any constants, fold them together.
2533 unsigned Idx = 0;
2534 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Val: Ops[0])) {
2535 ++Idx;
2536 assert(Idx < Ops.size());
2537 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Val: Ops[Idx])) {
2538 // We found two constants, fold them together!
2539 Ops[0] = getConstant(Val: LHSC->getAPInt() + RHSC->getAPInt());
2540 if (Ops.size() == 2) return Ops[0];
2541 Ops.erase(CI: Ops.begin()+1); // Erase the folded element
2542 LHSC = cast<SCEVConstant>(Val: Ops[0]);
2543 }
2544
2545 // If we are left with a constant zero being added, strip it off.
2546 if (LHSC->getValue()->isZero()) {
2547 Ops.erase(CI: Ops.begin());
2548 --Idx;
2549 }
2550
2551 if (Ops.size() == 1) return Ops[0];
2552 }
2553
2554 // Delay expensive flag strengthening until necessary.
2555 auto ComputeFlags = [this, OrigFlags](const ArrayRef<const SCEV *> Ops) {
2556 return StrengthenNoWrapFlags(SE: this, Type: scAddExpr, Ops, Flags: OrigFlags);
2557 };
2558
2559 // Limit recursion calls depth.
2560 if (Depth > MaxArithDepth || hasHugeExpression(Ops))
2561 return getOrCreateAddExpr(Ops, Flags: ComputeFlags(Ops));
2562
2563 if (SCEV *S = findExistingSCEVInCache(SCEVType: scAddExpr, Ops)) {
2564 // Don't strengthen flags if we have no new information.
2565 SCEVAddExpr *Add = static_cast<SCEVAddExpr *>(S);
2566 if (Add->getNoWrapFlags(Mask: OrigFlags) != OrigFlags)
2567 Add->setNoWrapFlags(ComputeFlags(Ops));
2568 return S;
2569 }
2570
2571 // Okay, check to see if the same value occurs in the operand list more than
2572 // once. If so, merge them together into an multiply expression. Since we
2573 // sorted the list, these values are required to be adjacent.
2574 Type *Ty = Ops[0]->getType();
2575 bool FoundMatch = false;
2576 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2577 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2578 // Scan ahead to count how many equal operands there are.
2579 unsigned Count = 2;
2580 while (i+Count != e && Ops[i+Count] == Ops[i])
2581 ++Count;
2582 // Merge the values into a multiply.
2583 const SCEV *Scale = getConstant(Ty, V: Count);
2584 const SCEV *Mul = getMulExpr(LHS: Scale, RHS: Ops[i], Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2585 if (Ops.size() == Count)
2586 return Mul;
2587 Ops[i] = Mul;
2588 Ops.erase(CS: Ops.begin()+i+1, CE: Ops.begin()+i+Count);
2589 --i; e -= Count - 1;
2590 FoundMatch = true;
2591 }
2592 if (FoundMatch)
2593 return getAddExpr(Ops, OrigFlags, Depth: Depth + 1);
2594
2595 // Check for truncates. If all the operands are truncated from the same
2596 // type, see if factoring out the truncate would permit the result to be
2597 // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
2598 // if the contents of the resulting outer trunc fold to something simple.
2599 auto FindTruncSrcType = [&]() -> Type * {
2600 // We're ultimately looking to fold an addrec of truncs and muls of only
2601 // constants and truncs, so if we find any other types of SCEV
2602 // as operands of the addrec then we bail and return nullptr here.
2603 // Otherwise, we return the type of the operand of a trunc that we find.
2604 if (auto *T = dyn_cast<SCEVTruncateExpr>(Val: Ops[Idx]))
2605 return T->getOperand()->getType();
2606 if (const auto *Mul = dyn_cast<SCEVMulExpr>(Val: Ops[Idx])) {
2607 const auto *LastOp = Mul->getOperand(i: Mul->getNumOperands() - 1);
2608 if (const auto *T = dyn_cast<SCEVTruncateExpr>(Val: LastOp))
2609 return T->getOperand()->getType();
2610 }
2611 return nullptr;
2612 };
2613 if (auto *SrcType = FindTruncSrcType()) {
2614 SmallVector<const SCEV *, 8> LargeOps;
2615 bool Ok = true;
2616 // Check all the operands to see if they can be represented in the
2617 // source type of the truncate.
2618 for (const SCEV *Op : Ops) {
2619 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Val: Op)) {
2620 if (T->getOperand()->getType() != SrcType) {
2621 Ok = false;
2622 break;
2623 }
2624 LargeOps.push_back(Elt: T->getOperand());
2625 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Val: Op)) {
2626 LargeOps.push_back(Elt: getAnyExtendExpr(Op: C, Ty: SrcType));
2627 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Val: Op)) {
2628 SmallVector<const SCEV *, 8> LargeMulOps;
2629 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2630 if (const SCEVTruncateExpr *T =
2631 dyn_cast<SCEVTruncateExpr>(Val: M->getOperand(i: j))) {
2632 if (T->getOperand()->getType() != SrcType) {
2633 Ok = false;
2634 break;
2635 }
2636 LargeMulOps.push_back(Elt: T->getOperand());
2637 } else if (const auto *C = dyn_cast<SCEVConstant>(Val: M->getOperand(i: j))) {
2638 LargeMulOps.push_back(Elt: getAnyExtendExpr(Op: C, Ty: SrcType));
2639 } else {
2640 Ok = false;
2641 break;
2642 }
2643 }
2644 if (Ok)
2645 LargeOps.push_back(Elt: getMulExpr(Ops&: LargeMulOps, Flags: SCEV::FlagAnyWrap, Depth: Depth + 1));
2646 } else {
2647 Ok = false;
2648 break;
2649 }
2650 }
2651 if (Ok) {
2652 // Evaluate the expression in the larger type.
2653 const SCEV *Fold = getAddExpr(Ops&: LargeOps, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2654 // If it folds to something simple, use it. Otherwise, don't.
2655 if (isa<SCEVConstant>(Val: Fold) || isa<SCEVUnknown>(Val: Fold))
2656 return getTruncateExpr(Op: Fold, Ty);
2657 }
2658 }
2659
2660 if (Ops.size() == 2) {
2661 // Check if we have an expression of the form ((X + C1) - C2), where C1 and
2662 // C2 can be folded in a way that allows retaining wrapping flags of (X +
2663 // C1).
2664 const SCEV *A = Ops[0];
2665 const SCEV *B = Ops[1];
2666 auto *AddExpr = dyn_cast<SCEVAddExpr>(Val: B);
2667 auto *C = dyn_cast<SCEVConstant>(Val: A);
2668 if (AddExpr && C && isa<SCEVConstant>(Val: AddExpr->getOperand(i: 0))) {
2669 auto C1 = cast<SCEVConstant>(Val: AddExpr->getOperand(i: 0))->getAPInt();
2670 auto C2 = C->getAPInt();
2671 SCEV::NoWrapFlags PreservedFlags = SCEV::FlagAnyWrap;
2672
2673 APInt ConstAdd = C1 + C2;
2674 auto AddFlags = AddExpr->getNoWrapFlags();
2675 // Adding a smaller constant is NUW if the original AddExpr was NUW.
2676 if (ScalarEvolution::hasFlags(Flags: AddFlags, TestFlags: SCEV::FlagNUW) &&
2677 ConstAdd.ule(RHS: C1)) {
2678 PreservedFlags =
2679 ScalarEvolution::setFlags(Flags: PreservedFlags, OnFlags: SCEV::FlagNUW);
2680 }
2681
2682 // Adding a constant with the same sign and small magnitude is NSW, if the
2683 // original AddExpr was NSW.
2684 if (ScalarEvolution::hasFlags(Flags: AddFlags, TestFlags: SCEV::FlagNSW) &&
2685 C1.isSignBitSet() == ConstAdd.isSignBitSet() &&
2686 ConstAdd.abs().ule(RHS: C1.abs())) {
2687 PreservedFlags =
2688 ScalarEvolution::setFlags(Flags: PreservedFlags, OnFlags: SCEV::FlagNSW);
2689 }
2690
2691 if (PreservedFlags != SCEV::FlagAnyWrap) {
2692 SmallVector<const SCEV *, 4> NewOps(AddExpr->operands());
2693 NewOps[0] = getConstant(Val: ConstAdd);
2694 return getAddExpr(Ops&: NewOps, OrigFlags: PreservedFlags);
2695 }
2696 }
2697 }
2698
2699 // Canonicalize (-1 * urem X, Y) + X --> (Y * X/Y)
2700 if (Ops.size() == 2) {
2701 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Val: Ops[0]);
2702 if (Mul && Mul->getNumOperands() == 2 &&
2703 Mul->getOperand(i: 0)->isAllOnesValue()) {
2704 const SCEV *X;
2705 const SCEV *Y;
2706 if (matchURem(Expr: Mul->getOperand(i: 1), LHS&: X, RHS&: Y) && X == Ops[1]) {
2707 return getMulExpr(LHS: Y, RHS: getUDivExpr(LHS: X, RHS: Y));
2708 }
2709 }
2710 }
2711
2712 // Skip past any other cast SCEVs.
2713 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2714 ++Idx;
2715
2716 // If there are add operands they would be next.
2717 if (Idx < Ops.size()) {
2718 bool DeletedAdd = false;
2719 // If the original flags and all inlined SCEVAddExprs are NUW, use the
2720 // common NUW flag for expression after inlining. Other flags cannot be
2721 // preserved, because they may depend on the original order of operations.
2722 SCEV::NoWrapFlags CommonFlags = maskFlags(Flags: OrigFlags, Mask: SCEV::FlagNUW);
2723 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Val: Ops[Idx])) {
2724 if (Ops.size() > AddOpsInlineThreshold ||
2725 Add->getNumOperands() > AddOpsInlineThreshold)
2726 break;
2727 // If we have an add, expand the add operands onto the end of the operands
2728 // list.
2729 Ops.erase(CI: Ops.begin()+Idx);
2730 append_range(C&: Ops, R: Add->operands());
2731 DeletedAdd = true;
2732 CommonFlags = maskFlags(Flags: CommonFlags, Mask: Add->getNoWrapFlags());
2733 }
2734
2735 // If we deleted at least one add, we added operands to the end of the list,
2736 // and they are not necessarily sorted. Recurse to resort and resimplify
2737 // any operands we just acquired.
2738 if (DeletedAdd)
2739 return getAddExpr(Ops, OrigFlags: CommonFlags, Depth: Depth + 1);
2740 }
2741
2742 // Skip over the add expression until we get to a multiply.
2743 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2744 ++Idx;
2745
2746 // Check to see if there are any folding opportunities present with
2747 // operands multiplied by constant values.
2748 if (Idx < Ops.size() && isa<SCEVMulExpr>(Val: Ops[Idx])) {
2749 uint64_t BitWidth = getTypeSizeInBits(Ty);
2750 DenseMap<const SCEV *, APInt> M;
2751 SmallVector<const SCEV *, 8> NewOps;
2752 APInt AccumulatedConstant(BitWidth, 0);
2753 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2754 Ops, Scale: APInt(BitWidth, 1), SE&: *this)) {
2755 struct APIntCompare {
2756 bool operator()(const APInt &LHS, const APInt &RHS) const {
2757 return LHS.ult(RHS);
2758 }
2759 };
2760
2761 // Some interesting folding opportunity is present, so its worthwhile to
2762 // re-generate the operands list. Group the operands by constant scale,
2763 // to avoid multiplying by the same constant scale multiple times.
2764 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2765 for (const SCEV *NewOp : NewOps)
2766 MulOpLists[M.find(Val: NewOp)->second].push_back(Elt: NewOp);
2767 // Re-generate the operands list.
2768 Ops.clear();
2769 if (AccumulatedConstant != 0)
2770 Ops.push_back(Elt: getConstant(Val: AccumulatedConstant));
2771 for (auto &MulOp : MulOpLists) {
2772 if (MulOp.first == 1) {
2773 Ops.push_back(Elt: getAddExpr(Ops&: MulOp.second, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1));
2774 } else if (MulOp.first != 0) {
2775 Ops.push_back(Elt: getMulExpr(
2776 LHS: getConstant(Val: MulOp.first),
2777 RHS: getAddExpr(Ops&: MulOp.second, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1),
2778 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1));
2779 }
2780 }
2781 if (Ops.empty())
2782 return getZero(Ty);
2783 if (Ops.size() == 1)
2784 return Ops[0];
2785 return getAddExpr(Ops, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2786 }
2787 }
2788
2789 // If we are adding something to a multiply expression, make sure the
2790 // something is not already an operand of the multiply. If so, merge it into
2791 // the multiply.
2792 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Val: Ops[Idx]); ++Idx) {
2793 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Val: Ops[Idx]);
2794 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2795 const SCEV *MulOpSCEV = Mul->getOperand(i: MulOp);
2796 if (isa<SCEVConstant>(Val: MulOpSCEV))
2797 continue;
2798 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2799 if (MulOpSCEV == Ops[AddOp]) {
2800 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2801 const SCEV *InnerMul = Mul->getOperand(i: MulOp == 0);
2802 if (Mul->getNumOperands() != 2) {
2803 // If the multiply has more than two operands, we must get the
2804 // Y*Z term.
2805 SmallVector<const SCEV *, 4> MulOps(
2806 Mul->operands().take_front(N: MulOp));
2807 append_range(C&: MulOps, R: Mul->operands().drop_front(N: MulOp + 1));
2808 InnerMul = getMulExpr(Ops&: MulOps, Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2809 }
2810 SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
2811 const SCEV *AddOne = getAddExpr(Ops&: TwoOps, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2812 const SCEV *OuterMul = getMulExpr(LHS: AddOne, RHS: MulOpSCEV,
2813 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2814 if (Ops.size() == 2) return OuterMul;
2815 if (AddOp < Idx) {
2816 Ops.erase(CI: Ops.begin()+AddOp);
2817 Ops.erase(CI: Ops.begin()+Idx-1);
2818 } else {
2819 Ops.erase(CI: Ops.begin()+Idx);
2820 Ops.erase(CI: Ops.begin()+AddOp-1);
2821 }
2822 Ops.push_back(Elt: OuterMul);
2823 return getAddExpr(Ops, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2824 }
2825
2826 // Check this multiply against other multiplies being added together.
2827 for (unsigned OtherMulIdx = Idx+1;
2828 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Val: Ops[OtherMulIdx]);
2829 ++OtherMulIdx) {
2830 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Val: Ops[OtherMulIdx]);
2831 // If MulOp occurs in OtherMul, we can fold the two multiplies
2832 // together.
2833 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2834 OMulOp != e; ++OMulOp)
2835 if (OtherMul->getOperand(i: OMulOp) == MulOpSCEV) {
2836 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2837 const SCEV *InnerMul1 = Mul->getOperand(i: MulOp == 0);
2838 if (Mul->getNumOperands() != 2) {
2839 SmallVector<const SCEV *, 4> MulOps(
2840 Mul->operands().take_front(N: MulOp));
2841 append_range(C&: MulOps, R: Mul->operands().drop_front(N: MulOp+1));
2842 InnerMul1 = getMulExpr(Ops&: MulOps, Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2843 }
2844 const SCEV *InnerMul2 = OtherMul->getOperand(i: OMulOp == 0);
2845 if (OtherMul->getNumOperands() != 2) {
2846 SmallVector<const SCEV *, 4> MulOps(
2847 OtherMul->operands().take_front(N: OMulOp));
2848 append_range(C&: MulOps, R: OtherMul->operands().drop_front(N: OMulOp+1));
2849 InnerMul2 = getMulExpr(Ops&: MulOps, Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2850 }
2851 SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
2852 const SCEV *InnerMulSum =
2853 getAddExpr(Ops&: TwoOps, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2854 const SCEV *OuterMul = getMulExpr(LHS: MulOpSCEV, RHS: InnerMulSum,
2855 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2856 if (Ops.size() == 2) return OuterMul;
2857 Ops.erase(CI: Ops.begin()+Idx);
2858 Ops.erase(CI: Ops.begin()+OtherMulIdx-1);
2859 Ops.push_back(Elt: OuterMul);
2860 return getAddExpr(Ops, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2861 }
2862 }
2863 }
2864 }
2865
2866 // If there are any add recurrences in the operands list, see if any other
2867 // added values are loop invariant. If so, we can fold them into the
2868 // recurrence.
2869 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2870 ++Idx;
2871
2872 // Scan over all recurrences, trying to fold loop invariants into them.
2873 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Val: Ops[Idx]); ++Idx) {
2874 // Scan all of the other operands to this add and add them to the vector if
2875 // they are loop invariant w.r.t. the recurrence.
2876 SmallVector<const SCEV *, 8> LIOps;
2877 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Val: Ops[Idx]);
2878 const Loop *AddRecLoop = AddRec->getLoop();
2879 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2880 if (isAvailableAtLoopEntry(S: Ops[i], L: AddRecLoop)) {
2881 LIOps.push_back(Elt: Ops[i]);
2882 Ops.erase(CI: Ops.begin()+i);
2883 --i; --e;
2884 }
2885
2886 // If we found some loop invariants, fold them into the recurrence.
2887 if (!LIOps.empty()) {
2888 // Compute nowrap flags for the addition of the loop-invariant ops and
2889 // the addrec. Temporarily push it as an operand for that purpose. These
2890 // flags are valid in the scope of the addrec only.
2891 LIOps.push_back(Elt: AddRec);
2892 SCEV::NoWrapFlags Flags = ComputeFlags(LIOps);
2893 LIOps.pop_back();
2894
2895 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2896 LIOps.push_back(Elt: AddRec->getStart());
2897
2898 SmallVector<const SCEV *, 4> AddRecOps(AddRec->operands());
2899
2900 // It is not in general safe to propagate flags valid on an add within
2901 // the addrec scope to one outside it. We must prove that the inner
2902 // scope is guaranteed to execute if the outer one does to be able to
2903 // safely propagate. We know the program is undefined if poison is
2904 // produced on the inner scoped addrec. We also know that *for this use*
2905 // the outer scoped add can't overflow (because of the flags we just
2906 // computed for the inner scoped add) without the program being undefined.
2907 // Proving that entry to the outer scope neccesitates entry to the inner
2908 // scope, thus proves the program undefined if the flags would be violated
2909 // in the outer scope.
2910 SCEV::NoWrapFlags AddFlags = Flags;
2911 if (AddFlags != SCEV::FlagAnyWrap) {
2912 auto *DefI = getDefiningScopeBound(Ops: LIOps);
2913 auto *ReachI = &*AddRecLoop->getHeader()->begin();
2914 if (!isGuaranteedToTransferExecutionTo(A: DefI, B: ReachI))
2915 AddFlags = SCEV::FlagAnyWrap;
2916 }
2917 AddRecOps[0] = getAddExpr(Ops&: LIOps, OrigFlags: AddFlags, Depth: Depth + 1);
2918
2919 // Build the new addrec. Propagate the NUW and NSW flags if both the
2920 // outer add and the inner addrec are guaranteed to have no overflow.
2921 // Always propagate NW.
2922 Flags = AddRec->getNoWrapFlags(Mask: setFlags(Flags, OnFlags: SCEV::FlagNW));
2923 const SCEV *NewRec = getAddRecExpr(Operands&: AddRecOps, L: AddRecLoop, Flags);
2924
2925 // If all of the other operands were loop invariant, we are done.
2926 if (Ops.size() == 1) return NewRec;
2927
2928 // Otherwise, add the folded AddRec by the non-invariant parts.
2929 for (unsigned i = 0;; ++i)
2930 if (Ops[i] == AddRec) {
2931 Ops[i] = NewRec;
2932 break;
2933 }
2934 return getAddExpr(Ops, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2935 }
2936
2937 // Okay, if there weren't any loop invariants to be folded, check to see if
2938 // there are multiple AddRec's with the same loop induction variable being
2939 // added together. If so, we can fold them.
2940 for (unsigned OtherIdx = Idx+1;
2941 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Val: Ops[OtherIdx]);
2942 ++OtherIdx) {
2943 // We expect the AddRecExpr's to be sorted in reverse dominance order,
2944 // so that the 1st found AddRecExpr is dominated by all others.
2945 assert(DT.dominates(
2946 cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
2947 AddRec->getLoop()->getHeader()) &&
2948 "AddRecExprs are not sorted in reverse dominance order?");
2949 if (AddRecLoop == cast<SCEVAddRecExpr>(Val: Ops[OtherIdx])->getLoop()) {
2950 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2951 SmallVector<const SCEV *, 4> AddRecOps(AddRec->operands());
2952 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Val: Ops[OtherIdx]);
2953 ++OtherIdx) {
2954 const auto *OtherAddRec = cast<SCEVAddRecExpr>(Val: Ops[OtherIdx]);
2955 if (OtherAddRec->getLoop() == AddRecLoop) {
2956 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2957 i != e; ++i) {
2958 if (i >= AddRecOps.size()) {
2959 append_range(C&: AddRecOps, R: OtherAddRec->operands().drop_front(N: i));
2960 break;
2961 }
2962 SmallVector<const SCEV *, 2> TwoOps = {
2963 AddRecOps[i], OtherAddRec->getOperand(i)};
2964 AddRecOps[i] = getAddExpr(Ops&: TwoOps, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2965 }
2966 Ops.erase(CI: Ops.begin() + OtherIdx); --OtherIdx;
2967 }
2968 }
2969 // Step size has changed, so we cannot guarantee no self-wraparound.
2970 Ops[Idx] = getAddRecExpr(Operands&: AddRecOps, L: AddRecLoop, Flags: SCEV::FlagAnyWrap);
2971 return getAddExpr(Ops, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
2972 }
2973 }
2974
2975 // Otherwise couldn't fold anything into this recurrence. Move onto the
2976 // next one.
2977 }
2978
2979 // Okay, it looks like we really DO need an add expr. Check to see if we
2980 // already have one, otherwise create a new one.
2981 return getOrCreateAddExpr(Ops, Flags: ComputeFlags(Ops));
2982}
2983
2984const SCEV *
2985ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
2986 SCEV::NoWrapFlags Flags) {
2987 FoldingSetNodeID ID;
2988 ID.AddInteger(I: scAddExpr);
2989 for (const SCEV *Op : Ops)
2990 ID.AddPointer(Ptr: Op);
2991 void *IP = nullptr;
2992 SCEVAddExpr *S =
2993 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP));
2994 if (!S) {
2995 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Num: Ops.size());
2996 std::uninitialized_copy(first: Ops.begin(), last: Ops.end(), result: O);
2997 S = new (SCEVAllocator)
2998 SCEVAddExpr(ID.Intern(Allocator&: SCEVAllocator), O, Ops.size());
2999 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
3000 registerUser(User: S, Ops);
3001 }
3002 S->setNoWrapFlags(Flags);
3003 return S;
3004}
3005
3006const SCEV *
3007ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
3008 const Loop *L, SCEV::NoWrapFlags Flags) {
3009 FoldingSetNodeID ID;
3010 ID.AddInteger(I: scAddRecExpr);
3011 for (const SCEV *Op : Ops)
3012 ID.AddPointer(Ptr: Op);
3013 ID.AddPointer(Ptr: L);
3014 void *IP = nullptr;
3015 SCEVAddRecExpr *S =
3016 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP));
3017 if (!S) {
3018 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Num: Ops.size());
3019 std::uninitialized_copy(first: Ops.begin(), last: Ops.end(), result: O);
3020 S = new (SCEVAllocator)
3021 SCEVAddRecExpr(ID.Intern(Allocator&: SCEVAllocator), O, Ops.size(), L);
3022 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
3023 LoopUsers[L].push_back(Elt: S);
3024 registerUser(User: S, Ops);
3025 }
3026 setNoWrapFlags(AddRec: S, Flags);
3027 return S;
3028}
3029
3030const SCEV *
3031ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
3032 SCEV::NoWrapFlags Flags) {
3033 FoldingSetNodeID ID;
3034 ID.AddInteger(I: scMulExpr);
3035 for (const SCEV *Op : Ops)
3036 ID.AddPointer(Ptr: Op);
3037 void *IP = nullptr;
3038 SCEVMulExpr *S =
3039 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP));
3040 if (!S) {
3041 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Num: Ops.size());
3042 std::uninitialized_copy(first: Ops.begin(), last: Ops.end(), result: O);
3043 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(Allocator&: SCEVAllocator),
3044 O, Ops.size());
3045 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
3046 registerUser(User: S, Ops);
3047 }
3048 S->setNoWrapFlags(Flags);
3049 return S;
3050}
3051
3052static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
3053 uint64_t k = i*j;
3054 if (j > 1 && k / j != i) Overflow = true;
3055 return k;
3056}
3057
3058/// Compute the result of "n choose k", the binomial coefficient. If an
3059/// intermediate computation overflows, Overflow will be set and the return will
3060/// be garbage. Overflow is not cleared on absence of overflow.
3061static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
3062 // We use the multiplicative formula:
3063 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
3064 // At each iteration, we take the n-th term of the numeral and divide by the
3065 // (k-n)th term of the denominator. This division will always produce an
3066 // integral result, and helps reduce the chance of overflow in the
3067 // intermediate computations. However, we can still overflow even when the
3068 // final result would fit.
3069
3070 if (n == 0 || n == k) return 1;
3071 if (k > n) return 0;
3072
3073 if (k > n/2)
3074 k = n-k;
3075
3076 uint64_t r = 1;
3077 for (uint64_t i = 1; i <= k; ++i) {
3078 r = umul_ov(i: r, j: n-(i-1), Overflow);
3079 r /= i;
3080 }
3081 return r;
3082}
3083
3084/// Determine if any of the operands in this SCEV are a constant or if
3085/// any of the add or multiply expressions in this SCEV contain a constant.
3086static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
3087 struct FindConstantInAddMulChain {
3088 bool FoundConstant = false;
3089
3090 bool follow(const SCEV *S) {
3091 FoundConstant |= isa<SCEVConstant>(Val: S);
3092 return isa<SCEVAddExpr>(Val: S) || isa<SCEVMulExpr>(Val: S);
3093 }
3094
3095 bool isDone() const {
3096 return FoundConstant;
3097 }
3098 };
3099
3100 FindConstantInAddMulChain F;
3101 SCEVTraversal<FindConstantInAddMulChain> ST(F);
3102 ST.visitAll(Root: StartExpr);
3103 return F.FoundConstant;
3104}
3105
3106/// Get a canonical multiply expression, or something simpler if possible.
3107const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
3108 SCEV::NoWrapFlags OrigFlags,
3109 unsigned Depth) {
3110 assert(OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) &&
3111 "only nuw or nsw allowed");
3112 assert(!Ops.empty() && "Cannot get empty mul!");
3113 if (Ops.size() == 1) return Ops[0];
3114#ifndef NDEBUG
3115 Type *ETy = Ops[0]->getType();
3116 assert(!ETy->isPointerTy());
3117 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3118 assert(Ops[i]->getType() == ETy &&
3119 "SCEVMulExpr operand types don't match!");
3120#endif
3121
3122 // Sort by complexity, this groups all similar expression types together.
3123 GroupByComplexity(Ops, LI: &LI, DT);
3124
3125 // If there are any constants, fold them together.
3126 unsigned Idx = 0;
3127 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Val: Ops[0])) {
3128 ++Idx;
3129 assert(Idx < Ops.size());
3130 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Val: Ops[Idx])) {
3131 // We found two constants, fold them together!
3132 Ops[0] = getConstant(Val: LHSC->getAPInt() * RHSC->getAPInt());
3133 if (Ops.size() == 2) return Ops[0];
3134 Ops.erase(CI: Ops.begin()+1); // Erase the folded element
3135 LHSC = cast<SCEVConstant>(Val: Ops[0]);
3136 }
3137
3138 // If we have a multiply of zero, it will always be zero.
3139 if (LHSC->getValue()->isZero())
3140 return LHSC;
3141
3142 // If we are left with a constant one being multiplied, strip it off.
3143 if (LHSC->getValue()->isOne()) {
3144 Ops.erase(CI: Ops.begin());
3145 --Idx;
3146 }
3147
3148 if (Ops.size() == 1)
3149 return Ops[0];
3150 }
3151
3152 // Delay expensive flag strengthening until necessary.
3153 auto ComputeFlags = [this, OrigFlags](const ArrayRef<const SCEV *> Ops) {
3154 return StrengthenNoWrapFlags(SE: this, Type: scMulExpr, Ops, Flags: OrigFlags);
3155 };
3156
3157 // Limit recursion calls depth.
3158 if (Depth > MaxArithDepth || hasHugeExpression(Ops))
3159 return getOrCreateMulExpr(Ops, Flags: ComputeFlags(Ops));
3160
3161 if (SCEV *S = findExistingSCEVInCache(SCEVType: scMulExpr, Ops)) {
3162 // Don't strengthen flags if we have no new information.
3163 SCEVMulExpr *Mul = static_cast<SCEVMulExpr *>(S);
3164 if (Mul->getNoWrapFlags(Mask: OrigFlags) != OrigFlags)
3165 Mul->setNoWrapFlags(ComputeFlags(Ops));
3166 return S;
3167 }
3168
3169 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Val: Ops[0])) {
3170 if (Ops.size() == 2) {
3171 // C1*(C2+V) -> C1*C2 + C1*V
3172 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Val: Ops[1]))
3173 // If any of Add's ops are Adds or Muls with a constant, apply this
3174 // transformation as well.
3175 //
3176 // TODO: There are some cases where this transformation is not
3177 // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
3178 // this transformation should be narrowed down.
3179 if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(StartExpr: Add)) {
3180 const SCEV *LHS = getMulExpr(LHS: LHSC, RHS: Add->getOperand(i: 0),
3181 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
3182 const SCEV *RHS = getMulExpr(LHS: LHSC, RHS: Add->getOperand(i: 1),
3183 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
3184 return getAddExpr(LHS, RHS, Flags: SCEV::FlagAnyWrap, Depth: Depth + 1);
3185 }
3186
3187 if (Ops[0]->isAllOnesValue()) {
3188 // If we have a mul by -1 of an add, try distributing the -1 among the
3189 // add operands.
3190 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Val: Ops[1])) {
3191 SmallVector<const SCEV *, 4> NewOps;
3192 bool AnyFolded = false;
3193 for (const SCEV *AddOp : Add->operands()) {
3194 const SCEV *Mul = getMulExpr(LHS: Ops[0], RHS: AddOp, Flags: SCEV::FlagAnyWrap,
3195 Depth: Depth + 1);
3196 if (!isa<SCEVMulExpr>(Val: Mul)) AnyFolded = true;
3197 NewOps.push_back(Elt: Mul);
3198 }
3199 if (AnyFolded)
3200 return getAddExpr(Ops&: NewOps, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
3201 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Val: Ops[1])) {
3202 // Negation preserves a recurrence's no self-wrap property.
3203 SmallVector<const SCEV *, 4> Operands;
3204 for (const SCEV *AddRecOp : AddRec->operands())
3205 Operands.push_back(Elt: getMulExpr(LHS: Ops[0], RHS: AddRecOp, Flags: SCEV::FlagAnyWrap,
3206 Depth: Depth + 1));
3207 // Let M be the minimum representable signed value. AddRec with nsw
3208 // multiplied by -1 can have signed overflow if and only if it takes a
3209 // value of M: M * (-1) would stay M and (M + 1) * (-1) would be the
3210 // maximum signed value. In all other cases signed overflow is
3211 // impossible.
3212 auto FlagsMask = SCEV::FlagNW;
3213 if (hasFlags(Flags: AddRec->getNoWrapFlags(), TestFlags: SCEV::FlagNSW)) {
3214 auto MinInt =
3215 APInt::getSignedMinValue(numBits: getTypeSizeInBits(Ty: AddRec->getType()));
3216 if (getSignedRangeMin(S: AddRec) != MinInt)
3217 FlagsMask = setFlags(Flags: FlagsMask, OnFlags: SCEV::FlagNSW);
3218 }
3219 return getAddRecExpr(Operands, L: AddRec->getLoop(),
3220 Flags: AddRec->getNoWrapFlags(Mask: FlagsMask));
3221 }
3222 }
3223 }
3224 }
3225
3226 // Skip over the add expression until we get to a multiply.
3227 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
3228 ++Idx;
3229
3230 // If there are mul operands inline them all into this expression.
3231 if (Idx < Ops.size()) {
3232 bool DeletedMul = false;
3233 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Val: Ops[Idx])) {
3234 if (Ops.size() > MulOpsInlineThreshold)
3235 break;
3236 // If we have an mul, expand the mul operands onto the end of the
3237 // operands list.
3238 Ops.erase(CI: Ops.begin()+Idx);
3239 append_range(C&: Ops, R: Mul->operands());
3240 DeletedMul = true;
3241 }
3242
3243 // If we deleted at least one mul, we added operands to the end of the
3244 // list, and they are not necessarily sorted. Recurse to resort and
3245 // resimplify any operands we just acquired.
3246 if (DeletedMul)
3247 return getMulExpr(Ops, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
3248 }
3249
3250 // If there are any add recurrences in the operands list, see if any other
3251 // added values are loop invariant. If so, we can fold them into the
3252 // recurrence.
3253 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
3254 ++Idx;
3255
3256 // Scan over all recurrences, trying to fold loop invariants into them.
3257 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Val: Ops[Idx]); ++Idx) {
3258 // Scan all of the other operands to this mul and add them to the vector
3259 // if they are loop invariant w.r.t. the recurrence.
3260 SmallVector<const SCEV *, 8> LIOps;
3261 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Val: Ops[Idx]);
3262 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3263 if (isAvailableAtLoopEntry(S: Ops[i], L: AddRec->getLoop())) {
3264 LIOps.push_back(Elt: Ops[i]);
3265 Ops.erase(CI: Ops.begin()+i);
3266 --i; --e;
3267 }
3268
3269 // If we found some loop invariants, fold them into the recurrence.
3270 if (!LIOps.empty()) {
3271 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
3272 SmallVector<const SCEV *, 4> NewOps;
3273 NewOps.reserve(N: AddRec->getNumOperands());
3274 const SCEV *Scale = getMulExpr(Ops&: LIOps, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
3275
3276 // If both the mul and addrec are nuw, we can preserve nuw.
3277 // If both the mul and addrec are nsw, we can only preserve nsw if either
3278 // a) they are also nuw, or
3279 // b) all multiplications of addrec operands with scale are nsw.
3280 SCEV::NoWrapFlags Flags =
3281 AddRec->getNoWrapFlags(Mask: ComputeFlags({Scale, AddRec}));
3282
3283 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3284 NewOps.push_back(Elt: getMulExpr(LHS: Scale, RHS: AddRec->getOperand(i),
3285 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1));
3286
3287 if (hasFlags(Flags, TestFlags: SCEV::FlagNSW) && !hasFlags(Flags, TestFlags: SCEV::FlagNUW)) {
3288 ConstantRange NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3289 BinOp: Instruction::Mul, Other: getSignedRange(S: Scale),
3290 NoWrapKind: OverflowingBinaryOperator::NoSignedWrap);
3291 if (!NSWRegion.contains(CR: getSignedRange(S: AddRec->getOperand(i))))
3292 Flags = clearFlags(Flags, OffFlags: SCEV::FlagNSW);
3293 }
3294 }
3295
3296 const SCEV *NewRec = getAddRecExpr(Operands&: NewOps, L: AddRec->getLoop(), Flags);
3297
3298 // If all of the other operands were loop invariant, we are done.
3299 if (Ops.size() == 1) return NewRec;
3300
3301 // Otherwise, multiply the folded AddRec by the non-invariant parts.
3302 for (unsigned i = 0;; ++i)
3303 if (Ops[i] == AddRec) {
3304 Ops[i] = NewRec;
3305 break;
3306 }
3307 return getMulExpr(Ops, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
3308 }
3309
3310 // Okay, if there weren't any loop invariants to be folded, check to see
3311 // if there are multiple AddRec's with the same loop induction variable
3312 // being multiplied together. If so, we can fold them.
3313
3314 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
3315 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
3316 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
3317 // ]]],+,...up to x=2n}.
3318 // Note that the arguments to choose() are always integers with values
3319 // known at compile time, never SCEV objects.
3320 //
3321 // The implementation avoids pointless extra computations when the two
3322 // addrec's are of different length (mathematically, it's equivalent to
3323 // an infinite stream of zeros on the right).
3324 bool OpsModified = false;
3325 for (unsigned OtherIdx = Idx+1;
3326 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Val: Ops[OtherIdx]);
3327 ++OtherIdx) {
3328 const SCEVAddRecExpr *OtherAddRec =
3329 dyn_cast<SCEVAddRecExpr>(Val: Ops[OtherIdx]);
3330 if (!OtherAddRec || OtherAddRec->getLoop() != AddRec->getLoop())
3331 continue;
3332
3333 // Limit max number of arguments to avoid creation of unreasonably big
3334 // SCEVAddRecs with very complex operands.
3335 if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
3336 MaxAddRecSize || hasHugeExpression(Ops: {AddRec, OtherAddRec}))
3337 continue;
3338
3339 bool Overflow = false;
3340 Type *Ty = AddRec->getType();
3341 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
3342 SmallVector<const SCEV*, 7> AddRecOps;
3343 for (int x = 0, xe = AddRec->getNumOperands() +
3344 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
3345 SmallVector <const SCEV *, 7> SumOps;
3346 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
3347 uint64_t Coeff1 = Choose(n: x, k: 2*x - y, Overflow);
3348 for (int z = std::max(a: y-x, b: y-(int)AddRec->getNumOperands()+1),
3349 ze = std::min(a: x+1, b: (int)OtherAddRec->getNumOperands());
3350 z < ze && !Overflow; ++z) {
3351 uint64_t Coeff2 = Choose(n: 2*x - y, k: x-z, Overflow);
3352 uint64_t Coeff;
3353 if (LargerThan64Bits)
3354 Coeff = umul_ov(i: Coeff1, j: Coeff2, Overflow);
3355 else
3356 Coeff = Coeff1*Coeff2;
3357 const SCEV *CoeffTerm = getConstant(Ty, V: Coeff);
3358 const SCEV *Term1 = AddRec->getOperand(i: y-z);
3359 const SCEV *Term2 = OtherAddRec->getOperand(i: z);
3360 SumOps.push_back(Elt: getMulExpr(Op0: CoeffTerm, Op1: Term1, Op2: Term2,
3361 Flags: SCEV::FlagAnyWrap, Depth: Depth + 1));
3362 }
3363 }
3364 if (SumOps.empty())
3365 SumOps.push_back(Elt: getZero(Ty));
3366 AddRecOps.push_back(Elt: getAddExpr(Ops&: SumOps, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1));
3367 }
3368 if (!Overflow) {
3369 const SCEV *NewAddRec = getAddRecExpr(Operands&: AddRecOps, L: AddRec->getLoop(),
3370 Flags: SCEV::FlagAnyWrap);
3371 if (Ops.size() == 2) return NewAddRec;
3372 Ops[Idx] = NewAddRec;
3373 Ops.erase(CI: Ops.begin() + OtherIdx); --OtherIdx;
3374 OpsModified = true;
3375 AddRec = dyn_cast<SCEVAddRecExpr>(Val: NewAddRec);
3376 if (!AddRec)
3377 break;
3378 }
3379 }
3380 if (OpsModified)
3381 return getMulExpr(Ops, OrigFlags: SCEV::FlagAnyWrap, Depth: Depth + 1);
3382
3383 // Otherwise couldn't fold anything into this recurrence. Move onto the
3384 // next one.
3385 }
3386
3387 // Okay, it looks like we really DO need an mul expr. Check to see if we
3388 // already have one, otherwise create a new one.
3389 return getOrCreateMulExpr(Ops, Flags: ComputeFlags(Ops));
3390}
3391
3392/// Represents an unsigned remainder expression based on unsigned division.
3393const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
3394 const SCEV *RHS) {
3395 assert(getEffectiveSCEVType(LHS->getType()) ==
3396 getEffectiveSCEVType(RHS->getType()) &&
3397 "SCEVURemExpr operand types don't match!");
3398
3399 // Short-circuit easy cases
3400 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Val: RHS)) {
3401 // If constant is one, the result is trivial
3402 if (RHSC->getValue()->isOne())
3403 return getZero(Ty: LHS->getType()); // X urem 1 --> 0
3404
3405 // If constant is a power of two, fold into a zext(trunc(LHS)).
3406 if (RHSC->getAPInt().isPowerOf2()) {
3407 Type *FullTy = LHS->getType();
3408 Type *TruncTy =
3409 IntegerType::get(C&: getContext(), NumBits: RHSC->getAPInt().logBase2());
3410 return getZeroExtendExpr(Op: getTruncateExpr(Op: LHS, Ty: TruncTy), Ty: FullTy);
3411 }
3412 }
3413
3414 // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
3415 const SCEV *UDiv = getUDivExpr(LHS, RHS);
3416 const SCEV *Mult = getMulExpr(LHS: UDiv, RHS, Flags: SCEV::FlagNUW);
3417 return getMinusSCEV(LHS, RHS: Mult, Flags: SCEV::FlagNUW);
3418}
3419
3420/// Get a canonical unsigned division expression, or something simpler if
3421/// possible.
3422const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
3423 const SCEV *RHS) {
3424 assert(!LHS->getType()->isPointerTy() &&
3425 "SCEVUDivExpr operand can't be pointer!");
3426 assert(LHS->getType() == RHS->getType() &&
3427 "SCEVUDivExpr operand types don't match!");
3428
3429 FoldingSetNodeID ID;
3430 ID.AddInteger(I: scUDivExpr);
3431 ID.AddPointer(Ptr: LHS);
3432 ID.AddPointer(Ptr: RHS);
3433 void *IP = nullptr;
3434 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP))
3435 return S;
3436
3437 // 0 udiv Y == 0
3438 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Val: LHS))
3439 if (LHSC->getValue()->isZero())
3440 return LHS;
3441
3442 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Val: RHS)) {
3443 if (RHSC->getValue()->isOne())
3444 return LHS; // X udiv 1 --> x
3445 // If the denominator is zero, the result of the udiv is undefined. Don't
3446 // try to analyze it, because the resolution chosen here may differ from
3447 // the resolution chosen in other parts of the compiler.
3448 if (!RHSC->getValue()->isZero()) {
3449 // Determine if the division can be folded into the operands of
3450 // its operands.
3451 // TODO: Generalize this to non-constants by using known-bits information.
3452 Type *Ty = LHS->getType();
3453 unsigned LZ = RHSC->getAPInt().countl_zero();
3454 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
3455 // For non-power-of-two values, effectively round the value up to the
3456 // nearest power of two.
3457 if (!RHSC->getAPInt().isPowerOf2())
3458 ++MaxShiftAmt;
3459 IntegerType *ExtTy =
3460 IntegerType::get(C&: getContext(), NumBits: getTypeSizeInBits(Ty) + MaxShiftAmt);
3461 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Val: LHS))
3462 if (const SCEVConstant *Step =
3463 dyn_cast<SCEVConstant>(Val: AR->getStepRecurrence(SE&: *this))) {
3464 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
3465 const APInt &StepInt = Step->getAPInt();
3466 const APInt &DivInt = RHSC->getAPInt();
3467 if (!StepInt.urem(RHS: DivInt) &&
3468 getZeroExtendExpr(Op: AR, Ty: ExtTy) ==
3469 getAddRecExpr(Start: getZeroExtendExpr(Op: AR->getStart(), Ty: ExtTy),
3470 Step: getZeroExtendExpr(Op: Step, Ty: ExtTy),
3471 L: AR->getLoop(), Flags: SCEV::FlagAnyWrap)) {
3472 SmallVector<const SCEV *, 4> Operands;
3473 for (const SCEV *Op : AR->operands())
3474 Operands.push_back(Elt: getUDivExpr(LHS: Op, RHS));
3475 return getAddRecExpr(Operands, L: AR->getLoop(), Flags: SCEV::FlagNW);
3476 }
3477 /// Get a canonical UDivExpr for a recurrence.
3478 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
3479 // We can currently only fold X%N if X is constant.
3480 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Val: AR->getStart());
3481 if (StartC && !DivInt.urem(RHS: StepInt) &&
3482 getZeroExtendExpr(Op: AR, Ty: ExtTy) ==
3483 getAddRecExpr(Start: getZeroExtendExpr(Op: AR->getStart(), Ty: ExtTy),
3484 Step: getZeroExtendExpr(Op: Step, Ty: ExtTy),
3485 L: AR->getLoop(), Flags: SCEV::FlagAnyWrap)) {
3486 const APInt &StartInt = StartC->getAPInt();
3487 const APInt &StartRem = StartInt.urem(RHS: StepInt);
3488 if (StartRem != 0) {
3489 const SCEV *NewLHS =
3490 getAddRecExpr(Start: getConstant(Val: StartInt - StartRem), Step,
3491 L: AR->getLoop(), Flags: SCEV::FlagNW);
3492 if (LHS != NewLHS) {
3493 LHS = NewLHS;
3494
3495 // Reset the ID to include the new LHS, and check if it is
3496 // already cached.
3497 ID.clear();
3498 ID.AddInteger(I: scUDivExpr);
3499 ID.AddPointer(Ptr: LHS);
3500 ID.AddPointer(Ptr: RHS);
3501 IP = nullptr;
3502 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP))
3503 return S;
3504 }
3505 }
3506 }
3507 }
3508 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
3509 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Val: LHS)) {
3510 SmallVector<const SCEV *, 4> Operands;
3511 for (const SCEV *Op : M->operands())
3512 Operands.push_back(Elt: getZeroExtendExpr(Op, Ty: ExtTy));
3513 if (getZeroExtendExpr(Op: M, Ty: ExtTy) == getMulExpr(Ops&: Operands))
3514 // Find an operand that's safely divisible.
3515 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
3516 const SCEV *Op = M->getOperand(i);
3517 const SCEV *Div = getUDivExpr(LHS: Op, RHS: RHSC);
3518 if (!isa<SCEVUDivExpr>(Val: Div) && getMulExpr(LHS: Div, RHS: RHSC) == Op) {
3519 Operands = SmallVector<const SCEV *, 4>(M->operands());
3520 Operands[i] = Div;
3521 return getMulExpr(Ops&: Operands);
3522 }
3523 }
3524 }
3525
3526 // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
3527 if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(Val: LHS)) {
3528 if (auto *DivisorConstant =
3529 dyn_cast<SCEVConstant>(Val: OtherDiv->getRHS())) {
3530 bool Overflow = false;
3531 APInt NewRHS =
3532 DivisorConstant->getAPInt().umul_ov(RHS: RHSC->getAPInt(), Overflow);
3533 if (Overflow) {
3534 return getConstant(Ty: RHSC->getType(), V: 0, isSigned: false);
3535 }
3536 return getUDivExpr(LHS: OtherDiv->getLHS(), RHS: getConstant(Val: NewRHS));
3537 }
3538 }
3539
3540 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
3541 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(Val: LHS)) {
3542 SmallVector<const SCEV *, 4> Operands;
3543 for (const SCEV *Op : A->operands())
3544 Operands.push_back(Elt: getZeroExtendExpr(Op, Ty: ExtTy));
3545 if (getZeroExtendExpr(Op: A, Ty: ExtTy) == getAddExpr(Ops&: Operands)) {
3546 Operands.clear();
3547 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
3548 const SCEV *Op = getUDivExpr(LHS: A->getOperand(i), RHS);
3549 if (isa<SCEVUDivExpr>(Val: Op) ||
3550 getMulExpr(LHS: Op, RHS) != A->getOperand(i))
3551 break;
3552 Operands.push_back(Elt: Op);
3553 }
3554 if (Operands.size() == A->getNumOperands())
3555 return getAddExpr(Ops&: Operands);
3556 }
3557 }
3558
3559 // Fold if both operands are constant.
3560 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Val: LHS))
3561 return getConstant(Val: LHSC->getAPInt().udiv(RHS: RHSC->getAPInt()));
3562 }
3563 }
3564
3565 // The Insertion Point (IP) might be invalid by now (due to UniqueSCEVs
3566 // changes). Make sure we get a new one.
3567 IP = nullptr;
3568 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP)) return S;
3569 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(Allocator&: SCEVAllocator),
3570 LHS, RHS);
3571 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
3572 registerUser(User: S, Ops: {LHS, RHS});
3573 return S;
3574}
3575
3576APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
3577 APInt A = C1->getAPInt().abs();
3578 APInt B = C2->getAPInt().abs();
3579 uint32_t ABW = A.getBitWidth();
3580 uint32_t BBW = B.getBitWidth();
3581
3582 if (ABW > BBW)
3583 B = B.zext(width: ABW);
3584 else if (ABW < BBW)
3585 A = A.zext(width: BBW);
3586
3587 return APIntOps::GreatestCommonDivisor(A: std::move(A), B: std::move(B));
3588}
3589
3590/// Get a canonical unsigned division expression, or something simpler if
3591/// possible. There is no representation for an exact udiv in SCEV IR, but we
3592/// can attempt to remove factors from the LHS and RHS. We can't do this when
3593/// it's not exact because the udiv may be clearing bits.
3594const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
3595 const SCEV *RHS) {
3596 // TODO: we could try to find factors in all sorts of things, but for now we
3597 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
3598 // end of this file for inspiration.
3599
3600 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Val: LHS);
3601 if (!Mul || !Mul->hasNoUnsignedWrap())
3602 return getUDivExpr(LHS, RHS);
3603
3604 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(Val: RHS)) {
3605 // If the mulexpr multiplies by a constant, then that constant must be the
3606 // first element of the mulexpr.
3607 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Val: Mul->getOperand(i: 0))) {
3608 if (LHSCst == RHSCst) {
3609 SmallVector<const SCEV *, 2> Operands(drop_begin(RangeOrContainer: Mul->operands()));
3610 return getMulExpr(Ops&: Operands);
3611 }
3612
3613 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
3614 // that there's a factor provided by one of the other terms. We need to
3615 // check.
3616 APInt Factor = gcd(C1: LHSCst, C2: RHSCst);
3617 if (!Factor.isIntN(N: 1)) {
3618 LHSCst =
3619 cast<SCEVConstant>(Val: getConstant(Val: LHSCst->getAPInt().udiv(RHS: Factor)));
3620 RHSCst =
3621 cast<SCEVConstant>(Val: getConstant(Val: RHSCst->getAPInt().udiv(RHS: Factor)));
3622 SmallVector<const SCEV *, 2> Operands;
3623 Operands.push_back(Elt: LHSCst);
3624 append_range(C&: Operands, R: Mul->operands().drop_front());
3625 LHS = getMulExpr(Ops&: Operands);
3626 RHS = RHSCst;
3627 Mul = dyn_cast<SCEVMulExpr>(Val: LHS);
3628 if (!Mul)
3629 return getUDivExactExpr(LHS, RHS);
3630 }
3631 }
3632 }
3633
3634 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
3635 if (Mul->getOperand(i) == RHS) {
3636 SmallVector<const SCEV *, 2> Operands;
3637 append_range(C&: Operands, R: Mul->operands().take_front(N: i));
3638 append_range(C&: Operands, R: Mul->operands().drop_front(N: i + 1));
3639 return getMulExpr(Ops&: Operands);
3640 }
3641 }
3642
3643 return getUDivExpr(LHS, RHS);
3644}
3645
3646/// Get an add recurrence expression for the specified loop. Simplify the
3647/// expression as much as possible.
3648const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
3649 const Loop *L,
3650 SCEV::NoWrapFlags Flags) {
3651 SmallVector<const SCEV *, 4> Operands;
3652 Operands.push_back(Elt: Start);
3653 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Val: Step))
3654 if (StepChrec->getLoop() == L) {
3655 append_range(C&: Operands, R: StepChrec->operands());
3656 return getAddRecExpr(Operands, L, Flags: maskFlags(Flags, Mask: SCEV::FlagNW));
3657 }
3658
3659 Operands.push_back(Elt: Step);
3660 return getAddRecExpr(Operands, L, Flags);
3661}
3662
3663/// Get an add recurrence expression for the specified loop. Simplify the
3664/// expression as much as possible.
3665const SCEV *
3666ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
3667 const Loop *L, SCEV::NoWrapFlags Flags) {
3668 if (Operands.size() == 1) return Operands[0];
3669#ifndef NDEBUG
3670 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
3671 for (const SCEV *Op : llvm::drop_begin(Operands)) {
3672 assert(getEffectiveSCEVType(Op->getType()) == ETy &&
3673 "SCEVAddRecExpr operand types don't match!");
3674 assert(!Op->getType()->isPointerTy() && "Step must be integer");
3675 }
3676 for (const SCEV *Op : Operands)
3677 assert(isAvailableAtLoopEntry(Op, L) &&
3678 "SCEVAddRecExpr operand is not available at loop entry!");
3679#endif
3680
3681 if (Operands.back()->isZero()) {
3682 Operands.pop_back();
3683 return getAddRecExpr(Operands, L, Flags: SCEV::FlagAnyWrap); // {X,+,0} --> X
3684 }
3685
3686 // It's tempting to want to call getConstantMaxBackedgeTakenCount count here and
3687 // use that information to infer NUW and NSW flags. However, computing a
3688 // BE count requires calling getAddRecExpr, so we may not yet have a
3689 // meaningful BE count at this point (and if we don't, we'd be stuck
3690 // with a SCEVCouldNotCompute as the cached BE count).
3691
3692 Flags = StrengthenNoWrapFlags(SE: this, Type: scAddRecExpr, Ops: Operands, Flags);
3693
3694 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
3695 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Val: Operands[0])) {
3696 const Loop *NestedLoop = NestedAR->getLoop();
3697 if (L->contains(L: NestedLoop)
3698 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
3699 : (!NestedLoop->contains(L) &&
3700 DT.dominates(A: L->getHeader(), B: NestedLoop->getHeader()))) {
3701 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->operands());
3702 Operands[0] = NestedAR->getStart();
3703 // AddRecs require their operands be loop-invariant with respect to their
3704 // loops. Don't perform this transformation if it would break this
3705 // requirement.
3706 bool AllInvariant = all_of(
3707 Range&: Operands, P: [&](const SCEV *Op) { return isLoopInvariant(S: Op, L); });
3708
3709 if (AllInvariant) {
3710 // Create a recurrence for the outer loop with the same step size.
3711 //
3712 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3713 // inner recurrence has the same property.
3714 SCEV::NoWrapFlags OuterFlags =
3715 maskFlags(Flags, Mask: SCEV::FlagNW | NestedAR->getNoWrapFlags());
3716
3717 NestedOperands[0] = getAddRecExpr(Operands, L, Flags: OuterFlags);
3718 AllInvariant = all_of(Range&: NestedOperands, P: [&](const SCEV *Op) {
3719 return isLoopInvariant(S: Op, L: NestedLoop);
3720 });
3721
3722 if (AllInvariant) {
3723 // Ok, both add recurrences are valid after the transformation.
3724 //
3725 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3726 // the outer recurrence has the same property.
3727 SCEV::NoWrapFlags InnerFlags =
3728 maskFlags(Flags: NestedAR->getNoWrapFlags(), Mask: SCEV::FlagNW | Flags);
3729 return getAddRecExpr(Operands&: NestedOperands, L: NestedLoop, Flags: InnerFlags);
3730 }
3731 }
3732 // Reset Operands to its original state.
3733 Operands[0] = NestedAR;
3734 }
3735 }
3736
3737 // Okay, it looks like we really DO need an addrec expr. Check to see if we
3738 // already have one, otherwise create a new one.
3739 return getOrCreateAddRecExpr(Ops: Operands, L, Flags);
3740}
3741
3742const SCEV *
3743ScalarEvolution::getGEPExpr(GEPOperator *GEP,
3744 const SmallVectorImpl<const SCEV *> &IndexExprs) {
3745 const SCEV *BaseExpr = getSCEV(V: GEP->getPointerOperand());
3746 // getSCEV(Base)->getType() has the same address space as Base->getType()
3747 // because SCEV::getType() preserves the address space.
3748 Type *IntIdxTy = getEffectiveSCEVType(Ty: BaseExpr->getType());
3749 GEPNoWrapFlags NW = GEP->getNoWrapFlags();
3750 if (NW != GEPNoWrapFlags::none()) {
3751 // We'd like to propagate flags from the IR to the corresponding SCEV nodes,
3752 // but to do that, we have to ensure that said flag is valid in the entire
3753 // defined scope of the SCEV.
3754 // TODO: non-instructions have global scope. We might be able to prove
3755 // some global scope cases
3756 auto *GEPI = dyn_cast<Instruction>(Val: GEP);
3757 if (!GEPI || !isSCEVExprNeverPoison(I: GEPI))
3758 NW = GEPNoWrapFlags::none();
3759 }
3760
3761 SCEV::NoWrapFlags OffsetWrap = SCEV::FlagAnyWrap;
3762 if (NW.hasNoUnsignedSignedWrap())
3763 OffsetWrap = setFlags(Flags: OffsetWrap, OnFlags: SCEV::FlagNSW);
3764 if (NW.hasNoUnsignedWrap())
3765 OffsetWrap = setFlags(Flags: OffsetWrap, OnFlags: SCEV::FlagNUW);
3766
3767 Type *CurTy = GEP->getType();
3768 bool FirstIter = true;
3769 SmallVector<const SCEV *, 4> Offsets;
3770 for (const SCEV *IndexExpr : IndexExprs) {
3771 // Compute the (potentially symbolic) offset in bytes for this index.
3772 if (StructType *STy = dyn_cast<StructType>(Val: CurTy)) {
3773 // For a struct, add the member offset.
3774 ConstantInt *Index = cast<SCEVConstant>(Val: IndexExpr)->getValue();
3775 unsigned FieldNo = Index->getZExtValue();
3776 const SCEV *FieldOffset = getOffsetOfExpr(IntTy: IntIdxTy, STy, FieldNo);
3777 Offsets.push_back(Elt: FieldOffset);
3778
3779 // Update CurTy to the type of the field at Index.
3780 CurTy = STy->getTypeAtIndex(V: Index);
3781 } else {
3782 // Update CurTy to its element type.
3783 if (FirstIter) {
3784 assert(isa<PointerType>(CurTy) &&
3785 "The first index of a GEP indexes a pointer");
3786 CurTy = GEP->getSourceElementType();
3787 FirstIter = false;
3788 } else {
3789 CurTy = GetElementPtrInst::getTypeAtIndex(Ty: CurTy, Idx: (uint64_t)0);
3790 }
3791 // For an array, add the element offset, explicitly scaled.
3792 const SCEV *ElementSize = getSizeOfExpr(IntTy: IntIdxTy, AllocTy: CurTy);
3793 // Getelementptr indices are signed.
3794 IndexExpr = getTruncateOrSignExtend(V: IndexExpr, Ty: IntIdxTy);
3795
3796 // Multiply the index by the element size to compute the element offset.
3797 const SCEV *LocalOffset = getMulExpr(LHS: IndexExpr, RHS: ElementSize, Flags: OffsetWrap);
3798 Offsets.push_back(Elt: LocalOffset);
3799 }
3800 }
3801
3802 // Handle degenerate case of GEP without offsets.
3803 if (Offsets.empty())
3804 return BaseExpr;
3805
3806 // Add the offsets together, assuming nsw if inbounds.
3807 const SCEV *Offset = getAddExpr(Ops&: Offsets, OrigFlags: OffsetWrap);
3808 // Add the base address and the offset. We cannot use the nsw flag, as the
3809 // base address is unsigned. However, if we know that the offset is
3810 // non-negative, we can use nuw.
3811 bool NUW = NW.hasNoUnsignedWrap() ||
3812 (NW.hasNoUnsignedSignedWrap() && isKnownNonNegative(S: Offset));
3813 SCEV::NoWrapFlags BaseWrap = NUW ? SCEV::FlagNUW : SCEV::FlagAnyWrap;
3814 auto *GEPExpr = getAddExpr(LHS: BaseExpr, RHS: Offset, Flags: BaseWrap);
3815 assert(BaseExpr->getType() == GEPExpr->getType() &&
3816 "GEP should not change type mid-flight.");
3817 return GEPExpr;
3818}
3819
3820SCEV *ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType,
3821 ArrayRef<const SCEV *> Ops) {
3822 FoldingSetNodeID ID;
3823 ID.AddInteger(I: SCEVType);
3824 for (const SCEV *Op : Ops)
3825 ID.AddPointer(Ptr: Op);
3826 void *IP = nullptr;
3827 return UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP);
3828}
3829
3830const SCEV *ScalarEvolution::getAbsExpr(const SCEV *Op, bool IsNSW) {
3831 SCEV::NoWrapFlags Flags = IsNSW ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3832 return getSMaxExpr(LHS: Op, RHS: getNegativeSCEV(V: Op, Flags));
3833}
3834
3835const SCEV *ScalarEvolution::getMinMaxExpr(SCEVTypes Kind,
3836 SmallVectorImpl<const SCEV *> &Ops) {
3837 assert(SCEVMinMaxExpr::isMinMaxType(Kind) && "Not a SCEVMinMaxExpr!");
3838 assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!");
3839 if (Ops.size() == 1) return Ops[0];
3840#ifndef NDEBUG
3841 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3842 for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
3843 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3844 "Operand types don't match!");
3845 assert(Ops[0]->getType()->isPointerTy() ==
3846 Ops[i]->getType()->isPointerTy() &&
3847 "min/max should be consistently pointerish");
3848 }
3849#endif
3850
3851 bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
3852 bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;
3853
3854 // Sort by complexity, this groups all similar expression types together.
3855 GroupByComplexity(Ops, LI: &LI, DT);
3856
3857 // Check if we have created the same expression before.
3858 if (const SCEV *S = findExistingSCEVInCache(SCEVType: Kind, Ops)) {
3859 return S;
3860 }
3861
3862 // If there are any constants, fold them together.
3863 unsigned Idx = 0;
3864 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Val: Ops[0])) {
3865 ++Idx;
3866 assert(Idx < Ops.size());
3867 auto FoldOp = [&](const APInt &LHS, const APInt &RHS) {
3868 switch (Kind) {
3869 case scSMaxExpr:
3870 return APIntOps::smax(A: LHS, B: RHS);
3871 case scSMinExpr:
3872 return APIntOps::smin(A: LHS, B: RHS);
3873 case scUMaxExpr:
3874 return APIntOps::umax(A: LHS, B: RHS);
3875 case scUMinExpr:
3876 return APIntOps::umin(A: LHS, B: RHS);
3877 default:
3878 llvm_unreachable("Unknown SCEV min/max opcode");
3879 }
3880 };
3881
3882 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Val: Ops[Idx])) {
3883 // We found two constants, fold them together!
3884 ConstantInt *Fold = ConstantInt::get(
3885 Context&: getContext(), V: FoldOp(LHSC->getAPInt(), RHSC->getAPInt()));
3886 Ops[0] = getConstant(V: Fold);
3887 Ops.erase(CI: Ops.begin()+1); // Erase the folded element
3888 if (Ops.size() == 1) return Ops[0];
3889 LHSC = cast<SCEVConstant>(Val: Ops[0]);
3890 }
3891
3892 bool IsMinV = LHSC->getValue()->isMinValue(IsSigned);
3893 bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned);
3894
3895 if (IsMax ? IsMinV : IsMaxV) {
3896 // If we are left with a constant minimum(/maximum)-int, strip it off.
3897 Ops.erase(CI: Ops.begin());
3898 --Idx;
3899 } else if (IsMax ? IsMaxV : IsMinV) {
3900 // If we have a max(/min) with a constant maximum(/minimum)-int,
3901 // it will always be the extremum.
3902 return LHSC;
3903 }
3904
3905 if (Ops.size() == 1) return Ops[0];
3906 }
3907
3908 // Find the first operation of the same kind
3909 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
3910 ++Idx;
3911
3912 // Check to see if one of the operands is of the same kind. If so, expand its
3913 // operands onto our operand list, and recurse to simplify.
3914 if (Idx < Ops.size()) {
3915 bool DeletedAny = false;
3916 while (Ops[Idx]->getSCEVType() == Kind) {
3917 const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Val: Ops[Idx]);
3918 Ops.erase(CI: Ops.begin()+Idx);
3919 append_range(C&: Ops, R: SMME->operands());
3920 DeletedAny = true;
3921 }
3922
3923 if (DeletedAny)
3924 return getMinMaxExpr(Kind, Ops);
3925 }
3926
3927 // Okay, check to see if the same value occurs in the operand list twice. If
3928 // so, delete one. Since we sorted the list, these values are required to
3929 // be adjacent.
3930 llvm::CmpInst::Predicate GEPred =
3931 IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
3932 llvm::CmpInst::Predicate LEPred =
3933 IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
3934 llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
3935 llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
3936 for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
3937 if (Ops[i] == Ops[i + 1] ||
3938 isKnownViaNonRecursiveReasoning(Pred: FirstPred, LHS: Ops[i], RHS: Ops[i + 1])) {
3939 // X op Y op Y --> X op Y
3940 // X op Y --> X, if we know X, Y are ordered appropriately
3941 Ops.erase(CS: Ops.begin() + i + 1, CE: Ops.begin() + i + 2);
3942 --i;
3943 --e;
3944 } else if (isKnownViaNonRecursiveReasoning(Pred: SecondPred, LHS: Ops[i],
3945 RHS: Ops[i + 1])) {
3946 // X op Y --> Y, if we know X, Y are ordered appropriately
3947 Ops.erase(CS: Ops.begin() + i, CE: Ops.begin() + i + 1);
3948 --i;
3949 --e;
3950 }
3951 }
3952
3953 if (Ops.size() == 1) return Ops[0];
3954
3955 assert(!Ops.empty() && "Reduced smax down to nothing!");
3956
3957 // Okay, it looks like we really DO need an expr. Check to see if we
3958 // already have one, otherwise create a new one.
3959 FoldingSetNodeID ID;
3960 ID.AddInteger(I: Kind);
3961 for (const SCEV *Op : Ops)
3962 ID.AddPointer(Ptr: Op);
3963 void *IP = nullptr;
3964 const SCEV *ExistingSCEV = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP);
3965 if (ExistingSCEV)
3966 return ExistingSCEV;
3967 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Num: Ops.size());
3968 std::uninitialized_copy(first: Ops.begin(), last: Ops.end(), result: O);
3969 SCEV *S = new (SCEVAllocator)
3970 SCEVMinMaxExpr(ID.Intern(Allocator&: SCEVAllocator), Kind, O, Ops.size());
3971
3972 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
3973 registerUser(User: S, Ops);
3974 return S;
3975}
3976
3977namespace {
3978
3979class SCEVSequentialMinMaxDeduplicatingVisitor final
3980 : public SCEVVisitor<SCEVSequentialMinMaxDeduplicatingVisitor,
3981 std::optional<const SCEV *>> {
3982 using RetVal = std::optional<const SCEV *>;
3983 using Base = SCEVVisitor<SCEVSequentialMinMaxDeduplicatingVisitor, RetVal>;
3984
3985 ScalarEvolution &SE;
3986 const SCEVTypes RootKind; // Must be a sequential min/max expression.
3987 const SCEVTypes NonSequentialRootKind; // Non-sequential variant of RootKind.
3988 SmallPtrSet<const SCEV *, 16> SeenOps;
3989
3990 bool canRecurseInto(SCEVTypes Kind) const {
3991 // We can only recurse into the SCEV expression of the same effective type
3992 // as the type of our root SCEV expression.
3993 return RootKind == Kind || NonSequentialRootKind == Kind;
3994 };
3995
3996 RetVal visitAnyMinMaxExpr(const SCEV *S) {
3997 assert((isa<SCEVMinMaxExpr>(S) || isa<SCEVSequentialMinMaxExpr>(S)) &&
3998 "Only for min/max expressions.");
3999 SCEVTypes Kind = S->getSCEVType();
4000
4001 if (!canRecurseInto(Kind))
4002 return S;
4003
4004 auto *NAry = cast<SCEVNAryExpr>(Val: S);
4005 SmallVector<const SCEV *> NewOps;
4006 bool Changed = visit(Kind, OrigOps: NAry->operands(), NewOps);
4007
4008 if (!Changed)
4009 return S;
4010 if (NewOps.empty())
4011 return std::nullopt;
4012
4013 return isa<SCEVSequentialMinMaxExpr>(Val: S)
4014 ? SE.getSequentialMinMaxExpr(Kind, Operands&: NewOps)
4015 : SE.getMinMaxExpr(Kind, Ops&: NewOps);
4016 }
4017
4018 RetVal visit(const SCEV *S) {
4019 // Has the whole operand been seen already?
4020 if (!SeenOps.insert(Ptr: S).second)
4021 return std::nullopt;
4022 return Base::visit(S);
4023 }
4024
4025public:
4026 SCEVSequentialMinMaxDeduplicatingVisitor(ScalarEvolution &SE,
4027 SCEVTypes RootKind)
4028 : SE(SE), RootKind(RootKind),
4029 NonSequentialRootKind(
4030 SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(
4031 Ty: RootKind)) {}
4032
4033 bool /*Changed*/ visit(SCEVTypes Kind, ArrayRef<const SCEV *> OrigOps,
4034 SmallVectorImpl<const SCEV *> &NewOps) {
4035 bool Changed = false;
4036 SmallVector<const SCEV *> Ops;
4037 Ops.reserve(N: OrigOps.size());
4038
4039 for (const SCEV *Op : OrigOps) {
4040 RetVal NewOp = visit(S: Op);
4041 if (NewOp != Op)
4042 Changed = true;
4043 if (NewOp)
4044 Ops.emplace_back(Args&: *NewOp);
4045 }
4046
4047 if (Changed)
4048 NewOps = std::move(Ops);
4049 return Changed;
4050 }
4051
4052 RetVal visitConstant(const SCEVConstant *Constant) { return Constant; }
4053
4054 RetVal visitVScale(const SCEVVScale *VScale) { return VScale; }
4055
4056 RetVal visitPtrToIntExpr(const SCEVPtrToIntExpr *Expr) { return Expr; }
4057
4058 RetVal visitTruncateExpr(const SCEVTruncateExpr *Expr) { return Expr; }
4059
4060 RetVal visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) { return Expr; }
4061
4062 RetVal visitSignExtendExpr(const SCEVSignExtendExpr *Expr) { return Expr; }
4063
4064 RetVal visitAddExpr(const SCEVAddExpr *Expr) { return Expr; }
4065
4066 RetVal visitMulExpr(const SCEVMulExpr *Expr) { return Expr; }
4067
4068 RetVal visitUDivExpr(const SCEVUDivExpr *Expr) { return Expr; }
4069
4070 RetVal visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; }
4071
4072 RetVal visitSMaxExpr(const SCEVSMaxExpr *Expr) {
4073 return visitAnyMinMaxExpr(S: Expr);
4074 }
4075
4076 RetVal visitUMaxExpr(const SCEVUMaxExpr *Expr) {
4077 return visitAnyMinMaxExpr(S: Expr);
4078 }
4079
4080 RetVal visitSMinExpr(const SCEVSMinExpr *Expr) {
4081 return visitAnyMinMaxExpr(S: Expr);
4082 }
4083
4084 RetVal visitUMinExpr(const SCEVUMinExpr *Expr) {
4085 return visitAnyMinMaxExpr(S: Expr);
4086 }
4087
4088 RetVal visitSequentialUMinExpr(const SCEVSequentialUMinExpr *Expr) {
4089 return visitAnyMinMaxExpr(S: Expr);
4090 }
4091
4092 RetVal visitUnknown(const SCEVUnknown *Expr) { return Expr; }
4093
4094 RetVal visitCouldNotCompute(const SCEVCouldNotCompute *Expr) { return Expr; }
4095};
4096
4097} // namespace
4098
4099static bool scevUnconditionallyPropagatesPoisonFromOperands(SCEVTypes Kind) {
4100 switch (Kind) {
4101 case scConstant:
4102 case scVScale:
4103 case scTruncate:
4104 case scZeroExtend:
4105 case scSignExtend:
4106 case scPtrToInt:
4107 case scAddExpr:
4108 case scMulExpr:
4109 case scUDivExpr:
4110 case scAddRecExpr:
4111 case scUMaxExpr:
4112 case scSMaxExpr:
4113 case scUMinExpr:
4114 case scSMinExpr:
4115 case scUnknown:
4116 // If any operand is poison, the whole expression is poison.
4117 return true;
4118 case scSequentialUMinExpr:
4119 // FIXME: if the *first* operand is poison, the whole expression is poison.
4120 return false; // Pessimistically, say that it does not propagate poison.
4121 case scCouldNotCompute:
4122 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
4123 }
4124 llvm_unreachable("Unknown SCEV kind!");
4125}
4126
4127namespace {
4128// The only way poison may be introduced in a SCEV expression is from a
4129// poison SCEVUnknown (ConstantExprs are also represented as SCEVUnknown,
4130// not SCEVConstant). Notably, nowrap flags in SCEV nodes can *not*
4131// introduce poison -- they encode guaranteed, non-speculated knowledge.
4132//
4133// Additionally, all SCEV nodes propagate poison from inputs to outputs,
4134// with the notable exception of umin_seq, where only poison from the first
4135// operand is (unconditionally) propagated.
4136struct SCEVPoisonCollector {
4137 bool LookThroughMaybePoisonBlocking;
4138 SmallPtrSet<const SCEVUnknown *, 4> MaybePoison;
4139 SCEVPoisonCollector(bool LookThroughMaybePoisonBlocking)
4140 : LookThroughMaybePoisonBlocking(LookThroughMaybePoisonBlocking) {}
4141
4142 bool follow(const SCEV *S) {
4143 if (!LookThroughMaybePoisonBlocking &&
4144 !scevUnconditionallyPropagatesPoisonFromOperands(Kind: S->getSCEVType()))
4145 return false;
4146
4147 if (auto *SU = dyn_cast<SCEVUnknown>(Val: S)) {
4148 if (!isGuaranteedNotToBePoison(V: SU->getValue()))
4149 MaybePoison.insert(Ptr: SU);
4150 }
4151 return true;
4152 }
4153 bool isDone() const { return false; }
4154};
4155} // namespace
4156
4157/// Return true if V is poison given that AssumedPoison is already poison.
4158static bool impliesPoison(const SCEV *AssumedPoison, const SCEV *S) {
4159 // First collect all SCEVs that might result in AssumedPoison to be poison.
4160 // We need to look through potentially poison-blocking operations here,
4161 // because we want to find all SCEVs that *might* result in poison, not only
4162 // those that are *required* to.
4163 SCEVPoisonCollector PC1(/* LookThroughMaybePoisonBlocking */ true);
4164 visitAll(Root: AssumedPoison, Visitor&: PC1);
4165
4166 // AssumedPoison is never poison. As the assumption is false, the implication
4167 // is true. Don't bother walking the other SCEV in this case.
4168 if (PC1.MaybePoison.empty())
4169 return true;
4170
4171 // Collect all SCEVs in S that, if poison, *will* result in S being poison
4172 // as well. We cannot look through potentially poison-blocking operations
4173 // here, as their arguments only *may* make the result poison.
4174 SCEVPoisonCollector PC2(/* LookThroughMaybePoisonBlocking */ false);
4175 visitAll(Root: S, Visitor&: PC2);
4176
4177 // Make sure that no matter which SCEV in PC1.MaybePoison is actually poison,
4178 // it will also make S poison by being part of PC2.MaybePoison.
4179 return all_of(Range&: PC1.MaybePoison, P: [&](const SCEVUnknown *S) {
4180 return PC2.MaybePoison.contains(Ptr: S);
4181 });
4182}
4183
4184void ScalarEvolution::getPoisonGeneratingValues(
4185 SmallPtrSetImpl<const Value *> &Result, const SCEV *S) {
4186 SCEVPoisonCollector PC(/* LookThroughMaybePoisonBlocking */ false);
4187 visitAll(Root: S, Visitor&: PC);
4188 for (const SCEVUnknown *SU : PC.MaybePoison)
4189 Result.insert(Ptr: SU->getValue());
4190}
4191
4192bool ScalarEvolution::canReuseInstruction(
4193 const SCEV *S, Instruction *I,
4194 SmallVectorImpl<Instruction *> &DropPoisonGeneratingInsts) {
4195 // If the instruction cannot be poison, it's always safe to reuse.
4196 if (programUndefinedIfPoison(Inst: I))
4197 return true;
4198
4199 // Otherwise, it is possible that I is more poisonous that S. Collect the
4200 // poison-contributors of S, and then check whether I has any additional
4201 // poison-contributors. Poison that is contributed through poison-generating
4202 // flags is handled by dropping those flags instead.
4203 SmallPtrSet<const Value *, 8> PoisonVals;
4204 getPoisonGeneratingValues(Result&: PoisonVals, S);
4205
4206 SmallVector<Value *> Worklist;
4207 SmallPtrSet<Value *, 8> Visited;
4208 Worklist.push_back(Elt: I);
4209 while (!Worklist.empty()) {
4210 Value *V = Worklist.pop_back_val();
4211 if (!Visited.insert(Ptr: V).second)
4212 continue;
4213
4214 // Avoid walking large instruction graphs.
4215 if (Visited.size() > 16)
4216 return false;
4217
4218 // Either the value can't be poison, or the S would also be poison if it
4219 // is.
4220 if (PoisonVals.contains(Ptr: V) || isGuaranteedNotToBePoison(V))
4221 continue;
4222
4223 auto *I = dyn_cast<Instruction>(Val: V);
4224 if (!I)
4225 return false;
4226
4227 // Disjoint or instructions are interpreted as adds by SCEV. However, we
4228 // can't replace an arbitrary add with disjoint or, even if we drop the
4229 // flag. We would need to convert the or into an add.
4230 if (auto *PDI = dyn_cast<PossiblyDisjointInst>(Val: I))
4231 if (PDI->isDisjoint())
4232 return false;
4233
4234 // FIXME: Ignore vscale, even though it technically could be poison. Do this
4235 // because SCEV currently assumes it can't be poison. Remove this special
4236 // case once we proper model when vscale can be poison.
4237 if (auto *II = dyn_cast<IntrinsicInst>(Val: I);
4238 II && II->getIntrinsicID() == Intrinsic::vscale)
4239 continue;
4240
4241 if (canCreatePoison(Op: cast<Operator>(Val: I), /*ConsiderFlagsAndMetadata*/ false))
4242 return false;
4243
4244 // If the instruction can't create poison, we can recurse to its operands.
4245 if (I->hasPoisonGeneratingAnnotations())
4246 DropPoisonGeneratingInsts.push_back(Elt: I);
4247
4248 for (Value *Op : I->operands())
4249 Worklist.push_back(Elt: Op);
4250 }
4251 return true;
4252}
4253
4254const SCEV *
4255ScalarEvolution::getSequentialMinMaxExpr(SCEVTypes Kind,
4256 SmallVectorImpl<const SCEV *> &Ops) {
4257 assert(SCEVSequentialMinMaxExpr::isSequentialMinMaxType(Kind) &&
4258 "Not a SCEVSequentialMinMaxExpr!");
4259 assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!");
4260 if (Ops.size() == 1)
4261 return Ops[0];
4262#ifndef NDEBUG
4263 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
4264 for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
4265 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
4266 "Operand types don't match!");
4267 assert(Ops[0]->getType()->isPointerTy() ==
4268 Ops[i]->getType()->isPointerTy() &&
4269 "min/max should be consistently pointerish");
4270 }
4271#endif
4272
4273 // Note that SCEVSequentialMinMaxExpr is *NOT* commutative,
4274 // so we can *NOT* do any kind of sorting of the expressions!
4275
4276 // Check if we have created the same expression before.
4277 if (const SCEV *S = findExistingSCEVInCache(SCEVType: Kind, Ops))
4278 return S;
4279
4280 // FIXME: there are *some* simplifications that we can do here.
4281
4282 // Keep only the first instance of an operand.
4283 {
4284 SCEVSequentialMinMaxDeduplicatingVisitor Deduplicator(*this, Kind);
4285 bool Changed = Deduplicator.visit(Kind, OrigOps: Ops, NewOps&: Ops);
4286 if (Changed)
4287 return getSequentialMinMaxExpr(Kind, Ops);
4288 }
4289
4290 // Check to see if one of the operands is of the same kind. If so, expand its
4291 // operands onto our operand list, and recurse to simplify.
4292 {
4293 unsigned Idx = 0;
4294 bool DeletedAny = false;
4295 while (Idx < Ops.size()) {
4296 if (Ops[Idx]->getSCEVType() != Kind) {
4297 ++Idx;
4298 continue;
4299 }
4300 const auto *SMME = cast<SCEVSequentialMinMaxExpr>(Val: Ops[Idx]);
4301 Ops.erase(CI: Ops.begin() + Idx);
4302 Ops.insert(I: Ops.begin() + Idx, From: SMME->operands().begin(),
4303 To: SMME->operands().end());
4304 DeletedAny = true;
4305 }
4306
4307 if (DeletedAny)
4308 return getSequentialMinMaxExpr(Kind, Ops);
4309 }
4310
4311 const SCEV *SaturationPoint;
4312 ICmpInst::Predicate Pred;
4313 switch (Kind) {
4314 case scSequentialUMinExpr:
4315 SaturationPoint = getZero(Ty: Ops[0]->getType());
4316 Pred = ICmpInst::ICMP_ULE;
4317 break;
4318 default:
4319 llvm_unreachable("Not a sequential min/max type.");
4320 }
4321
4322 for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
4323 // We can replace %x umin_seq %y with %x umin %y if either:
4324 // * %y being poison implies %x is also poison.
4325 // * %x cannot be the saturating value (e.g. zero for umin).
4326 if (::impliesPoison(AssumedPoison: Ops[i], S: Ops[i - 1]) ||
4327 isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_NE, LHS: Ops[i - 1],
4328 RHS: SaturationPoint)) {
4329 SmallVector<const SCEV *> SeqOps = {Ops[i - 1], Ops[i]};
4330 Ops[i - 1] = getMinMaxExpr(
4331 Kind: SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(Ty: Kind),
4332 Ops&: SeqOps);
4333 Ops.erase(CI: Ops.begin() + i);
4334 return getSequentialMinMaxExpr(Kind, Ops);
4335 }
4336 // Fold %x umin_seq %y to %x if %x ule %y.
4337 // TODO: We might be able to prove the predicate for a later operand.
4338 if (isKnownViaNonRecursiveReasoning(Pred, LHS: Ops[i - 1], RHS: Ops[i])) {
4339 Ops.erase(CI: Ops.begin() + i);
4340 return getSequentialMinMaxExpr(Kind, Ops);
4341 }
4342 }
4343
4344 // Okay, it looks like we really DO need an expr. Check to see if we
4345 // already have one, otherwise create a new one.
4346 FoldingSetNodeID ID;
4347 ID.AddInteger(I: Kind);
4348 for (const SCEV *Op : Ops)
4349 ID.AddPointer(Ptr: Op);
4350 void *IP = nullptr;
4351 const SCEV *ExistingSCEV = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP);
4352 if (ExistingSCEV)
4353 return ExistingSCEV;
4354
4355 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Num: Ops.size());
4356 std::uninitialized_copy(first: Ops.begin(), last: Ops.end(), result: O);
4357 SCEV *S = new (SCEVAllocator)
4358 SCEVSequentialMinMaxExpr(ID.Intern(Allocator&: SCEVAllocator), Kind, O, Ops.size());
4359
4360 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
4361 registerUser(User: S, Ops);
4362 return S;
4363}
4364
4365const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) {
4366 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
4367 return getSMaxExpr(Operands&: Ops);
4368}
4369
4370const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
4371 return getMinMaxExpr(Kind: scSMaxExpr, Ops);
4372}
4373
4374const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) {
4375 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
4376 return getUMaxExpr(Operands&: Ops);
4377}
4378
4379const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
4380 return getMinMaxExpr(Kind: scUMaxExpr, Ops);
4381}
4382
4383const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
4384 const SCEV *RHS) {
4385 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
4386 return getSMinExpr(Operands&: Ops);
4387}
4388
4389const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
4390 return getMinMaxExpr(Kind: scSMinExpr, Ops);
4391}
4392
4393const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, const SCEV *RHS,
4394 bool Sequential) {
4395 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
4396 return getUMinExpr(Operands&: Ops, Sequential);
4397}
4398
4399const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops,
4400 bool Sequential) {
4401 return Sequential ? getSequentialMinMaxExpr(Kind: scSequentialUMinExpr, Ops)
4402 : getMinMaxExpr(Kind: scUMinExpr, Ops);
4403}
4404
4405const SCEV *
4406ScalarEvolution::getSizeOfExpr(Type *IntTy, TypeSize Size) {
4407 const SCEV *Res = getConstant(Ty: IntTy, V: Size.getKnownMinValue());
4408 if (Size.isScalable())
4409 Res = getMulExpr(LHS: Res, RHS: getVScale(Ty: IntTy));
4410 return Res;
4411}
4412
4413const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
4414 return getSizeOfExpr(IntTy, Size: getDataLayout().getTypeAllocSize(Ty: AllocTy));
4415}
4416
4417const SCEV *ScalarEvolution::getStoreSizeOfExpr(Type *IntTy, Type *StoreTy) {
4418 return getSizeOfExpr(IntTy, Size: getDataLayout().getTypeStoreSize(Ty: StoreTy));
4419}
4420
4421const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
4422 StructType *STy,
4423 unsigned FieldNo) {
4424 // We can bypass creating a target-independent constant expression and then
4425 // folding it back into a ConstantInt. This is just a compile-time
4426 // optimization.
4427 const StructLayout *SL = getDataLayout().getStructLayout(Ty: STy);
4428 assert(!SL->getSizeInBits().isScalable() &&
4429 "Cannot get offset for structure containing scalable vector types");
4430 return getConstant(Ty: IntTy, V: SL->getElementOffset(Idx: FieldNo));
4431}
4432
4433const SCEV *ScalarEvolution::getUnknown(Value *V) {
4434 // Don't attempt to do anything other than create a SCEVUnknown object
4435 // here. createSCEV only calls getUnknown after checking for all other
4436 // interesting possibilities, and any other code that calls getUnknown
4437 // is doing so in order to hide a value from SCEV canonicalization.
4438
4439 FoldingSetNodeID ID;
4440 ID.AddInteger(I: scUnknown);
4441 ID.AddPointer(Ptr: V);
4442 void *IP = nullptr;
4443 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, InsertPos&: IP)) {
4444 assert(cast<SCEVUnknown>(S)->getValue() == V &&
4445 "Stale SCEVUnknown in uniquing map!");
4446 return S;
4447 }
4448 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(Allocator&: SCEVAllocator), V, this,
4449 FirstUnknown);
4450 FirstUnknown = cast<SCEVUnknown>(Val: S);
4451 UniqueSCEVs.InsertNode(N: S, InsertPos: IP);
4452 return S;
4453}
4454
4455//===----------------------------------------------------------------------===//
4456// Basic SCEV Analysis and PHI Idiom Recognition Code
4457//
4458
4459/// Test if values of the given type are analyzable within the SCEV
4460/// framework. This primarily includes integer types, and it can optionally
4461/// include pointer types if the ScalarEvolution class has access to
4462/// target-specific information.
4463bool ScalarEvolution::isSCEVable(Type *Ty) const {
4464 // Integers and pointers are always SCEVable.
4465 return Ty->isIntOrPtrTy();
4466}
4467
4468/// Return the size in bits of the specified type, for which isSCEVable must
4469/// return true.
4470uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
4471 assert(isSCEVable(Ty) && "Type is not SCEVable!");
4472 if (Ty->isPointerTy())
4473 return getDataLayout().getIndexTypeSizeInBits(Ty);
4474 return getDataLayout().getTypeSizeInBits(Ty);
4475}
4476
4477/// Return a type with the same bitwidth as the given type and which represents
4478/// how SCEV will treat the given type, for which isSCEVable must return
4479/// true. For pointer types, this is the pointer index sized integer type.
4480Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
4481 assert(isSCEVable(Ty) && "Type is not SCEVable!");
4482
4483 if (Ty->isIntegerTy())
4484 return Ty;
4485
4486 // The only other support type is pointer.
4487 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
4488 return getDataLayout().getIndexType(PtrTy: Ty);
4489}
4490
4491Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
4492 return getTypeSizeInBits(Ty: T1) >= getTypeSizeInBits(Ty: T2) ? T1 : T2;
4493}
4494
4495bool ScalarEvolution::instructionCouldExistWithOperands(const SCEV *A,
4496 const SCEV *B) {
4497 /// For a valid use point to exist, the defining scope of one operand
4498 /// must dominate the other.
4499 bool PreciseA, PreciseB;
4500 auto *ScopeA = getDefiningScopeBound(Ops: {A}, Precise&: PreciseA);
4501 auto *ScopeB = getDefiningScopeBound(Ops: {B}, Precise&: PreciseB);
4502 if (!PreciseA || !PreciseB)
4503 // Can't tell.
4504 return false;
4505 return (ScopeA == ScopeB) || DT.dominates(Def: ScopeA, User: ScopeB) ||
4506 DT.dominates(Def: ScopeB, User: ScopeA);
4507}
4508
4509const SCEV *ScalarEvolution::getCouldNotCompute() {
4510 return CouldNotCompute.get();
4511}
4512
4513bool ScalarEvolution::checkValidity(const SCEV *S) const {
4514 bool ContainsNulls = SCEVExprContains(Root: S, Pred: [](const SCEV *S) {
4515 auto *SU = dyn_cast<SCEVUnknown>(Val: S);
4516 return SU && SU->getValue() == nullptr;
4517 });
4518
4519 return !ContainsNulls;
4520}
4521
4522bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
4523 HasRecMapType::iterator I = HasRecMap.find(Val: S);
4524 if (I != HasRecMap.end())
4525 return I->second;
4526
4527 bool FoundAddRec =
4528 SCEVExprContains(Root: S, Pred: [](const SCEV *S) { return isa<SCEVAddRecExpr>(Val: S); });
4529 HasRecMap.insert(KV: {S, FoundAddRec});
4530 return FoundAddRec;
4531}
4532
4533/// Return the ValueOffsetPair set for \p S. \p S can be represented
4534/// by the value and offset from any ValueOffsetPair in the set.
4535ArrayRef<Value *> ScalarEvolution::getSCEVValues(const SCEV *S) {
4536 ExprValueMapType::iterator SI = ExprValueMap.find_as(Val: S);
4537 if (SI == ExprValueMap.end())
4538 return std::nullopt;
4539 return SI->second.getArrayRef();
4540}
4541
4542/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
4543/// cannot be used separately. eraseValueFromMap should be used to remove
4544/// V from ValueExprMap and ExprValueMap at the same time.
4545void ScalarEvolution::eraseValueFromMap(Value *V) {
4546 ValueExprMapType::iterator I = ValueExprMap.find_as(Val: V);
4547 if (I != ValueExprMap.end()) {
4548 auto EVIt = ExprValueMap.find(Val: I->second);
4549 bool Removed = EVIt->second.remove(X: V);
4550 (void) Removed;
4551 assert(Removed && "Value not in ExprValueMap?");
4552 ValueExprMap.erase(I);
4553 }
4554}
4555
4556void ScalarEvolution::insertValueToMap(Value *V, const SCEV *S) {
4557 // A recursive query may have already computed the SCEV. It should be
4558 // equivalent, but may not necessarily be exactly the same, e.g. due to lazily
4559 // inferred nowrap flags.
4560 auto It = ValueExprMap.find_as(Val: V);
4561 if (It == ValueExprMap.end()) {
4562 ValueExprMap.insert(KV: {SCEVCallbackVH(V, this), S});
4563 ExprValueMap[S].insert(X: V);
4564 }
4565}
4566
4567/// Return an existing SCEV if it exists, otherwise analyze the expression and
4568/// create a new one.
4569const SCEV *ScalarEvolution::getSCEV(Value *V) {
4570 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
4571
4572 if (const SCEV *S = getExistingSCEV(V))
4573 return S;
4574 return createSCEVIter(V);
4575}
4576
4577const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
4578 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
4579
4580 ValueExprMapType::iterator I = ValueExprMap.find_as(Val: V);
4581 if (I != ValueExprMap.end()) {
4582 const SCEV *S = I->second;
4583 assert(checkValidity(S) &&
4584 "existing SCEV has not been properly invalidated");
4585 return S;
4586 }
4587 return nullptr;
4588}
4589
4590/// Return a SCEV corresponding to -V = -1*V
4591const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
4592 SCEV::NoWrapFlags Flags) {
4593 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(Val: V))
4594 return getConstant(
4595 V: cast<ConstantInt>(Val: ConstantExpr::getNeg(C: VC->getValue())));
4596
4597 Type *Ty = V->getType();
4598 Ty = getEffectiveSCEVType(Ty);
4599 return getMulExpr(LHS: V, RHS: getMinusOne(Ty), Flags);
4600}
4601
4602/// If Expr computes ~A, return A else return nullptr
4603static const SCEV *MatchNotExpr(const SCEV *Expr) {
4604 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Val: Expr);
4605 if (!Add || Add->getNumOperands() != 2 ||
4606 !Add->getOperand(i: 0)->isAllOnesValue())
4607 return nullptr;
4608
4609 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Val: Add->getOperand(i: 1));
4610 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
4611 !AddRHS->getOperand(i: 0)->isAllOnesValue())
4612 return nullptr;
4613
4614 return AddRHS->getOperand(i: 1);
4615}
4616
4617/// Return a SCEV corresponding to ~V = -1-V
4618const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
4619 assert(!V->getType()->isPointerTy() && "Can't negate pointer");
4620
4621 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(Val: V))
4622 return getConstant(
4623 V: cast<ConstantInt>(Val: ConstantExpr::getNot(C: VC->getValue())));
4624
4625 // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
4626 if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(Val: V)) {
4627 auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
4628 SmallVector<const SCEV *, 2> MatchedOperands;
4629 for (const SCEV *Operand : MME->operands()) {
4630 const SCEV *Matched = MatchNotExpr(Expr: Operand);
4631 if (!Matched)
4632 return (const SCEV *)nullptr;
4633 MatchedOperands.push_back(Elt: Matched);
4634 }
4635 return getMinMaxExpr(Kind: SCEVMinMaxExpr::negate(T: MME->getSCEVType()),
4636 Ops&: MatchedOperands);
4637 };
4638 if (const SCEV *Replaced = MatchMinMaxNegation(MME))
4639 return Replaced;
4640 }
4641
4642 Type *Ty = V->getType();
4643 Ty = getEffectiveSCEVType(Ty);
4644 return getMinusSCEV(LHS: getMinusOne(Ty), RHS: V);
4645}
4646
4647const SCEV *ScalarEvolution::removePointerBase(const SCEV *P) {
4648 assert(P->getType()->isPointerTy());
4649
4650 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Val: P)) {
4651 // The base of an AddRec is the first operand.
4652 SmallVector<const SCEV *> Ops{AddRec->operands()};
4653 Ops[0] = removePointerBase(P: Ops[0]);
4654 // Don't try to transfer nowrap flags for now. We could in some cases
4655 // (for example, if pointer operand of the AddRec is a SCEVUnknown).
4656 return getAddRecExpr(Operands&: Ops, L: AddRec->getLoop(), Flags: SCEV::FlagAnyWrap);
4657 }
4658 if (auto *Add = dyn_cast<SCEVAddExpr>(Val: P)) {
4659 // The base of an Add is the pointer operand.
4660 SmallVector<const SCEV *> Ops{Add->operands()};
4661 const SCEV **PtrOp = nullptr;
4662 for (const SCEV *&AddOp : Ops) {
4663 if (AddOp->getType()->isPointerTy()) {
4664 assert(!PtrOp && "Cannot have multiple pointer ops");
4665 PtrOp = &AddOp;
4666 }
4667 }
4668 *PtrOp = removePointerBase(P: *PtrOp);
4669 // Don't try to transfer nowrap flags for now. We could in some cases
4670 // (for example, if the pointer operand of the Add is a SCEVUnknown).
4671 return getAddExpr(Ops);
4672 }
4673 // Any other expression must be a pointer base.
4674 return getZero(Ty: P->getType());
4675}
4676
4677const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
4678 SCEV::NoWrapFlags Flags,
4679 unsigned Depth) {
4680 // Fast path: X - X --> 0.
4681 if (LHS == RHS)
4682 return getZero(Ty: LHS->getType());
4683
4684 // If we subtract two pointers with different pointer bases, bail.
4685 // Eventually, we're going to add an assertion to getMulExpr that we
4686 // can't multiply by a pointer.
4687 if (RHS->getType()->isPointerTy()) {
4688 if (!LHS->getType()->isPointerTy() ||
4689 getPointerBase(V: LHS) != getPointerBase(V: RHS))
4690 return getCouldNotCompute();
4691 LHS = removePointerBase(P: LHS);
4692 RHS = removePointerBase(P: RHS);
4693 }
4694
4695 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
4696 // makes it so that we cannot make much use of NUW.
4697 auto AddFlags = SCEV::FlagAnyWrap;
4698 const bool RHSIsNotMinSigned =
4699 !getSignedRangeMin(S: RHS).isMinSignedValue();
4700 if (hasFlags(Flags, TestFlags: SCEV::FlagNSW)) {
4701 // Let M be the minimum representable signed value. Then (-1)*RHS
4702 // signed-wraps if and only if RHS is M. That can happen even for
4703 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
4704 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
4705 // (-1)*RHS, we need to prove that RHS != M.
4706 //
4707 // If LHS is non-negative and we know that LHS - RHS does not
4708 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
4709 // either by proving that RHS > M or that LHS >= 0.
4710 if (RHSIsNotMinSigned || isKnownNonNegative(S: LHS)) {
4711 AddFlags = SCEV::FlagNSW;
4712 }
4713 }
4714
4715 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
4716 // RHS is NSW and LHS >= 0.
4717 //
4718 // The difficulty here is that the NSW flag may have been proven
4719 // relative to a loop that is to be found in a recurrence in LHS and
4720 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
4721 // larger scope than intended.
4722 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
4723
4724 return getAddExpr(LHS, RHS: getNegativeSCEV(V: RHS, Flags: NegFlags), Flags: AddFlags, Depth);
4725}
4726
4727const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
4728 unsigned Depth) {
4729 Type *SrcTy = V->getType();
4730 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
4731 "Cannot truncate or zero extend with non-integer arguments!");
4732 if (getTypeSizeInBits(Ty: SrcTy) == getTypeSizeInBits(Ty))
4733 return V; // No conversion
4734 if (getTypeSizeInBits(Ty: SrcTy) > getTypeSizeInBits(Ty))
4735 return getTruncateExpr(Op: V, Ty, Depth);
4736 return getZeroExtendExpr(Op: V, Ty, Depth);
4737}
4738
4739const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
4740 unsigned Depth) {
4741 Type *SrcTy = V->getType();
4742 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
4743 "Cannot truncate or zero extend with non-integer arguments!");
4744 if (getTypeSizeInBits(Ty: SrcTy) == getTypeSizeInBits(Ty))
4745 return V; // No conversion
4746 if (getTypeSizeInBits(Ty: SrcTy) > getTypeSizeInBits(Ty))
4747 return getTruncateExpr(Op: V, Ty, Depth);
4748 return getSignExtendExpr(Op: V, Ty, Depth);
4749}
4750
4751const SCEV *
4752ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
4753 Type *SrcTy = V->getType();
4754 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
4755 "Cannot noop or zero extend with non-integer arguments!");
4756 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
4757 "getNoopOrZeroExtend cannot truncate!");
4758 if (getTypeSizeInBits(Ty: SrcTy) == getTypeSizeInBits(Ty))
4759 return V; // No conversion
4760 return getZeroExtendExpr(Op: V, Ty);
4761}
4762
4763const SCEV *
4764ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
4765 Type *SrcTy = V->getType();
4766 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
4767 "Cannot noop or sign extend with non-integer arguments!");
4768 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
4769 "getNoopOrSignExtend cannot truncate!");
4770 if (getTypeSizeInBits(Ty: SrcTy) == getTypeSizeInBits(Ty))
4771 return V; // No conversion
4772 return getSignExtendExpr(Op: V, Ty);
4773}
4774
4775const SCEV *
4776ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
4777 Type *SrcTy = V->getType();
4778 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
4779 "Cannot noop or any extend with non-integer arguments!");
4780 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
4781 "getNoopOrAnyExtend cannot truncate!");
4782 if (getTypeSizeInBits(Ty: SrcTy) == getTypeSizeInBits(Ty))
4783 return V; // No conversion
4784 return getAnyExtendExpr(Op: V, Ty);
4785}
4786
4787const SCEV *
4788ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
4789 Type *SrcTy = V->getType();
4790 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
4791 "Cannot truncate or noop with non-integer arguments!");
4792 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
4793 "getTruncateOrNoop cannot extend!");
4794 if (getTypeSizeInBits(Ty: SrcTy) == getTypeSizeInBits(Ty))
4795 return V; // No conversion
4796 return getTruncateExpr(Op: V, Ty);
4797}
4798
4799const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
4800 const SCEV *RHS) {
4801 const SCEV *PromotedLHS = LHS;
4802 const SCEV *PromotedRHS = RHS;
4803
4804 if (getTypeSizeInBits(Ty: LHS->getType()) > getTypeSizeInBits(Ty: RHS->getType()))
4805 PromotedRHS = getZeroExtendExpr(Op: RHS, Ty: LHS->getType());
4806 else
4807 PromotedLHS = getNoopOrZeroExtend(V: LHS, Ty: RHS->getType());
4808
4809 return getUMaxExpr(LHS: PromotedLHS, RHS: PromotedRHS);
4810}
4811
4812const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
4813 const SCEV *RHS,
4814 bool Sequential) {
4815 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
4816 return getUMinFromMismatchedTypes(Ops, Sequential);
4817}
4818
4819const SCEV *
4820ScalarEvolution::getUMinFromMismatchedTypes(SmallVectorImpl<const SCEV *> &Ops,
4821 bool Sequential) {
4822 assert(!Ops.empty() && "At least one operand must be!");
4823 // Trivial case.
4824 if (Ops.size() == 1)
4825 return Ops[0];
4826
4827 // Find the max type first.
4828 Type *MaxType = nullptr;
4829 for (const auto *S : Ops)
4830 if (MaxType)
4831 MaxType = getWiderType(T1: MaxType, T2: S->getType());
4832 else
4833 MaxType = S->getType();
4834 assert(MaxType && "Failed to find maximum type!");
4835
4836 // Extend all ops to max type.
4837 SmallVector<const SCEV *, 2> PromotedOps;
4838 for (const auto *S : Ops)
4839 PromotedOps.push_back(Elt: getNoopOrZeroExtend(V: S, Ty: MaxType));
4840
4841 // Generate umin.
4842 return getUMinExpr(Ops&: PromotedOps, Sequential);
4843}
4844
4845const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
4846 // A pointer operand may evaluate to a nonpointer expression, such as null.
4847 if (!V->getType()->isPointerTy())
4848 return V;
4849
4850 while (true) {
4851 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Val: V)) {
4852 V = AddRec->getStart();
4853 } else if (auto *Add = dyn_cast<SCEVAddExpr>(Val: V)) {
4854 const SCEV *PtrOp = nullptr;
4855 for (const SCEV *AddOp : Add->operands()) {
4856 if (AddOp->getType()->isPointerTy()) {
4857 assert(!PtrOp && "Cannot have multiple pointer ops");
4858 PtrOp = AddOp;
4859 }
4860 }
4861 assert(PtrOp && "Must have pointer op");
4862 V = PtrOp;
4863 } else // Not something we can look further into.
4864 return V;
4865 }
4866}
4867
4868/// Push users of the given Instruction onto the given Worklist.
4869static void PushDefUseChildren(Instruction *I,
4870 SmallVectorImpl<Instruction *> &Worklist,
4871 SmallPtrSetImpl<Instruction *> &Visited) {
4872 // Push the def-use children onto the Worklist stack.
4873 for (User *U : I->users()) {
4874 auto *UserInsn = cast<Instruction>(Val: U);
4875 if (Visited.insert(Ptr: UserInsn).second)
4876 Worklist.push_back(Elt: UserInsn);
4877 }
4878}
4879
4880namespace {
4881
4882/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
4883/// expression in case its Loop is L. If it is not L then
4884/// if IgnoreOtherLoops is true then use AddRec itself
4885/// otherwise rewrite cannot be done.
4886/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4887class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4888public:
4889 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
4890 bool IgnoreOtherLoops = true) {
4891 SCEVInitRewriter Rewriter(L, SE);
4892 const SCEV *Result = Rewriter.visit(S);
4893 if (Rewriter.hasSeenLoopVariantSCEVUnknown())
4894 return SE.getCouldNotCompute();
4895 return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
4896 ? SE.getCouldNotCompute()
4897 : Result;
4898 }
4899
4900 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4901 if (!SE.isLoopInvariant(S: Expr, L))
4902 SeenLoopVariantSCEVUnknown = true;
4903 return Expr;
4904 }
4905
4906 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4907 // Only re-write AddRecExprs for this loop.
4908 if (Expr->getLoop() == L)
4909 return Expr->getStart();
4910 SeenOtherLoops = true;
4911 return Expr;
4912 }
4913
4914 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4915
4916 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4917
4918private:
4919 explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
4920 : SCEVRewriteVisitor(SE), L(L) {}
4921
4922 const Loop *L;
4923 bool SeenLoopVariantSCEVUnknown = false;
4924 bool SeenOtherLoops = false;
4925};
4926
4927/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
4928/// increment expression in case its Loop is L. If it is not L then
4929/// use AddRec itself.
4930/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4931class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
4932public:
4933 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
4934 SCEVPostIncRewriter Rewriter(L, SE);
4935 const SCEV *Result = Rewriter.visit(S);
4936 return Rewriter.hasSeenLoopVariantSCEVUnknown()
4937 ? SE.getCouldNotCompute()
4938 : Result;
4939 }
4940
4941 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4942 if (!SE.isLoopInvariant(S: Expr, L))
4943 SeenLoopVariantSCEVUnknown = true;
4944 return Expr;
4945 }
4946
4947 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4948 // Only re-write AddRecExprs for this loop.
4949 if (Expr->getLoop() == L)
4950 return Expr->getPostIncExpr(SE);
4951 SeenOtherLoops = true;
4952 return Expr;
4953 }
4954
4955 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4956
4957 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4958
4959private:
4960 explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
4961 : SCEVRewriteVisitor(SE), L(L) {}
4962
4963 const Loop *L;
4964 bool SeenLoopVariantSCEVUnknown = false;
4965 bool SeenOtherLoops = false;
4966};
4967
4968/// This class evaluates the compare condition by matching it against the
4969/// condition of loop latch. If there is a match we assume a true value
4970/// for the condition while building SCEV nodes.
4971class SCEVBackedgeConditionFolder
4972 : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4973public:
4974 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4975 ScalarEvolution &SE) {
4976 bool IsPosBECond = false;
4977 Value *BECond = nullptr;
4978 if (BasicBlock *Latch = L->getLoopLatch()) {
4979 BranchInst *BI = dyn_cast<BranchInst>(Val: Latch->getTerminator());
4980 if (BI && BI->isConditional()) {
4981 assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&
4982 "Both outgoing branches should not target same header!");
4983 BECond = BI->getCondition();
4984 IsPosBECond = BI->getSuccessor(i: 0) == L->getHeader();
4985 } else {
4986 return S;
4987 }
4988 }
4989 SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
4990 return Rewriter.visit(S);
4991 }
4992
4993 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4994 const SCEV *Result = Expr;
4995 bool InvariantF = SE.isLoopInvariant(S: Expr, L);
4996
4997 if (!InvariantF) {
4998 Instruction *I = cast<Instruction>(Val: Expr->getValue());
4999 switch (I->getOpcode()) {
5000 case Instruction::Select: {
5001 SelectInst *SI = cast<SelectInst>(Val: I);
5002 std::optional<const SCEV *> Res =
5003 compareWithBackedgeCondition(IC: SI->getCondition());
5004 if (Res) {
5005 bool IsOne = cast<SCEVConstant>(Val: *Res)->getValue()->isOne();
5006 Result = SE.getSCEV(V: IsOne ? SI->getTrueValue() : SI->getFalseValue());
5007 }
5008 break;
5009 }
5010 default: {
5011 std::optional<const SCEV *> Res = compareWithBackedgeCondition(IC: I);
5012 if (Res)
5013 Result = *Res;
5014 break;
5015 }
5016 }
5017 }
5018 return Result;
5019 }
5020
5021private:
5022 explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
5023 bool IsPosBECond, ScalarEvolution &SE)
5024 : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
5025 IsPositiveBECond(IsPosBECond) {}
5026
5027 std::optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
5028
5029 const Loop *L;
5030 /// Loop back condition.
5031 Value *BackedgeCond = nullptr;
5032 /// Set to true if loop back is on positive branch condition.
5033 bool IsPositiveBECond;
5034};
5035
5036std::optional<const SCEV *>
5037SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
5038
5039 // If value matches the backedge condition for loop latch,
5040 // then return a constant evolution node based on loopback
5041 // branch taken.
5042 if (BackedgeCond == IC)
5043 return IsPositiveBECond ? SE.getOne(Ty: Type::getInt1Ty(C&: SE.getContext()))
5044 : SE.getZero(Ty: Type::getInt1Ty(C&: SE.getContext()));
5045 return std::nullopt;
5046}
5047
5048class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
5049public:
5050 static const SCEV *rewrite(const SCEV *S, const Loop *L,
5051 ScalarEvolution &SE) {
5052 SCEVShiftRewriter Rewriter(L, SE);
5053 const SCEV *Result = Rewriter.visit(S);
5054 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
5055 }
5056
5057 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
5058 // Only allow AddRecExprs for this loop.
5059 if (!SE.isLoopInvariant(S: Expr, L))
5060 Valid = false;
5061 return Expr;
5062 }
5063
5064 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
5065 if (Expr->getLoop() == L && Expr->isAffine())
5066 return SE.getMinusSCEV(LHS: Expr, RHS: Expr->getStepRecurrence(SE));
5067 Valid = false;
5068 return Expr;
5069 }
5070
5071 bool isValid() { return Valid; }
5072
5073private:
5074 explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
5075 : SCEVRewriteVisitor(SE), L(L) {}
5076
5077 const Loop *L;
5078 bool Valid = true;
5079};
5080
5081} // end anonymous namespace
5082
5083SCEV::NoWrapFlags
5084ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
5085 if (!AR->isAffine())
5086 return SCEV::FlagAnyWrap;
5087
5088 using OBO = OverflowingBinaryOperator;
5089
5090 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
5091
5092 if (!AR->hasNoSelfWrap()) {
5093 const SCEV *BECount = getConstantMaxBackedgeTakenCount(L: AR->getLoop());
5094 if (const SCEVConstant *BECountMax = dyn_cast<SCEVConstant>(Val: BECount)) {
5095 ConstantRange StepCR = getSignedRange(S: AR->getStepRecurrence(SE&: *this));
5096 const APInt &BECountAP = BECountMax->getAPInt();
5097 unsigned NoOverflowBitWidth =
5098 BECountAP.getActiveBits() + StepCR.getMinSignedBits();
5099 if (NoOverflowBitWidth <= getTypeSizeInBits(Ty: AR->getType()))
5100 Result = ScalarEvolution::setFlags(Flags: Result, OnFlags: SCEV::FlagNW);
5101 }
5102 }
5103
5104 if (!AR->hasNoSignedWrap()) {
5105 ConstantRange AddRecRange = getSignedRange(S: AR);
5106 ConstantRange IncRange = getSignedRange(S: AR->getStepRecurrence(SE&: *this));
5107
5108 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
5109 BinOp: Instruction::Add, Other: IncRange, NoWrapKind: OBO::NoSignedWrap);
5110 if (NSWRegion.contains(CR: AddRecRange))
5111 Result = ScalarEvolution::setFlags(Flags: Result, OnFlags: SCEV::FlagNSW);
5112 }
5113
5114 if (!AR->hasNoUnsignedWrap()) {
5115 ConstantRange AddRecRange = getUnsignedRange(S: AR);
5116 ConstantRange IncRange = getUnsignedRange(S: AR->getStepRecurrence(SE&: *this));
5117
5118 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
5119 BinOp: Instruction::Add, Other: IncRange, NoWrapKind: OBO::NoUnsignedWrap);
5120 if (NUWRegion.contains(CR: AddRecRange))
5121 Result = ScalarEvolution::setFlags(Flags: Result, OnFlags: SCEV::FlagNUW);
5122 }
5123
5124 return Result;
5125}
5126
5127SCEV::NoWrapFlags
5128ScalarEvolution::proveNoSignedWrapViaInduction(const SCEVAddRecExpr *AR) {
5129 SCEV::NoWrapFlags Result = AR->getNoWrapFlags();
5130
5131 if (AR->hasNoSignedWrap())
5132 return Result;
5133
5134 if (!AR->isAffine())
5135 return Result;
5136
5137 // This function can be expensive, only try to prove NSW once per AddRec.
5138 if (!SignedWrapViaInductionTried.insert(Ptr: AR).second)
5139 return Result;
5140
5141 const SCEV *Step = AR->getStepRecurrence(SE&: *this);
5142 const Loop *L = AR->getLoop();
5143
5144 // Check whether the backedge-taken count is SCEVCouldNotCompute.
5145 // Note that this serves two purposes: It filters out loops that are
5146 // simply not analyzable, and it covers the case where this code is
5147 // being called from within backedge-taken count analysis, such that
5148 // attempting to ask for the backedge-taken count would likely result
5149 // in infinite recursion. In the later case, the analysis code will
5150 // cope with a conservative value, and it will take care to purge
5151 // that value once it has finished.
5152 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
5153
5154 // Normally, in the cases we can prove no-overflow via a
5155 // backedge guarding condition, we can also compute a backedge
5156 // taken count for the loop. The exceptions are assumptions and
5157 // guards present in the loop -- SCEV is not great at exploiting
5158 // these to compute max backedge taken counts, but can still use
5159 // these to prove lack of overflow. Use this fact to avoid
5160 // doing extra work that may not pay off.
5161
5162 if (isa<SCEVCouldNotCompute>(Val: MaxBECount) && !HasGuards &&
5163 AC.assumptions().empty())
5164 return Result;
5165
5166 // If the backedge is guarded by a comparison with the pre-inc value the
5167 // addrec is safe. Also, if the entry is guarded by a comparison with the
5168 // start value and the backedge is guarded by a comparison with the post-inc
5169 // value, the addrec is safe.
5170 ICmpInst::Predicate Pred;
5171 const SCEV *OverflowLimit =
5172 getSignedOverflowLimitForStep(Step, Pred: &Pred, SE: this);
5173 if (OverflowLimit &&
5174 (isLoopBackedgeGuardedByCond(L, Pred, LHS: AR, RHS: OverflowLimit) ||
5175 isKnownOnEveryIteration(Pred, LHS: AR, RHS: OverflowLimit))) {
5176 Result = setFlags(Flags: Result, OnFlags: SCEV::FlagNSW);
5177 }
5178 return Result;
5179}
5180SCEV::NoWrapFlags
5181ScalarEvolution::proveNoUnsignedWrapViaInduction(const SCEVAddRecExpr *AR) {
5182 SCEV::NoWrapFlags Result = AR->getNoWrapFlags();
5183
5184 if (AR->hasNoUnsignedWrap())
5185 return Result;
5186
5187 if (!AR->isAffine())
5188 return Result;
5189
5190 // This function can be expensive, only try to prove NUW once per AddRec.
5191 if (!UnsignedWrapViaInductionTried.insert(Ptr: AR).second)
5192 return Result;
5193
5194 const SCEV *Step = AR->getStepRecurrence(SE&: *this);
5195 unsigned BitWidth = getTypeSizeInBits(Ty: AR->getType());
5196 const Loop *L = AR->getLoop();
5197
5198 // Check whether the backedge-taken count is SCEVCouldNotCompute.
5199 // Note that this serves two purposes: It filters out loops that are
5200 // simply not analyzable, and it covers the case where this code is
5201 // being called from within backedge-taken count analysis, such that
5202 // attempting to ask for the backedge-taken count would likely result
5203 // in infinite recursion. In the later case, the analysis code will
5204 // cope with a conservative value, and it will take care to purge
5205 // that value once it has finished.
5206 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
5207
5208 // Normally, in the cases we can prove no-overflow via a
5209 // backedge guarding condition, we can also compute a backedge
5210 // taken count for the loop. The exceptions are assumptions and
5211 // guards present in the loop -- SCEV is not great at exploiting
5212 // these to compute max backedge taken counts, but can still use
5213 // these to prove lack of overflow. Use this fact to avoid
5214 // doing extra work that may not pay off.
5215
5216 if (isa<SCEVCouldNotCompute>(Val: MaxBECount) && !HasGuards &&
5217 AC.assumptions().empty())
5218 return Result;
5219
5220 // If the backedge is guarded by a comparison with the pre-inc value the
5221 // addrec is safe. Also, if the entry is guarded by a comparison with the
5222 // start value and the backedge is guarded by a comparison with the post-inc
5223 // value, the addrec is safe.
5224 if (isKnownPositive(S: Step)) {
5225 const SCEV *N = getConstant(Val: APInt::getMinValue(numBits: BitWidth) -
5226 getUnsignedRangeMax(S: Step));
5227 if (isLoopBackedgeGuardedByCond(L, Pred: ICmpInst::ICMP_ULT, LHS: AR, RHS: N) ||
5228 isKnownOnEveryIteration(Pred: ICmpInst::ICMP_ULT, LHS: AR, RHS: N)) {
5229 Result = setFlags(Flags: Result, OnFlags: SCEV::FlagNUW);
5230 }
5231 }
5232
5233 return Result;
5234}
5235
5236namespace {
5237
5238/// Represents an abstract binary operation. This may exist as a
5239/// normal instruction or constant expression, or may have been
5240/// derived from an expression tree.
5241struct BinaryOp {
5242 unsigned Opcode;
5243 Value *LHS;
5244 Value *RHS;
5245 bool IsNSW = false;
5246 bool IsNUW = false;
5247
5248 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
5249 /// constant expression.
5250 Operator *Op = nullptr;
5251
5252 explicit BinaryOp(Operator *Op)
5253 : Opcode(Op->getOpcode()), LHS(Op->getOperand(i: 0)), RHS(Op->getOperand(i: 1)),
5254 Op(Op) {
5255 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Val: Op)) {
5256 IsNSW = OBO->hasNoSignedWrap();
5257 IsNUW = OBO->hasNoUnsignedWrap();
5258 }
5259 }
5260
5261 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
5262 bool IsNUW = false)
5263 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
5264};
5265
5266} // end anonymous namespace
5267
5268/// Try to map \p V into a BinaryOp, and return \c std::nullopt on failure.
5269static std::optional<BinaryOp> MatchBinaryOp(Value *V, const DataLayout &DL,
5270 AssumptionCache &AC,
5271 const DominatorTree &DT,
5272 const Instruction *CxtI) {
5273 auto *Op = dyn_cast<Operator>(Val: V);
5274 if (!Op)
5275 return std::nullopt;
5276
5277 // Implementation detail: all the cleverness here should happen without
5278 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
5279 // SCEV expressions when possible, and we should not break that.
5280
5281 switch (Op->getOpcode()) {
5282 case Instruction::Add:
5283 case Instruction::Sub:
5284 case Instruction::Mul:
5285 case Instruction::UDiv:
5286 case Instruction::URem:
5287 case Instruction::And:
5288 case Instruction::AShr:
5289 case Instruction::Shl:
5290 return BinaryOp(Op);
5291
5292 case Instruction::Or: {
5293 // Convert or disjoint into add nuw nsw.
5294 if (cast<PossiblyDisjointInst>(Val: Op)->isDisjoint())
5295 return BinaryOp(Instruction::Add, Op->getOperand(i: 0), Op->getOperand(i: 1),
5296 /*IsNSW=*/true, /*IsNUW=*/true);
5297 return BinaryOp(Op);
5298 }
5299
5300 case Instruction::Xor:
5301 if (auto *RHSC = dyn_cast<ConstantInt>(Val: Op->getOperand(i: 1)))
5302 // If the RHS of the xor is a signmask, then this is just an add.
5303 // Instcombine turns add of signmask into xor as a strength reduction step.
5304 if (RHSC->getValue().isSignMask())
5305 return BinaryOp(Instruction::Add, Op->getOperand(i: 0), Op->getOperand(i: 1));
5306 // Binary `xor` is a bit-wise `add`.
5307 if (V->getType()->isIntegerTy(Bitwidth: 1))
5308 return BinaryOp(Instruction::Add, Op->getOperand(i: 0), Op->getOperand(i: 1));
5309 return BinaryOp(Op);
5310
5311 case Instruction::LShr:
5312 // Turn logical shift right of a constant into a unsigned divide.
5313 if (ConstantInt *SA = dyn_cast<ConstantInt>(Val: Op->getOperand(i: 1))) {
5314 uint32_t BitWidth = cast<IntegerType>(Val: Op->getType())->getBitWidth();
5315
5316 // If the shift count is not less than the bitwidth, the result of
5317 // the shift is undefined. Don't try to analyze it, because the
5318 // resolution chosen here may differ from the resolution chosen in
5319 // other parts of the compiler.
5320 if (SA->getValue().ult(RHS: BitWidth)) {
5321 Constant *X =
5322 ConstantInt::get(Context&: SA->getContext(),
5323 V: APInt::getOneBitSet(numBits: BitWidth, BitNo: SA->getZExtValue()));
5324 return BinaryOp(Instruction::UDiv, Op->getOperand(i: 0), X);
5325 }
5326 }
5327 return BinaryOp(Op);
5328
5329 case Instruction::ExtractValue: {
5330 auto *EVI = cast<ExtractValueInst>(Val: Op);
5331 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
5332 break;
5333
5334 auto *WO = dyn_cast<WithOverflowInst>(Val: EVI->getAggregateOperand());
5335 if (!WO)
5336 break;
5337
5338 Instruction::BinaryOps BinOp = WO->getBinaryOp();
5339 bool Signed = WO->isSigned();
5340 // TODO: Should add nuw/nsw flags for mul as well.
5341 if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
5342 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());
5343
5344 // Now that we know that all uses of the arithmetic-result component of
5345 // CI are guarded by the overflow check, we can go ahead and pretend
5346 // that the arithmetic is non-overflowing.
5347 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
5348 /* IsNSW = */ Signed, /* IsNUW = */ !Signed);
5349 }
5350
5351 default:
5352 break;
5353 }
5354
5355 // Recognise intrinsic loop.decrement.reg, and as this has exactly the same
5356 // semantics as a Sub, return a binary sub expression.
5357 if (auto *II = dyn_cast<IntrinsicInst>(Val: V))
5358 if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg)
5359 return BinaryOp(Instruction::Sub, II->getOperand(i_nocapture: 0), II->getOperand(i_nocapture: 1));
5360
5361 return std::nullopt;
5362}
5363
5364/// Helper function to createAddRecFromPHIWithCasts. We have a phi
5365/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
5366/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
5367/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
5368/// follows one of the following patterns:
5369/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
5370/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
5371/// If the SCEV expression of \p Op conforms with one of the expected patterns
5372/// we return the type of the truncation operation, and indicate whether the
5373/// truncated type should be treated as signed/unsigned by setting
5374/// \p Signed to true/false, respectively.
5375static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
5376 bool &Signed, ScalarEvolution &SE) {
5377 // The case where Op == SymbolicPHI (that is, with no type conversions on
5378 // the way) is handled by the regular add recurrence creating logic and
5379 // would have already been triggered in createAddRecForPHI. Reaching it here
5380 // means that createAddRecFromPHI had failed for this PHI before (e.g.,
5381 // because one of the other operands of the SCEVAddExpr updating this PHI is
5382 // not invariant).
5383 //
5384 // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
5385 // this case predicates that allow us to prove that Op == SymbolicPHI will
5386 // be added.
5387 if (Op == SymbolicPHI)
5388 return nullptr;
5389
5390 unsigned SourceBits = SE.getTypeSizeInBits(Ty: SymbolicPHI->getType());
5391 unsigned NewBits = SE.getTypeSizeInBits(Ty: Op->getType());
5392 if (SourceBits != NewBits)
5393 return nullptr;
5394
5395 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Val: Op);
5396 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Val: Op);
5397 if (!SExt && !ZExt)
5398 return nullptr;
5399 const SCEVTruncateExpr *Trunc =
5400 SExt ? dyn_cast<SCEVTruncateExpr>(Val: SExt->getOperand())
5401 : dyn_cast<SCEVTruncateExpr>(Val: ZExt->getOperand());
5402 if (!Trunc)
5403 return nullptr;
5404 const SCEV *X = Trunc->getOperand();
5405 if (X != SymbolicPHI)
5406 return nullptr;
5407 Signed = SExt != nullptr;
5408 return Trunc->getType();
5409}
5410
5411static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
5412 if (!PN->getType()->isIntegerTy())
5413 return nullptr;
5414 const Loop *L = LI.getLoopFor(BB: PN->getParent());
5415 if (!L || L->getHeader() != PN->getParent())
5416 return nullptr;
5417 return L;
5418}
5419
5420// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
5421// computation that updates the phi follows the following pattern:
5422// (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
5423// which correspond to a phi->trunc->sext/zext->add->phi update chain.
5424// If so, try to see if it can be rewritten as an AddRecExpr under some
5425// Predicates. If successful, return them as a pair. Also cache the results
5426// of the analysis.
5427//
5428// Example usage scenario:
5429// Say the Rewriter is called for the following SCEV:
5430// 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
5431// where:
5432// %X = phi i64 (%Start, %BEValue)
5433// It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
5434// and call this function with %SymbolicPHI = %X.
5435//
5436// The analysis will find that the value coming around the backedge has
5437// the following SCEV:
5438// BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
5439// Upon concluding that this matches the desired pattern, the function
5440// will return the pair {NewAddRec, SmallPredsVec} where:
5441// NewAddRec = {%Start,+,%Step}
5442// SmallPredsVec = {P1, P2, P3} as follows:
5443// P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
5444// P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
5445// P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
5446// The returned pair means that SymbolicPHI can be rewritten into NewAddRec
5447// under the predicates {P1,P2,P3}.
5448// This predicated rewrite will be cached in PredicatedSCEVRewrites:
5449// PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
5450//
5451// TODO's:
5452//
5453// 1) Extend the Induction descriptor to also support inductions that involve
5454// casts: When needed (namely, when we are called in the context of the
5455// vectorizer induction analysis), a Set of cast instructions will be
5456// populated by this method, and provided back to isInductionPHI. This is
5457// needed to allow the vectorizer to properly record them to be ignored by
5458// the cost model and to avoid vectorizing them (otherwise these casts,
5459// which are redundant under the runtime overflow checks, will be
5460// vectorized, which can be costly).
5461//
5462// 2) Support additional induction/PHISCEV patterns: We also want to support
5463// inductions where the sext-trunc / zext-trunc operations (partly) occur
5464// after the induction update operation (the induction increment):
5465//
5466// (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
5467// which correspond to a phi->add->trunc->sext/zext->phi update chain.
5468//
5469// (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
5470// which correspond to a phi->trunc->add->sext/zext->phi update chain.
5471//
5472// 3) Outline common code with createAddRecFromPHI to avoid duplication.
5473std::optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
5474ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
5475 SmallVector<const SCEVPredicate *, 3> Predicates;
5476
5477 // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
5478 // return an AddRec expression under some predicate.
5479
5480 auto *PN = cast<PHINode>(Val: SymbolicPHI->getValue());
5481 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
5482 assert(L && "Expecting an integer loop header phi");
5483
5484 // The loop may have multiple entrances or multiple exits; we can analyze
5485 // this phi as an addrec if it has a unique entry value and a unique
5486 // backedge value.
5487 Value *BEValueV = nullptr, *StartValueV = nullptr;
5488 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5489 Value *V = PN->getIncomingValue(i);
5490 if (L->contains(BB: PN->getIncomingBlock(i))) {
5491 if (!BEValueV) {
5492 BEValueV = V;
5493 } else if (BEValueV != V) {
5494 BEValueV = nullptr;
5495 break;
5496 }
5497 } else if (!StartValueV) {
5498 StartValueV = V;
5499 } else if (StartValueV != V) {
5500 StartValueV = nullptr;
5501 break;
5502 }
5503 }
5504 if (!BEValueV || !StartValueV)
5505 return std::nullopt;
5506
5507 const SCEV *BEValue = getSCEV(V: BEValueV);
5508
5509 // If the value coming around the backedge is an add with the symbolic
5510 // value we just inserted, possibly with casts that we can ignore under
5511 // an appropriate runtime guard, then we found a simple induction variable!
5512 const auto *Add = dyn_cast<SCEVAddExpr>(Val: BEValue);
5513 if (!Add)
5514 return std::nullopt;
5515
5516 // If there is a single occurrence of the symbolic value, possibly
5517 // casted, replace it with a recurrence.
5518 unsigned FoundIndex = Add->getNumOperands();
5519 Type *TruncTy = nullptr;
5520 bool Signed;
5521 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5522 if ((TruncTy =
5523 isSimpleCastedPHI(Op: Add->getOperand(i), SymbolicPHI, Signed, SE&: *this)))
5524 if (FoundIndex == e) {
5525 FoundIndex = i;
5526 break;
5527 }
5528
5529 if (FoundIndex == Add->getNumOperands())
5530 return std::nullopt;
5531
5532 // Create an add with everything but the specified operand.
5533 SmallVector<const SCEV *, 8> Ops;
5534 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5535 if (i != FoundIndex)
5536 Ops.push_back(Elt: Add->getOperand(i));
5537 const SCEV *Accum = getAddExpr(Ops);
5538
5539 // The runtime checks will not be valid if the step amount is
5540 // varying inside the loop.
5541 if (!isLoopInvariant(S: Accum, L))
5542 return std::nullopt;
5543
5544 // *** Part2: Create the predicates
5545
5546 // Analysis was successful: we have a phi-with-cast pattern for which we
5547 // can return an AddRec expression under the following predicates:
5548 //
5549 // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
5550 // fits within the truncated type (does not overflow) for i = 0 to n-1.
5551 // P2: An Equal predicate that guarantees that
5552 // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
5553 // P3: An Equal predicate that guarantees that
5554 // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
5555 //
5556 // As we next prove, the above predicates guarantee that:
5557 // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
5558 //
5559 //
5560 // More formally, we want to prove that:
5561 // Expr(i+1) = Start + (i+1) * Accum
5562 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
5563 //
5564 // Given that:
5565 // 1) Expr(0) = Start
5566 // 2) Expr(1) = Start + Accum
5567 // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
5568 // 3) Induction hypothesis (step i):
5569 // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
5570 //
5571 // Proof:
5572 // Expr(i+1) =
5573 // = Start + (i+1)*Accum
5574 // = (Start + i*Accum) + Accum
5575 // = Expr(i) + Accum
5576 // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
5577 // :: from step i
5578 //
5579 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
5580 //
5581 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
5582 // + (Ext ix (Trunc iy (Accum) to ix) to iy)
5583 // + Accum :: from P3
5584 //
5585 // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
5586 // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
5587 //
5588 // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
5589 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
5590 //
5591 // By induction, the same applies to all iterations 1<=i<n:
5592 //
5593
5594 // Create a truncated addrec for which we will add a no overflow check (P1).
5595 const SCEV *StartVal = getSCEV(V: StartValueV);
5596 const SCEV *PHISCEV =
5597 getAddRecExpr(Start: getTruncateExpr(Op: StartVal, Ty: TruncTy),
5598 Step: getTruncateExpr(Op: Accum, Ty: TruncTy), L, Flags: SCEV::FlagAnyWrap);
5599
5600 // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
5601 // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
5602 // will be constant.
5603 //
5604 // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
5605 // add P1.
5606 if (const auto *AR = dyn_cast<SCEVAddRecExpr>(Val: PHISCEV)) {
5607 SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
5608 Signed ? SCEVWrapPredicate::IncrementNSSW
5609 : SCEVWrapPredicate::IncrementNUSW;
5610 const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
5611 Predicates.push_back(Elt: AddRecPred);
5612 }
5613
5614 // Create the Equal Predicates P2,P3:
5615
5616 // It is possible that the predicates P2 and/or P3 are computable at
5617 // compile time due to StartVal and/or Accum being constants.
5618 // If either one is, then we can check that now and escape if either P2
5619 // or P3 is false.
5620
5621 // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
5622 // for each of StartVal and Accum
5623 auto getExtendedExpr = [&](const SCEV *Expr,
5624 bool CreateSignExtend) -> const SCEV * {
5625 assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
5626 const SCEV *TruncatedExpr = getTruncateExpr(Op: Expr, Ty: TruncTy);
5627 const SCEV *ExtendedExpr =
5628 CreateSignExtend ? getSignExtendExpr(Op: TruncatedExpr, Ty: Expr->getType())
5629 : getZeroExtendExpr(Op: TruncatedExpr, Ty: Expr->getType());
5630 return ExtendedExpr;
5631 };
5632
5633 // Given:
5634 // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
5635 // = getExtendedExpr(Expr)
5636 // Determine whether the predicate P: Expr == ExtendedExpr
5637 // is known to be false at compile time
5638 auto PredIsKnownFalse = [&](const SCEV *Expr,
5639 const SCEV *ExtendedExpr) -> bool {
5640 return Expr != ExtendedExpr &&
5641 isKnownPredicate(Pred: ICmpInst::ICMP_NE, LHS: Expr, RHS: ExtendedExpr);
5642 };
5643
5644 const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
5645 if (PredIsKnownFalse(StartVal, StartExtended)) {
5646 LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";);
5647 return std::nullopt;
5648 }
5649
5650 // The Step is always Signed (because the overflow checks are either
5651 // NSSW or NUSW)
5652 const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
5653 if (PredIsKnownFalse(Accum, AccumExtended)) {
5654 LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";);
5655 return std::nullopt;
5656 }
5657
5658 auto AppendPredicate = [&](const SCEV *Expr,
5659 const SCEV *ExtendedExpr) -> void {
5660 if (Expr != ExtendedExpr &&
5661 !isKnownPredicate(Pred: ICmpInst::ICMP_EQ, LHS: Expr, RHS: ExtendedExpr)) {
5662 const SCEVPredicate *Pred = getEqualPredicate(LHS: Expr, RHS: ExtendedExpr);
5663 LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred);
5664 Predicates.push_back(Elt: Pred);
5665 }
5666 };
5667
5668 AppendPredicate(StartVal, StartExtended);
5669 AppendPredicate(Accum, AccumExtended);
5670
5671 // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
5672 // which the casts had been folded away. The caller can rewrite SymbolicPHI
5673 // into NewAR if it will also add the runtime overflow checks specified in
5674 // Predicates.
5675 auto *NewAR = getAddRecExpr(Start: StartVal, Step: Accum, L, Flags: SCEV::FlagAnyWrap);
5676
5677 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
5678 std::make_pair(x&: NewAR, y&: Predicates);
5679 // Remember the result of the analysis for this SCEV at this locayyytion.
5680 PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
5681 return PredRewrite;
5682}
5683
5684std::optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
5685ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
5686 auto *PN = cast<PHINode>(Val: SymbolicPHI->getValue());
5687 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
5688 if (!L)
5689 return std::nullopt;
5690
5691 // Check to see if we already analyzed this PHI.
5692 auto I = PredicatedSCEVRewrites.find(Val: {SymbolicPHI, L});
5693 if (I != PredicatedSCEVRewrites.end()) {
5694 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
5695 I->second;
5696 // Analysis was done before and failed to create an AddRec:
5697 if (Rewrite.first == SymbolicPHI)
5698 return std::nullopt;
5699 // Analysis was done before and succeeded to create an AddRec under
5700 // a predicate:
5701 assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
5702 assert(!(Rewrite.second).empty() && "Expected to find Predicates");
5703 return Rewrite;
5704 }
5705
5706 std::optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
5707 Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
5708
5709 // Record in the cache that the analysis failed
5710 if (!Rewrite) {
5711 SmallVector<const SCEVPredicate *, 3> Predicates;
5712 PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
5713 return std::nullopt;
5714 }
5715
5716 return Rewrite;
5717}
5718
5719// FIXME: This utility is currently required because the Rewriter currently
5720// does not rewrite this expression:
5721// {0, +, (sext ix (trunc iy to ix) to iy)}
5722// into {0, +, %step},
5723// even when the following Equal predicate exists:
5724// "%step == (sext ix (trunc iy to ix) to iy)".
5725bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
5726 const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
5727 if (AR1 == AR2)
5728 return true;
5729
5730 auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
5731 if (Expr1 != Expr2 && !Preds->implies(N: SE.getEqualPredicate(LHS: Expr1, RHS: Expr2)) &&
5732 !Preds->implies(N: SE.getEqualPredicate(LHS: Expr2, RHS: Expr1)))
5733 return false;
5734 return true;
5735 };
5736
5737 if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
5738 !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
5739 return false;
5740 return true;
5741}
5742
5743/// A helper function for createAddRecFromPHI to handle simple cases.
5744///
5745/// This function tries to find an AddRec expression for the simplest (yet most
5746/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
5747/// If it fails, createAddRecFromPHI will use a more general, but slow,
5748/// technique for finding the AddRec expression.
5749const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
5750 Value *BEValueV,
5751 Value *StartValueV) {
5752 const Loop *L = LI.getLoopFor(BB: PN->getParent());
5753 assert(L && L->getHeader() == PN->getParent());
5754 assert(BEValueV && StartValueV);
5755
5756 auto BO = MatchBinaryOp(V: BEValueV, DL: getDataLayout(), AC, DT, CxtI: PN);
5757 if (!BO)
5758 return nullptr;
5759
5760 if (BO->Opcode != Instruction::Add)
5761 return nullptr;
5762
5763 const SCEV *Accum = nullptr;
5764 if (BO->LHS == PN && L->isLoopInvariant(V: BO->RHS))
5765 Accum = getSCEV(V: BO->RHS);
5766 else if (BO->RHS == PN && L->isLoopInvariant(V: BO->LHS))
5767 Accum = getSCEV(V: BO->LHS);
5768
5769 if (!Accum)
5770 return nullptr;
5771
5772 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5773 if (BO->IsNUW)
5774 Flags = setFlags(Flags, OnFlags: SCEV::FlagNUW);
5775 if (BO->IsNSW)
5776 Flags = setFlags(Flags, OnFlags: SCEV::FlagNSW);
5777
5778 const SCEV *StartVal = getSCEV(V: StartValueV);
5779 const SCEV *PHISCEV = getAddRecExpr(Start: StartVal, Step: Accum, L, Flags);
5780 insertValueToMap(V: PN, S: PHISCEV);
5781
5782 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Val: PHISCEV)) {
5783 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR),
5784 Flags: (SCEV::NoWrapFlags)(AR->getNoWrapFlags() |
5785 proveNoWrapViaConstantRanges(AR)));
5786 }
5787
5788 // We can add Flags to the post-inc expression only if we
5789 // know that it is *undefined behavior* for BEValueV to
5790 // overflow.
5791 if (auto *BEInst = dyn_cast<Instruction>(Val: BEValueV)) {
5792 assert(isLoopInvariant(Accum, L) &&
5793 "Accum is defined outside L, but is not invariant?");
5794 if (isAddRecNeverPoison(I: BEInst, L))
5795 (void)getAddRecExpr(Start: getAddExpr(LHS: StartVal, RHS: Accum), Step: Accum, L, Flags);
5796 }
5797
5798 return PHISCEV;
5799}
5800
5801const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
5802 const Loop *L = LI.getLoopFor(BB: PN->getParent());
5803 if (!L || L->getHeader() != PN->getParent())
5804 return nullptr;
5805
5806 // The loop may have multiple entrances or multiple exits; we can analyze
5807 // this phi as an addrec if it has a unique entry value and a unique
5808 // backedge value.
5809 Value *BEValueV = nullptr, *StartValueV = nullptr;
5810 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5811 Value *V = PN->getIncomingValue(i);
5812 if (L->contains(BB: PN->getIncomingBlock(i))) {
5813 if (!BEValueV) {
5814 BEValueV = V;
5815 } else if (BEValueV != V) {
5816 BEValueV = nullptr;
5817 break;
5818 }
5819 } else if (!StartValueV) {
5820 StartValueV = V;
5821 } else if (StartValueV != V) {
5822 StartValueV = nullptr;
5823 break;
5824 }
5825 }
5826 if (!BEValueV || !StartValueV)
5827 return nullptr;
5828
5829 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
5830 "PHI node already processed?");
5831
5832 // First, try to find AddRec expression without creating a fictituos symbolic
5833 // value for PN.
5834 if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
5835 return S;
5836
5837 // Handle PHI node value symbolically.
5838 const SCEV *SymbolicName = getUnknown(V: PN);
5839 insertValueToMap(V: PN, S: SymbolicName);
5840
5841 // Using this symbolic name for the PHI, analyze the value coming around
5842 // the back-edge.
5843 const SCEV *BEValue = getSCEV(V: BEValueV);
5844
5845 // NOTE: If BEValue is loop invariant, we know that the PHI node just
5846 // has a special value for the first iteration of the loop.
5847
5848 // If the value coming around the backedge is an add with the symbolic
5849 // value we just inserted, then we found a simple induction variable!
5850 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Val: BEValue)) {
5851 // If there is a single occurrence of the symbolic value, replace it
5852 // with a recurrence.
5853 unsigned FoundIndex = Add->getNumOperands();
5854 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5855 if (Add->getOperand(i) == SymbolicName)
5856 if (FoundIndex == e) {
5857 FoundIndex = i;
5858 break;
5859 }
5860
5861 if (FoundIndex != Add->getNumOperands()) {
5862 // Create an add with everything but the specified operand.
5863 SmallVector<const SCEV *, 8> Ops;
5864 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5865 if (i != FoundIndex)
5866 Ops.push_back(Elt: SCEVBackedgeConditionFolder::rewrite(S: Add->getOperand(i),
5867 L, SE&: *this));
5868 const SCEV *Accum = getAddExpr(Ops);
5869
5870 // This is not a valid addrec if the step amount is varying each
5871 // loop iteration, but is not itself an addrec in this loop.
5872 if (isLoopInvariant(S: Accum, L) ||
5873 (isa<SCEVAddRecExpr>(Val: Accum) &&
5874 cast<SCEVAddRecExpr>(Val: Accum)->getLoop() == L)) {
5875 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5876
5877 if (auto BO = MatchBinaryOp(V: BEValueV, DL: getDataLayout(), AC, DT, CxtI: PN)) {
5878 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
5879 if (BO->IsNUW)
5880 Flags = setFlags(Flags, OnFlags: SCEV::FlagNUW);
5881 if (BO->IsNSW)
5882 Flags = setFlags(Flags, OnFlags: SCEV::FlagNSW);
5883 }
5884 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(Val: BEValueV)) {
5885 if (GEP->getOperand(i_nocapture: 0) == PN) {
5886 GEPNoWrapFlags NW = GEP->getNoWrapFlags();
5887 // If the increment has any nowrap flags, then we know the address
5888 // space cannot be wrapped around.
5889 if (NW != GEPNoWrapFlags::none())
5890 Flags = setFlags(Flags, OnFlags: SCEV::FlagNW);
5891 // If the GEP is nuw or nusw with non-negative offset, we know that
5892 // no unsigned wrap occurs. We cannot set the nsw flag as only the
5893 // offset is treated as signed, while the base is unsigned.
5894 if (NW.hasNoUnsignedWrap() ||
5895 (NW.hasNoUnsignedSignedWrap() && isKnownNonNegative(S: Accum)))
5896 Flags = setFlags(Flags, OnFlags: SCEV::FlagNUW);
5897 }
5898
5899 // We cannot transfer nuw and nsw flags from subtraction
5900 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
5901 // for instance.
5902 }
5903
5904 const SCEV *StartVal = getSCEV(V: StartValueV);
5905 const SCEV *PHISCEV = getAddRecExpr(Start: StartVal, Step: Accum, L, Flags);
5906
5907 // Okay, for the entire analysis of this edge we assumed the PHI
5908 // to be symbolic. We now need to go back and purge all of the
5909 // entries for the scalars that use the symbolic expression.
5910 forgetMemoizedResults(SCEVs: SymbolicName);
5911 insertValueToMap(V: PN, S: PHISCEV);
5912
5913 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Val: PHISCEV)) {
5914 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR),
5915 Flags: (SCEV::NoWrapFlags)(AR->getNoWrapFlags() |
5916 proveNoWrapViaConstantRanges(AR)));
5917 }
5918
5919 // We can add Flags to the post-inc expression only if we
5920 // know that it is *undefined behavior* for BEValueV to
5921 // overflow.
5922 if (auto *BEInst = dyn_cast<Instruction>(Val: BEValueV))
5923 if (isLoopInvariant(S: Accum, L) && isAddRecNeverPoison(I: BEInst, L))
5924 (void)getAddRecExpr(Start: getAddExpr(LHS: StartVal, RHS: Accum), Step: Accum, L, Flags);
5925
5926 return PHISCEV;
5927 }
5928 }
5929 } else {
5930 // Otherwise, this could be a loop like this:
5931 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
5932 // In this case, j = {1,+,1} and BEValue is j.
5933 // Because the other in-value of i (0) fits the evolution of BEValue
5934 // i really is an addrec evolution.
5935 //
5936 // We can generalize this saying that i is the shifted value of BEValue
5937 // by one iteration:
5938 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
5939 const SCEV *Shifted = SCEVShiftRewriter::rewrite(S: BEValue, L, SE&: *this);
5940 const SCEV *Start = SCEVInitRewriter::rewrite(S: Shifted, L, SE&: *this, IgnoreOtherLoops: false);
5941 if (Shifted != getCouldNotCompute() &&
5942 Start != getCouldNotCompute()) {
5943 const SCEV *StartVal = getSCEV(V: StartValueV);
5944 if (Start == StartVal) {
5945 // Okay, for the entire analysis of this edge we assumed the PHI
5946 // to be symbolic. We now need to go back and purge all of the
5947 // entries for the scalars that use the symbolic expression.
5948 forgetMemoizedResults(SCEVs: SymbolicName);
5949 insertValueToMap(V: PN, S: Shifted);
5950 return Shifted;
5951 }
5952 }
5953 }
5954
5955 // Remove the temporary PHI node SCEV that has been inserted while intending
5956 // to create an AddRecExpr for this PHI node. We can not keep this temporary
5957 // as it will prevent later (possibly simpler) SCEV expressions to be added
5958 // to the ValueExprMap.
5959 eraseValueFromMap(V: PN);
5960
5961 return nullptr;
5962}
5963
5964// Try to match a control flow sequence that branches out at BI and merges back
5965// at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
5966// match.
5967static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
5968 Value *&C, Value *&LHS, Value *&RHS) {
5969 C = BI->getCondition();
5970
5971 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(i: 0));
5972 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(i: 1));
5973
5974 if (!LeftEdge.isSingleEdge())
5975 return false;
5976
5977 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
5978
5979 Use &LeftUse = Merge->getOperandUse(i: 0);
5980 Use &RightUse = Merge->getOperandUse(i: 1);
5981
5982 if (DT.dominates(BBE: LeftEdge, U: LeftUse) && DT.dominates(BBE: RightEdge, U: RightUse)) {
5983 LHS = LeftUse;
5984 RHS = RightUse;
5985 return true;
5986 }
5987
5988 if (DT.dominates(BBE: LeftEdge, U: RightUse) && DT.dominates(BBE: RightEdge, U: LeftUse)) {
5989 LHS = RightUse;
5990 RHS = LeftUse;
5991 return true;
5992 }
5993
5994 return false;
5995}
5996
5997const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
5998 auto IsReachable =
5999 [&](BasicBlock *BB) { return DT.isReachableFromEntry(A: BB); };
6000 if (PN->getNumIncomingValues() == 2 && all_of(Range: PN->blocks(), P: IsReachable)) {
6001 // Try to match
6002 //
6003 // br %cond, label %left, label %right
6004 // left:
6005 // br label %merge
6006 // right:
6007 // br label %merge
6008 // merge:
6009 // V = phi [ %x, %left ], [ %y, %right ]
6010 //
6011 // as "select %cond, %x, %y"
6012
6013 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
6014 assert(IDom && "At least the entry block should dominate PN");
6015
6016 auto *BI = dyn_cast<BranchInst>(Val: IDom->getTerminator());
6017 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
6018
6019 if (BI && BI->isConditional() &&
6020 BrPHIToSelect(DT, BI, Merge: PN, C&: Cond, LHS, RHS) &&
6021 properlyDominates(S: getSCEV(V: LHS), BB: PN->getParent()) &&
6022 properlyDominates(S: getSCEV(V: RHS), BB: PN->getParent()))
6023 return createNodeForSelectOrPHI(V: PN, Cond, TrueVal: LHS, FalseVal: RHS);
6024 }
6025
6026 return nullptr;
6027}
6028
6029const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
6030 if (const SCEV *S = createAddRecFromPHI(PN))
6031 return S;
6032
6033 if (Value *V = simplifyInstruction(I: PN, Q: {getDataLayout(), &TLI, &DT, &AC}))
6034 return getSCEV(V);
6035
6036 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
6037 return S;
6038
6039 // If it's not a loop phi, we can't handle it yet.
6040 return getUnknown(V: PN);
6041}
6042
6043bool SCEVMinMaxExprContains(const SCEV *Root, const SCEV *OperandToFind,
6044 SCEVTypes RootKind) {
6045 struct FindClosure {
6046 const SCEV *OperandToFind;
6047 const SCEVTypes RootKind; // Must be a sequential min/max expression.
6048 const SCEVTypes NonSequentialRootKind; // Non-seq variant of RootKind.
6049
6050 bool Found = false;
6051
6052 bool canRecurseInto(SCEVTypes Kind) const {
6053 // We can only recurse into the SCEV expression of the same effective type
6054 // as the type of our root SCEV expression, and into zero-extensions.
6055 return RootKind == Kind || NonSequentialRootKind == Kind ||
6056 scZeroExtend == Kind;
6057 };
6058
6059 FindClosure(const SCEV *OperandToFind, SCEVTypes RootKind)
6060 : OperandToFind(OperandToFind), RootKind(RootKind),
6061 NonSequentialRootKind(
6062 SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(
6063 Ty: RootKind)) {}
6064
6065 bool follow(const SCEV *S) {
6066 Found = S == OperandToFind;
6067
6068 return !isDone() && canRecurseInto(Kind: S->getSCEVType());
6069 }
6070
6071 bool isDone() const { return Found; }
6072 };
6073
6074 FindClosure FC(OperandToFind, RootKind);
6075 visitAll(Root, Visitor&: FC);
6076 return FC.Found;
6077}
6078
6079std::optional<const SCEV *>
6080ScalarEvolution::createNodeForSelectOrPHIInstWithICmpInstCond(Type *Ty,
6081 ICmpInst *Cond,
6082 Value *TrueVal,
6083 Value *FalseVal) {
6084 // Try to match some simple smax or umax patterns.
6085 auto *ICI = Cond;
6086
6087 Value *LHS = ICI->getOperand(i_nocapture: 0);
6088 Value *RHS = ICI->getOperand(i_nocapture: 1);
6089
6090 switch (ICI->getPredicate()) {
6091 case ICmpInst::ICMP_SLT:
6092 case ICmpInst::ICMP_SLE:
6093 case ICmpInst::ICMP_ULT:
6094 case ICmpInst::ICMP_ULE:
6095 std::swap(a&: LHS, b&: RHS);
6096 [[fallthrough]];
6097 case ICmpInst::ICMP_SGT:
6098 case ICmpInst::ICMP_SGE:
6099 case ICmpInst::ICMP_UGT:
6100 case ICmpInst::ICMP_UGE:
6101 // a > b ? a+x : b+x -> max(a, b)+x
6102 // a > b ? b+x : a+x -> min(a, b)+x
6103 if (getTypeSizeInBits(Ty: LHS->getType()) <= getTypeSizeInBits(Ty)) {
6104 bool Signed = ICI->isSigned();
6105 const SCEV *LA = getSCEV(V: TrueVal);
6106 const SCEV *RA = getSCEV(V: FalseVal);
6107 const SCEV *LS = getSCEV(V: LHS);
6108 const SCEV *RS = getSCEV(V: RHS);
6109 if (LA->getType()->isPointerTy()) {
6110 // FIXME: Handle cases where LS/RS are pointers not equal to LA/RA.
6111 // Need to make sure we can't produce weird expressions involving
6112 // negated pointers.
6113 if (LA == LS && RA == RS)
6114 return Signed ? getSMaxExpr(LHS: LS, RHS: RS) : getUMaxExpr(LHS: LS, RHS: RS);
6115 if (LA == RS && RA == LS)
6116 return Signed ? getSMinExpr(LHS: LS, RHS: RS) : getUMinExpr(LHS: LS, RHS: RS);
6117 }
6118 auto CoerceOperand = [&](const SCEV *Op) -> const SCEV * {
6119 if (Op->getType()->isPointerTy()) {
6120 Op = getLosslessPtrToIntExpr(Op);
6121 if (isa<SCEVCouldNotCompute>(Val: Op))
6122 return Op;
6123 }
6124 if (Signed)
6125 Op = getNoopOrSignExtend(V: Op, Ty);
6126 else
6127 Op = getNoopOrZeroExtend(V: Op, Ty);
6128 return Op;
6129 };
6130 LS = CoerceOperand(LS);
6131 RS = CoerceOperand(RS);
6132 if (isa<SCEVCouldNotCompute>(Val: LS) || isa<SCEVCouldNotCompute>(Val: RS))
6133 break;
6134 const SCEV *LDiff = getMinusSCEV(LHS: LA, RHS: LS);
6135 const SCEV *RDiff = getMinusSCEV(LHS: RA, RHS: RS);
6136 if (LDiff == RDiff)
6137 return getAddExpr(LHS: Signed ? getSMaxExpr(LHS: LS, RHS: RS) : getUMaxExpr(LHS: LS, RHS: RS),
6138 RHS: LDiff);
6139 LDiff = getMinusSCEV(LHS: LA, RHS: RS);
6140 RDiff = getMinusSCEV(LHS: RA, RHS: LS);
6141 if (LDiff == RDiff)
6142 return getAddExpr(LHS: Signed ? getSMinExpr(LHS: LS, RHS: RS) : getUMinExpr(LHS: LS, RHS: RS),
6143 RHS: LDiff);
6144 }
6145 break;
6146 case ICmpInst::ICMP_NE:
6147 // x != 0 ? x+y : C+y -> x == 0 ? C+y : x+y
6148 std::swap(a&: TrueVal, b&: FalseVal);
6149 [[fallthrough]];
6150 case ICmpInst::ICMP_EQ:
6151 // x == 0 ? C+y : x+y -> umax(x, C)+y iff C u<= 1
6152 if (getTypeSizeInBits(Ty: LHS->getType()) <= getTypeSizeInBits(Ty) &&
6153 isa<ConstantInt>(Val: RHS) && cast<ConstantInt>(Val: RHS)->isZero()) {
6154 const SCEV *X = getNoopOrZeroExtend(V: getSCEV(V: LHS), Ty);
6155 const SCEV *TrueValExpr = getSCEV(V: TrueVal); // C+y
6156 const SCEV *FalseValExpr = getSCEV(V: FalseVal); // x+y
6157 const SCEV *Y = getMinusSCEV(LHS: FalseValExpr, RHS: X); // y = (x+y)-x
6158 const SCEV *C = getMinusSCEV(LHS: TrueValExpr, RHS: Y); // C = (C+y)-y
6159 if (isa<SCEVConstant>(Val: C) && cast<SCEVConstant>(Val: C)->getAPInt().ule(RHS: 1))
6160 return getAddExpr(LHS: getUMaxExpr(LHS: X, RHS: C), RHS: Y);
6161 }
6162 // x == 0 ? 0 : umin (..., x, ...) -> umin_seq(x, umin (...))
6163 // x == 0 ? 0 : umin_seq(..., x, ...) -> umin_seq(x, umin_seq(...))
6164 // x == 0 ? 0 : umin (..., umin_seq(..., x, ...), ...)
6165 // -> umin_seq(x, umin (..., umin_seq(...), ...))
6166 if (isa<ConstantInt>(Val: RHS) && cast<ConstantInt>(Val: RHS)->isZero() &&
6167 isa<ConstantInt>(Val: TrueVal) && cast<ConstantInt>(Val: TrueVal)->isZero()) {
6168 const SCEV *X = getSCEV(V: LHS);
6169 while (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(Val: X))
6170 X = ZExt->getOperand();
6171 if (getTypeSizeInBits(Ty: X->getType()) <= getTypeSizeInBits(Ty)) {
6172 const SCEV *FalseValExpr = getSCEV(V: FalseVal);
6173 if (SCEVMinMaxExprContains(Root: FalseValExpr, OperandToFind: X, RootKind: scSequentialUMinExpr))
6174 return getUMinExpr(LHS: getNoopOrZeroExtend(V: X, Ty), RHS: FalseValExpr,
6175 /*Sequential=*/true);
6176 }
6177 }
6178 break;
6179 default:
6180 break;
6181 }
6182
6183 return std::nullopt;
6184}
6185
6186static std::optional<const SCEV *>
6187createNodeForSelectViaUMinSeq(ScalarEvolution *SE, const SCEV *CondExpr,
6188 const SCEV *TrueExpr, const SCEV *FalseExpr) {
6189 assert(CondExpr->getType()->isIntegerTy(1) &&
6190 TrueExpr->getType() == FalseExpr->getType() &&
6191 TrueExpr->getType()->isIntegerTy(1) &&
6192 "Unexpected operands of a select.");
6193
6194 // i1 cond ? i1 x : i1 C --> C + (i1 cond ? (i1 x - i1 C) : i1 0)
6195 // --> C + (umin_seq cond, x - C)
6196 //
6197 // i1 cond ? i1 C : i1 x --> C + (i1 cond ? i1 0 : (i1 x - i1 C))
6198 // --> C + (i1 ~cond ? (i1 x - i1 C) : i1 0)
6199 // --> C + (umin_seq ~cond, x - C)
6200
6201 // FIXME: while we can't legally model the case where both of the hands
6202 // are fully variable, we only require that the *difference* is constant.
6203 if (!isa<SCEVConstant>(Val: TrueExpr) && !isa<SCEVConstant>(Val: FalseExpr))
6204 return std::nullopt;
6205
6206 const SCEV *X, *C;
6207 if (isa<SCEVConstant>(Val: TrueExpr)) {
6208 CondExpr = SE->getNotSCEV(V: CondExpr);
6209 X = FalseExpr;
6210 C = TrueExpr;
6211 } else {
6212 X = TrueExpr;
6213 C = FalseExpr;
6214 }
6215 return SE->getAddExpr(LHS: C, RHS: SE->getUMinExpr(LHS: CondExpr, RHS: SE->getMinusSCEV(LHS: X, RHS: C),
6216 /*Sequential=*/true));
6217}
6218
6219static std::optional<const SCEV *>
6220createNodeForSelectViaUMinSeq(ScalarEvolution *SE, Value *Cond, Value *TrueVal,
6221 Value *FalseVal) {
6222 if (!isa<ConstantInt>(Val: TrueVal) && !isa<ConstantInt>(Val: FalseVal))
6223 return std::nullopt;
6224
6225 const auto *SECond = SE->getSCEV(V: Cond);
6226 const auto *SETrue = SE->getSCEV(V: TrueVal);
6227 const auto *SEFalse = SE->getSCEV(V: FalseVal);
6228 return createNodeForSelectViaUMinSeq(SE, CondExpr: SECond, TrueExpr: SETrue, FalseExpr: SEFalse);
6229}
6230
6231const SCEV *ScalarEvolution::createNodeForSelectOrPHIViaUMinSeq(
6232 Value *V, Value *Cond, Value *TrueVal, Value *FalseVal) {
6233 assert(Cond->getType()->isIntegerTy(1) && "Select condition is not an i1?");
6234 assert(TrueVal->getType() == FalseVal->getType() &&
6235 V->getType() == TrueVal->getType() &&
6236 "Types of select hands and of the result must match.");
6237
6238 // For now, only deal with i1-typed `select`s.
6239 if (!V->getType()->isIntegerTy(Bitwidth: 1))
6240 return getUnknown(V);
6241
6242 if (std::optional<const SCEV *> S =
6243 createNodeForSelectViaUMinSeq(SE: this, Cond, TrueVal, FalseVal))
6244 return *S;
6245
6246 return getUnknown(V);
6247}
6248
6249const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Value *V, Value *Cond,
6250 Value *TrueVal,
6251 Value *FalseVal) {
6252 // Handle "constant" branch or select. This can occur for instance when a
6253 // loop pass transforms an inner loop and moves on to process the outer loop.
6254 if (auto *CI = dyn_cast<ConstantInt>(Val: Cond))
6255 return getSCEV(V: CI->isOne() ? TrueVal : FalseVal);
6256
6257 if (auto *I = dyn_cast<Instruction>(Val: V)) {
6258 if (auto *ICI = dyn_cast<ICmpInst>(Val: Cond)) {
6259 if (std::optional<const SCEV *> S =
6260 createNodeForSelectOrPHIInstWithICmpInstCond(Ty: I->getType(), Cond: ICI,
6261 TrueVal, FalseVal))
6262 return *S;
6263 }
6264 }
6265
6266 return createNodeForSelectOrPHIViaUMinSeq(V, Cond, TrueVal, FalseVal);
6267}
6268
6269/// Expand GEP instructions into add and multiply operations. This allows them
6270/// to be analyzed by regular SCEV code.
6271const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
6272 assert(GEP->getSourceElementType()->isSized() &&
6273 "GEP source element type must be sized");
6274
6275 SmallVector<const SCEV *, 4> IndexExprs;
6276 for (Value *Index : GEP->indices())
6277 IndexExprs.push_back(Elt: getSCEV(V: Index));
6278 return getGEPExpr(GEP, IndexExprs);
6279}
6280
6281APInt ScalarEvolution::getConstantMultipleImpl(const SCEV *S) {
6282 uint64_t BitWidth = getTypeSizeInBits(Ty: S->getType());
6283 auto GetShiftedByZeros = [BitWidth](uint32_t TrailingZeros) {
6284 return TrailingZeros >= BitWidth
6285 ? APInt::getZero(numBits: BitWidth)
6286 : APInt::getOneBitSet(numBits: BitWidth, BitNo: TrailingZeros);
6287 };
6288 auto GetGCDMultiple = [this](const SCEVNAryExpr *N) {
6289 // The result is GCD of all operands results.
6290 APInt Res = getConstantMultiple(S: N->getOperand(i: 0));
6291 for (unsigned I = 1, E = N->getNumOperands(); I < E && Res != 1; ++I)
6292 Res = APIntOps::GreatestCommonDivisor(
6293 A: Res, B: getConstantMultiple(S: N->getOperand(i: I)));
6294 return Res;
6295 };
6296
6297 switch (S->getSCEVType()) {
6298 case scConstant:
6299 return cast<SCEVConstant>(Val: S)->getAPInt();
6300 case scPtrToInt:
6301 return getConstantMultiple(S: cast<SCEVPtrToIntExpr>(Val: S)->getOperand());
6302 case scUDivExpr:
6303 case scVScale:
6304 return APInt(BitWidth, 1);
6305 case scTruncate: {
6306 // Only multiples that are a power of 2 will hold after truncation.
6307 const SCEVTruncateExpr *T = cast<SCEVTruncateExpr>(Val: S);
6308 uint32_t TZ = getMinTrailingZeros(S: T->getOperand());
6309 return GetShiftedByZeros(TZ);
6310 }
6311 case scZeroExtend: {
6312 const SCEVZeroExtendExpr *Z = cast<SCEVZeroExtendExpr>(Val: S);
6313 return getConstantMultiple(S: Z->getOperand()).zext(width: BitWidth);
6314 }
6315 case scSignExtend: {
6316 const SCEVSignExtendExpr *E = cast<SCEVSignExtendExpr>(Val: S);
6317 return getConstantMultiple(S: E->getOperand()).sext(width: BitWidth);
6318 }
6319 case scMulExpr: {
6320 const SCEVMulExpr *M = cast<SCEVMulExpr>(Val: S);
6321 if (M->hasNoUnsignedWrap()) {
6322 // The result is the product of all operand results.
6323 APInt Res = getConstantMultiple(S: M->getOperand(i: 0));
6324 for (const SCEV *Operand : M->operands().drop_front())
6325 Res = Res * getConstantMultiple(S: Operand);
6326 return Res;
6327 }
6328
6329 // If there are no wrap guarentees, find the trailing zeros, which is the
6330 // sum of trailing zeros for all its operands.
6331 uint32_t TZ = 0;
6332 for (const SCEV *Operand : M->operands())
6333 TZ += getMinTrailingZeros(S: Operand);
6334 return GetShiftedByZeros(TZ);
6335 }
6336 case scAddExpr:
6337 case scAddRecExpr: {
6338 const SCEVNAryExpr *N = cast<SCEVNAryExpr>(Val: S);
6339 if (N->hasNoUnsignedWrap())
6340 return GetGCDMultiple(N);
6341 // Find the trailing bits, which is the minimum of its operands.
6342 uint32_t TZ = getMinTrailingZeros(S: N->getOperand(i: 0));
6343 for (const SCEV *Operand : N->operands().drop_front())
6344 TZ = std::min(a: TZ, b: getMinTrailingZeros(S: Operand));
6345 return GetShiftedByZeros(TZ);
6346 }
6347 case scUMaxExpr:
6348 case scSMaxExpr:
6349 case scUMinExpr:
6350 case scSMinExpr:
6351 case scSequentialUMinExpr:
6352 return GetGCDMultiple(cast<SCEVNAryExpr>(Val: S));
6353 case scUnknown: {
6354 // ask ValueTracking for known bits
6355 const SCEVUnknown *U = cast<SCEVUnknown>(Val: S);
6356 unsigned Known =
6357 computeKnownBits(V: U->getValue(), DL: getDataLayout(), Depth: 0, AC: &AC, CxtI: nullptr, DT: &DT)
6358 .countMinTrailingZeros();
6359 return GetShiftedByZeros(Known);
6360 }
6361 case scCouldNotCompute:
6362 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6363 }
6364 llvm_unreachable("Unknown SCEV kind!");
6365}
6366
6367APInt ScalarEvolution::getConstantMultiple(const SCEV *S) {
6368 auto I = ConstantMultipleCache.find(Val: S);
6369 if (I != ConstantMultipleCache.end())
6370 return I->second;
6371
6372 APInt Result = getConstantMultipleImpl(S);
6373 auto InsertPair = ConstantMultipleCache.insert(KV: {S, Result});
6374 assert(InsertPair.second && "Should insert a new key");
6375 return InsertPair.first->second;
6376}
6377
6378APInt ScalarEvolution::getNonZeroConstantMultiple(const SCEV *S) {
6379 APInt Multiple = getConstantMultiple(S);
6380 return Multiple == 0 ? APInt(Multiple.getBitWidth(), 1) : Multiple;
6381}
6382
6383uint32_t ScalarEvolution::getMinTrailingZeros(const SCEV *S) {
6384 return std::min(a: getConstantMultiple(S).countTrailingZeros(),
6385 b: (unsigned)getTypeSizeInBits(Ty: S->getType()));
6386}
6387
6388/// Helper method to assign a range to V from metadata present in the IR.
6389static std::optional<ConstantRange> GetRangeFromMetadata(Value *V) {
6390 if (Instruction *I = dyn_cast<Instruction>(Val: V)) {
6391 if (MDNode *MD = I->getMetadata(KindID: LLVMContext::MD_range))
6392 return getConstantRangeFromMetadata(RangeMD: *MD);
6393 if (const auto *CB = dyn_cast<CallBase>(Val: V))
6394 if (std::optional<ConstantRange> Range = CB->getRange())
6395 return Range;
6396 }
6397 if (auto *A = dyn_cast<Argument>(Val: V))
6398 if (std::optional<ConstantRange> Range = A->getRange())
6399 return Range;
6400
6401 return std::nullopt;
6402}
6403
6404void ScalarEvolution::setNoWrapFlags(SCEVAddRecExpr *AddRec,
6405 SCEV::NoWrapFlags Flags) {
6406 if (AddRec->getNoWrapFlags(Mask: Flags) != Flags) {
6407 AddRec->setNoWrapFlags(Flags);
6408 UnsignedRanges.erase(Val: AddRec);
6409 SignedRanges.erase(Val: AddRec);
6410 ConstantMultipleCache.erase(Val: AddRec);
6411 }
6412}
6413
6414ConstantRange ScalarEvolution::
6415getRangeForUnknownRecurrence(const SCEVUnknown *U) {
6416 const DataLayout &DL = getDataLayout();
6417
6418 unsigned BitWidth = getTypeSizeInBits(Ty: U->getType());
6419 const ConstantRange FullSet(BitWidth, /*isFullSet=*/true);
6420
6421 // Match a simple recurrence of the form: <start, ShiftOp, Step>, and then
6422 // use information about the trip count to improve our available range. Note
6423 // that the trip count independent cases are already handled by known bits.
6424 // WARNING: The definition of recurrence used here is subtly different than
6425 // the one used by AddRec (and thus most of this file). Step is allowed to
6426 // be arbitrarily loop varying here, where AddRec allows only loop invariant
6427 // and other addrecs in the same loop (for non-affine addrecs). The code
6428 // below intentionally handles the case where step is not loop invariant.
6429 auto *P = dyn_cast<PHINode>(Val: U->getValue());
6430 if (!P)
6431 return FullSet;
6432
6433 // Make sure that no Phi input comes from an unreachable block. Otherwise,
6434 // even the values that are not available in these blocks may come from them,
6435 // and this leads to false-positive recurrence test.
6436 for (auto *Pred : predecessors(BB: P->getParent()))
6437 if (!DT.isReachableFromEntry(A: Pred))
6438 return FullSet;
6439
6440 BinaryOperator *BO;
6441 Value *Start, *Step;
6442 if (!matchSimpleRecurrence(P, BO, Start, Step))
6443 return FullSet;
6444
6445 // If we found a recurrence in reachable code, we must be in a loop. Note
6446 // that BO might be in some subloop of L, and that's completely okay.
6447 auto *L = LI.getLoopFor(BB: P->getParent());
6448 assert(L && L->getHeader() == P->getParent());
6449 if (!L->contains(BB: BO->getParent()))
6450 // NOTE: This bailout should be an assert instead. However, asserting
6451 // the condition here exposes a case where LoopFusion is querying SCEV
6452 // with malformed loop information during the midst of the transform.
6453 // There doesn't appear to be an obvious fix, so for the moment bailout
6454 // until the caller issue can be fixed. PR49566 tracks the bug.
6455 return FullSet;
6456
6457 // TODO: Extend to other opcodes such as mul, and div
6458 switch (BO->getOpcode()) {
6459 default:
6460 return FullSet;
6461 case Instruction::AShr:
6462 case Instruction::LShr:
6463 case Instruction::Shl:
6464 break;
6465 };
6466
6467 if (BO->getOperand(i_nocapture: 0) != P)
6468 // TODO: Handle the power function forms some day.
6469 return FullSet;
6470
6471 unsigned TC = getSmallConstantMaxTripCount(L);
6472 if (!TC || TC >= BitWidth)
6473 return FullSet;
6474
6475 auto KnownStart = computeKnownBits(V: Start, DL, Depth: 0, AC: &AC, CxtI: nullptr, DT: &DT);
6476 auto KnownStep = computeKnownBits(V: Step, DL, Depth: 0, AC: &AC, CxtI: nullptr, DT: &DT);
6477 assert(KnownStart.getBitWidth() == BitWidth &&
6478 KnownStep.getBitWidth() == BitWidth);
6479
6480 // Compute total shift amount, being careful of overflow and bitwidths.
6481 auto MaxShiftAmt = KnownStep.getMaxValue();
6482 APInt TCAP(BitWidth, TC-1);
6483 bool Overflow = false;
6484 auto TotalShift = MaxShiftAmt.umul_ov(RHS: TCAP, Overflow);
6485 if (Overflow)
6486 return FullSet;
6487
6488 switch (BO->getOpcode()) {
6489 default:
6490 llvm_unreachable("filtered out above");
6491 case Instruction::AShr: {
6492 // For each ashr, three cases:
6493 // shift = 0 => unchanged value
6494 // saturation => 0 or -1
6495 // other => a value closer to zero (of the same sign)
6496 // Thus, the end value is closer to zero than the start.
6497 auto KnownEnd = KnownBits::ashr(LHS: KnownStart,
6498 RHS: KnownBits::makeConstant(C: TotalShift));
6499 if (KnownStart.isNonNegative())
6500 // Analogous to lshr (simply not yet canonicalized)
6501 return ConstantRange::getNonEmpty(Lower: KnownEnd.getMinValue(),
6502 Upper: KnownStart.getMaxValue() + 1);
6503 if (KnownStart.isNegative())
6504 // End >=u Start && End <=s Start
6505 return ConstantRange::getNonEmpty(Lower: KnownStart.getMinValue(),
6506 Upper: KnownEnd.getMaxValue() + 1);
6507 break;
6508 }
6509 case Instruction::LShr: {
6510 // For each lshr, three cases:
6511 // shift = 0 => unchanged value
6512 // saturation => 0
6513 // other => a smaller positive number
6514 // Thus, the low end of the unsigned range is the last value produced.
6515 auto KnownEnd = KnownBits::lshr(LHS: KnownStart,
6516 RHS: KnownBits::makeConstant(C: TotalShift));
6517 return ConstantRange::getNonEmpty(Lower: KnownEnd.getMinValue(),
6518 Upper: KnownStart.getMaxValue() + 1);
6519 }
6520 case Instruction::Shl: {
6521 // Iff no bits are shifted out, value increases on every shift.
6522 auto KnownEnd = KnownBits::shl(LHS: KnownStart,
6523 RHS: KnownBits::makeConstant(C: TotalShift));
6524 if (TotalShift.ult(RHS: KnownStart.countMinLeadingZeros()))
6525 return ConstantRange(KnownStart.getMinValue(),
6526 KnownEnd.getMaxValue() + 1);
6527 break;
6528 }
6529 };
6530 return FullSet;
6531}
6532
6533const ConstantRange &
6534ScalarEvolution::getRangeRefIter(const SCEV *S,
6535 ScalarEvolution::RangeSignHint SignHint) {
6536 DenseMap<const SCEV *, ConstantRange> &Cache =
6537 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
6538 : SignedRanges;
6539 SmallVector<const SCEV *> WorkList;
6540 SmallPtrSet<const SCEV *, 8> Seen;
6541
6542 // Add Expr to the worklist, if Expr is either an N-ary expression or a
6543 // SCEVUnknown PHI node.
6544 auto AddToWorklist = [&WorkList, &Seen, &Cache](const SCEV *Expr) {
6545 if (!Seen.insert(Ptr: Expr).second)
6546 return;
6547 if (Cache.contains(Val: Expr))
6548 return;
6549 switch (Expr->getSCEVType()) {
6550 case scUnknown:
6551 if (!isa<PHINode>(Val: cast<SCEVUnknown>(Val: Expr)->getValue()))
6552 break;
6553 [[fallthrough]];
6554 case scConstant:
6555 case scVScale:
6556 case scTruncate:
6557 case scZeroExtend:
6558 case scSignExtend:
6559 case scPtrToInt:
6560 case scAddExpr:
6561 case scMulExpr:
6562 case scUDivExpr:
6563 case scAddRecExpr:
6564 case scUMaxExpr:
6565 case scSMaxExpr:
6566 case scUMinExpr:
6567 case scSMinExpr:
6568 case scSequentialUMinExpr:
6569 WorkList.push_back(Elt: Expr);
6570 break;
6571 case scCouldNotCompute:
6572 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6573 }
6574 };
6575 AddToWorklist(S);
6576
6577 // Build worklist by queuing operands of N-ary expressions and phi nodes.
6578 for (unsigned I = 0; I != WorkList.size(); ++I) {
6579 const SCEV *P = WorkList[I];
6580 auto *UnknownS = dyn_cast<SCEVUnknown>(Val: P);
6581 // If it is not a `SCEVUnknown`, just recurse into operands.
6582 if (!UnknownS) {
6583 for (const SCEV *Op : P->operands())
6584 AddToWorklist(Op);
6585 continue;
6586 }
6587 // `SCEVUnknown`'s require special treatment.
6588 if (const PHINode *P = dyn_cast<PHINode>(Val: UnknownS->getValue())) {
6589 if (!PendingPhiRangesIter.insert(Ptr: P).second)
6590 continue;
6591 for (auto &Op : reverse(C: P->operands()))
6592 AddToWorklist(getSCEV(V: Op));
6593 }
6594 }
6595
6596 if (!WorkList.empty()) {
6597 // Use getRangeRef to compute ranges for items in the worklist in reverse
6598 // order. This will force ranges for earlier operands to be computed before
6599 // their users in most cases.
6600 for (const SCEV *P : reverse(C: drop_begin(RangeOrContainer&: WorkList))) {
6601 getRangeRef(S: P, Hint: SignHint);
6602
6603 if (auto *UnknownS = dyn_cast<SCEVUnknown>(Val: P))
6604 if (const PHINode *P = dyn_cast<PHINode>(Val: UnknownS->getValue()))
6605 PendingPhiRangesIter.erase(Ptr: P);
6606 }
6607 }
6608
6609 return getRangeRef(S, Hint: SignHint, Depth: 0);
6610}
6611
6612/// Determine the range for a particular SCEV. If SignHint is
6613/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
6614/// with a "cleaner" unsigned (resp. signed) representation.
6615const ConstantRange &ScalarEvolution::getRangeRef(
6616 const SCEV *S, ScalarEvolution::RangeSignHint SignHint, unsigned Depth) {
6617 DenseMap<const SCEV *, ConstantRange> &Cache =
6618 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
6619 : SignedRanges;
6620 ConstantRange::PreferredRangeType RangeType =
6621 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? ConstantRange::Unsigned
6622 : ConstantRange::Signed;
6623
6624 // See if we've computed this range already.
6625 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(Val: S);
6626 if (I != Cache.end())
6627 return I->second;
6628
6629 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Val: S))
6630 return setRange(S: C, Hint: SignHint, CR: ConstantRange(C->getAPInt()));
6631
6632 // Switch to iteratively computing the range for S, if it is part of a deeply
6633 // nested expression.
6634 if (Depth > RangeIterThreshold)
6635 return getRangeRefIter(S, SignHint);
6636
6637 unsigned BitWidth = getTypeSizeInBits(Ty: S->getType());
6638 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
6639 using OBO = OverflowingBinaryOperator;
6640
6641 // If the value has known zeros, the maximum value will have those known zeros
6642 // as well.
6643 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
6644 APInt Multiple = getNonZeroConstantMultiple(S);
6645 APInt Remainder = APInt::getMaxValue(numBits: BitWidth).urem(RHS: Multiple);
6646 if (!Remainder.isZero())
6647 ConservativeResult =
6648 ConstantRange(APInt::getMinValue(numBits: BitWidth),
6649 APInt::getMaxValue(numBits: BitWidth) - Remainder + 1);
6650 }
6651 else {
6652 uint32_t TZ = getMinTrailingZeros(S);
6653 if (TZ != 0) {
6654 ConservativeResult = ConstantRange(
6655 APInt::getSignedMinValue(numBits: BitWidth),
6656 APInt::getSignedMaxValue(numBits: BitWidth).ashr(ShiftAmt: TZ).shl(shiftAmt: TZ) + 1);
6657 }
6658 }
6659
6660 switch (S->getSCEVType()) {
6661 case scConstant:
6662 llvm_unreachable("Already handled above.");
6663 case scVScale:
6664 return setRange(S, Hint: SignHint, CR: getVScaleRange(F: &F, BitWidth));
6665 case scTruncate: {
6666 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Val: S);
6667 ConstantRange X = getRangeRef(S: Trunc->getOperand(), SignHint, Depth: Depth + 1);
6668 return setRange(
6669 S: Trunc, Hint: SignHint,
6670 CR: ConservativeResult.intersectWith(CR: X.truncate(BitWidth), Type: RangeType));
6671 }
6672 case scZeroExtend: {
6673 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(Val: S);
6674 ConstantRange X = getRangeRef(S: ZExt->getOperand(), SignHint, Depth: Depth + 1);
6675 return setRange(
6676 S: ZExt, Hint: SignHint,
6677 CR: ConservativeResult.intersectWith(CR: X.zeroExtend(BitWidth), Type: RangeType));
6678 }
6679 case scSignExtend: {
6680 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(Val: S);
6681 ConstantRange X = getRangeRef(S: SExt->getOperand(), SignHint, Depth: Depth + 1);
6682 return setRange(
6683 S: SExt, Hint: SignHint,
6684 CR: ConservativeResult.intersectWith(CR: X.signExtend(BitWidth), Type: RangeType));
6685 }
6686 case scPtrToInt: {
6687 const SCEVPtrToIntExpr *PtrToInt = cast<SCEVPtrToIntExpr>(Val: S);
6688 ConstantRange X = getRangeRef(S: PtrToInt->getOperand(), SignHint, Depth: Depth + 1);
6689 return setRange(S: PtrToInt, Hint: SignHint, CR: X);
6690 }
6691 case scAddExpr: {
6692 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Val: S);
6693 ConstantRange X = getRangeRef(S: Add->getOperand(i: 0), SignHint, Depth: Depth + 1);
6694 unsigned WrapType = OBO::AnyWrap;
6695 if (Add->hasNoSignedWrap())
6696 WrapType |= OBO::NoSignedWrap;
6697 if (Add->hasNoUnsignedWrap())
6698 WrapType |= OBO::NoUnsignedWrap;
6699 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
6700 X = X.addWithNoWrap(Other: getRangeRef(S: Add->getOperand(i), SignHint, Depth: Depth + 1),
6701 NoWrapKind: WrapType, RangeType);
6702 return setRange(S: Add, Hint: SignHint,
6703 CR: ConservativeResult.intersectWith(CR: X, Type: RangeType));
6704 }
6705 case scMulExpr: {
6706 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Val: S);
6707 ConstantRange X = getRangeRef(S: Mul->getOperand(i: 0), SignHint, Depth: Depth + 1);
6708 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
6709 X = X.multiply(Other: getRangeRef(S: Mul->getOperand(i), SignHint, Depth: Depth + 1));
6710 return setRange(S: Mul, Hint: SignHint,
6711 CR: ConservativeResult.intersectWith(CR: X, Type: RangeType));
6712 }
6713 case scUDivExpr: {
6714 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(Val: S);
6715 ConstantRange X = getRangeRef(S: UDiv->getLHS(), SignHint, Depth: Depth + 1);
6716 ConstantRange Y = getRangeRef(S: UDiv->getRHS(), SignHint, Depth: Depth + 1);
6717 return setRange(S: UDiv, Hint: SignHint,
6718 CR: ConservativeResult.intersectWith(CR: X.udiv(Other: Y), Type: RangeType));
6719 }
6720 case scAddRecExpr: {
6721 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Val: S);
6722 // If there's no unsigned wrap, the value will never be less than its
6723 // initial value.
6724 if (AddRec->hasNoUnsignedWrap()) {
6725 APInt UnsignedMinValue = getUnsignedRangeMin(S: AddRec->getStart());
6726 if (!UnsignedMinValue.isZero())
6727 ConservativeResult = ConservativeResult.intersectWith(
6728 CR: ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), Type: RangeType);
6729 }
6730
6731 // If there's no signed wrap, and all the operands except initial value have
6732 // the same sign or zero, the value won't ever be:
6733 // 1: smaller than initial value if operands are non negative,
6734 // 2: bigger than initial value if operands are non positive.
6735 // For both cases, value can not cross signed min/max boundary.
6736 if (AddRec->hasNoSignedWrap()) {
6737 bool AllNonNeg = true;
6738 bool AllNonPos = true;
6739 for (unsigned i = 1, e = AddRec->getNumOperands(); i != e; ++i) {
6740 if (!isKnownNonNegative(S: AddRec->getOperand(i)))
6741 AllNonNeg = false;
6742 if (!isKnownNonPositive(S: AddRec->getOperand(i)))
6743 AllNonPos = false;
6744 }
6745 if (AllNonNeg)
6746 ConservativeResult = ConservativeResult.intersectWith(
6747 CR: ConstantRange::getNonEmpty(Lower: getSignedRangeMin(S: AddRec->getStart()),
6748 Upper: APInt::getSignedMinValue(numBits: BitWidth)),
6749 Type: RangeType);
6750 else if (AllNonPos)
6751 ConservativeResult = ConservativeResult.intersectWith(
6752 CR: ConstantRange::getNonEmpty(Lower: APInt::getSignedMinValue(numBits: BitWidth),
6753 Upper: getSignedRangeMax(S: AddRec->getStart()) +
6754 1),
6755 Type: RangeType);
6756 }
6757
6758 // TODO: non-affine addrec
6759 if (AddRec->isAffine()) {
6760 const SCEV *MaxBEScev =
6761 getConstantMaxBackedgeTakenCount(L: AddRec->getLoop());
6762 if (!isa<SCEVCouldNotCompute>(Val: MaxBEScev)) {
6763 APInt MaxBECount = cast<SCEVConstant>(Val: MaxBEScev)->getAPInt();
6764
6765 // Adjust MaxBECount to the same bitwidth as AddRec. We can truncate if
6766 // MaxBECount's active bits are all <= AddRec's bit width.
6767 if (MaxBECount.getBitWidth() > BitWidth &&
6768 MaxBECount.getActiveBits() <= BitWidth)
6769 MaxBECount = MaxBECount.trunc(width: BitWidth);
6770 else if (MaxBECount.getBitWidth() < BitWidth)
6771 MaxBECount = MaxBECount.zext(width: BitWidth);
6772
6773 if (MaxBECount.getBitWidth() == BitWidth) {
6774 auto RangeFromAffine = getRangeForAffineAR(
6775 Start: AddRec->getStart(), Step: AddRec->getStepRecurrence(SE&: *this), MaxBECount);
6776 ConservativeResult =
6777 ConservativeResult.intersectWith(CR: RangeFromAffine, Type: RangeType);
6778
6779 auto RangeFromFactoring = getRangeViaFactoring(
6780 Start: AddRec->getStart(), Step: AddRec->getStepRecurrence(SE&: *this), MaxBECount);
6781 ConservativeResult =
6782 ConservativeResult.intersectWith(CR: RangeFromFactoring, Type: RangeType);
6783 }
6784 }
6785
6786 // Now try symbolic BE count and more powerful methods.
6787 if (UseExpensiveRangeSharpening) {
6788 const SCEV *SymbolicMaxBECount =
6789 getSymbolicMaxBackedgeTakenCount(L: AddRec->getLoop());
6790 if (!isa<SCEVCouldNotCompute>(Val: SymbolicMaxBECount) &&
6791 getTypeSizeInBits(Ty: MaxBEScev->getType()) <= BitWidth &&
6792 AddRec->hasNoSelfWrap()) {
6793 auto RangeFromAffineNew = getRangeForAffineNoSelfWrappingAR(
6794 AddRec, MaxBECount: SymbolicMaxBECount, BitWidth, SignHint);
6795 ConservativeResult =
6796 ConservativeResult.intersectWith(CR: RangeFromAffineNew, Type: RangeType);
6797 }
6798 }
6799 }
6800
6801 return setRange(S: AddRec, Hint: SignHint, CR: std::move(ConservativeResult));
6802 }
6803 case scUMaxExpr:
6804 case scSMaxExpr:
6805 case scUMinExpr:
6806 case scSMinExpr:
6807 case scSequentialUMinExpr: {
6808 Intrinsic::ID ID;
6809 switch (S->getSCEVType()) {
6810 case scUMaxExpr:
6811 ID = Intrinsic::umax;
6812 break;
6813 case scSMaxExpr:
6814 ID = Intrinsic::smax;
6815 break;
6816 case scUMinExpr:
6817 case scSequentialUMinExpr:
6818 ID = Intrinsic::umin;
6819 break;
6820 case scSMinExpr:
6821 ID = Intrinsic::smin;
6822 break;
6823 default:
6824 llvm_unreachable("Unknown SCEVMinMaxExpr/SCEVSequentialMinMaxExpr.");
6825 }
6826
6827 const auto *NAry = cast<SCEVNAryExpr>(Val: S);
6828 ConstantRange X = getRangeRef(S: NAry->getOperand(i: 0), SignHint, Depth: Depth + 1);
6829 for (unsigned i = 1, e = NAry->getNumOperands(); i != e; ++i)
6830 X = X.intrinsic(
6831 IntrinsicID: ID, Ops: {X, getRangeRef(S: NAry->getOperand(i), SignHint, Depth: Depth + 1)});
6832 return setRange(S, Hint: SignHint,
6833 CR: ConservativeResult.intersectWith(CR: X, Type: RangeType));
6834 }
6835 case scUnknown: {
6836 const SCEVUnknown *U = cast<SCEVUnknown>(Val: S);
6837 Value *V = U->getValue();
6838
6839 // Check if the IR explicitly contains !range metadata.
6840 std::optional<ConstantRange> MDRange = GetRangeFromMetadata(V);
6841 if (MDRange)
6842 ConservativeResult =
6843 ConservativeResult.intersectWith(CR: *MDRange, Type: RangeType);
6844
6845 // Use facts about recurrences in the underlying IR. Note that add
6846 // recurrences are AddRecExprs and thus don't hit this path. This
6847 // primarily handles shift recurrences.
6848 auto CR = getRangeForUnknownRecurrence(U);
6849 ConservativeResult = ConservativeResult.intersectWith(CR);
6850
6851 // See if ValueTracking can give us a useful range.
6852 const DataLayout &DL = getDataLayout();
6853 KnownBits Known = computeKnownBits(V, DL, Depth: 0, AC: &AC, CxtI: nullptr, DT: &DT);
6854 if (Known.getBitWidth() != BitWidth)
6855 Known = Known.zextOrTrunc(BitWidth);
6856
6857 // ValueTracking may be able to compute a tighter result for the number of
6858 // sign bits than for the value of those sign bits.
6859 unsigned NS = ComputeNumSignBits(Op: V, DL, Depth: 0, AC: &AC, CxtI: nullptr, DT: &DT);
6860 if (U->getType()->isPointerTy()) {
6861 // If the pointer size is larger than the index size type, this can cause
6862 // NS to be larger than BitWidth. So compensate for this.
6863 unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType());
6864 int ptrIdxDiff = ptrSize - BitWidth;
6865 if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff)
6866 NS -= ptrIdxDiff;
6867 }
6868
6869 if (NS > 1) {
6870 // If we know any of the sign bits, we know all of the sign bits.
6871 if (!Known.Zero.getHiBits(numBits: NS).isZero())
6872 Known.Zero.setHighBits(NS);
6873 if (!Known.One.getHiBits(numBits: NS).isZero())
6874 Known.One.setHighBits(NS);
6875 }
6876
6877 if (Known.getMinValue() != Known.getMaxValue() + 1)
6878 ConservativeResult = ConservativeResult.intersectWith(
6879 CR: ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1),
6880 Type: RangeType);
6881 if (NS > 1)
6882 ConservativeResult = ConservativeResult.intersectWith(
6883 CR: ConstantRange(APInt::getSignedMinValue(numBits: BitWidth).ashr(ShiftAmt: NS - 1),
6884 APInt::getSignedMaxValue(numBits: BitWidth).ashr(ShiftAmt: NS - 1) + 1),
6885 Type: RangeType);
6886
6887 if (U->getType()->isPointerTy() && SignHint == HINT_RANGE_UNSIGNED) {
6888 // Strengthen the range if the underlying IR value is a
6889 // global/alloca/heap allocation using the size of the object.
6890 ObjectSizeOpts Opts;
6891 Opts.RoundToAlign = false;
6892 Opts.NullIsUnknownSize = true;
6893 uint64_t ObjSize;
6894 if ((isa<GlobalVariable>(Val: V) || isa<AllocaInst>(Val: V) ||
6895 isAllocationFn(V, TLI: &TLI)) &&
6896 getObjectSize(Ptr: V, Size&: ObjSize, DL, TLI: &TLI, Opts) && ObjSize > 1) {
6897 // The highest address the object can start is ObjSize bytes before the
6898 // end (unsigned max value). If this value is not a multiple of the
6899 // alignment, the last possible start value is the next lowest multiple
6900 // of the alignment. Note: The computations below cannot overflow,
6901 // because if they would there's no possible start address for the
6902 // object.
6903 APInt MaxVal = APInt::getMaxValue(numBits: BitWidth) - APInt(BitWidth, ObjSize);
6904 uint64_t Align = U->getValue()->getPointerAlignment(DL).value();
6905 uint64_t Rem = MaxVal.urem(RHS: Align);
6906 MaxVal -= APInt(BitWidth, Rem);
6907 APInt MinVal = APInt::getZero(numBits: BitWidth);
6908 if (llvm::isKnownNonZero(V, Q: DL))
6909 MinVal = Align;
6910 ConservativeResult = ConservativeResult.intersectWith(
6911 CR: ConstantRange::getNonEmpty(Lower: MinVal, Upper: MaxVal + 1), Type: RangeType);
6912 }
6913 }
6914
6915 // A range of Phi is a subset of union of all ranges of its input.
6916 if (PHINode *Phi = dyn_cast<PHINode>(Val: V)) {
6917 // Make sure that we do not run over cycled Phis.
6918 if (PendingPhiRanges.insert(Ptr: Phi).second) {
6919 ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
6920
6921 for (const auto &Op : Phi->operands()) {
6922 auto OpRange = getRangeRef(S: getSCEV(V: Op), SignHint, Depth: Depth + 1);
6923 RangeFromOps = RangeFromOps.unionWith(CR: OpRange);
6924 // No point to continue if we already have a full set.
6925 if (RangeFromOps.isFullSet())
6926 break;
6927 }
6928 ConservativeResult =
6929 ConservativeResult.intersectWith(CR: RangeFromOps, Type: RangeType);
6930 bool Erased = PendingPhiRanges.erase(Ptr: Phi);
6931 assert(Erased && "Failed to erase Phi properly?");
6932 (void)Erased;
6933 }
6934 }
6935
6936 // vscale can't be equal to zero
6937 if (const auto *II = dyn_cast<IntrinsicInst>(Val: V))
6938 if (II->getIntrinsicID() == Intrinsic::vscale) {
6939 ConstantRange Disallowed = APInt::getZero(numBits: BitWidth);
6940 ConservativeResult = ConservativeResult.difference(CR: Disallowed);
6941 }
6942
6943 return setRange(S: U, Hint: SignHint, CR: std::move(ConservativeResult));
6944 }
6945 case scCouldNotCompute:
6946 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6947 }
6948
6949 return setRange(S, Hint: SignHint, CR: std::move(ConservativeResult));
6950}
6951
6952// Given a StartRange, Step and MaxBECount for an expression compute a range of
6953// values that the expression can take. Initially, the expression has a value
6954// from StartRange and then is changed by Step up to MaxBECount times. Signed
6955// argument defines if we treat Step as signed or unsigned.
6956static ConstantRange getRangeForAffineARHelper(APInt Step,
6957 const ConstantRange &StartRange,
6958 const APInt &MaxBECount,
6959 bool Signed) {
6960 unsigned BitWidth = Step.getBitWidth();
6961 assert(BitWidth == StartRange.getBitWidth() &&
6962 BitWidth == MaxBECount.getBitWidth() && "mismatched bit widths");
6963 // If either Step or MaxBECount is 0, then the expression won't change, and we
6964 // just need to return the initial range.
6965 if (Step == 0 || MaxBECount == 0)
6966 return StartRange;
6967
6968 // If we don't know anything about the initial value (i.e. StartRange is
6969 // FullRange), then we don't know anything about the final range either.
6970 // Return FullRange.
6971 if (StartRange.isFullSet())
6972 return ConstantRange::getFull(BitWidth);
6973
6974 // If Step is signed and negative, then we use its absolute value, but we also
6975 // note that we're moving in the opposite direction.
6976 bool Descending = Signed && Step.isNegative();
6977
6978 if (Signed)
6979 // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
6980 // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
6981 // This equations hold true due to the well-defined wrap-around behavior of
6982 // APInt.
6983 Step = Step.abs();
6984
6985 // Check if Offset is more than full span of BitWidth. If it is, the
6986 // expression is guaranteed to overflow.
6987 if (APInt::getMaxValue(numBits: StartRange.getBitWidth()).udiv(RHS: Step).ult(RHS: MaxBECount))
6988 return ConstantRange::getFull(BitWidth);
6989
6990 // Offset is by how much the expression can change. Checks above guarantee no
6991 // overflow here.
6992 APInt Offset = Step * MaxBECount;
6993
6994 // Minimum value of the final range will match the minimal value of StartRange
6995 // if the expression is increasing and will be decreased by Offset otherwise.
6996 // Maximum value of the final range will match the maximal value of StartRange
6997 // if the expression is decreasing and will be increased by Offset otherwise.
6998 APInt StartLower = StartRange.getLower();
6999 APInt StartUpper = StartRange.getUpper() - 1;
7000 APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
7001 : (StartUpper + std::move(Offset));
7002
7003 // It's possible that the new minimum/maximum value will fall into the initial
7004 // range (due to wrap around). This means that the expression can take any
7005 // value in this bitwidth, and we have to return full range.
7006 if (StartRange.contains(Val: MovedBoundary))
7007 return ConstantRange::getFull(BitWidth);
7008
7009 APInt NewLower =
7010 Descending ? std::move(MovedBoundary) : std::move(StartLower);
7011 APInt NewUpper =
7012 Descending ? std::move(StartUpper) : std::move(MovedBoundary);
7013 NewUpper += 1;
7014
7015 // No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
7016 return ConstantRange::getNonEmpty(Lower: std::move(NewLower), Upper: std::move(NewUpper));
7017}
7018
7019ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
7020 const SCEV *Step,
7021 const APInt &MaxBECount) {
7022 assert(getTypeSizeInBits(Start->getType()) ==
7023 getTypeSizeInBits(Step->getType()) &&
7024 getTypeSizeInBits(Start->getType()) == MaxBECount.getBitWidth() &&
7025 "mismatched bit widths");
7026
7027 // First, consider step signed.
7028 ConstantRange StartSRange = getSignedRange(S: Start);
7029 ConstantRange StepSRange = getSignedRange(S: Step);
7030
7031 // If Step can be both positive and negative, we need to find ranges for the
7032 // maximum absolute step values in both directions and union them.
7033 ConstantRange SR = getRangeForAffineARHelper(
7034 Step: StepSRange.getSignedMin(), StartRange: StartSRange, MaxBECount, /* Signed = */ true);
7035 SR = SR.unionWith(CR: getRangeForAffineARHelper(Step: StepSRange.getSignedMax(),
7036 StartRange: StartSRange, MaxBECount,
7037 /* Signed = */ true));
7038
7039 // Next, consider step unsigned.
7040 ConstantRange UR = getRangeForAffineARHelper(
7041 Step: getUnsignedRangeMax(S: Step), StartRange: getUnsignedRange(S: Start), MaxBECount,
7042 /* Signed = */ false);
7043
7044 // Finally, intersect signed and unsigned ranges.
7045 return SR.intersectWith(CR: UR, Type: ConstantRange::Smallest);
7046}
7047
7048ConstantRange ScalarEvolution::getRangeForAffineNoSelfWrappingAR(
7049 const SCEVAddRecExpr *AddRec, const SCEV *MaxBECount, unsigned BitWidth,
7050 ScalarEvolution::RangeSignHint SignHint) {
7051 assert(AddRec->isAffine() && "Non-affine AddRecs are not suppored!\n");
7052 assert(AddRec->hasNoSelfWrap() &&
7053 "This only works for non-self-wrapping AddRecs!");
7054 const bool IsSigned = SignHint == HINT_RANGE_SIGNED;
7055 const SCEV *Step = AddRec->getStepRecurrence(SE&: *this);
7056 // Only deal with constant step to save compile time.
7057 if (!isa<SCEVConstant>(Val: Step))
7058 return ConstantRange::getFull(BitWidth);
7059 // Let's make sure that we can prove that we do not self-wrap during
7060 // MaxBECount iterations. We need this because MaxBECount is a maximum
7061 // iteration count estimate, and we might infer nw from some exit for which we
7062 // do not know max exit count (or any other side reasoning).
7063 // TODO: Turn into assert at some point.
7064 if (getTypeSizeInBits(Ty: MaxBECount->getType()) >
7065 getTypeSizeInBits(Ty: AddRec->getType()))
7066 return ConstantRange::getFull(BitWidth);
7067 MaxBECount = getNoopOrZeroExtend(V: MaxBECount, Ty: AddRec->getType());
7068 const SCEV *RangeWidth = getMinusOne(Ty: AddRec->getType());
7069 const SCEV *StepAbs = getUMinExpr(LHS: Step, RHS: getNegativeSCEV(V: Step));
7070 const SCEV *MaxItersWithoutWrap = getUDivExpr(LHS: RangeWidth, RHS: StepAbs);
7071 if (!isKnownPredicateViaConstantRanges(Pred: ICmpInst::ICMP_ULE, LHS: MaxBECount,
7072 RHS: MaxItersWithoutWrap))
7073 return ConstantRange::getFull(BitWidth);
7074
7075 ICmpInst::Predicate LEPred =
7076 IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
7077 ICmpInst::Predicate GEPred =
7078 IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
7079 const SCEV *End = AddRec->evaluateAtIteration(It: MaxBECount, SE&: *this);
7080
7081 // We know that there is no self-wrap. Let's take Start and End values and
7082 // look at all intermediate values V1, V2, ..., Vn that IndVar takes during
7083 // the iteration. They either lie inside the range [Min(Start, End),
7084 // Max(Start, End)] or outside it:
7085 //
7086 // Case 1: RangeMin ... Start V1 ... VN End ... RangeMax;
7087 // Case 2: RangeMin Vk ... V1 Start ... End Vn ... Vk + 1 RangeMax;
7088 //
7089 // No self wrap flag guarantees that the intermediate values cannot be BOTH
7090 // outside and inside the range [Min(Start, End), Max(Start, End)]. Using that
7091 // knowledge, let's try to prove that we are dealing with Case 1. It is so if
7092 // Start <= End and step is positive, or Start >= End and step is negative.
7093 const SCEV *Start = applyLoopGuards(Expr: AddRec->getStart(), L: AddRec->getLoop());
7094 ConstantRange StartRange = getRangeRef(S: Start, SignHint);
7095 ConstantRange EndRange = getRangeRef(S: End, SignHint);
7096 ConstantRange RangeBetween = StartRange.unionWith(CR: EndRange);
7097 // If they already cover full iteration space, we will know nothing useful
7098 // even if we prove what we want to prove.
7099 if (RangeBetween.isFullSet())
7100 return RangeBetween;
7101 // Only deal with ranges that do not wrap (i.e. RangeMin < RangeMax).
7102 bool IsWrappedSet = IsSigned ? RangeBetween.isSignWrappedSet()
7103 : RangeBetween.isWrappedSet();
7104 if (IsWrappedSet)
7105 return ConstantRange::getFull(BitWidth);
7106
7107 if (isKnownPositive(S: Step) &&
7108 isKnownPredicateViaConstantRanges(Pred: LEPred, LHS: Start, RHS: End))
7109 return RangeBetween;
7110 if (isKnownNegative(S: Step) &&
7111 isKnownPredicateViaConstantRanges(Pred: GEPred, LHS: Start, RHS: End))
7112 return RangeBetween;
7113 return ConstantRange::getFull(BitWidth);
7114}
7115
7116ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
7117 const SCEV *Step,
7118 const APInt &MaxBECount) {
7119 // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
7120 // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
7121
7122 unsigned BitWidth = MaxBECount.getBitWidth();
7123 assert(getTypeSizeInBits(Start->getType()) == BitWidth &&
7124 getTypeSizeInBits(Step->getType()) == BitWidth &&
7125 "mismatched bit widths");
7126
7127 struct SelectPattern {
7128 Value *Condition = nullptr;
7129 APInt TrueValue;
7130 APInt FalseValue;
7131
7132 explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
7133 const SCEV *S) {
7134 std::optional<unsigned> CastOp;
7135 APInt Offset(BitWidth, 0);
7136
7137 assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
7138 "Should be!");
7139
7140 // Peel off a constant offset:
7141 if (auto *SA = dyn_cast<SCEVAddExpr>(Val: S)) {
7142 // In the future we could consider being smarter here and handle
7143 // {Start+Step,+,Step} too.
7144 if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(Val: SA->getOperand(i: 0)))
7145 return;
7146
7147 Offset = cast<SCEVConstant>(Val: SA->getOperand(i: 0))->getAPInt();
7148 S = SA->getOperand(i: 1);
7149 }
7150
7151 // Peel off a cast operation
7152 if (auto *SCast = dyn_cast<SCEVIntegralCastExpr>(Val: S)) {
7153 CastOp = SCast->getSCEVType();
7154 S = SCast->getOperand();
7155 }
7156
7157 using namespace llvm::PatternMatch;
7158
7159 auto *SU = dyn_cast<SCEVUnknown>(Val: S);
7160 const APInt *TrueVal, *FalseVal;
7161 if (!SU ||
7162 !match(V: SU->getValue(), P: m_Select(C: m_Value(V&: Condition), L: m_APInt(Res&: TrueVal),
7163 R: m_APInt(Res&: FalseVal)))) {
7164 Condition = nullptr;
7165 return;
7166 }
7167
7168 TrueValue = *TrueVal;
7169 FalseValue = *FalseVal;
7170
7171 // Re-apply the cast we peeled off earlier
7172 if (CastOp)
7173 switch (*CastOp) {
7174 default:
7175 llvm_unreachable("Unknown SCEV cast type!");
7176
7177 case scTruncate:
7178 TrueValue = TrueValue.trunc(width: BitWidth);
7179 FalseValue = FalseValue.trunc(width: BitWidth);
7180 break;
7181 case scZeroExtend:
7182 TrueValue = TrueValue.zext(width: BitWidth);
7183 FalseValue = FalseValue.zext(width: BitWidth);
7184 break;
7185 case scSignExtend:
7186 TrueValue = TrueValue.sext(width: BitWidth);
7187 FalseValue = FalseValue.sext(width: BitWidth);
7188 break;
7189 }
7190
7191 // Re-apply the constant offset we peeled off earlier
7192 TrueValue += Offset;
7193 FalseValue += Offset;
7194 }
7195
7196 bool isRecognized() { return Condition != nullptr; }
7197 };
7198
7199 SelectPattern StartPattern(*this, BitWidth, Start);
7200 if (!StartPattern.isRecognized())
7201 return ConstantRange::getFull(BitWidth);
7202
7203 SelectPattern StepPattern(*this, BitWidth, Step);
7204 if (!StepPattern.isRecognized())
7205 return ConstantRange::getFull(BitWidth);
7206
7207 if (StartPattern.Condition != StepPattern.Condition) {
7208 // We don't handle this case today; but we could, by considering four
7209 // possibilities below instead of two. I'm not sure if there are cases where
7210 // that will help over what getRange already does, though.
7211 return ConstantRange::getFull(BitWidth);
7212 }
7213
7214 // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
7215 // construct arbitrary general SCEV expressions here. This function is called
7216 // from deep in the call stack, and calling getSCEV (on a sext instruction,
7217 // say) can end up caching a suboptimal value.
7218
7219 // FIXME: without the explicit `this` receiver below, MSVC errors out with
7220 // C2352 and C2512 (otherwise it isn't needed).
7221
7222 const SCEV *TrueStart = this->getConstant(Val: StartPattern.TrueValue);
7223 const SCEV *TrueStep = this->getConstant(Val: StepPattern.TrueValue);
7224 const SCEV *FalseStart = this->getConstant(Val: StartPattern.FalseValue);
7225 const SCEV *FalseStep = this->getConstant(Val: StepPattern.FalseValue);
7226
7227 ConstantRange TrueRange =
7228 this->getRangeForAffineAR(Start: TrueStart, Step: TrueStep, MaxBECount);
7229 ConstantRange FalseRange =
7230 this->getRangeForAffineAR(Start: FalseStart, Step: FalseStep, MaxBECount);
7231
7232 return TrueRange.unionWith(CR: FalseRange);
7233}
7234
7235SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
7236 if (isa<ConstantExpr>(Val: V)) return SCEV::FlagAnyWrap;
7237 const BinaryOperator *BinOp = cast<BinaryOperator>(Val: V);
7238
7239 // Return early if there are no flags to propagate to the SCEV.
7240 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
7241 if (BinOp->hasNoUnsignedWrap())
7242 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNUW);
7243 if (BinOp->hasNoSignedWrap())
7244 Flags = ScalarEvolution::setFlags(Flags, OnFlags: SCEV::FlagNSW);
7245 if (Flags == SCEV::FlagAnyWrap)
7246 return SCEV::FlagAnyWrap;
7247
7248 return isSCEVExprNeverPoison(I: BinOp) ? Flags : SCEV::FlagAnyWrap;
7249}
7250
7251const Instruction *
7252ScalarEvolution::getNonTrivialDefiningScopeBound(const SCEV *S) {
7253 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Val: S))
7254 return &*AddRec->getLoop()->getHeader()->begin();
7255 if (auto *U = dyn_cast<SCEVUnknown>(Val: S))
7256 if (auto *I = dyn_cast<Instruction>(Val: U->getValue()))
7257 return I;
7258 return nullptr;
7259}
7260
7261const Instruction *
7262ScalarEvolution::getDefiningScopeBound(ArrayRef<const SCEV *> Ops,
7263 bool &Precise) {
7264 Precise = true;
7265 // Do a bounded search of the def relation of the requested SCEVs.
7266 SmallSet<const SCEV *, 16> Visited;
7267 SmallVector<const SCEV *> Worklist;
7268 auto pushOp = [&](const SCEV *S) {
7269 if (!Visited.insert(Ptr: S).second)
7270 return;
7271 // Threshold of 30 here is arbitrary.
7272 if (Visited.size() > 30) {
7273 Precise = false;
7274 return;
7275 }
7276 Worklist.push_back(Elt: S);
7277 };
7278
7279 for (const auto *S : Ops)
7280 pushOp(S);
7281
7282 const Instruction *Bound = nullptr;
7283 while (!Worklist.empty()) {
7284 auto *S = Worklist.pop_back_val();
7285 if (auto *DefI = getNonTrivialDefiningScopeBound(S)) {
7286 if (!Bound || DT.dominates(Def: Bound, User: DefI))
7287 Bound = DefI;
7288 } else {
7289 for (const auto *Op : S->operands())
7290 pushOp(Op);
7291 }
7292 }
7293 return Bound ? Bound : &*F.getEntryBlock().begin();
7294}
7295
7296const Instruction *
7297ScalarEvolution::getDefiningScopeBound(ArrayRef<const SCEV *> Ops) {
7298 bool Discard;
7299 return getDefiningScopeBound(Ops, Precise&: Discard);
7300}
7301
7302bool ScalarEvolution::isGuaranteedToTransferExecutionTo(const Instruction *A,
7303 const Instruction *B) {
7304 if (A->getParent() == B->getParent() &&
7305 isGuaranteedToTransferExecutionToSuccessor(Begin: A->getIterator(),
7306 End: B->getIterator()))
7307 return true;
7308
7309 auto *BLoop = LI.getLoopFor(BB: B->getParent());
7310 if (BLoop && BLoop->getHeader() == B->getParent() &&
7311 BLoop->getLoopPreheader() == A->getParent() &&
7312 isGuaranteedToTransferExecutionToSuccessor(Begin: A->getIterator(),
7313 End: A->getParent()->end()) &&
7314 isGuaranteedToTransferExecutionToSuccessor(Begin: B->getParent()->begin(),
7315 End: B->getIterator()))
7316 return true;
7317 return false;
7318}
7319
7320
7321bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
7322 // Only proceed if we can prove that I does not yield poison.
7323 if (!programUndefinedIfPoison(Inst: I))
7324 return false;
7325
7326 // At this point we know that if I is executed, then it does not wrap
7327 // according to at least one of NSW or NUW. If I is not executed, then we do
7328 // not know if the calculation that I represents would wrap. Multiple
7329 // instructions can map to the same SCEV. If we apply NSW or NUW from I to
7330 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
7331 // derived from other instructions that map to the same SCEV. We cannot make
7332 // that guarantee for cases where I is not executed. So we need to find a
7333 // upper bound on the defining scope for the SCEV, and prove that I is
7334 // executed every time we enter that scope. When the bounding scope is a
7335 // loop (the common case), this is equivalent to proving I executes on every
7336 // iteration of that loop.
7337 SmallVector<const SCEV *> SCEVOps;
7338 for (const Use &Op : I->operands()) {
7339 // I could be an extractvalue from a call to an overflow intrinsic.
7340 // TODO: We can do better here in some cases.
7341 if (isSCEVable(Ty: Op->getType()))
7342 SCEVOps.push_back(Elt: getSCEV(V: Op));
7343 }
7344 auto *DefI = getDefiningScopeBound(Ops: SCEVOps);
7345 return isGuaranteedToTransferExecutionTo(A: DefI, B: I);
7346}
7347
7348bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
7349 // If we know that \c I can never be poison period, then that's enough.
7350 if (isSCEVExprNeverPoison(I))
7351 return true;
7352
7353 // If the loop only has one exit, then we know that, if the loop is entered,
7354 // any instruction dominating that exit will be executed. If any such
7355 // instruction would result in UB, the addrec cannot be poison.
7356 //
7357 // This is basically the same reasoning as in isSCEVExprNeverPoison(), but
7358 // also handles uses outside the loop header (they just need to dominate the
7359 // single exit).
7360
7361 auto *ExitingBB = L->getExitingBlock();
7362 if (!ExitingBB || !loopHasNoAbnormalExits(L))
7363 return false;
7364
7365 SmallPtrSet<const Value *, 16> KnownPoison;
7366 SmallVector<const Instruction *, 8> Worklist;
7367
7368 // We start by assuming \c I, the post-inc add recurrence, is poison. Only
7369 // things that are known to be poison under that assumption go on the
7370 // Worklist.
7371 KnownPoison.insert(Ptr: I);
7372 Worklist.push_back(Elt: I);
7373
7374 while (!Worklist.empty()) {
7375 const Instruction *Poison = Worklist.pop_back_val();
7376
7377 for (const Use &U : Poison->uses()) {
7378 const Instruction *PoisonUser = cast<Instruction>(Val: U.getUser());
7379 if (mustTriggerUB(I: PoisonUser, KnownPoison) &&
7380 DT.dominates(A: PoisonUser->getParent(), B: ExitingBB))
7381 return true;
7382
7383 if (propagatesPoison(PoisonOp: U) && L->contains(Inst: PoisonUser))
7384 if (KnownPoison.insert(Ptr: PoisonUser).second)
7385 Worklist.push_back(Elt: PoisonUser);
7386 }
7387 }
7388
7389 return false;
7390}
7391
7392ScalarEvolution::LoopProperties
7393ScalarEvolution::getLoopProperties(const Loop *L) {
7394 using LoopProperties = ScalarEvolution::LoopProperties;
7395
7396 auto Itr = LoopPropertiesCache.find(Val: L);
7397 if (Itr == LoopPropertiesCache.end()) {
7398 auto HasSideEffects = [](Instruction *I) {
7399 if (auto *SI = dyn_cast<StoreInst>(Val: I))
7400 return !SI->isSimple();
7401
7402 return I->mayThrow() || I->mayWriteToMemory();
7403 };
7404
7405 LoopProperties LP = {/* HasNoAbnormalExits */ true,
7406 /*HasNoSideEffects*/ true};
7407
7408 for (auto *BB : L->getBlocks())
7409 for (auto &I : *BB) {
7410 if (!isGuaranteedToTransferExecutionToSuccessor(I: &I))
7411 LP.HasNoAbnormalExits = false;
7412 if (HasSideEffects(&I))
7413 LP.HasNoSideEffects = false;
7414 if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
7415 break; // We're already as pessimistic as we can get.
7416 }
7417
7418 auto InsertPair = LoopPropertiesCache.insert(KV: {L, LP});
7419 assert(InsertPair.second && "We just checked!");
7420 Itr = InsertPair.first;
7421 }
7422
7423 return Itr->second;
7424}
7425
7426bool ScalarEvolution::loopIsFiniteByAssumption(const Loop *L) {
7427 // A mustprogress loop without side effects must be finite.
7428 // TODO: The check used here is very conservative. It's only *specific*
7429 // side effects which are well defined in infinite loops.
7430 return isFinite(L) || (isMustProgress(L) && loopHasNoSideEffects(L));
7431}
7432
7433const SCEV *ScalarEvolution::createSCEVIter(Value *V) {
7434 // Worklist item with a Value and a bool indicating whether all operands have
7435 // been visited already.
7436 using PointerTy = PointerIntPair<Value *, 1, bool>;
7437 SmallVector<PointerTy> Stack;
7438
7439 Stack.emplace_back(Args&: V, Args: true);
7440 Stack.emplace_back(Args&: V, Args: false);
7441 while (!Stack.empty()) {
7442 auto E = Stack.pop_back_val();
7443 Value *CurV = E.getPointer();
7444
7445 if (getExistingSCEV(V: CurV))
7446 continue;
7447
7448 SmallVector<Value *> Ops;
7449 const SCEV *CreatedSCEV = nullptr;
7450 // If all operands have been visited already, create the SCEV.
7451 if (E.getInt()) {
7452 CreatedSCEV = createSCEV(V: CurV);
7453 } else {
7454 // Otherwise get the operands we need to create SCEV's for before creating
7455 // the SCEV for CurV. If the SCEV for CurV can be constructed trivially,
7456 // just use it.
7457 CreatedSCEV = getOperandsToCreate(V: CurV, Ops);
7458 }
7459
7460 if (CreatedSCEV) {
7461 insertValueToMap(V: CurV, S: CreatedSCEV);
7462 } else {
7463 // Queue CurV for SCEV creation, followed by its's operands which need to
7464 // be constructed first.
7465 Stack.emplace_back(Args&: CurV, Args: true);
7466 for (Value *Op : Ops)
7467 Stack.emplace_back(Args&: Op, Args: false);
7468 }
7469 }
7470
7471 return getExistingSCEV(V);
7472}
7473
7474const SCEV *
7475ScalarEvolution::getOperandsToCreate(Value *V, SmallVectorImpl<Value *> &Ops) {
7476 if (!isSCEVable(Ty: V->getType()))
7477 return getUnknown(V);
7478
7479 if (Instruction *I = dyn_cast<Instruction>(Val: V)) {
7480 // Don't attempt to analyze instructions in blocks that aren't
7481 // reachable. Such instructions don't matter, and they aren't required
7482 // to obey basic rules for definitions dominating uses which this
7483 // analysis depends on.
7484 if (!DT.isReachableFromEntry(A: I->getParent()))
7485 return getUnknown(V: PoisonValue::get(T: V->getType()));
7486 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(Val: V))
7487 return getConstant(V: CI);
7488 else if (isa<GlobalAlias>(Val: V))
7489 return getUnknown(V);
7490 else if (!isa<ConstantExpr>(Val: V))
7491 return getUnknown(V);
7492
7493 Operator *U = cast<Operator>(Val: V);
7494 if (auto BO =
7495 MatchBinaryOp(V: U, DL: getDataLayout(), AC, DT, CxtI: dyn_cast<Instruction>(Val: V))) {
7496 bool IsConstArg = isa<ConstantInt>(Val: BO->RHS);
7497 switch (BO->Opcode) {
7498 case Instruction::Add:
7499 case Instruction::Mul: {
7500 // For additions and multiplications, traverse add/mul chains for which we
7501 // can potentially create a single SCEV, to reduce the number of
7502 // get{Add,Mul}Expr calls.
7503 do {
7504 if (BO->Op) {
7505 if (BO->Op != V && getExistingSCEV(V: BO->Op)) {
7506 Ops.push_back(Elt: BO->Op);
7507 break;
7508 }
7509 }
7510 Ops.push_back(Elt: BO->RHS);
7511 auto NewBO = MatchBinaryOp(V: BO->LHS, DL: getDataLayout(), AC, DT,
7512 CxtI: dyn_cast<Instruction>(Val: V));
7513 if (!NewBO ||
7514 (BO->Opcode == Instruction::Add &&
7515 (NewBO->Opcode != Instruction::Add &&
7516 NewBO->Opcode != Instruction::Sub)) ||
7517 (BO->Opcode == Instruction::Mul &&
7518 NewBO->Opcode != Instruction::Mul)) {
7519 Ops.push_back(Elt: BO->LHS);
7520 break;
7521 }
7522 // CreateSCEV calls getNoWrapFlagsFromUB, which under certain conditions
7523 // requires a SCEV for the LHS.
7524 if (BO->Op && (BO->IsNSW || BO->IsNUW)) {
7525 auto *I = dyn_cast<Instruction>(Val: BO->Op);
7526 if (I && programUndefinedIfPoison(Inst: I)) {
7527 Ops.push_back(Elt: BO->LHS);
7528 break;
7529 }
7530 }
7531 BO = NewBO;
7532 } while (true);
7533 return nullptr;
7534 }
7535 case Instruction::Sub:
7536 case Instruction::UDiv:
7537 case Instruction::URem:
7538 break;
7539 case Instruction::AShr:
7540 case Instruction::Shl:
7541 case Instruction::Xor:
7542 if (!IsConstArg)
7543 return nullptr;
7544 break;
7545 case Instruction::And:
7546 case Instruction::Or:
7547 if (!IsConstArg && !BO->LHS->getType()->isIntegerTy(Bitwidth: 1))
7548 return nullptr;
7549 break;
7550 case Instruction::LShr:
7551 return getUnknown(V);
7552 default:
7553 llvm_unreachable("Unhandled binop");
7554 break;
7555 }
7556
7557 Ops.push_back(Elt: BO->LHS);
7558 Ops.push_back(Elt: BO->RHS);
7559 return nullptr;
7560 }
7561
7562 switch (U->getOpcode()) {
7563 case Instruction::Trunc:
7564 case Instruction::ZExt:
7565 case Instruction::SExt:
7566 case Instruction::PtrToInt:
7567 Ops.push_back(Elt: U->getOperand(i: 0));
7568 return nullptr;
7569
7570 case Instruction::BitCast:
7571 if (isSCEVable(Ty: U->getType()) && isSCEVable(Ty: U->getOperand(i: 0)->getType())) {
7572 Ops.push_back(Elt: U->getOperand(i: 0));
7573 return nullptr;
7574 }
7575 return getUnknown(V);
7576
7577 case Instruction::SDiv:
7578 case Instruction::SRem:
7579 Ops.push_back(Elt: U->getOperand(i: 0));
7580 Ops.push_back(Elt: U->getOperand(i: 1));
7581 return nullptr;
7582
7583 case Instruction::GetElementPtr:
7584 assert(cast<GEPOperator>(U)->getSourceElementType()->isSized() &&
7585 "GEP source element type must be sized");
7586 for (Value *Index : U->operands())
7587 Ops.push_back(Elt: Index);
7588 return nullptr;
7589
7590 case Instruction::IntToPtr:
7591 return getUnknown(V);
7592
7593 case Instruction::PHI:
7594 // Keep constructing SCEVs' for phis recursively for now.
7595 return nullptr;
7596
7597 case Instruction::Select: {
7598 // Check if U is a select that can be simplified to a SCEVUnknown.
7599 auto CanSimplifyToUnknown = [this, U]() {
7600 if (U->getType()->isIntegerTy(Bitwidth: 1) || isa<ConstantInt>(Val: U->getOperand(i: 0)))
7601 return false;
7602
7603 auto *ICI = dyn_cast<ICmpInst>(Val: U->getOperand(i: 0));
7604 if (!ICI)
7605 return false;
7606 Value *LHS = ICI->getOperand(i_nocapture: 0);
7607 Value *RHS = ICI->getOperand(i_nocapture: 1);
7608 if (ICI->getPredicate() == CmpInst::ICMP_EQ ||
7609 ICI->getPredicate() == CmpInst::ICMP_NE) {
7610 if (!(isa<ConstantInt>(Val: RHS) && cast<ConstantInt>(Val: RHS)->isZero()))
7611 return true;
7612 } else if (getTypeSizeInBits(Ty: LHS->getType()) >
7613 getTypeSizeInBits(Ty: U->getType()))
7614 return true;
7615 return false;
7616 };
7617 if (CanSimplifyToUnknown())
7618 return getUnknown(V: U);
7619
7620 for (Value *Inc : U->operands())
7621 Ops.push_back(Elt: Inc);
7622 return nullptr;
7623 break;
7624 }
7625 case Instruction::Call:
7626 case Instruction::Invoke:
7627 if (Value *RV = cast<CallBase>(Val: U)->getReturnedArgOperand()) {
7628 Ops.push_back(Elt: RV);
7629 return nullptr;
7630 }
7631
7632 if (auto *II = dyn_cast<IntrinsicInst>(Val: U)) {
7633 switch (II->getIntrinsicID()) {
7634 case Intrinsic::abs:
7635 Ops.push_back(Elt: II->getArgOperand(i: 0));
7636 return nullptr;
7637 case Intrinsic::umax:
7638 case Intrinsic::umin:
7639 case Intrinsic::smax:
7640 case Intrinsic::smin:
7641 case Intrinsic::usub_sat:
7642 case Intrinsic::uadd_sat:
7643 Ops.push_back(Elt: II->getArgOperand(i: 0));
7644 Ops.push_back(Elt: II->getArgOperand(i: 1));
7645 return nullptr;
7646 case Intrinsic::start_loop_iterations:
7647 case Intrinsic::annotation:
7648 case Intrinsic::ptr_annotation:
7649 Ops.push_back(Elt: II->getArgOperand(i: 0));
7650 return nullptr;
7651 default:
7652 break;
7653 }
7654 }
7655 break;
7656 }
7657
7658 return nullptr;
7659}
7660
7661const SCEV *ScalarEvolution::createSCEV(Value *V) {
7662 if (!isSCEVable(Ty: V->getType()))
7663 return getUnknown(V);
7664
7665 if (Instruction *I = dyn_cast<Instruction>(Val: V)) {
7666 // Don't attempt to analyze instructions in blocks that aren't
7667 // reachable. Such instructions don't matter, and they aren't required
7668 // to obey basic rules for definitions dominating uses which this
7669 // analysis depends on.
7670 if (!DT.isReachableFromEntry(A: I->getParent()))
7671 return getUnknown(V: PoisonValue::get(T: V->getType()));
7672 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(Val: V))
7673 return getConstant(V: CI);
7674 else if (isa<GlobalAlias>(Val: V))
7675 return getUnknown(V);
7676 else if (!isa<ConstantExpr>(Val: V))
7677 return getUnknown(V);
7678
7679 const SCEV *LHS;
7680 const SCEV *RHS;
7681
7682 Operator *U = cast<Operator>(Val: V);
7683 if (auto BO =
7684 MatchBinaryOp(V: U, DL: getDataLayout(), AC, DT, CxtI: dyn_cast<Instruction>(Val: V))) {
7685 switch (BO->Opcode) {
7686 case Instruction::Add: {
7687 // The simple thing to do would be to just call getSCEV on both operands
7688 // and call getAddExpr with the result. However if we're looking at a
7689 // bunch of things all added together, this can be quite inefficient,
7690 // because it leads to N-1 getAddExpr calls for N ultimate operands.
7691 // Instead, gather up all the operands and make a single getAddExpr call.
7692 // LLVM IR canonical form means we need only traverse the left operands.
7693 SmallVector<const SCEV *, 4> AddOps;
7694 do {
7695 if (BO->Op) {
7696 if (auto *OpSCEV = getExistingSCEV(V: BO->Op)) {
7697 AddOps.push_back(Elt: OpSCEV);
7698 break;
7699 }
7700
7701 // If a NUW or NSW flag can be applied to the SCEV for this
7702 // addition, then compute the SCEV for this addition by itself
7703 // with a separate call to getAddExpr. We need to do that
7704 // instead of pushing the operands of the addition onto AddOps,
7705 // since the flags are only known to apply to this particular
7706 // addition - they may not apply to other additions that can be
7707 // formed with operands from AddOps.
7708 const SCEV *RHS = getSCEV(V: BO->RHS);
7709 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(V: BO->Op);
7710 if (Flags != SCEV::FlagAnyWrap) {
7711 const SCEV *LHS = getSCEV(V: BO->LHS);
7712 if (BO->Opcode == Instruction::Sub)
7713 AddOps.push_back(Elt: getMinusSCEV(LHS, RHS, Flags));
7714 else
7715 AddOps.push_back(Elt: getAddExpr(LHS, RHS, Flags));
7716 break;
7717 }
7718 }
7719
7720 if (BO->Opcode == Instruction::Sub)
7721 AddOps.push_back(Elt: getNegativeSCEV(V: getSCEV(V: BO->RHS)));
7722 else
7723 AddOps.push_back(Elt: getSCEV(V: BO->RHS));
7724
7725 auto NewBO = MatchBinaryOp(V: BO->LHS, DL: getDataLayout(), AC, DT,
7726 CxtI: dyn_cast<Instruction>(Val: V));
7727 if (!NewBO || (NewBO->Opcode != Instruction::Add &&
7728 NewBO->Opcode != Instruction::Sub)) {
7729 AddOps.push_back(Elt: getSCEV(V: BO->LHS));
7730 break;
7731 }
7732 BO = NewBO;
7733 } while (true);
7734
7735 return getAddExpr(Ops&: AddOps);
7736 }
7737
7738 case Instruction::Mul: {
7739 SmallVector<const SCEV *, 4> MulOps;
7740 do {
7741 if (BO->Op) {
7742 if (auto *OpSCEV = getExistingSCEV(V: BO->Op)) {
7743 MulOps.push_back(Elt: OpSCEV);
7744 break;
7745 }
7746
7747 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(V: BO->Op);
7748 if (Flags != SCEV::FlagAnyWrap) {
7749 LHS = getSCEV(V: BO->LHS);
7750 RHS = getSCEV(V: BO->RHS);
7751 MulOps.push_back(Elt: getMulExpr(LHS, RHS, Flags));
7752 break;
7753 }
7754 }
7755
7756 MulOps.push_back(Elt: getSCEV(V: BO->RHS));
7757 auto NewBO = MatchBinaryOp(V: BO->LHS, DL: getDataLayout(), AC, DT,
7758 CxtI: dyn_cast<Instruction>(Val: V));
7759 if (!NewBO || NewBO->Opcode != Instruction::Mul) {
7760 MulOps.push_back(Elt: getSCEV(V: BO->LHS));
7761 break;
7762 }
7763 BO = NewBO;
7764 } while (true);
7765
7766 return getMulExpr(Ops&: MulOps);
7767 }
7768 case Instruction::UDiv:
7769 LHS = getSCEV(V: BO->LHS);
7770 RHS = getSCEV(V: BO->RHS);
7771 return getUDivExpr(LHS, RHS);
7772 case Instruction::URem:
7773 LHS = getSCEV(V: BO->LHS);
7774 RHS = getSCEV(V: BO->RHS);
7775 return getURemExpr(LHS, RHS);
7776 case Instruction::Sub: {
7777 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
7778 if (BO->Op)
7779 Flags = getNoWrapFlagsFromUB(V: BO->Op);
7780 LHS = getSCEV(V: BO->LHS);
7781 RHS = getSCEV(V: BO->RHS);
7782 return getMinusSCEV(LHS, RHS, Flags);
7783 }
7784 case Instruction::And:
7785 // For an expression like x&255 that merely masks off the high bits,
7786 // use zext(trunc(x)) as the SCEV expression.
7787 if (ConstantInt *CI = dyn_cast<ConstantInt>(Val: BO->RHS)) {
7788 if (CI->isZero())
7789 return getSCEV(V: BO->RHS);
7790 if (CI->isMinusOne())
7791 return getSCEV(V: BO->LHS);
7792 const APInt &A = CI->getValue();
7793
7794 // Instcombine's ShrinkDemandedConstant may strip bits out of
7795 // constants, obscuring what would otherwise be a low-bits mask.
7796 // Use computeKnownBits to compute what ShrinkDemandedConstant
7797 // knew about to reconstruct a low-bits mask value.
7798 unsigned LZ = A.countl_zero();
7799 unsigned TZ = A.countr_zero();
7800 unsigned BitWidth = A.getBitWidth();
7801 KnownBits Known(BitWidth);
7802 computeKnownBits(V: BO->LHS, Known, DL: getDataLayout(),
7803 Depth: 0, AC: &AC, CxtI: nullptr, DT: &DT);
7804
7805 APInt EffectiveMask =
7806 APInt::getLowBitsSet(numBits: BitWidth, loBitsSet: BitWidth - LZ - TZ).shl(shiftAmt: TZ);
7807 if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
7808 const SCEV *MulCount = getConstant(Val: APInt::getOneBitSet(numBits: BitWidth, BitNo: TZ));
7809 const SCEV *LHS = getSCEV(V: BO->LHS);
7810 const SCEV *ShiftedLHS = nullptr;
7811 if (auto *LHSMul = dyn_cast<SCEVMulExpr>(Val: LHS)) {
7812 if (auto *OpC = dyn_cast<SCEVConstant>(Val: LHSMul->getOperand(i: 0))) {
7813 // For an expression like (x * 8) & 8, simplify the multiply.
7814 unsigned MulZeros = OpC->getAPInt().countr_zero();
7815 unsigned GCD = std::min(a: MulZeros, b: TZ);
7816 APInt DivAmt = APInt::getOneBitSet(numBits: BitWidth, BitNo: TZ - GCD);
7817 SmallVector<const SCEV*, 4> MulOps;
7818 MulOps.push_back(Elt: getConstant(Val: OpC->getAPInt().lshr(shiftAmt: GCD)));
7819 append_range(C&: MulOps, R: LHSMul->operands().drop_front());
7820 auto *NewMul = getMulExpr(Ops&: MulOps, OrigFlags: LHSMul->getNoWrapFlags());
7821 ShiftedLHS = getUDivExpr(LHS: NewMul, RHS: getConstant(Val: DivAmt));
7822 }
7823 }
7824 if (!ShiftedLHS)
7825 ShiftedLHS = getUDivExpr(LHS, RHS: MulCount);
7826 return getMulExpr(
7827 LHS: getZeroExtendExpr(
7828 Op: getTruncateExpr(Op: ShiftedLHS,
7829 Ty: IntegerType::get(C&: getContext(), NumBits: BitWidth - LZ - TZ)),
7830 Ty: BO->LHS->getType()),
7831 RHS: MulCount);
7832 }
7833 }
7834 // Binary `and` is a bit-wise `umin`.
7835 if (BO->LHS->getType()->isIntegerTy(Bitwidth: 1)) {
7836 LHS = getSCEV(V: BO->LHS);
7837 RHS = getSCEV(V: BO->RHS);
7838 return getUMinExpr(LHS, RHS);
7839 }
7840 break;
7841
7842 case Instruction::Or:
7843 // Binary `or` is a bit-wise `umax`.
7844 if (BO->LHS->getType()->isIntegerTy(Bitwidth: 1)) {
7845 LHS = getSCEV(V: BO->LHS);
7846 RHS = getSCEV(V: BO->RHS);
7847 return getUMaxExpr(LHS, RHS);
7848 }
7849 break;
7850
7851 case Instruction::Xor:
7852 if (ConstantInt *CI = dyn_cast<ConstantInt>(Val: BO->RHS)) {
7853 // If the RHS of xor is -1, then this is a not operation.
7854 if (CI->isMinusOne())
7855 return getNotSCEV(V: getSCEV(V: BO->LHS));
7856
7857 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
7858 // This is a variant of the check for xor with -1, and it handles
7859 // the case where instcombine has trimmed non-demanded bits out
7860 // of an xor with -1.
7861 if (auto *LBO = dyn_cast<BinaryOperator>(Val: BO->LHS))
7862 if (ConstantInt *LCI = dyn_cast<ConstantInt>(Val: LBO->getOperand(i_nocapture: 1)))
7863 if (LBO->getOpcode() == Instruction::And &&
7864 LCI->getValue() == CI->getValue())
7865 if (const SCEVZeroExtendExpr *Z =
7866 dyn_cast<SCEVZeroExtendExpr>(Val: getSCEV(V: BO->LHS))) {
7867 Type *UTy = BO->LHS->getType();
7868 const SCEV *Z0 = Z->getOperand();
7869 Type *Z0Ty = Z0->getType();
7870 unsigned Z0TySize = getTypeSizeInBits(Ty: Z0Ty);
7871
7872 // If C is a low-bits mask, the zero extend is serving to
7873 // mask off the high bits. Complement the operand and
7874 // re-apply the zext.
7875 if (CI->getValue().isMask(numBits: Z0TySize))
7876 return getZeroExtendExpr(Op: getNotSCEV(V: Z0), Ty: UTy);
7877
7878 // If C is a single bit, it may be in the sign-bit position
7879 // before the zero-extend. In this case, represent the xor
7880 // using an add, which is equivalent, and re-apply the zext.
7881 APInt Trunc = CI->getValue().trunc(width: Z0TySize);
7882 if (Trunc.zext(width: getTypeSizeInBits(Ty: UTy)) == CI->getValue() &&
7883 Trunc.isSignMask())
7884 return getZeroExtendExpr(Op: getAddExpr(LHS: Z0, RHS: getConstant(Val: Trunc)),
7885 Ty: UTy);
7886 }
7887 }
7888 break;
7889
7890 case Instruction::Shl:
7891 // Turn shift left of a constant amount into a multiply.
7892 if (ConstantInt *SA = dyn_cast<ConstantInt>(Val: BO->RHS)) {
7893 uint32_t BitWidth = cast<IntegerType>(Val: SA->getType())->getBitWidth();
7894
7895 // If the shift count is not less than the bitwidth, the result of
7896 // the shift is undefined. Don't try to analyze it, because the
7897 // resolution chosen here may differ from the resolution chosen in
7898 // other parts of the compiler.
7899 if (SA->getValue().uge(RHS: BitWidth))
7900 break;
7901
7902 // We can safely preserve the nuw flag in all cases. It's also safe to
7903 // turn a nuw nsw shl into a nuw nsw mul. However, nsw in isolation
7904 // requires special handling. It can be preserved as long as we're not
7905 // left shifting by bitwidth - 1.
7906 auto Flags = SCEV::FlagAnyWrap;
7907 if (BO->Op) {
7908 auto MulFlags = getNoWrapFlagsFromUB(V: BO->Op);
7909 if ((MulFlags & SCEV::FlagNSW) &&
7910 ((MulFlags & SCEV::FlagNUW) || SA->getValue().ult(RHS: BitWidth - 1)))
7911 Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNSW);
7912 if (MulFlags & SCEV::FlagNUW)
7913 Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNUW);
7914 }
7915
7916 ConstantInt *X = ConstantInt::get(
7917 Context&: getContext(), V: APInt::getOneBitSet(numBits: BitWidth, BitNo: SA->getZExtValue()));
7918 return getMulExpr(LHS: getSCEV(V: BO->LHS), RHS: getConstant(V: X), Flags);
7919 }
7920 break;
7921
7922 case Instruction::AShr:
7923 // AShr X, C, where C is a constant.
7924 ConstantInt *CI = dyn_cast<ConstantInt>(Val: BO->RHS);
7925 if (!CI)
7926 break;
7927
7928 Type *OuterTy = BO->LHS->getType();
7929 uint64_t BitWidth = getTypeSizeInBits(Ty: OuterTy);
7930 // If the shift count is not less than the bitwidth, the result of
7931 // the shift is undefined. Don't try to analyze it, because the
7932 // resolution chosen here may differ from the resolution chosen in
7933 // other parts of the compiler.
7934 if (CI->getValue().uge(RHS: BitWidth))
7935 break;
7936
7937 if (CI->isZero())
7938 return getSCEV(V: BO->LHS); // shift by zero --> noop
7939
7940 uint64_t AShrAmt = CI->getZExtValue();
7941 Type *TruncTy = IntegerType::get(C&: getContext(), NumBits: BitWidth - AShrAmt);
7942
7943 Operator *L = dyn_cast<Operator>(Val: BO->LHS);
7944 const SCEV *AddTruncateExpr = nullptr;
7945 ConstantInt *ShlAmtCI = nullptr;
7946 const SCEV *AddConstant = nullptr;
7947
7948 if (L && L->getOpcode() == Instruction::Add) {
7949 // X = Shl A, n
7950 // Y = Add X, c
7951 // Z = AShr Y, m
7952 // n, c and m are constants.
7953
7954 Operator *LShift = dyn_cast<Operator>(Val: L->getOperand(i: 0));
7955 ConstantInt *AddOperandCI = dyn_cast<ConstantInt>(Val: L->getOperand(i: 1));
7956 if (LShift && LShift->getOpcode() == Instruction::Shl) {
7957 if (AddOperandCI) {
7958 const SCEV *ShlOp0SCEV = getSCEV(V: LShift->getOperand(i: 0));
7959 ShlAmtCI = dyn_cast<ConstantInt>(Val: LShift->getOperand(i: 1));
7960 // since we truncate to TruncTy, the AddConstant should be of the
7961 // same type, so create a new Constant with type same as TruncTy.
7962 // Also, the Add constant should be shifted right by AShr amount.
7963 APInt AddOperand = AddOperandCI->getValue().ashr(ShiftAmt: AShrAmt);
7964 AddConstant = getConstant(Val: AddOperand.trunc(width: BitWidth - AShrAmt));
7965 // we model the expression as sext(add(trunc(A), c << n)), since the
7966 // sext(trunc) part is already handled below, we create a
7967 // AddExpr(TruncExp) which will be used later.
7968 AddTruncateExpr = getTruncateExpr(Op: ShlOp0SCEV, Ty: TruncTy);
7969 }
7970 }
7971 } else if (L && L->getOpcode() == Instruction::Shl) {
7972 // X = Shl A, n
7973 // Y = AShr X, m
7974 // Both n and m are constant.
7975
7976 const SCEV *ShlOp0SCEV = getSCEV(V: L->getOperand(i: 0));
7977 ShlAmtCI = dyn_cast<ConstantInt>(Val: L->getOperand(i: 1));
7978 AddTruncateExpr = getTruncateExpr(Op: ShlOp0SCEV, Ty: TruncTy);
7979 }
7980
7981 if (AddTruncateExpr && ShlAmtCI) {
7982 // We can merge the two given cases into a single SCEV statement,
7983 // incase n = m, the mul expression will be 2^0, so it gets resolved to
7984 // a simpler case. The following code handles the two cases:
7985 //
7986 // 1) For a two-shift sext-inreg, i.e. n = m,
7987 // use sext(trunc(x)) as the SCEV expression.
7988 //
7989 // 2) When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
7990 // expression. We already checked that ShlAmt < BitWidth, so
7991 // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
7992 // ShlAmt - AShrAmt < Amt.
7993 const APInt &ShlAmt = ShlAmtCI->getValue();
7994 if (ShlAmt.ult(RHS: BitWidth) && ShlAmt.uge(RHS: AShrAmt)) {
7995 APInt Mul = APInt::getOneBitSet(numBits: BitWidth - AShrAmt,
7996 BitNo: ShlAmtCI->getZExtValue() - AShrAmt);
7997 const SCEV *CompositeExpr =
7998 getMulExpr(LHS: AddTruncateExpr, RHS: getConstant(Val: Mul));
7999 if (L->getOpcode() != Instruction::Shl)
8000 CompositeExpr = getAddExpr(LHS: CompositeExpr, RHS: AddConstant);
8001
8002 return getSignExtendExpr(Op: CompositeExpr, Ty: OuterTy);
8003 }
8004 }
8005 break;
8006 }
8007 }
8008
8009 switch (U->getOpcode()) {
8010 case Instruction::Trunc:
8011 return getTruncateExpr(Op: getSCEV(V: U->getOperand(i: 0)), Ty: U->getType());
8012
8013 case Instruction::ZExt:
8014 return getZeroExtendExpr(Op: getSCEV(V: U->getOperand(i: 0)), Ty: U->getType());
8015
8016 case Instruction::SExt:
8017 if (auto BO = MatchBinaryOp(V: U->getOperand(i: 0), DL: getDataLayout(), AC, DT,
8018 CxtI: dyn_cast<Instruction>(Val: V))) {
8019 // The NSW flag of a subtract does not always survive the conversion to
8020 // A + (-1)*B. By pushing sign extension onto its operands we are much
8021 // more likely to preserve NSW and allow later AddRec optimisations.
8022 //
8023 // NOTE: This is effectively duplicating this logic from getSignExtend:
8024 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
8025 // but by that point the NSW information has potentially been lost.
8026 if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
8027 Type *Ty = U->getType();
8028 auto *V1 = getSignExtendExpr(Op: getSCEV(V: BO->LHS), Ty);
8029 auto *V2 = getSignExtendExpr(Op: getSCEV(V: BO->RHS), Ty);
8030 return getMinusSCEV(LHS: V1, RHS: V2, Flags: SCEV::FlagNSW);
8031 }
8032 }
8033 return getSignExtendExpr(Op: getSCEV(V: U->getOperand(i: 0)), Ty: U->getType());
8034
8035 case Instruction::BitCast:
8036 // BitCasts are no-op casts so we just eliminate the cast.
8037 if (isSCEVable(Ty: U->getType()) && isSCEVable(Ty: U->getOperand(i: 0)->getType()))
8038 return getSCEV(V: U->getOperand(i: 0));
8039 break;
8040
8041 case Instruction::PtrToInt: {
8042 // Pointer to integer cast is straight-forward, so do model it.
8043 const SCEV *Op = getSCEV(V: U->getOperand(i: 0));
8044 Type *DstIntTy = U->getType();
8045 // But only if effective SCEV (integer) type is wide enough to represent
8046 // all possible pointer values.
8047 const SCEV *IntOp = getPtrToIntExpr(Op, Ty: DstIntTy);
8048 if (isa<SCEVCouldNotCompute>(Val: IntOp))
8049 return getUnknown(V);
8050 return IntOp;
8051 }
8052 case Instruction::IntToPtr:
8053 // Just don't deal with inttoptr casts.
8054 return getUnknown(V);
8055
8056 case Instruction::SDiv:
8057 // If both operands are non-negative, this is just an udiv.
8058 if (isKnownNonNegative(S: getSCEV(V: U->getOperand(i: 0))) &&
8059 isKnownNonNegative(S: getSCEV(V: U->getOperand(i: 1))))
8060 return getUDivExpr(LHS: getSCEV(V: U->getOperand(i: 0)), RHS: getSCEV(V: U->getOperand(i: 1)));
8061 break;
8062
8063 case Instruction::SRem:
8064 // If both operands are non-negative, this is just an urem.
8065 if (isKnownNonNegative(S: getSCEV(V: U->getOperand(i: 0))) &&
8066 isKnownNonNegative(S: getSCEV(V: U->getOperand(i: 1))))
8067 return getURemExpr(LHS: getSCEV(V: U->getOperand(i: 0)), RHS: getSCEV(V: U->getOperand(i: 1)));
8068 break;
8069
8070 case Instruction::GetElementPtr:
8071 return createNodeForGEP(GEP: cast<GEPOperator>(Val: U));
8072
8073 case Instruction::PHI:
8074 return createNodeForPHI(PN: cast<PHINode>(Val: U));
8075
8076 case Instruction::Select:
8077 return createNodeForSelectOrPHI(V: U, Cond: U->getOperand(i: 0), TrueVal: U->getOperand(i: 1),
8078 FalseVal: U->getOperand(i: 2));
8079
8080 case Instruction::Call:
8081 case Instruction::Invoke:
8082 if (Value *RV = cast<CallBase>(Val: U)->getReturnedArgOperand())
8083 return getSCEV(V: RV);
8084
8085 if (auto *II = dyn_cast<IntrinsicInst>(Val: U)) {
8086 switch (II->getIntrinsicID()) {
8087 case Intrinsic::abs:
8088 return getAbsExpr(
8089 Op: getSCEV(V: II->getArgOperand(i: 0)),
8090 /*IsNSW=*/cast<ConstantInt>(Val: II->getArgOperand(i: 1))->isOne());
8091 case Intrinsic::umax:
8092 LHS = getSCEV(V: II->getArgOperand(i: 0));
8093 RHS = getSCEV(V: II->getArgOperand(i: 1));
8094 return getUMaxExpr(LHS, RHS);
8095 case Intrinsic::umin:
8096 LHS = getSCEV(V: II->getArgOperand(i: 0));
8097 RHS = getSCEV(V: II->getArgOperand(i: 1));
8098 return getUMinExpr(LHS, RHS);
8099 case Intrinsic::smax:
8100 LHS = getSCEV(V: II->getArgOperand(i: 0));
8101 RHS = getSCEV(V: II->getArgOperand(i: 1));
8102 return getSMaxExpr(LHS, RHS);
8103 case Intrinsic::smin:
8104 LHS = getSCEV(V: II->getArgOperand(i: 0));
8105 RHS = getSCEV(V: II->getArgOperand(i: 1));
8106 return getSMinExpr(LHS, RHS);
8107 case Intrinsic::usub_sat: {
8108 const SCEV *X = getSCEV(V: II->getArgOperand(i: 0));
8109 const SCEV *Y = getSCEV(V: II->getArgOperand(i: 1));
8110 const SCEV *ClampedY = getUMinExpr(LHS: X, RHS: Y);
8111 return getMinusSCEV(LHS: X, RHS: ClampedY, Flags: SCEV::FlagNUW);
8112 }
8113 case Intrinsic::uadd_sat: {
8114 const SCEV *X = getSCEV(V: II->getArgOperand(i: 0));
8115 const SCEV *Y = getSCEV(V: II->getArgOperand(i: 1));
8116 const SCEV *ClampedX = getUMinExpr(LHS: X, RHS: getNotSCEV(V: Y));
8117 return getAddExpr(LHS: ClampedX, RHS: Y, Flags: SCEV::FlagNUW);
8118 }
8119 case Intrinsic::start_loop_iterations:
8120 case Intrinsic::annotation:
8121 case Intrinsic::ptr_annotation:
8122 // A start_loop_iterations or llvm.annotation or llvm.prt.annotation is
8123 // just eqivalent to the first operand for SCEV purposes.
8124 return getSCEV(V: II->getArgOperand(i: 0));
8125 case Intrinsic::vscale:
8126 return getVScale(Ty: II->getType());
8127 default:
8128 break;
8129 }
8130 }
8131 break;
8132 }
8133
8134 return getUnknown(V);
8135}
8136
8137//===----------------------------------------------------------------------===//
8138// Iteration Count Computation Code
8139//
8140
8141const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount) {
8142 if (isa<SCEVCouldNotCompute>(Val: ExitCount))
8143 return getCouldNotCompute();
8144
8145 auto *ExitCountType = ExitCount->getType();
8146 assert(ExitCountType->isIntegerTy());
8147 auto *EvalTy = Type::getIntNTy(C&: ExitCountType->getContext(),
8148 N: 1 + ExitCountType->getScalarSizeInBits());
8149 return getTripCountFromExitCount(ExitCount, EvalTy, L: nullptr);
8150}
8151
8152const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount,
8153 Type *EvalTy,
8154 const Loop *L) {
8155 if (isa<SCEVCouldNotCompute>(Val: ExitCount))
8156 return getCouldNotCompute();
8157
8158 unsigned ExitCountSize = getTypeSizeInBits(Ty: ExitCount->getType());
8159 unsigned EvalSize = EvalTy->getPrimitiveSizeInBits();
8160
8161 auto CanAddOneWithoutOverflow = [&]() {
8162 ConstantRange ExitCountRange =
8163 getRangeRef(S: ExitCount, SignHint: RangeSignHint::HINT_RANGE_UNSIGNED);
8164 if (!ExitCountRange.contains(Val: APInt::getMaxValue(numBits: ExitCountSize)))
8165 return true;
8166
8167 return L && isLoopEntryGuardedByCond(L, Pred: ICmpInst::ICMP_NE, LHS: ExitCount,
8168 RHS: getMinusOne(Ty: ExitCount->getType()));
8169 };
8170
8171 // If we need to zero extend the backedge count, check if we can add one to
8172 // it prior to zero extending without overflow. Provided this is safe, it
8173 // allows better simplification of the +1.
8174 if (EvalSize > ExitCountSize && CanAddOneWithoutOverflow())
8175 return getZeroExtendExpr(
8176 Op: getAddExpr(LHS: ExitCount, RHS: getOne(Ty: ExitCount->getType())), Ty: EvalTy);
8177
8178 // Get the total trip count from the count by adding 1. This may wrap.
8179 return getAddExpr(LHS: getTruncateOrZeroExtend(V: ExitCount, Ty: EvalTy), RHS: getOne(Ty: EvalTy));
8180}
8181
8182static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
8183 if (!ExitCount)
8184 return 0;
8185
8186 ConstantInt *ExitConst = ExitCount->getValue();
8187
8188 // Guard against huge trip counts.
8189 if (ExitConst->getValue().getActiveBits() > 32)
8190 return 0;
8191
8192 // In case of integer overflow, this returns 0, which is correct.
8193 return ((unsigned)ExitConst->getZExtValue()) + 1;
8194}
8195
8196unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
8197 auto *ExitCount = dyn_cast<SCEVConstant>(Val: getBackedgeTakenCount(L, Kind: Exact));
8198 return getConstantTripCount(ExitCount);
8199}
8200
8201unsigned
8202ScalarEvolution::getSmallConstantTripCount(const Loop *L,
8203 const BasicBlock *ExitingBlock) {
8204 assert(ExitingBlock && "Must pass a non-null exiting block!");
8205 assert(L->isLoopExiting(ExitingBlock) &&
8206 "Exiting block must actually branch out of the loop!");
8207 const SCEVConstant *ExitCount =
8208 dyn_cast<SCEVConstant>(Val: getExitCount(L, ExitingBlock));
8209 return getConstantTripCount(ExitCount);
8210}
8211
8212unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) {
8213 const auto *MaxExitCount =
8214 dyn_cast<SCEVConstant>(Val: getConstantMaxBackedgeTakenCount(L));
8215 return getConstantTripCount(ExitCount: MaxExitCount);
8216}
8217
8218unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
8219 SmallVector<BasicBlock *, 8> ExitingBlocks;
8220 L->getExitingBlocks(ExitingBlocks);
8221
8222 std::optional<unsigned> Res;
8223 for (auto *ExitingBB : ExitingBlocks) {
8224 unsigned Multiple = getSmallConstantTripMultiple(L, ExitingBlock: ExitingBB);
8225 if (!Res)
8226 Res = Multiple;
8227 Res = (unsigned)std::gcd(m: *Res, n: Multiple);
8228 }
8229 return Res.value_or(u: 1);
8230}
8231
8232unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
8233 const SCEV *ExitCount) {
8234 if (ExitCount == getCouldNotCompute())
8235 return 1;
8236
8237 // Get the trip count
8238 const SCEV *TCExpr = getTripCountFromExitCount(ExitCount: applyLoopGuards(Expr: ExitCount, L));
8239
8240 APInt Multiple = getNonZeroConstantMultiple(S: TCExpr);
8241 // If a trip multiple is huge (>=2^32), the trip count is still divisible by
8242 // the greatest power of 2 divisor less than 2^32.
8243 return Multiple.getActiveBits() > 32
8244 ? 1U << std::min(a: (unsigned)31, b: Multiple.countTrailingZeros())
8245 : (unsigned)Multiple.zextOrTrunc(width: 32).getZExtValue();
8246}
8247
8248/// Returns the largest constant divisor of the trip count of this loop as a
8249/// normal unsigned value, if possible. This means that the actual trip count is
8250/// always a multiple of the returned value (don't forget the trip count could
8251/// very well be zero as well!).
8252///
8253/// Returns 1 if the trip count is unknown or not guaranteed to be the
8254/// multiple of a constant (which is also the case if the trip count is simply
8255/// constant, use getSmallConstantTripCount for that case), Will also return 1
8256/// if the trip count is very large (>= 2^32).
8257///
8258/// As explained in the comments for getSmallConstantTripCount, this assumes
8259/// that control exits the loop via ExitingBlock.
8260unsigned
8261ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
8262 const BasicBlock *ExitingBlock) {
8263 assert(ExitingBlock && "Must pass a non-null exiting block!");
8264 assert(L->isLoopExiting(ExitingBlock) &&
8265 "Exiting block must actually branch out of the loop!");
8266 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
8267 return getSmallConstantTripMultiple(L, ExitCount);
8268}
8269
8270const SCEV *ScalarEvolution::getExitCount(const Loop *L,
8271 const BasicBlock *ExitingBlock,
8272 ExitCountKind Kind) {
8273 switch (Kind) {
8274 case Exact:
8275 return getBackedgeTakenInfo(L).getExact(ExitingBlock, SE: this);
8276 case SymbolicMaximum:
8277 return getBackedgeTakenInfo(L).getSymbolicMax(ExitingBlock, SE: this);
8278 case ConstantMaximum:
8279 return getBackedgeTakenInfo(L).getConstantMax(ExitingBlock, SE: this);
8280 };
8281 llvm_unreachable("Invalid ExitCountKind!");
8282}
8283
8284const SCEV *
8285ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
8286 SmallVector<const SCEVPredicate *, 4> &Preds) {
8287 return getPredicatedBackedgeTakenInfo(L).getExact(L, SE: this, Predicates: &Preds);
8288}
8289
8290const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L,
8291 ExitCountKind Kind) {
8292 switch (Kind) {
8293 case Exact:
8294 return getBackedgeTakenInfo(L).getExact(L, SE: this);
8295 case ConstantMaximum:
8296 return getBackedgeTakenInfo(L).getConstantMax(SE: this);
8297 case SymbolicMaximum:
8298 return getBackedgeTakenInfo(L).getSymbolicMax(L, SE: this);
8299 };
8300 llvm_unreachable("Invalid ExitCountKind!");
8301}
8302
8303const SCEV *ScalarEvolution::getPredicatedSymbolicMaxBackedgeTakenCount(
8304 const Loop *L, SmallVector<const SCEVPredicate *, 4> &Preds) {
8305 return getPredicatedBackedgeTakenInfo(L).getSymbolicMax(L, SE: this, Predicates: &Preds);
8306}
8307
8308bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
8309 return getBackedgeTakenInfo(L).isConstantMaxOrZero(SE: this);
8310}
8311
8312/// Push PHI nodes in the header of the given loop onto the given Worklist.
8313static void PushLoopPHIs(const Loop *L,
8314 SmallVectorImpl<Instruction *> &Worklist,
8315 SmallPtrSetImpl<Instruction *> &Visited) {
8316 BasicBlock *Header = L->getHeader();
8317
8318 // Push all Loop-header PHIs onto the Worklist stack.
8319 for (PHINode &PN : Header->phis())
8320 if (Visited.insert(Ptr: &PN).second)
8321 Worklist.push_back(Elt: &PN);
8322}
8323
8324ScalarEvolution::BackedgeTakenInfo &
8325ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
8326 auto &BTI = getBackedgeTakenInfo(L);
8327 if (BTI.hasFullInfo())
8328 return BTI;
8329
8330 auto Pair = PredicatedBackedgeTakenCounts.insert(KV: {L, BackedgeTakenInfo()});
8331
8332 if (!Pair.second)
8333 return Pair.first->second;
8334
8335 BackedgeTakenInfo Result =
8336 computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
8337
8338 return PredicatedBackedgeTakenCounts.find(Val: L)->second = std::move(Result);
8339}
8340
8341ScalarEvolution::BackedgeTakenInfo &
8342ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
8343 // Initially insert an invalid entry for this loop. If the insertion
8344 // succeeds, proceed to actually compute a backedge-taken count and
8345 // update the value. The temporary CouldNotCompute value tells SCEV
8346 // code elsewhere that it shouldn't attempt to request a new
8347 // backedge-taken count, which could result in infinite recursion.
8348 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
8349 BackedgeTakenCounts.insert(KV: {L, BackedgeTakenInfo()});
8350 if (!Pair.second)
8351 return Pair.first->second;
8352
8353 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
8354 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
8355 // must be cleared in this scope.
8356 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
8357
8358 // Now that we know more about the trip count for this loop, forget any
8359 // existing SCEV values for PHI nodes in this loop since they are only
8360 // conservative estimates made without the benefit of trip count
8361 // information. This invalidation is not necessary for correctness, and is
8362 // only done to produce more precise results.
8363 if (Result.hasAnyInfo()) {
8364 // Invalidate any expression using an addrec in this loop.
8365 SmallVector<const SCEV *, 8> ToForget;
8366 auto LoopUsersIt = LoopUsers.find(Val: L);
8367 if (LoopUsersIt != LoopUsers.end())
8368 append_range(C&: ToForget, R&: LoopUsersIt->second);
8369 forgetMemoizedResults(SCEVs: ToForget);
8370
8371 // Invalidate constant-evolved loop header phis.
8372 for (PHINode &PN : L->getHeader()->phis())
8373 ConstantEvolutionLoopExitValue.erase(Val: &PN);
8374 }
8375
8376 // Re-lookup the insert position, since the call to
8377 // computeBackedgeTakenCount above could result in a
8378 // recusive call to getBackedgeTakenInfo (on a different
8379 // loop), which would invalidate the iterator computed
8380 // earlier.
8381 return BackedgeTakenCounts.find(Val: L)->second = std::move(Result);
8382}
8383
8384void ScalarEvolution::forgetAllLoops() {
8385 // This method is intended to forget all info about loops. It should
8386 // invalidate caches as if the following happened:
8387 // - The trip counts of all loops have changed arbitrarily
8388 // - Every llvm::Value has been updated in place to produce a different
8389 // result.
8390 BackedgeTakenCounts.clear();
8391 PredicatedBackedgeTakenCounts.clear();
8392 BECountUsers.clear();
8393 LoopPropertiesCache.clear();
8394 ConstantEvolutionLoopExitValue.clear();
8395 ValueExprMap.clear();
8396 ValuesAtScopes.clear();
8397 ValuesAtScopesUsers.clear();
8398 LoopDispositions.clear();
8399 BlockDispositions.clear();
8400 UnsignedRanges.clear();
8401 SignedRanges.clear();
8402 ExprValueMap.clear();
8403 HasRecMap.clear();
8404 ConstantMultipleCache.clear();
8405 PredicatedSCEVRewrites.clear();
8406 FoldCache.clear();
8407 FoldCacheUser.clear();
8408}
8409void ScalarEvolution::visitAndClearUsers(
8410 SmallVectorImpl<Instruction *> &Worklist,
8411 SmallPtrSetImpl<Instruction *> &Visited,
8412 SmallVectorImpl<const SCEV *> &ToForget) {
8413 while (!Worklist.empty()) {
8414 Instruction *I = Worklist.pop_back_val();
8415 if (!isSCEVable(Ty: I->getType()) && !isa<WithOverflowInst>(Val: I))
8416 continue;
8417
8418 ValueExprMapType::iterator It =
8419 ValueExprMap.find_as(Val: static_cast<Value *>(I));
8420 if (It != ValueExprMap.end()) {
8421 eraseValueFromMap(V: It->first);
8422 ToForget.push_back(Elt: It->second);
8423 if (PHINode *PN = dyn_cast<PHINode>(Val: I))
8424 ConstantEvolutionLoopExitValue.erase(Val: PN);
8425 }
8426
8427 PushDefUseChildren(I, Worklist, Visited);
8428 }
8429}
8430
8431void ScalarEvolution::forgetLoop(const Loop *L) {
8432 SmallVector<const Loop *, 16> LoopWorklist(1, L);
8433 SmallVector<Instruction *, 32> Worklist;
8434 SmallPtrSet<Instruction *, 16> Visited;
8435 SmallVector<const SCEV *, 16> ToForget;
8436
8437 // Iterate over all the loops and sub-loops to drop SCEV information.
8438 while (!LoopWorklist.empty()) {
8439 auto *CurrL = LoopWorklist.pop_back_val();
8440
8441 // Drop any stored trip count value.
8442 forgetBackedgeTakenCounts(L: CurrL, /* Predicated */ false);
8443 forgetBackedgeTakenCounts(L: CurrL, /* Predicated */ true);
8444
8445 // Drop information about predicated SCEV rewrites for this loop.
8446 for (auto I = PredicatedSCEVRewrites.begin();
8447 I != PredicatedSCEVRewrites.end();) {
8448 std::pair<const SCEV *, const Loop *> Entry = I->first;
8449 if (Entry.second == CurrL)
8450 PredicatedSCEVRewrites.erase(I: I++);
8451 else
8452 ++I;
8453 }
8454
8455 auto LoopUsersItr = LoopUsers.find(Val: CurrL);
8456 if (LoopUsersItr != LoopUsers.end()) {
8457 ToForget.insert(I: ToForget.end(), From: LoopUsersItr->second.begin(),
8458 To: LoopUsersItr->second.end());
8459 }
8460
8461 // Drop information about expressions based on loop-header PHIs.
8462 PushLoopPHIs(L: CurrL, Worklist, Visited);
8463 visitAndClearUsers(Worklist, Visited, ToForget);
8464
8465 LoopPropertiesCache.erase(Val: CurrL);
8466 // Forget all contained loops too, to avoid dangling entries in the
8467 // ValuesAtScopes map.
8468 LoopWorklist.append(in_start: CurrL->begin(), in_end: CurrL->end());
8469 }
8470 forgetMemoizedResults(SCEVs: ToForget);
8471}
8472
8473void ScalarEvolution::forgetTopmostLoop(const Loop *L) {
8474 forgetLoop(L: L->getOutermostLoop());
8475}
8476
8477void ScalarEvolution::forgetValue(Value *V) {
8478 Instruction *I = dyn_cast<Instruction>(Val: V);
8479 if (!I) return;
8480
8481 // Drop information about expressions based on loop-header PHIs.
8482 SmallVector<Instruction *, 16> Worklist;
8483 SmallPtrSet<Instruction *, 8> Visited;
8484 SmallVector<const SCEV *, 8> ToForget;
8485 Worklist.push_back(Elt: I);
8486 Visited.insert(Ptr: I);
8487 visitAndClearUsers(Worklist, Visited, ToForget);
8488
8489 forgetMemoizedResults(SCEVs: ToForget);
8490}
8491
8492void ScalarEvolution::forgetLcssaPhiWithNewPredecessor(Loop *L, PHINode *V) {
8493 if (!isSCEVable(Ty: V->getType()))
8494 return;
8495
8496 // If SCEV looked through a trivial LCSSA phi node, we might have SCEV's
8497 // directly using a SCEVUnknown/SCEVAddRec defined in the loop. After an
8498 // extra predecessor is added, this is no longer valid. Find all Unknowns and
8499 // AddRecs defined in the loop and invalidate any SCEV's making use of them.
8500 if (const SCEV *S = getExistingSCEV(V)) {
8501 struct InvalidationRootCollector {
8502 Loop *L;
8503 SmallVector<const SCEV *, 8> Roots;
8504
8505 InvalidationRootCollector(Loop *L) : L(L) {}
8506
8507 bool follow(const SCEV *S) {
8508 if (auto *SU = dyn_cast<SCEVUnknown>(Val: S)) {
8509 if (auto *I = dyn_cast<Instruction>(Val: SU->getValue()))
8510 if (L->contains(Inst: I))
8511 Roots.push_back(Elt: S);
8512 } else if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Val: S)) {
8513 if (L->contains(L: AddRec->getLoop()))
8514 Roots.push_back(Elt: S);
8515 }
8516 return true;
8517 }
8518 bool isDone() const { return false; }
8519 };
8520
8521 InvalidationRootCollector C(L);
8522 visitAll(Root: S, Visitor&: C);
8523 forgetMemoizedResults(SCEVs: C.Roots);
8524 }
8525
8526 // Also perform the normal invalidation.
8527 forgetValue(V);
8528}
8529
8530void ScalarEvolution::forgetLoopDispositions() { LoopDispositions.clear(); }
8531
8532void ScalarEvolution::forgetBlockAndLoopDispositions(Value *V) {
8533 // Unless a specific value is passed to invalidation, completely clear both
8534 // caches.
8535 if (!V) {
8536 BlockDispositions.clear();
8537 LoopDispositions.clear();
8538 return;
8539 }
8540
8541 if (!isSCEVable(Ty: V->getType()))
8542 return;
8543
8544 const SCEV *S = getExistingSCEV(V);
8545 if (!S)
8546 return;
8547
8548 // Invalidate the block and loop dispositions cached for S. Dispositions of
8549 // S's users may change if S's disposition changes (i.e. a user may change to
8550 // loop-invariant, if S changes to loop invariant), so also invalidate
8551 // dispositions of S's users recursively.
8552 SmallVector<const SCEV *, 8> Worklist = {S};
8553 SmallPtrSet<const SCEV *, 8> Seen = {S};
8554 while (!Worklist.empty()) {
8555 const SCEV *Curr = Worklist.pop_back_val();
8556 bool LoopDispoRemoved = LoopDispositions.erase(Val: Curr);
8557 bool BlockDispoRemoved = BlockDispositions.erase(Val: Curr);
8558 if (!LoopDispoRemoved && !BlockDispoRemoved)
8559 continue;
8560 auto Users = SCEVUsers.find(Val: Curr);
8561 if (Users != SCEVUsers.end())
8562 for (const auto *User : Users->second)
8563 if (Seen.insert(Ptr: User).second)
8564 Worklist.push_back(Elt: User);
8565 }
8566}
8567
8568/// Get the exact loop backedge taken count considering all loop exits. A
8569/// computable result can only be returned for loops with all exiting blocks
8570/// dominating the latch. howFarToZero assumes that the limit of each loop test
8571/// is never skipped. This is a valid assumption as long as the loop exits via
8572/// that test. For precise results, it is the caller's responsibility to specify
8573/// the relevant loop exiting block using getExact(ExitingBlock, SE).
8574const SCEV *
8575ScalarEvolution::BackedgeTakenInfo::getExact(const Loop *L, ScalarEvolution *SE,
8576 SmallVector<const SCEVPredicate *, 4> *Preds) const {
8577 // If any exits were not computable, the loop is not computable.
8578 if (!isComplete() || ExitNotTaken.empty())
8579 return SE->getCouldNotCompute();
8580
8581 const BasicBlock *Latch = L->getLoopLatch();
8582 // All exiting blocks we have collected must dominate the only backedge.
8583 if (!Latch)
8584 return SE->getCouldNotCompute();
8585
8586 // All exiting blocks we have gathered dominate loop's latch, so exact trip
8587 // count is simply a minimum out of all these calculated exit counts.
8588 SmallVector<const SCEV *, 2> Ops;
8589 for (const auto &ENT : ExitNotTaken) {
8590 const SCEV *BECount = ENT.ExactNotTaken;
8591 assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!");
8592 assert(SE->DT.dominates(ENT.ExitingBlock, Latch) &&
8593 "We should only have known counts for exiting blocks that dominate "
8594 "latch!");
8595
8596 Ops.push_back(Elt: BECount);
8597
8598 if (Preds)
8599 for (const auto *P : ENT.Predicates)
8600 Preds->push_back(Elt: P);
8601
8602 assert((Preds || ENT.hasAlwaysTruePredicate()) &&
8603 "Predicate should be always true!");
8604 }
8605
8606 // If an earlier exit exits on the first iteration (exit count zero), then
8607 // a later poison exit count should not propagate into the result. This are
8608 // exactly the semantics provided by umin_seq.
8609 return SE->getUMinFromMismatchedTypes(Ops, /* Sequential */ true);
8610}
8611
8612/// Get the exact not taken count for this loop exit.
8613const SCEV *
8614ScalarEvolution::BackedgeTakenInfo::getExact(const BasicBlock *ExitingBlock,
8615 ScalarEvolution *SE) const {
8616 for (const auto &ENT : ExitNotTaken)
8617 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
8618 return ENT.ExactNotTaken;
8619
8620 return SE->getCouldNotCompute();
8621}
8622
8623const SCEV *ScalarEvolution::BackedgeTakenInfo::getConstantMax(
8624 const BasicBlock *ExitingBlock, ScalarEvolution *SE) const {
8625 for (const auto &ENT : ExitNotTaken)
8626 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
8627 return ENT.ConstantMaxNotTaken;
8628
8629 return SE->getCouldNotCompute();
8630}
8631
8632const SCEV *ScalarEvolution::BackedgeTakenInfo::getSymbolicMax(
8633 const BasicBlock *ExitingBlock, ScalarEvolution *SE) const {
8634 for (const auto &ENT : ExitNotTaken)
8635 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
8636 return ENT.SymbolicMaxNotTaken;
8637
8638 return SE->getCouldNotCompute();
8639}
8640
8641/// getConstantMax - Get the constant max backedge taken count for the loop.
8642const SCEV *
8643ScalarEvolution::BackedgeTakenInfo::getConstantMax(ScalarEvolution *SE) const {
8644 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
8645 return !ENT.hasAlwaysTruePredicate();
8646 };
8647
8648 if (!getConstantMax() || any_of(Range: ExitNotTaken, P: PredicateNotAlwaysTrue))
8649 return SE->getCouldNotCompute();
8650
8651 assert((isa<SCEVCouldNotCompute>(getConstantMax()) ||
8652 isa<SCEVConstant>(getConstantMax())) &&
8653 "No point in having a non-constant max backedge taken count!");
8654 return getConstantMax();
8655}
8656
8657const SCEV *ScalarEvolution::BackedgeTakenInfo::getSymbolicMax(
8658 const Loop *L, ScalarEvolution *SE,
8659 SmallVector<const SCEVPredicate *, 4> *Predicates) {
8660 if (!SymbolicMax) {
8661 // Form an expression for the maximum exit count possible for this loop. We
8662 // merge the max and exact information to approximate a version of
8663 // getConstantMaxBackedgeTakenCount which isn't restricted to just
8664 // constants.
8665 SmallVector<const SCEV *, 4> ExitCounts;
8666
8667 for (const auto &ENT : ExitNotTaken) {
8668 const SCEV *ExitCount = ENT.SymbolicMaxNotTaken;
8669 if (!isa<SCEVCouldNotCompute>(Val: ExitCount)) {
8670 assert(SE->DT.dominates(ENT.ExitingBlock, L->getLoopLatch()) &&
8671 "We should only have known counts for exiting blocks that "
8672 "dominate latch!");
8673 ExitCounts.push_back(Elt: ExitCount);
8674 if (Predicates)
8675 for (const auto *P : ENT.Predicates)
8676 Predicates->push_back(Elt: P);
8677
8678 assert((Predicates || ENT.hasAlwaysTruePredicate()) &&
8679 "Predicate should be always true!");
8680 }
8681 }
8682 if (ExitCounts.empty())
8683 SymbolicMax = SE->getCouldNotCompute();
8684 else
8685 SymbolicMax =
8686 SE->getUMinFromMismatchedTypes(Ops&: ExitCounts, /*Sequential*/ true);
8687 }
8688 return SymbolicMax;
8689}
8690
8691bool ScalarEvolution::BackedgeTakenInfo::isConstantMaxOrZero(
8692 ScalarEvolution *SE) const {
8693 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
8694 return !ENT.hasAlwaysTruePredicate();
8695 };
8696 return MaxOrZero && !any_of(Range: ExitNotTaken, P: PredicateNotAlwaysTrue);
8697}
8698
8699ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
8700 : ExitLimit(E, E, E, false, std::nullopt) {}
8701
8702ScalarEvolution::ExitLimit::ExitLimit(
8703 const SCEV *E, const SCEV *ConstantMaxNotTaken,
8704 const SCEV *SymbolicMaxNotTaken, bool MaxOrZero,
8705 ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList)
8706 : ExactNotTaken(E), ConstantMaxNotTaken(ConstantMaxNotTaken),
8707 SymbolicMaxNotTaken(SymbolicMaxNotTaken), MaxOrZero(MaxOrZero) {
8708 // If we prove the max count is zero, so is the symbolic bound. This happens
8709 // in practice due to differences in a) how context sensitive we've chosen
8710 // to be and b) how we reason about bounds implied by UB.
8711 if (ConstantMaxNotTaken->isZero()) {
8712 this->ExactNotTaken = E = ConstantMaxNotTaken;
8713 this->SymbolicMaxNotTaken = SymbolicMaxNotTaken = ConstantMaxNotTaken;
8714 }
8715
8716 assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
8717 !isa<SCEVCouldNotCompute>(ConstantMaxNotTaken)) &&
8718 "Exact is not allowed to be less precise than Constant Max");
8719 assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
8720 !isa<SCEVCouldNotCompute>(SymbolicMaxNotTaken)) &&
8721 "Exact is not allowed to be less precise than Symbolic Max");
8722 assert((isa<SCEVCouldNotCompute>(SymbolicMaxNotTaken) ||
8723 !isa<SCEVCouldNotCompute>(ConstantMaxNotTaken)) &&
8724 "Symbolic Max is not allowed to be less precise than Constant Max");
8725 assert((isa<SCEVCouldNotCompute>(ConstantMaxNotTaken) ||
8726 isa<SCEVConstant>(ConstantMaxNotTaken)) &&
8727 "No point in having a non-constant max backedge taken count!");
8728 for (const auto *PredSet : PredSetList)
8729 for (const auto *P : *PredSet)
8730 addPredicate(P);
8731 assert((isa<SCEVCouldNotCompute>(E) || !E->getType()->isPointerTy()) &&
8732 "Backedge count should be int");
8733 assert((isa<SCEVCouldNotCompute>(ConstantMaxNotTaken) ||
8734 !ConstantMaxNotTaken->getType()->isPointerTy()) &&
8735 "Max backedge count should be int");
8736}
8737
8738ScalarEvolution::ExitLimit::ExitLimit(
8739 const SCEV *E, const SCEV *ConstantMaxNotTaken,
8740 const SCEV *SymbolicMaxNotTaken, bool MaxOrZero,
8741 const SmallPtrSetImpl<const SCEVPredicate *> &PredSet)
8742 : ExitLimit(E, ConstantMaxNotTaken, SymbolicMaxNotTaken, MaxOrZero,
8743 { &PredSet }) {}
8744
8745/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
8746/// computable exit into a persistent ExitNotTakenInfo array.
8747ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
8748 ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo> ExitCounts,
8749 bool IsComplete, const SCEV *ConstantMax, bool MaxOrZero)
8750 : ConstantMax(ConstantMax), IsComplete(IsComplete), MaxOrZero(MaxOrZero) {
8751 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
8752
8753 ExitNotTaken.reserve(N: ExitCounts.size());
8754 std::transform(first: ExitCounts.begin(), last: ExitCounts.end(),
8755 result: std::back_inserter(x&: ExitNotTaken),
8756 unary_op: [&](const EdgeExitInfo &EEI) {
8757 BasicBlock *ExitBB = EEI.first;
8758 const ExitLimit &EL = EEI.second;
8759 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken,
8760 EL.ConstantMaxNotTaken, EL.SymbolicMaxNotTaken,
8761 EL.Predicates);
8762 });
8763 assert((isa<SCEVCouldNotCompute>(ConstantMax) ||
8764 isa<SCEVConstant>(ConstantMax)) &&
8765 "No point in having a non-constant max backedge taken count!");
8766}
8767
8768/// Compute the number of times the backedge of the specified loop will execute.
8769ScalarEvolution::BackedgeTakenInfo
8770ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
8771 bool AllowPredicates) {
8772 SmallVector<BasicBlock *, 8> ExitingBlocks;
8773 L->getExitingBlocks(ExitingBlocks);
8774
8775 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
8776
8777 SmallVector<EdgeExitInfo, 4> ExitCounts;
8778 bool CouldComputeBECount = true;
8779 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
8780 const SCEV *MustExitMaxBECount = nullptr;
8781 const SCEV *MayExitMaxBECount = nullptr;
8782 bool MustExitMaxOrZero = false;
8783 bool IsOnlyExit = ExitingBlocks.size() == 1;
8784
8785 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
8786 // and compute maxBECount.
8787 // Do a union of all the predicates here.
8788 for (BasicBlock *ExitBB : ExitingBlocks) {
8789 // We canonicalize untaken exits to br (constant), ignore them so that
8790 // proving an exit untaken doesn't negatively impact our ability to reason
8791 // about the loop as whole.
8792 if (auto *BI = dyn_cast<BranchInst>(Val: ExitBB->getTerminator()))
8793 if (auto *CI = dyn_cast<ConstantInt>(Val: BI->getCondition())) {
8794 bool ExitIfTrue = !L->contains(BB: BI->getSuccessor(i: 0));
8795 if (ExitIfTrue == CI->isZero())
8796 continue;
8797 }
8798
8799 ExitLimit EL = computeExitLimit(L, ExitingBlock: ExitBB, IsOnlyExit, AllowPredicates);
8800
8801 assert((AllowPredicates || EL.Predicates.empty()) &&
8802 "Predicated exit limit when predicates are not allowed!");
8803
8804 // 1. For each exit that can be computed, add an entry to ExitCounts.
8805 // CouldComputeBECount is true only if all exits can be computed.
8806 if (EL.ExactNotTaken != getCouldNotCompute())
8807 ++NumExitCountsComputed;
8808 else
8809 // We couldn't compute an exact value for this exit, so
8810 // we won't be able to compute an exact value for the loop.
8811 CouldComputeBECount = false;
8812 // Remember exit count if either exact or symbolic is known. Because
8813 // Exact always implies symbolic, only check symbolic.
8814 if (EL.SymbolicMaxNotTaken != getCouldNotCompute())
8815 ExitCounts.emplace_back(Args&: ExitBB, Args&: EL);
8816 else {
8817 assert(EL.ExactNotTaken == getCouldNotCompute() &&
8818 "Exact is known but symbolic isn't?");
8819 ++NumExitCountsNotComputed;
8820 }
8821
8822 // 2. Derive the loop's MaxBECount from each exit's max number of
8823 // non-exiting iterations. Partition the loop exits into two kinds:
8824 // LoopMustExits and LoopMayExits.
8825 //
8826 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
8827 // is a LoopMayExit. If any computable LoopMustExit is found, then
8828 // MaxBECount is the minimum EL.ConstantMaxNotTaken of computable
8829 // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
8830 // EL.ConstantMaxNotTaken, where CouldNotCompute is considered greater than
8831 // any
8832 // computable EL.ConstantMaxNotTaken.
8833 if (EL.ConstantMaxNotTaken != getCouldNotCompute() && Latch &&
8834 DT.dominates(A: ExitBB, B: Latch)) {
8835 if (!MustExitMaxBECount) {
8836 MustExitMaxBECount = EL.ConstantMaxNotTaken;
8837 MustExitMaxOrZero = EL.MaxOrZero;
8838 } else {
8839 MustExitMaxBECount = getUMinFromMismatchedTypes(LHS: MustExitMaxBECount,
8840 RHS: EL.ConstantMaxNotTaken);
8841 }
8842 } else if (MayExitMaxBECount != getCouldNotCompute()) {
8843 if (!MayExitMaxBECount || EL.ConstantMaxNotTaken == getCouldNotCompute())
8844 MayExitMaxBECount = EL.ConstantMaxNotTaken;
8845 else {
8846 MayExitMaxBECount = getUMaxFromMismatchedTypes(LHS: MayExitMaxBECount,
8847 RHS: EL.ConstantMaxNotTaken);
8848 }
8849 }
8850 }
8851 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
8852 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
8853 // The loop backedge will be taken the maximum or zero times if there's
8854 // a single exit that must be taken the maximum or zero times.
8855 bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
8856
8857 // Remember which SCEVs are used in exit limits for invalidation purposes.
8858 // We only care about non-constant SCEVs here, so we can ignore
8859 // EL.ConstantMaxNotTaken
8860 // and MaxBECount, which must be SCEVConstant.
8861 for (const auto &Pair : ExitCounts) {
8862 if (!isa<SCEVConstant>(Val: Pair.second.ExactNotTaken))
8863 BECountUsers[Pair.second.ExactNotTaken].insert(Ptr: {L, AllowPredicates});
8864 if (!isa<SCEVConstant>(Val: Pair.second.SymbolicMaxNotTaken))
8865 BECountUsers[Pair.second.SymbolicMaxNotTaken].insert(
8866 Ptr: {L, AllowPredicates});
8867 }
8868 return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
8869 MaxBECount, MaxOrZero);
8870}
8871
8872ScalarEvolution::ExitLimit
8873ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
8874 bool IsOnlyExit, bool AllowPredicates) {
8875 assert(L->contains(ExitingBlock) && "Exit count for non-loop block?");
8876 // If our exiting block does not dominate the latch, then its connection with
8877 // loop's exit limit may be far from trivial.
8878 const BasicBlock *Latch = L->getLoopLatch();
8879 if (!Latch || !DT.dominates(A: ExitingBlock, B: Latch))
8880 return getCouldNotCompute();
8881
8882 Instruction *Term = ExitingBlock->getTerminator();
8883 if (BranchInst *BI = dyn_cast<BranchInst>(Val: Term)) {
8884 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
8885 bool ExitIfTrue = !L->contains(BB: BI->getSuccessor(i: 0));
8886 assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) &&
8887 "It should have one successor in loop and one exit block!");
8888 // Proceed to the next level to examine the exit condition expression.
8889 return computeExitLimitFromCond(L, ExitCond: BI->getCondition(), ExitIfTrue,
8890 /*ControlsOnlyExit=*/IsOnlyExit,
8891 AllowPredicates);
8892 }
8893
8894 if (SwitchInst *SI = dyn_cast<SwitchInst>(Val: Term)) {
8895 // For switch, make sure that there is a single exit from the loop.
8896 BasicBlock *Exit = nullptr;
8897 for (auto *SBB : successors(BB: ExitingBlock))
8898 if (!L->contains(BB: SBB)) {
8899 if (Exit) // Multiple exit successors.
8900 return getCouldNotCompute();
8901 Exit = SBB;
8902 }
8903 assert(Exit && "Exiting block must have at least one exit");
8904 return computeExitLimitFromSingleExitSwitch(
8905 L, Switch: SI, ExitingBB: Exit, /*ControlsOnlyExit=*/IsSubExpr: IsOnlyExit);
8906 }
8907
8908 return getCouldNotCompute();
8909}
8910
8911ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
8912 const Loop *L, Value *ExitCond, bool ExitIfTrue, bool ControlsOnlyExit,
8913 bool AllowPredicates) {
8914 ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates);
8915 return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue,
8916 ControlsOnlyExit, AllowPredicates);
8917}
8918
8919std::optional<ScalarEvolution::ExitLimit>
8920ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
8921 bool ExitIfTrue, bool ControlsOnlyExit,
8922 bool AllowPredicates) {
8923 (void)this->L;
8924 (void)this->ExitIfTrue;
8925 (void)this->AllowPredicates;
8926
8927 assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
8928 this->AllowPredicates == AllowPredicates &&
8929 "Variance in assumed invariant key components!");
8930 auto Itr = TripCountMap.find(Val: {ExitCond, ControlsOnlyExit});
8931 if (Itr == TripCountMap.end())
8932 return std::nullopt;
8933 return Itr->second;
8934}
8935
8936void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
8937 bool ExitIfTrue,
8938 bool ControlsOnlyExit,
8939 bool AllowPredicates,
8940 const ExitLimit &EL) {
8941 assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
8942 this->AllowPredicates == AllowPredicates &&
8943 "Variance in assumed invariant key components!");
8944
8945 auto InsertResult = TripCountMap.insert(KV: {{ExitCond, ControlsOnlyExit}, EL});
8946 assert(InsertResult.second && "Expected successful insertion!");
8947 (void)InsertResult;
8948 (void)ExitIfTrue;
8949}
8950
8951ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
8952 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
8953 bool ControlsOnlyExit, bool AllowPredicates) {
8954
8955 if (auto MaybeEL = Cache.find(L, ExitCond, ExitIfTrue, ControlsOnlyExit,
8956 AllowPredicates))
8957 return *MaybeEL;
8958
8959 ExitLimit EL = computeExitLimitFromCondImpl(
8960 Cache, L, ExitCond, ExitIfTrue, ControlsOnlyExit, AllowPredicates);
8961 Cache.insert(L, ExitCond, ExitIfTrue, ControlsOnlyExit, AllowPredicates, EL);
8962 return EL;
8963}
8964
8965ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
8966 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
8967 bool ControlsOnlyExit, bool AllowPredicates) {
8968 // Handle BinOp conditions (And, Or).
8969 if (auto LimitFromBinOp = computeExitLimitFromCondFromBinOp(
8970 Cache, L, ExitCond, ExitIfTrue, ControlsOnlyExit, AllowPredicates))
8971 return *LimitFromBinOp;
8972
8973 // With an icmp, it may be feasible to compute an exact backedge-taken count.
8974 // Proceed to the next level to examine the icmp.
8975 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(Val: ExitCond)) {
8976 ExitLimit EL =
8977 computeExitLimitFromICmp(L, ExitCond: ExitCondICmp, ExitIfTrue, IsSubExpr: ControlsOnlyExit);
8978 if (EL.hasFullInfo() || !AllowPredicates)
8979 return EL;
8980
8981 // Try again, but use SCEV predicates this time.
8982 return computeExitLimitFromICmp(L, ExitCond: ExitCondICmp, ExitIfTrue,
8983 IsSubExpr: ControlsOnlyExit,
8984 /*AllowPredicates=*/true);
8985 }
8986
8987 // Check for a constant condition. These are normally stripped out by
8988 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
8989 // preserve the CFG and is temporarily leaving constant conditions
8990 // in place.
8991 if (ConstantInt *CI = dyn_cast<ConstantInt>(Val: ExitCond)) {
8992 if (ExitIfTrue == !CI->getZExtValue())
8993 // The backedge is always taken.
8994 return getCouldNotCompute();
8995 // The backedge is never taken.
8996 return getZero(Ty: CI->getType());
8997 }
8998
8999 // If we're exiting based on the overflow flag of an x.with.overflow intrinsic
9000 // with a constant step, we can form an equivalent icmp predicate and figure
9001 // out how many iterations will be taken before we exit.
9002 const WithOverflowInst *WO;
9003 const APInt *C;
9004 if (match(V: ExitCond, P: m_ExtractValue<1>(V: m_WithOverflowInst(I&: WO))) &&
9005 match(V: WO->getRHS(), P: m_APInt(Res&: C))) {
9006 ConstantRange NWR =
9007 ConstantRange::makeExactNoWrapRegion(BinOp: WO->getBinaryOp(), Other: *C,
9008 NoWrapKind: WO->getNoWrapKind());
9009 CmpInst::Predicate Pred;
9010 APInt NewRHSC, Offset;
9011 NWR.getEquivalentICmp(Pred, RHS&: NewRHSC, Offset);
9012 if (!ExitIfTrue)
9013 Pred = ICmpInst::getInversePredicate(pred: Pred);
9014 auto *LHS = getSCEV(V: WO->getLHS());
9015 if (Offset != 0)
9016 LHS = getAddExpr(LHS, RHS: getConstant(Val: Offset));
9017 auto EL = computeExitLimitFromICmp(L, Pred, LHS, RHS: getConstant(Val: NewRHSC),
9018 IsSubExpr: ControlsOnlyExit, AllowPredicates);
9019 if (EL.hasAnyInfo())
9020 return EL;
9021 }
9022
9023 // If it's not an integer or pointer comparison then compute it the hard way.
9024 return computeExitCountExhaustively(L, Cond: ExitCond, ExitWhen: ExitIfTrue);
9025}
9026
9027std::optional<ScalarEvolution::ExitLimit>
9028ScalarEvolution::computeExitLimitFromCondFromBinOp(
9029 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
9030 bool ControlsOnlyExit, bool AllowPredicates) {
9031 // Check if the controlling expression for this loop is an And or Or.
9032 Value *Op0, *Op1;
9033 bool IsAnd = false;
9034 if (match(V: ExitCond, P: m_LogicalAnd(L: m_Value(V&: Op0), R: m_Value(V&: Op1))))
9035 IsAnd = true;
9036 else if (match(V: ExitCond, P: m_LogicalOr(L: m_Value(V&: Op0), R: m_Value(V&: Op1))))
9037 IsAnd = false;
9038 else
9039 return std::nullopt;
9040
9041 // EitherMayExit is true in these two cases:
9042 // br (and Op0 Op1), loop, exit
9043 // br (or Op0 Op1), exit, loop
9044 bool EitherMayExit = IsAnd ^ ExitIfTrue;
9045 ExitLimit EL0 = computeExitLimitFromCondCached(
9046 Cache, L, ExitCond: Op0, ExitIfTrue, ControlsOnlyExit: ControlsOnlyExit && !EitherMayExit,
9047 AllowPredicates);
9048 ExitLimit EL1 = computeExitLimitFromCondCached(
9049 Cache, L, ExitCond: Op1, ExitIfTrue, ControlsOnlyExit: ControlsOnlyExit && !EitherMayExit,
9050 AllowPredicates);
9051
9052 // Be robust against unsimplified IR for the form "op i1 X, NeutralElement"
9053 const Constant *NeutralElement = ConstantInt::get(Ty: ExitCond->getType(), V: IsAnd);
9054 if (isa<ConstantInt>(Val: Op1))
9055 return Op1 == NeutralElement ? EL0 : EL1;
9056 if (isa<ConstantInt>(Val: Op0))
9057 return Op0 == NeutralElement ? EL1 : EL0;
9058
9059 const SCEV *BECount = getCouldNotCompute();
9060 const SCEV *ConstantMaxBECount = getCouldNotCompute();
9061 const SCEV *SymbolicMaxBECount = getCouldNotCompute();
9062 if (EitherMayExit) {
9063 bool UseSequentialUMin = !isa<BinaryOperator>(Val: ExitCond);
9064 // Both conditions must be same for the loop to continue executing.
9065 // Choose the less conservative count.
9066 if (EL0.ExactNotTaken != getCouldNotCompute() &&
9067 EL1.ExactNotTaken != getCouldNotCompute()) {
9068 BECount = getUMinFromMismatchedTypes(LHS: EL0.ExactNotTaken, RHS: EL1.ExactNotTaken,
9069 Sequential: UseSequentialUMin);
9070 }
9071 if (EL0.ConstantMaxNotTaken == getCouldNotCompute())
9072 ConstantMaxBECount = EL1.ConstantMaxNotTaken;
9073 else if (EL1.ConstantMaxNotTaken == getCouldNotCompute())
9074 ConstantMaxBECount = EL0.ConstantMaxNotTaken;
9075 else
9076 ConstantMaxBECount = getUMinFromMismatchedTypes(LHS: EL0.ConstantMaxNotTaken,
9077 RHS: EL1.ConstantMaxNotTaken);
9078 if (EL0.SymbolicMaxNotTaken == getCouldNotCompute())
9079 SymbolicMaxBECount = EL1.SymbolicMaxNotTaken;
9080 else if (EL1.SymbolicMaxNotTaken == getCouldNotCompute())
9081 SymbolicMaxBECount = EL0.SymbolicMaxNotTaken;
9082 else
9083 SymbolicMaxBECount = getUMinFromMismatchedTypes(
9084 LHS: EL0.SymbolicMaxNotTaken, RHS: EL1.SymbolicMaxNotTaken, Sequential: UseSequentialUMin);
9085 } else {
9086 // Both conditions must be same at the same time for the loop to exit.
9087 // For now, be conservative.
9088 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
9089 BECount = EL0.ExactNotTaken;
9090 }
9091
9092 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
9093 // to be more aggressive when computing BECount than when computing
9094 // ConstantMaxBECount. In these cases it is possible for EL0.ExactNotTaken
9095 // and
9096 // EL1.ExactNotTaken to match, but for EL0.ConstantMaxNotTaken and
9097 // EL1.ConstantMaxNotTaken to not.
9098 if (isa<SCEVCouldNotCompute>(Val: ConstantMaxBECount) &&
9099 !isa<SCEVCouldNotCompute>(Val: BECount))
9100 ConstantMaxBECount = getConstant(Val: getUnsignedRangeMax(S: BECount));
9101 if (isa<SCEVCouldNotCompute>(Val: SymbolicMaxBECount))
9102 SymbolicMaxBECount =
9103 isa<SCEVCouldNotCompute>(Val: BECount) ? ConstantMaxBECount : BECount;
9104 return ExitLimit(BECount, ConstantMaxBECount, SymbolicMaxBECount, false,
9105 { &EL0.Predicates, &EL1.Predicates });
9106}
9107
9108ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromICmp(
9109 const Loop *L, ICmpInst *ExitCond, bool ExitIfTrue, bool ControlsOnlyExit,
9110 bool AllowPredicates) {
9111 // If the condition was exit on true, convert the condition to exit on false
9112 ICmpInst::Predicate Pred;
9113 if (!ExitIfTrue)
9114 Pred = ExitCond->getPredicate();
9115 else
9116 Pred = ExitCond->getInversePredicate();
9117 const ICmpInst::Predicate OriginalPred = Pred;
9118
9119 const SCEV *LHS = getSCEV(V: ExitCond->getOperand(i_nocapture: 0));
9120 const SCEV *RHS = getSCEV(V: ExitCond->getOperand(i_nocapture: 1));
9121
9122 ExitLimit EL = computeExitLimitFromICmp(L, Pred, LHS, RHS, IsSubExpr: ControlsOnlyExit,
9123 AllowPredicates);
9124 if (EL.hasAnyInfo())
9125 return EL;
9126
9127 auto *ExhaustiveCount =
9128 computeExitCountExhaustively(L, Cond: ExitCond, ExitWhen: ExitIfTrue);
9129
9130 if (!isa<SCEVCouldNotCompute>(Val: ExhaustiveCount))
9131 return ExhaustiveCount;
9132
9133 return computeShiftCompareExitLimit(LHS: ExitCond->getOperand(i_nocapture: 0),
9134 RHS: ExitCond->getOperand(i_nocapture: 1), L, Pred: OriginalPred);
9135}
9136ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromICmp(
9137 const Loop *L, ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
9138 bool ControlsOnlyExit, bool AllowPredicates) {
9139
9140 // Try to evaluate any dependencies out of the loop.
9141 LHS = getSCEVAtScope(S: LHS, L);
9142 RHS = getSCEVAtScope(S: RHS, L);
9143
9144 // At this point, we would like to compute how many iterations of the
9145 // loop the predicate will return true for these inputs.
9146 if (isLoopInvariant(S: LHS, L) && !isLoopInvariant(S: RHS, L)) {
9147 // If there is a loop-invariant, force it into the RHS.
9148 std::swap(a&: LHS, b&: RHS);
9149 Pred = ICmpInst::getSwappedPredicate(pred: Pred);
9150 }
9151
9152 bool ControllingFiniteLoop = ControlsOnlyExit && loopHasNoAbnormalExits(L) &&
9153 loopIsFiniteByAssumption(L);
9154 // Simplify the operands before analyzing them.
9155 (void)SimplifyICmpOperands(Pred, LHS, RHS, /*Depth=*/0);
9156
9157 // If we have a comparison of a chrec against a constant, try to use value
9158 // ranges to answer this query.
9159 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Val: RHS))
9160 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Val: LHS))
9161 if (AddRec->getLoop() == L) {
9162 // Form the constant range.
9163 ConstantRange CompRange =
9164 ConstantRange::makeExactICmpRegion(Pred, Other: RHSC->getAPInt());
9165
9166 const SCEV *Ret = AddRec->getNumIterationsInRange(Range: CompRange, SE&: *this);
9167 if (!isa<SCEVCouldNotCompute>(Val: Ret)) return Ret;
9168 }
9169
9170 // If this loop must exit based on this condition (or execute undefined
9171 // behaviour), and we can prove the test sequence produced must repeat
9172 // the same values on self-wrap of the IV, then we can infer that IV
9173 // doesn't self wrap because if it did, we'd have an infinite (undefined)
9174 // loop.
9175 if (ControllingFiniteLoop && isLoopInvariant(S: RHS, L)) {
9176 // TODO: We can peel off any functions which are invertible *in L*. Loop
9177 // invariant terms are effectively constants for our purposes here.
9178 auto *InnerLHS = LHS;
9179 if (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(Val: LHS))
9180 InnerLHS = ZExt->getOperand();
9181 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Val: InnerLHS)) {
9182 auto *StrideC = dyn_cast<SCEVConstant>(Val: AR->getStepRecurrence(SE&: *this));
9183 if (!AR->hasNoSelfWrap() && AR->getLoop() == L && AR->isAffine() &&
9184 StrideC && StrideC->getAPInt().isPowerOf2()) {
9185 auto Flags = AR->getNoWrapFlags();
9186 Flags = setFlags(Flags, OnFlags: SCEV::FlagNW);
9187 SmallVector<const SCEV*> Operands{AR->operands()};
9188 Flags = StrengthenNoWrapFlags(SE: this, Type: scAddRecExpr, Ops: Operands, Flags);
9189 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags);
9190 }
9191 }
9192 }
9193
9194 switch (Pred) {
9195 case ICmpInst::ICMP_NE: { // while (X != Y)
9196 // Convert to: while (X-Y != 0)
9197 if (LHS->getType()->isPointerTy()) {
9198 LHS = getLosslessPtrToIntExpr(Op: LHS);
9199 if (isa<SCEVCouldNotCompute>(Val: LHS))
9200 return LHS;
9201 }
9202 if (RHS->getType()->isPointerTy()) {
9203 RHS = getLosslessPtrToIntExpr(Op: RHS);
9204 if (isa<SCEVCouldNotCompute>(Val: RHS))
9205 return RHS;
9206 }
9207 ExitLimit EL = howFarToZero(V: getMinusSCEV(LHS, RHS), L, IsSubExpr: ControlsOnlyExit,
9208 AllowPredicates);
9209 if (EL.hasAnyInfo())
9210 return EL;
9211 break;
9212 }
9213 case ICmpInst::ICMP_EQ: { // while (X == Y)
9214 // Convert to: while (X-Y == 0)
9215 if (LHS->getType()->isPointerTy()) {
9216 LHS = getLosslessPtrToIntExpr(Op: LHS);
9217 if (isa<SCEVCouldNotCompute>(Val: LHS))
9218 return LHS;
9219 }
9220 if (RHS->getType()->isPointerTy()) {
9221 RHS = getLosslessPtrToIntExpr(Op: RHS);
9222 if (isa<SCEVCouldNotCompute>(Val: RHS))
9223 return RHS;
9224 }
9225 ExitLimit EL = howFarToNonZero(V: getMinusSCEV(LHS, RHS), L);
9226 if (EL.hasAnyInfo()) return EL;
9227 break;
9228 }
9229 case ICmpInst::ICMP_SLE:
9230 case ICmpInst::ICMP_ULE:
9231 // Since the loop is finite, an invariant RHS cannot include the boundary
9232 // value, otherwise it would loop forever.
9233 if (!EnableFiniteLoopControl || !ControllingFiniteLoop ||
9234 !isLoopInvariant(S: RHS, L)) {
9235 // Otherwise, perform the addition in a wider type, to avoid overflow.
9236 // If the LHS is an addrec with the appropriate nowrap flag, the
9237 // extension will be sunk into it and the exit count can be analyzed.
9238 auto *OldType = dyn_cast<IntegerType>(Val: LHS->getType());
9239 if (!OldType)
9240 break;
9241 // Prefer doubling the bitwidth over adding a single bit to make it more
9242 // likely that we use a legal type.
9243 auto *NewType =
9244 Type::getIntNTy(C&: OldType->getContext(), N: OldType->getBitWidth() * 2);
9245 if (ICmpInst::isSigned(predicate: Pred)) {
9246 LHS = getSignExtendExpr(Op: LHS, Ty: NewType);
9247 RHS = getSignExtendExpr(Op: RHS, Ty: NewType);
9248 } else {
9249 LHS = getZeroExtendExpr(Op: LHS, Ty: NewType);
9250 RHS = getZeroExtendExpr(Op: RHS, Ty: NewType);
9251 }
9252 }
9253 RHS = getAddExpr(LHS: getOne(Ty: RHS->getType()), RHS);
9254 [[fallthrough]];
9255 case ICmpInst::ICMP_SLT:
9256 case ICmpInst::ICMP_ULT: { // while (X < Y)
9257 bool IsSigned = ICmpInst::isSigned(predicate: Pred);
9258 ExitLimit EL = howManyLessThans(LHS, RHS, L, isSigned: IsSigned, ControlsOnlyExit,
9259 AllowPredicates);
9260 if (EL.hasAnyInfo())
9261 return EL;
9262 break;
9263 }
9264 case ICmpInst::ICMP_SGE:
9265 case ICmpInst::ICMP_UGE:
9266 // Since the loop is finite, an invariant RHS cannot include the boundary
9267 // value, otherwise it would loop forever.
9268 if (!EnableFiniteLoopControl || !ControllingFiniteLoop ||
9269 !isLoopInvariant(S: RHS, L))
9270 break;
9271 RHS = getAddExpr(LHS: getMinusOne(Ty: RHS->getType()), RHS);
9272 [[fallthrough]];
9273 case ICmpInst::ICMP_SGT:
9274 case ICmpInst::ICMP_UGT: { // while (X > Y)
9275 bool IsSigned = ICmpInst::isSigned(predicate: Pred);
9276 ExitLimit EL = howManyGreaterThans(LHS, RHS, L, isSigned: IsSigned, IsSubExpr: ControlsOnlyExit,
9277 AllowPredicates);
9278 if (EL.hasAnyInfo())
9279 return EL;
9280 break;
9281 }
9282 default:
9283 break;
9284 }
9285
9286 return getCouldNotCompute();
9287}
9288
9289ScalarEvolution::ExitLimit
9290ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
9291 SwitchInst *Switch,
9292 BasicBlock *ExitingBlock,
9293 bool ControlsOnlyExit) {
9294 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
9295
9296 // Give up if the exit is the default dest of a switch.
9297 if (Switch->getDefaultDest() == ExitingBlock)
9298 return getCouldNotCompute();
9299
9300 assert(L->contains(Switch->getDefaultDest()) &&
9301 "Default case must not exit the loop!");
9302 const SCEV *LHS = getSCEVAtScope(V: Switch->getCondition(), L);
9303 const SCEV *RHS = getConstant(V: Switch->findCaseDest(BB: ExitingBlock));
9304
9305 // while (X != Y) --> while (X-Y != 0)
9306 ExitLimit EL = howFarToZero(V: getMinusSCEV(LHS, RHS), L, IsSubExpr: ControlsOnlyExit);
9307 if (EL.hasAnyInfo())
9308 return EL;
9309
9310 return getCouldNotCompute();
9311}
9312
9313static ConstantInt *
9314EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
9315 ScalarEvolution &SE) {
9316 const SCEV *InVal = SE.getConstant(V: C);
9317 const SCEV *Val = AddRec->evaluateAtIteration(It: InVal, SE);
9318 assert(isa<SCEVConstant>(Val) &&
9319 "Evaluation of SCEV at constant didn't fold correctly?");
9320 return cast<SCEVConstant>(Val)->getValue();
9321}
9322
9323ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
9324 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
9325 ConstantInt *RHS = dyn_cast<ConstantInt>(Val: RHSV);
9326 if (!RHS)
9327 return getCouldNotCompute();
9328
9329 const BasicBlock *Latch = L->getLoopLatch();
9330 if (!Latch)
9331 return getCouldNotCompute();
9332
9333 const BasicBlock *Predecessor = L->getLoopPredecessor();
9334 if (!Predecessor)
9335 return getCouldNotCompute();
9336
9337 // Return true if V is of the form "LHS `shift_op` <positive constant>".
9338 // Return LHS in OutLHS and shift_opt in OutOpCode.
9339 auto MatchPositiveShift =
9340 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
9341
9342 using namespace PatternMatch;
9343
9344 ConstantInt *ShiftAmt;
9345 if (match(V, P: m_LShr(L: m_Value(V&: OutLHS), R: m_ConstantInt(CI&: ShiftAmt))))
9346 OutOpCode = Instruction::LShr;
9347 else if (match(V, P: m_AShr(L: m_Value(V&: OutLHS), R: m_ConstantInt(CI&: ShiftAmt))))
9348 OutOpCode = Instruction::AShr;
9349 else if (match(V, P: m_Shl(L: m_Value(V&: OutLHS), R: m_ConstantInt(CI&: ShiftAmt))))
9350 OutOpCode = Instruction::Shl;
9351 else
9352 return false;
9353
9354 return ShiftAmt->getValue().isStrictlyPositive();
9355 };
9356
9357 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
9358 //
9359 // loop:
9360 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
9361 // %iv.shifted = lshr i32 %iv, <positive constant>
9362 //
9363 // Return true on a successful match. Return the corresponding PHI node (%iv
9364 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
9365 auto MatchShiftRecurrence =
9366 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
9367 std::optional<Instruction::BinaryOps> PostShiftOpCode;
9368
9369 {
9370 Instruction::BinaryOps OpC;
9371 Value *V;
9372
9373 // If we encounter a shift instruction, "peel off" the shift operation,
9374 // and remember that we did so. Later when we inspect %iv's backedge
9375 // value, we will make sure that the backedge value uses the same
9376 // operation.
9377 //
9378 // Note: the peeled shift operation does not have to be the same
9379 // instruction as the one feeding into the PHI's backedge value. We only
9380 // really care about it being the same *kind* of shift instruction --
9381 // that's all that is required for our later inferences to hold.
9382 if (MatchPositiveShift(LHS, V, OpC)) {
9383 PostShiftOpCode = OpC;
9384 LHS = V;
9385 }
9386 }
9387
9388 PNOut = dyn_cast<PHINode>(Val: LHS);
9389 if (!PNOut || PNOut->getParent() != L->getHeader())
9390 return false;
9391
9392 Value *BEValue = PNOut->getIncomingValueForBlock(BB: Latch);
9393 Value *OpLHS;
9394
9395 return
9396 // The backedge value for the PHI node must be a shift by a positive
9397 // amount
9398 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
9399
9400 // of the PHI node itself
9401 OpLHS == PNOut &&
9402
9403 // and the kind of shift should be match the kind of shift we peeled
9404 // off, if any.
9405 (!PostShiftOpCode || *PostShiftOpCode == OpCodeOut);
9406 };
9407
9408 PHINode *PN;
9409 Instruction::BinaryOps OpCode;
9410 if (!MatchShiftRecurrence(LHS, PN, OpCode))
9411 return getCouldNotCompute();
9412
9413 const DataLayout &DL = getDataLayout();
9414
9415 // The key rationale for this optimization is that for some kinds of shift
9416 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
9417 // within a finite number of iterations. If the condition guarding the
9418 // backedge (in the sense that the backedge is taken if the condition is true)
9419 // is false for the value the shift recurrence stabilizes to, then we know
9420 // that the backedge is taken only a finite number of times.
9421
9422 ConstantInt *StableValue = nullptr;
9423 switch (OpCode) {
9424 default:
9425 llvm_unreachable("Impossible case!");
9426
9427 case Instruction::AShr: {
9428 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
9429 // bitwidth(K) iterations.
9430 Value *FirstValue = PN->getIncomingValueForBlock(BB: Predecessor);
9431 KnownBits Known = computeKnownBits(V: FirstValue, DL, Depth: 0, AC: &AC,
9432 CxtI: Predecessor->getTerminator(), DT: &DT);
9433 auto *Ty = cast<IntegerType>(Val: RHS->getType());
9434 if (Known.isNonNegative())
9435 StableValue = ConstantInt::get(Ty, V: 0);
9436 else if (Known.isNegative())
9437 StableValue = ConstantInt::get(Ty, V: -1, IsSigned: true);
9438 else
9439 return getCouldNotCompute();
9440
9441 break;
9442 }
9443 case Instruction::LShr:
9444 case Instruction::Shl:
9445 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
9446 // stabilize to 0 in at most bitwidth(K) iterations.
9447 StableValue = ConstantInt::get(Ty: cast<IntegerType>(Val: RHS->getType()), V: 0);
9448 break;
9449 }
9450
9451 auto *Result =
9452 ConstantFoldCompareInstOperands(Predicate: Pred, LHS: StableValue, RHS, DL, TLI: &TLI);
9453 assert(Result->getType()->isIntegerTy(1) &&
9454 "Otherwise cannot be an operand to a branch instruction");
9455
9456 if (Result->isZeroValue()) {
9457 unsigned BitWidth = getTypeSizeInBits(Ty: RHS->getType());
9458 const SCEV *UpperBound =
9459 getConstant(Ty: getEffectiveSCEVType(Ty: RHS->getType()), V: BitWidth);
9460 return ExitLimit(getCouldNotCompute(), UpperBound, UpperBound, false);
9461 }
9462
9463 return getCouldNotCompute();
9464}
9465
9466/// Return true if we can constant fold an instruction of the specified type,
9467/// assuming that all operands were constants.
9468static bool CanConstantFold(const Instruction *I) {
9469 if (isa<BinaryOperator>(Val: I) || isa<CmpInst>(Val: I) ||
9470 isa<SelectInst>(Val: I) || isa<CastInst>(Val: I) || isa<GetElementPtrInst>(Val: I) ||
9471 isa<LoadInst>(Val: I) || isa<ExtractValueInst>(Val: I))
9472 return true;
9473
9474 if (const CallInst *CI = dyn_cast<CallInst>(Val: I))
9475 if (const Function *F = CI->getCalledFunction())
9476 return canConstantFoldCallTo(Call: CI, F);
9477 return false;
9478}
9479
9480/// Determine whether this instruction can constant evolve within this loop
9481/// assuming its operands can all constant evolve.
9482static bool canConstantEvolve(Instruction *I, const Loop *L) {
9483 // An instruction outside of the loop can't be derived from a loop PHI.
9484 if (!L->contains(Inst: I)) return false;
9485
9486 if (isa<PHINode>(Val: I)) {
9487 // We don't currently keep track of the control flow needed to evaluate
9488 // PHIs, so we cannot handle PHIs inside of loops.
9489 return L->getHeader() == I->getParent();
9490 }
9491
9492 // If we won't be able to constant fold this expression even if the operands
9493 // are constants, bail early.
9494 return CanConstantFold(I);
9495}
9496
9497/// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
9498/// recursing through each instruction operand until reaching a loop header phi.
9499static PHINode *
9500getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
9501 DenseMap<Instruction *, PHINode *> &PHIMap,
9502 unsigned Depth) {
9503 if (Depth > MaxConstantEvolvingDepth)
9504 return nullptr;
9505
9506 // Otherwise, we can evaluate this instruction if all of its operands are
9507 // constant or derived from a PHI node themselves.
9508 PHINode *PHI = nullptr;
9509 for (Value *Op : UseInst->operands()) {
9510 if (isa<Constant>(Val: Op)) continue;
9511
9512 Instruction *OpInst = dyn_cast<Instruction>(Val: Op);
9513 if (!OpInst || !canConstantEvolve(I: OpInst, L)) return nullptr;
9514
9515 PHINode *P = dyn_cast<PHINode>(Val: OpInst);
9516 if (!P)
9517 // If this operand is already visited, reuse the prior result.
9518 // We may have P != PHI if this is the deepest point at which the
9519 // inconsistent paths meet.
9520 P = PHIMap.lookup(Val: OpInst);
9521 if (!P) {
9522 // Recurse and memoize the results, whether a phi is found or not.
9523 // This recursive call invalidates pointers into PHIMap.
9524 P = getConstantEvolvingPHIOperands(UseInst: OpInst, L, PHIMap, Depth: Depth + 1);
9525 PHIMap[OpInst] = P;
9526 }
9527 if (!P)
9528 return nullptr; // Not evolving from PHI
9529 if (PHI && PHI != P)
9530 return nullptr; // Evolving from multiple different PHIs.
9531 PHI = P;
9532 }
9533 // This is a expression evolving from a constant PHI!
9534 return PHI;
9535}
9536
9537/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
9538/// in the loop that V is derived from. We allow arbitrary operations along the
9539/// way, but the operands of an operation must either be constants or a value
9540/// derived from a constant PHI. If this expression does not fit with these
9541/// constraints, return null.
9542static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
9543 Instruction *I = dyn_cast<Instruction>(Val: V);
9544 if (!I || !canConstantEvolve(I, L)) return nullptr;
9545
9546 if (PHINode *PN = dyn_cast<PHINode>(Val: I))
9547 return PN;
9548
9549 // Record non-constant instructions contained by the loop.
9550 DenseMap<Instruction *, PHINode *> PHIMap;
9551 return getConstantEvolvingPHIOperands(UseInst: I, L, PHIMap, Depth: 0);
9552}
9553
9554/// EvaluateExpression - Given an expression that passes the
9555/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
9556/// in the loop has the value PHIVal. If we can't fold this expression for some
9557/// reason, return null.
9558static Constant *EvaluateExpression(Value *V, const Loop *L,
9559 DenseMap<Instruction *, Constant *> &Vals,
9560 const DataLayout &DL,
9561 const TargetLibraryInfo *TLI) {
9562 // Convenient constant check, but redundant for recursive calls.
9563 if (Constant *C = dyn_cast<Constant>(Val: V)) return C;
9564 Instruction *I = dyn_cast<Instruction>(Val: V);
9565 if (!I) return nullptr;
9566
9567 if (Constant *C = Vals.lookup(Val: I)) return C;
9568
9569 // An instruction inside the loop depends on a value outside the loop that we
9570 // weren't given a mapping for, or a value such as a call inside the loop.
9571 if (!canConstantEvolve(I, L)) return nullptr;
9572
9573 // An unmapped PHI can be due to a branch or another loop inside this loop,
9574 // or due to this not being the initial iteration through a loop where we
9575 // couldn't compute the evolution of this particular PHI last time.
9576 if (isa<PHINode>(Val: I)) return nullptr;
9577
9578 std::vector<Constant*> Operands(I->getNumOperands());
9579
9580 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
9581 Instruction *Operand = dyn_cast<Instruction>(Val: I->getOperand(i));
9582 if (!Operand) {
9583 Operands[i] = dyn_cast<Constant>(Val: I->getOperand(i));
9584 if (!Operands[i]) return nullptr;
9585 continue;
9586 }
9587 Constant *C = EvaluateExpression(V: Operand, L, Vals, DL, TLI);
9588 Vals[Operand] = C;
9589 if (!C) return nullptr;
9590 Operands[i] = C;
9591 }
9592
9593 return ConstantFoldInstOperands(I, Ops: Operands, DL, TLI,
9594 /*AllowNonDeterministic=*/false);
9595}
9596
9597
9598// If every incoming value to PN except the one for BB is a specific Constant,
9599// return that, else return nullptr.
9600static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
9601 Constant *IncomingVal = nullptr;
9602
9603 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
9604 if (PN->getIncomingBlock(i) == BB)
9605 continue;
9606
9607 auto *CurrentVal = dyn_cast<Constant>(Val: PN->getIncomingValue(i));
9608 if (!CurrentVal)
9609 return nullptr;
9610
9611 if (IncomingVal != CurrentVal) {
9612 if (IncomingVal)
9613 return nullptr;
9614 IncomingVal = CurrentVal;
9615 }
9616 }
9617
9618 return IncomingVal;
9619}
9620
9621/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
9622/// in the header of its containing loop, we know the loop executes a
9623/// constant number of times, and the PHI node is just a recurrence
9624/// involving constants, fold it.
9625Constant *
9626ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
9627 const APInt &BEs,
9628 const Loop *L) {
9629 auto I = ConstantEvolutionLoopExitValue.find(Val: PN);
9630 if (I != ConstantEvolutionLoopExitValue.end())
9631 return I->second;
9632
9633 if (BEs.ugt(RHS: MaxBruteForceIterations))
9634 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
9635
9636 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
9637
9638 DenseMap<Instruction *, Constant *> CurrentIterVals;
9639 BasicBlock *Header = L->getHeader();
9640 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
9641
9642 BasicBlock *Latch = L->getLoopLatch();
9643 if (!Latch)
9644 return nullptr;
9645
9646 for (PHINode &PHI : Header->phis()) {
9647 if (auto *StartCST = getOtherIncomingValue(PN: &PHI, BB: Latch))
9648 CurrentIterVals[&PHI] = StartCST;
9649 }
9650 if (!CurrentIterVals.count(Val: PN))
9651 return RetVal = nullptr;
9652
9653 Value *BEValue = PN->getIncomingValueForBlock(BB: Latch);
9654
9655 // Execute the loop symbolically to determine the exit value.
9656 assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&
9657 "BEs is <= MaxBruteForceIterations which is an 'unsigned'!");
9658
9659 unsigned NumIterations = BEs.getZExtValue(); // must be in range
9660 unsigned IterationNum = 0;
9661 const DataLayout &DL = getDataLayout();
9662 for (; ; ++IterationNum) {
9663 if (IterationNum == NumIterations)
9664 return RetVal = CurrentIterVals[PN]; // Got exit value!
9665
9666 // Compute the value of the PHIs for the next iteration.
9667 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
9668 DenseMap<Instruction *, Constant *> NextIterVals;
9669 Constant *NextPHI =
9670 EvaluateExpression(V: BEValue, L, Vals&: CurrentIterVals, DL, TLI: &TLI);
9671 if (!NextPHI)
9672 return nullptr; // Couldn't evaluate!
9673 NextIterVals[PN] = NextPHI;
9674
9675 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
9676
9677 // Also evaluate the other PHI nodes. However, we don't get to stop if we
9678 // cease to be able to evaluate one of them or if they stop evolving,
9679 // because that doesn't necessarily prevent us from computing PN.
9680 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
9681 for (const auto &I : CurrentIterVals) {
9682 PHINode *PHI = dyn_cast<PHINode>(Val: I.first);
9683 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
9684 PHIsToCompute.emplace_back(Args&: PHI, Args: I.second);
9685 }
9686 // We use two distinct loops because EvaluateExpression may invalidate any
9687 // iterators into CurrentIterVals.
9688 for (const auto &I : PHIsToCompute) {
9689 PHINode *PHI = I.first;
9690 Constant *&NextPHI = NextIterVals[PHI];
9691 if (!NextPHI) { // Not already computed.
9692 Value *BEValue = PHI->getIncomingValueForBlock(BB: Latch);
9693 NextPHI = EvaluateExpression(V: BEValue, L, Vals&: CurrentIterVals, DL, TLI: &TLI);
9694 }
9695 if (NextPHI != I.second)
9696 StoppedEvolving = false;
9697 }
9698
9699 // If all entries in CurrentIterVals == NextIterVals then we can stop
9700 // iterating, the loop can't continue to change.
9701 if (StoppedEvolving)
9702 return RetVal = CurrentIterVals[PN];
9703
9704 CurrentIterVals.swap(RHS&: NextIterVals);
9705 }
9706}
9707
9708const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
9709 Value *Cond,
9710 bool ExitWhen) {
9711 PHINode *PN = getConstantEvolvingPHI(V: Cond, L);
9712 if (!PN) return getCouldNotCompute();
9713
9714 // If the loop is canonicalized, the PHI will have exactly two entries.
9715 // That's the only form we support here.
9716 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
9717
9718 DenseMap<Instruction *, Constant *> CurrentIterVals;
9719 BasicBlock *Header = L->getHeader();
9720 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
9721
9722 BasicBlock *Latch = L->getLoopLatch();
9723 assert(Latch && "Should follow from NumIncomingValues == 2!");
9724
9725 for (PHINode &PHI : Header->phis()) {
9726 if (auto *StartCST = getOtherIncomingValue(PN: &PHI, BB: Latch))
9727 CurrentIterVals[&PHI] = StartCST;
9728 }
9729 if (!CurrentIterVals.count(Val: PN))
9730 return getCouldNotCompute();
9731
9732 // Okay, we find a PHI node that defines the trip count of this loop. Execute
9733 // the loop symbolically to determine when the condition gets a value of
9734 // "ExitWhen".
9735 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
9736 const DataLayout &DL = getDataLayout();
9737 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
9738 auto *CondVal = dyn_cast_or_null<ConstantInt>(
9739 Val: EvaluateExpression(V: Cond, L, Vals&: CurrentIterVals, DL, TLI: &TLI));
9740
9741 // Couldn't symbolically evaluate.
9742 if (!CondVal) return getCouldNotCompute();
9743
9744 if (CondVal->getValue() == uint64_t(ExitWhen)) {
9745 ++NumBruteForceTripCountsComputed;
9746 return getConstant(Ty: Type::getInt32Ty(C&: getContext()), V: IterationNum);
9747 }
9748
9749 // Update all the PHI nodes for the next iteration.
9750 DenseMap<Instruction *, Constant *> NextIterVals;
9751
9752 // Create a list of which PHIs we need to compute. We want to do this before
9753 // calling EvaluateExpression on them because that may invalidate iterators
9754 // into CurrentIterVals.
9755 SmallVector<PHINode *, 8> PHIsToCompute;
9756 for (const auto &I : CurrentIterVals) {
9757 PHINode *PHI = dyn_cast<PHINode>(Val: I.first);
9758 if (!PHI || PHI->getParent() != Header) continue;
9759 PHIsToCompute.push_back(Elt: PHI);
9760 }
9761 for (PHINode *PHI : PHIsToCompute) {
9762 Constant *&NextPHI = NextIterVals[PHI];
9763 if (NextPHI) continue; // Already computed!
9764
9765 Value *BEValue = PHI->getIncomingValueForBlock(BB: Latch);
9766 NextPHI = EvaluateExpression(V: BEValue, L, Vals&: CurrentIterVals, DL, TLI: &TLI);
9767 }
9768 CurrentIterVals.swap(RHS&: NextIterVals);
9769 }
9770
9771 // Too many iterations were needed to evaluate.
9772 return getCouldNotCompute();
9773}
9774
9775const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
9776 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
9777 ValuesAtScopes[V];
9778 // Check to see if we've folded this expression at this loop before.
9779 for (auto &LS : Values)
9780 if (LS.first == L)
9781 return LS.second ? LS.second : V;
9782
9783 Values.emplace_back(Args&: L, Args: nullptr);
9784
9785 // Otherwise compute it.
9786 const SCEV *C = computeSCEVAtScope(S: V, L);
9787 for (auto &LS : reverse(C&: ValuesAtScopes[V]))
9788 if (LS.first == L) {
9789 LS.second = C;
9790 if (!isa<SCEVConstant>(Val: C))
9791 ValuesAtScopesUsers[C].push_back(Elt: {L, V});
9792 break;
9793 }
9794 return C;
9795}
9796
9797/// This builds up a Constant using the ConstantExpr interface. That way, we
9798/// will return Constants for objects which aren't represented by a
9799/// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
9800/// Returns NULL if the SCEV isn't representable as a Constant.
9801static Constant *BuildConstantFromSCEV(const SCEV *V) {
9802 switch (V->getSCEVType()) {
9803 case scCouldNotCompute:
9804 case scAddRecExpr:
9805 case scVScale:
9806 return nullptr;
9807 case scConstant:
9808 return cast<SCEVConstant>(Val: V)->getValue();
9809 case scUnknown:
9810 return dyn_cast<Constant>(Val: cast<SCEVUnknown>(Val: V)->getValue());
9811 case scPtrToInt: {
9812 const SCEVPtrToIntExpr *P2I = cast<SCEVPtrToIntExpr>(Val: V);
9813 if (Constant *CastOp = BuildConstantFromSCEV(V: P2I->getOperand()))
9814 return ConstantExpr::getPtrToInt(C: CastOp, Ty: P2I->getType());
9815
9816 return nullptr;
9817 }
9818 case scTruncate: {
9819 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(Val: V);
9820 if (Constant *CastOp = BuildConstantFromSCEV(V: ST->getOperand()))
9821 return ConstantExpr::getTrunc(C: CastOp, Ty: ST->getType());
9822 return nullptr;
9823 }
9824 case scAddExpr: {
9825 const SCEVAddExpr *SA = cast<SCEVAddExpr>(Val: V);
9826 Constant *C = nullptr;
9827 for (const SCEV *Op : SA->operands()) {
9828 Constant *OpC = BuildConstantFromSCEV(V: Op);
9829 if (!OpC)
9830 return nullptr;
9831 if (!C) {
9832 C = OpC;
9833 continue;
9834 }
9835 assert(!C->getType()->isPointerTy() &&
9836 "Can only have one pointer, and it must be last");
9837 if (OpC->getType()->isPointerTy()) {
9838 // The offsets have been converted to bytes. We can add bytes using
9839 // an i8 GEP.
9840 C = ConstantExpr::getGetElementPtr(Ty: Type::getInt8Ty(C&: C->getContext()),
9841 C: OpC, Idx: C);
9842 } else {
9843 C = ConstantExpr::getAdd(C1: C, C2: OpC);
9844 }
9845 }
9846 return C;
9847 }
9848 case scMulExpr:
9849 case scSignExtend:
9850 case scZeroExtend:
9851 case scUDivExpr:
9852 case scSMaxExpr:
9853 case scUMaxExpr:
9854 case scSMinExpr:
9855 case scUMinExpr:
9856 case scSequentialUMinExpr:
9857 return nullptr;
9858 }
9859 llvm_unreachable("Unknown SCEV kind!");
9860}
9861
9862const SCEV *
9863ScalarEvolution::getWithOperands(const SCEV *S,
9864 SmallVectorImpl<const SCEV *> &NewOps) {
9865 switch (S->getSCEVType()) {
9866 case scTruncate:
9867 case scZeroExtend:
9868 case scSignExtend:
9869 case scPtrToInt:
9870 return getCastExpr(Kind: S->getSCEVType(), Op: NewOps[0], Ty: S->getType());
9871 case scAddRecExpr: {
9872 auto *AddRec = cast<SCEVAddRecExpr>(Val: S);
9873 return getAddRecExpr(Operands&: NewOps, L: AddRec->getLoop(), Flags: AddRec->getNoWrapFlags());
9874 }
9875 case scAddExpr:
9876 return getAddExpr(Ops&: NewOps, OrigFlags: cast<SCEVAddExpr>(Val: S)->getNoWrapFlags());
9877 case scMulExpr:
9878 return getMulExpr(Ops&: NewOps, OrigFlags: cast<SCEVMulExpr>(Val: S)->getNoWrapFlags());
9879 case scUDivExpr:
9880 return getUDivExpr(LHS: NewOps[0], RHS: NewOps[1]);
9881 case scUMaxExpr:
9882 case scSMaxExpr:
9883 case scUMinExpr:
9884 case scSMinExpr:
9885 return getMinMaxExpr(Kind: S->getSCEVType(), Ops&: NewOps);
9886 case scSequentialUMinExpr:
9887 return getSequentialMinMaxExpr(Kind: S->getSCEVType(), Ops&: NewOps);
9888 case scConstant:
9889 case scVScale:
9890 case scUnknown:
9891 return S;
9892 case scCouldNotCompute:
9893 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9894 }
9895 llvm_unreachable("Unknown SCEV kind!");
9896}
9897
9898const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
9899 switch (V->getSCEVType()) {
9900 case scConstant:
9901 case scVScale:
9902 return V;
9903 case scAddRecExpr: {
9904 // If this is a loop recurrence for a loop that does not contain L, then we
9905 // are dealing with the final value computed by the loop.
9906 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Val: V);
9907 // First, attempt to evaluate each operand.
9908 // Avoid performing the look-up in the common case where the specified
9909 // expression has no loop-variant portions.
9910 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
9911 const SCEV *OpAtScope = getSCEVAtScope(V: AddRec->getOperand(i), L);
9912 if (OpAtScope == AddRec->getOperand(i))
9913 continue;
9914
9915 // Okay, at least one of these operands is loop variant but might be
9916 // foldable. Build a new instance of the folded commutative expression.
9917 SmallVector<const SCEV *, 8> NewOps;
9918 NewOps.reserve(N: AddRec->getNumOperands());
9919 append_range(C&: NewOps, R: AddRec->operands().take_front(N: i));
9920 NewOps.push_back(Elt: OpAtScope);
9921 for (++i; i != e; ++i)
9922 NewOps.push_back(Elt: getSCEVAtScope(V: AddRec->getOperand(i), L));
9923
9924 const SCEV *FoldedRec = getAddRecExpr(
9925 Operands&: NewOps, L: AddRec->getLoop(), Flags: AddRec->getNoWrapFlags(Mask: SCEV::FlagNW));
9926 AddRec = dyn_cast<SCEVAddRecExpr>(Val: FoldedRec);
9927 // The addrec may be folded to a nonrecurrence, for example, if the
9928 // induction variable is multiplied by zero after constant folding. Go
9929 // ahead and return the folded value.
9930 if (!AddRec)
9931 return FoldedRec;
9932 break;
9933 }
9934
9935 // If the scope is outside the addrec's loop, evaluate it by using the
9936 // loop exit value of the addrec.
9937 if (!AddRec->getLoop()->contains(L)) {
9938 // To evaluate this recurrence, we need to know how many times the AddRec
9939 // loop iterates. Compute this now.
9940 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(L: AddRec->getLoop());
9941 if (BackedgeTakenCount == getCouldNotCompute())
9942 return AddRec;
9943
9944 // Then, evaluate the AddRec.
9945 return AddRec->evaluateAtIteration(It: BackedgeTakenCount, SE&: *this);
9946 }
9947
9948 return AddRec;
9949 }
9950 case scTruncate:
9951 case scZeroExtend:
9952 case scSignExtend:
9953 case scPtrToInt:
9954 case scAddExpr:
9955 case scMulExpr:
9956 case scUDivExpr:
9957 case scUMaxExpr:
9958 case scSMaxExpr:
9959 case scUMinExpr:
9960 case scSMinExpr:
9961 case scSequentialUMinExpr: {
9962 ArrayRef<const SCEV *> Ops = V->operands();
9963 // Avoid performing the look-up in the common case where the specified
9964 // expression has no loop-variant portions.
9965 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
9966 const SCEV *OpAtScope = getSCEVAtScope(V: Ops[i], L);
9967 if (OpAtScope != Ops[i]) {
9968 // Okay, at least one of these operands is loop variant but might be
9969 // foldable. Build a new instance of the folded commutative expression.
9970 SmallVector<const SCEV *, 8> NewOps;
9971 NewOps.reserve(N: Ops.size());
9972 append_range(C&: NewOps, R: Ops.take_front(N: i));
9973 NewOps.push_back(Elt: OpAtScope);
9974
9975 for (++i; i != e; ++i) {
9976 OpAtScope = getSCEVAtScope(V: Ops[i], L);
9977 NewOps.push_back(Elt: OpAtScope);
9978 }
9979
9980 return getWithOperands(S: V, NewOps);
9981 }
9982 }
9983 // If we got here, all operands are loop invariant.
9984 return V;
9985 }
9986 case scUnknown: {
9987 // If this instruction is evolved from a constant-evolving PHI, compute the
9988 // exit value from the loop without using SCEVs.
9989 const SCEVUnknown *SU = cast<SCEVUnknown>(Val: V);
9990 Instruction *I = dyn_cast<Instruction>(Val: SU->getValue());
9991 if (!I)
9992 return V; // This is some other type of SCEVUnknown, just return it.
9993
9994 if (PHINode *PN = dyn_cast<PHINode>(Val: I)) {
9995 const Loop *CurrLoop = this->LI[I->getParent()];
9996 // Looking for loop exit value.
9997 if (CurrLoop && CurrLoop->getParentLoop() == L &&
9998 PN->getParent() == CurrLoop->getHeader()) {
9999 // Okay, there is no closed form solution for the PHI node. Check
10000 // to see if the loop that contains it has a known backedge-taken
10001 // count. If so, we may be able to force computation of the exit
10002 // value.
10003 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(L: CurrLoop);
10004 // This trivial case can show up in some degenerate cases where
10005 // the incoming IR has not yet been fully simplified.
10006 if (BackedgeTakenCount->isZero()) {
10007 Value *InitValue = nullptr;
10008 bool MultipleInitValues = false;
10009 for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
10010 if (!CurrLoop->contains(BB: PN->getIncomingBlock(i))) {
10011 if (!InitValue)
10012 InitValue = PN->getIncomingValue(i);
10013 else if (InitValue != PN->getIncomingValue(i)) {
10014 MultipleInitValues = true;
10015 break;
10016 }
10017 }
10018 }
10019 if (!MultipleInitValues && InitValue)
10020 return getSCEV(V: InitValue);
10021 }
10022 // Do we have a loop invariant value flowing around the backedge
10023 // for a loop which must execute the backedge?
10024 if (!isa<SCEVCouldNotCompute>(Val: BackedgeTakenCount) &&
10025 isKnownNonZero(S: BackedgeTakenCount) &&
10026 PN->getNumIncomingValues() == 2) {
10027
10028 unsigned InLoopPred =
10029 CurrLoop->contains(BB: PN->getIncomingBlock(i: 0)) ? 0 : 1;
10030 Value *BackedgeVal = PN->getIncomingValue(i: InLoopPred);
10031 if (CurrLoop->isLoopInvariant(V: BackedgeVal))
10032 return getSCEV(V: BackedgeVal);
10033 }
10034 if (auto *BTCC = dyn_cast<SCEVConstant>(Val: BackedgeTakenCount)) {
10035 // Okay, we know how many times the containing loop executes. If
10036 // this is a constant evolving PHI node, get the final value at
10037 // the specified iteration number.
10038 Constant *RV =
10039 getConstantEvolutionLoopExitValue(PN, BEs: BTCC->getAPInt(), L: CurrLoop);
10040 if (RV)
10041 return getSCEV(V: RV);
10042 }
10043 }
10044 }
10045
10046 // Okay, this is an expression that we cannot symbolically evaluate
10047 // into a SCEV. Check to see if it's possible to symbolically evaluate
10048 // the arguments into constants, and if so, try to constant propagate the
10049 // result. This is particularly useful for computing loop exit values.
10050 if (!CanConstantFold(I))
10051 return V; // This is some other type of SCEVUnknown, just return it.
10052
10053 SmallVector<Constant *, 4> Operands;
10054 Operands.reserve(N: I->getNumOperands());
10055 bool MadeImprovement = false;
10056 for (Value *Op : I->operands()) {
10057 if (Constant *C = dyn_cast<Constant>(Val: Op)) {
10058 Operands.push_back(Elt: C);
10059 continue;
10060 }
10061
10062 // If any of the operands is non-constant and if they are
10063 // non-integer and non-pointer, don't even try to analyze them
10064 // with scev techniques.
10065 if (!isSCEVable(Ty: Op->getType()))
10066 return V;
10067
10068 const SCEV *OrigV = getSCEV(V: Op);
10069 const SCEV *OpV = getSCEVAtScope(V: OrigV, L);
10070 MadeImprovement |= OrigV != OpV;
10071
10072 Constant *C = BuildConstantFromSCEV(V: OpV);
10073 if (!C)
10074 return V;
10075 assert(C->getType() == Op->getType() && "Type mismatch");
10076 Operands.push_back(Elt: C);
10077 }
10078
10079 // Check to see if getSCEVAtScope actually made an improvement.
10080 if (!MadeImprovement)
10081 return V; // This is some other type of SCEVUnknown, just return it.
10082
10083 Constant *C = nullptr;
10084 const DataLayout &DL = getDataLayout();
10085 C = ConstantFoldInstOperands(I, Ops: Operands, DL, TLI: &TLI,
10086 /*AllowNonDeterministic=*/false);
10087 if (!C)
10088 return V;
10089 return getSCEV(V: C);
10090 }
10091 case scCouldNotCompute:
10092 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
10093 }
10094 llvm_unreachable("Unknown SCEV type!");
10095}
10096
10097const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
10098 return getSCEVAtScope(V: getSCEV(V), L);
10099}
10100
10101const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const {
10102 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Val: S))
10103 return stripInjectiveFunctions(S: ZExt->getOperand());
10104 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Val: S))
10105 return stripInjectiveFunctions(S: SExt->getOperand());
10106 return S;
10107}
10108
10109/// Finds the minimum unsigned root of the following equation:
10110///
10111/// A * X = B (mod N)
10112///
10113/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
10114/// A and B isn't important.
10115///
10116/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
10117static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
10118 ScalarEvolution &SE) {
10119 uint32_t BW = A.getBitWidth();
10120 assert(BW == SE.getTypeSizeInBits(B->getType()));
10121 assert(A != 0 && "A must be non-zero.");
10122
10123 // 1. D = gcd(A, N)
10124 //
10125 // The gcd of A and N may have only one prime factor: 2. The number of
10126 // trailing zeros in A is its multiplicity
10127 uint32_t Mult2 = A.countr_zero();
10128 // D = 2^Mult2
10129
10130 // 2. Check if B is divisible by D.
10131 //
10132 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
10133 // is not less than multiplicity of this prime factor for D.
10134 if (SE.getMinTrailingZeros(S: B) < Mult2)
10135 return SE.getCouldNotCompute();
10136
10137 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
10138 // modulo (N / D).
10139 //
10140 // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
10141 // (N / D) in general. The inverse itself always fits into BW bits, though,
10142 // so we immediately truncate it.
10143 APInt AD = A.lshr(shiftAmt: Mult2).trunc(width: BW - Mult2); // AD = A / D
10144 APInt I = AD.multiplicativeInverse().zext(width: BW);
10145
10146 // 4. Compute the minimum unsigned root of the equation:
10147 // I * (B / D) mod (N / D)
10148 // To simplify the computation, we factor out the divide by D:
10149 // (I * B mod N) / D
10150 const SCEV *D = SE.getConstant(Val: APInt::getOneBitSet(numBits: BW, BitNo: Mult2));
10151 return SE.getUDivExactExpr(LHS: SE.getMulExpr(LHS: B, RHS: SE.getConstant(Val: I)), RHS: D);
10152}
10153
10154/// For a given quadratic addrec, generate coefficients of the corresponding
10155/// quadratic equation, multiplied by a common value to ensure that they are
10156/// integers.
10157/// The returned value is a tuple { A, B, C, M, BitWidth }, where
10158/// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C
10159/// were multiplied by, and BitWidth is the bit width of the original addrec
10160/// coefficients.
10161/// This function returns std::nullopt if the addrec coefficients are not
10162/// compile- time constants.
10163static std::optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>>
10164GetQuadraticEquation(const SCEVAddRecExpr *AddRec) {
10165 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
10166 const SCEVConstant *LC = dyn_cast<SCEVConstant>(Val: AddRec->getOperand(i: 0));
10167 const SCEVConstant *MC = dyn_cast<SCEVConstant>(Val: AddRec->getOperand(i: 1));
10168 const SCEVConstant *NC = dyn_cast<SCEVConstant>(Val: AddRec->getOperand(i: 2));
10169 LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: "
10170 << *AddRec << '\n');
10171
10172 // We currently can only solve this if the coefficients are constants.
10173 if (!LC || !MC || !NC) {
10174 LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n");
10175 return std::nullopt;
10176 }
10177
10178 APInt L = LC->getAPInt();
10179 APInt M = MC->getAPInt();
10180 APInt N = NC->getAPInt();
10181 assert(!N.isZero() && "This is not a quadratic addrec");
10182
10183 unsigned BitWidth = LC->getAPInt().getBitWidth();
10184 unsigned NewWidth = BitWidth + 1;
10185 LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: "
10186 << BitWidth << '\n');
10187 // The sign-extension (as opposed to a zero-extension) here matches the
10188 // extension used in SolveQuadraticEquationWrap (with the same motivation).
10189 N = N.sext(width: NewWidth);
10190 M = M.sext(width: NewWidth);
10191 L = L.sext(width: NewWidth);
10192
10193 // The increments are M, M+N, M+2N, ..., so the accumulated values are
10194 // L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is,
10195 // L+M, L+2M+N, L+3M+3N, ...
10196 // After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N.
10197 //
10198 // The equation Acc = 0 is then
10199 // L + nM + n(n-1)/2 N = 0, or 2L + 2M n + n(n-1) N = 0.
10200 // In a quadratic form it becomes:
10201 // N n^2 + (2M-N) n + 2L = 0.
10202
10203 APInt A = N;
10204 APInt B = 2 * M - A;
10205 APInt C = 2 * L;
10206 APInt T = APInt(NewWidth, 2);
10207 LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << B
10208 << "x + " << C << ", coeff bw: " << NewWidth
10209 << ", multiplied by " << T << '\n');
10210 return std::make_tuple(args&: A, args&: B, args&: C, args&: T, args&: BitWidth);
10211}
10212
10213/// Helper function to compare optional APInts:
10214/// (a) if X and Y both exist, return min(X, Y),
10215/// (b) if neither X nor Y exist, return std::nullopt,
10216/// (c) if exactly one of X and Y exists, return that value.
10217static std::optional<APInt> MinOptional(std::optional<APInt> X,
10218 std::optional<APInt> Y) {
10219 if (X && Y) {
10220 unsigned W = std::max(a: X->getBitWidth(), b: Y->getBitWidth());
10221 APInt XW = X->sext(width: W);
10222 APInt YW = Y->sext(width: W);
10223 return XW.slt(RHS: YW) ? *X : *Y;
10224 }
10225 if (!X && !Y)
10226 return std::nullopt;
10227 return X ? *X : *Y;
10228}
10229
10230/// Helper function to truncate an optional APInt to a given BitWidth.
10231/// When solving addrec-related equations, it is preferable to return a value
10232/// that has the same bit width as the original addrec's coefficients. If the
10233/// solution fits in the original bit width, truncate it (except for i1).
10234/// Returning a value of a different bit width may inhibit some optimizations.
10235///
10236/// In general, a solution to a quadratic equation generated from an addrec
10237/// may require BW+1 bits, where BW is the bit width of the addrec's
10238/// coefficients. The reason is that the coefficients of the quadratic
10239/// equation are BW+1 bits wide (to avoid truncation when converting from
10240/// the addrec to the equation).
10241static std::optional<APInt> TruncIfPossible(std::optional<APInt> X,
10242 unsigned BitWidth) {
10243 if (!X)
10244 return std::nullopt;
10245 unsigned W = X->getBitWidth();
10246 if (BitWidth > 1 && BitWidth < W && X->isIntN(N: BitWidth))
10247 return X->trunc(width: BitWidth);
10248 return X;
10249}
10250
10251/// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n
10252/// iterations. The values L, M, N are assumed to be signed, and they
10253/// should all have the same bit widths.
10254/// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW,
10255/// where BW is the bit width of the addrec's coefficients.
10256/// If the calculated value is a BW-bit integer (for BW > 1), it will be
10257/// returned as such, otherwise the bit width of the returned value may
10258/// be greater than BW.
10259///
10260/// This function returns std::nullopt if
10261/// (a) the addrec coefficients are not constant, or
10262/// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases
10263/// like x^2 = 5, no integer solutions exist, in other cases an integer
10264/// solution may exist, but SolveQuadraticEquationWrap may fail to find it.
10265static std::optional<APInt>
10266SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
10267 APInt A, B, C, M;
10268 unsigned BitWidth;
10269 auto T = GetQuadraticEquation(AddRec);
10270 if (!T)
10271 return std::nullopt;
10272
10273 std::tie(args&: A, args&: B, args&: C, args&: M, args&: BitWidth) = *T;
10274 LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n");
10275 std::optional<APInt> X =
10276 APIntOps::SolveQuadraticEquationWrap(A, B, C, RangeWidth: BitWidth + 1);
10277 if (!X)
10278 return std::nullopt;
10279
10280 ConstantInt *CX = ConstantInt::get(Context&: SE.getContext(), V: *X);
10281 ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, C: CX, SE);
10282 if (!V->isZero())
10283 return std::nullopt;
10284
10285 return TruncIfPossible(X, BitWidth);
10286}
10287
10288/// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n
10289/// iterations. The values M, N are assumed to be signed, and they
10290/// should all have the same bit widths.
10291/// Find the least n such that c(n) does not belong to the given range,
10292/// while c(n-1) does.
10293///
10294/// This function returns std::nullopt if
10295/// (a) the addrec coefficients are not constant, or
10296/// (b) SolveQuadraticEquationWrap was unable to find a solution for the
10297/// bounds of the range.
10298static std::optional<APInt>
10299SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec,
10300 const ConstantRange &Range, ScalarEvolution &SE) {
10301 assert(AddRec->getOperand(0)->isZero() &&
10302 "Starting value of addrec should be 0");
10303 LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range "
10304 << Range << ", addrec " << *AddRec << '\n');
10305 // This case is handled in getNumIterationsInRange. Here we can assume that
10306 // we start in the range.
10307 assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) &&
10308 "Addrec's initial value should be in range");
10309
10310 APInt A, B, C, M;
10311 unsigned BitWidth;
10312 auto T = GetQuadraticEquation(AddRec);
10313 if (!T)
10314 return std::nullopt;
10315
10316 // Be careful about the return value: there can be two reasons for not
10317 // returning an actual number. First, if no solutions to the equations
10318 // were found, and second, if the solutions don't leave the given range.
10319 // The first case means that the actual solution is "unknown", the second
10320 // means that it's known, but not valid. If the solution is unknown, we
10321 // cannot make any conclusions.
10322 // Return a pair: the optional solution and a flag indicating if the
10323 // solution was found.
10324 auto SolveForBoundary =
10325 [&](APInt Bound) -> std::pair<std::optional<APInt>, bool> {
10326 // Solve for signed overflow and unsigned overflow, pick the lower
10327 // solution.
10328 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary "
10329 << Bound << " (before multiplying by " << M << ")\n");
10330 Bound *= M; // The quadratic equation multiplier.
10331
10332 std::optional<APInt> SO;
10333 if (BitWidth > 1) {
10334 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
10335 "signed overflow\n");
10336 SO = APIntOps::SolveQuadraticEquationWrap(A, B, C: -Bound, RangeWidth: BitWidth);
10337 }
10338 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
10339 "unsigned overflow\n");
10340 std::optional<APInt> UO =
10341 APIntOps::SolveQuadraticEquationWrap(A, B, C: -Bound, RangeWidth: BitWidth + 1);
10342
10343 auto LeavesRange = [&] (const APInt &X) {
10344 ConstantInt *C0 = ConstantInt::get(Context&: SE.getContext(), V: X);
10345 ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C: C0, SE);
10346 if (Range.contains(Val: V0->getValue()))
10347 return false;
10348 // X should be at least 1, so X-1 is non-negative.
10349 ConstantInt *C1 = ConstantInt::get(Context&: SE.getContext(), V: X-1);
10350 ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C: C1, SE);
10351 if (Range.contains(Val: V1->getValue()))
10352 return true;
10353 return false;
10354 };
10355
10356 // If SolveQuadraticEquationWrap returns std::nullopt, it means that there
10357 // can be a solution, but the function failed to find it. We cannot treat it
10358 // as "no solution".
10359 if (!SO || !UO)
10360 return {std::nullopt, false};
10361
10362 // Check the smaller value first to see if it leaves the range.
10363 // At this point, both SO and UO must have values.
10364 std::optional<APInt> Min = MinOptional(X: SO, Y: UO);
10365 if (LeavesRange(*Min))
10366 return { Min, true };
10367 std::optional<APInt> Max = Min == SO ? UO : SO;
10368 if (LeavesRange(*Max))
10369 return { Max, true };
10370
10371 // Solutions were found, but were eliminated, hence the "true".
10372 return {std::nullopt, true};
10373 };
10374
10375 std::tie(args&: A, args&: B, args&: C, args&: M, args&: BitWidth) = *T;
10376 // Lower bound is inclusive, subtract 1 to represent the exiting value.
10377 APInt Lower = Range.getLower().sext(width: A.getBitWidth()) - 1;
10378 APInt Upper = Range.getUpper().sext(width: A.getBitWidth());
10379 auto SL = SolveForBoundary(Lower);
10380 auto SU = SolveForBoundary(Upper);
10381 // If any of the solutions was unknown, no meaninigful conclusions can
10382 // be made.
10383 if (!SL.second || !SU.second)
10384 return std::nullopt;
10385
10386 // Claim: The correct solution is not some value between Min and Max.
10387 //
10388 // Justification: Assuming that Min and Max are different values, one of
10389 // them is when the first signed overflow happens, the other is when the
10390 // first unsigned overflow happens. Crossing the range boundary is only
10391 // possible via an overflow (treating 0 as a special case of it, modeling
10392 // an overflow as crossing k*2^W for some k).
10393 //
10394 // The interesting case here is when Min was eliminated as an invalid
10395 // solution, but Max was not. The argument is that if there was another
10396 // overflow between Min and Max, it would also have been eliminated if
10397 // it was considered.
10398 //
10399 // For a given boundary, it is possible to have two overflows of the same
10400 // type (signed/unsigned) without having the other type in between: this
10401 // can happen when the vertex of the parabola is between the iterations
10402 // corresponding to the overflows. This is only possible when the two
10403 // overflows cross k*2^W for the same k. In such case, if the second one
10404 // left the range (and was the first one to do so), the first overflow
10405 // would have to enter the range, which would mean that either we had left
10406 // the range before or that we started outside of it. Both of these cases
10407 // are contradictions.
10408 //
10409 // Claim: In the case where SolveForBoundary returns std::nullopt, the correct
10410 // solution is not some value between the Max for this boundary and the
10411 // Min of the other boundary.
10412 //
10413 // Justification: Assume that we had such Max_A and Min_B corresponding
10414 // to range boundaries A and B and such that Max_A < Min_B. If there was
10415 // a solution between Max_A and Min_B, it would have to be caused by an
10416 // overflow corresponding to either A or B. It cannot correspond to B,
10417 // since Min_B is the first occurrence of such an overflow. If it
10418 // corresponded to A, it would have to be either a signed or an unsigned
10419 // overflow that is larger than both eliminated overflows for A. But
10420 // between the eliminated overflows and this overflow, the values would
10421 // cover the entire value space, thus crossing the other boundary, which
10422 // is a contradiction.
10423
10424 return TruncIfPossible(X: MinOptional(X: SL.first, Y: SU.first), BitWidth);
10425}
10426
10427ScalarEvolution::ExitLimit ScalarEvolution::howFarToZero(const SCEV *V,
10428 const Loop *L,
10429 bool ControlsOnlyExit,
10430 bool AllowPredicates) {
10431
10432 // This is only used for loops with a "x != y" exit test. The exit condition
10433 // is now expressed as a single expression, V = x-y. So the exit test is
10434 // effectively V != 0. We know and take advantage of the fact that this
10435 // expression only being used in a comparison by zero context.
10436
10437 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
10438 // If the value is a constant
10439 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Val: V)) {
10440 // If the value is already zero, the branch will execute zero times.
10441 if (C->getValue()->isZero()) return C;
10442 return getCouldNotCompute(); // Otherwise it will loop infinitely.
10443 }
10444
10445 const SCEVAddRecExpr *AddRec =
10446 dyn_cast<SCEVAddRecExpr>(Val: stripInjectiveFunctions(S: V));
10447
10448 if (!AddRec && AllowPredicates)
10449 // Try to make this an AddRec using runtime tests, in the first X
10450 // iterations of this loop, where X is the SCEV expression found by the
10451 // algorithm below.
10452 AddRec = convertSCEVToAddRecWithPredicates(S: V, L, Preds&: Predicates);
10453
10454 if (!AddRec || AddRec->getLoop() != L)
10455 return getCouldNotCompute();
10456
10457 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
10458 // the quadratic equation to solve it.
10459 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
10460 // We can only use this value if the chrec ends up with an exact zero
10461 // value at this index. When solving for "X*X != 5", for example, we
10462 // should not accept a root of 2.
10463 if (auto S = SolveQuadraticAddRecExact(AddRec, SE&: *this)) {
10464 const auto *R = cast<SCEVConstant>(Val: getConstant(Val: *S));
10465 return ExitLimit(R, R, R, false, Predicates);
10466 }
10467 return getCouldNotCompute();
10468 }
10469
10470 // Otherwise we can only handle this if it is affine.
10471 if (!AddRec->isAffine())
10472 return getCouldNotCompute();
10473
10474 // If this is an affine expression, the execution count of this branch is
10475 // the minimum unsigned root of the following equation:
10476 //
10477 // Start + Step*N = 0 (mod 2^BW)
10478 //
10479 // equivalent to:
10480 //
10481 // Step*N = -Start (mod 2^BW)
10482 //
10483 // where BW is the common bit width of Start and Step.
10484
10485 // Get the initial value for the loop.
10486 const SCEV *Start = getSCEVAtScope(V: AddRec->getStart(), L: L->getParentLoop());
10487 const SCEV *Step = getSCEVAtScope(V: AddRec->getOperand(i: 1), L: L->getParentLoop());
10488 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Val: Step);
10489
10490 if (!isLoopInvariant(S: Step, L))
10491 return getCouldNotCompute();
10492
10493 LoopGuards Guards = LoopGuards::collect(L, SE&: *this);
10494 // Specialize step for this loop so we get context sensitive facts below.
10495 const SCEV *StepWLG = applyLoopGuards(Expr: Step, Guards);
10496
10497 // For positive steps (counting up until unsigned overflow):
10498 // N = -Start/Step (as unsigned)
10499 // For negative steps (counting down to zero):
10500 // N = Start/-Step
10501 // First compute the unsigned distance from zero in the direction of Step.
10502 bool CountDown = isKnownNegative(S: StepWLG);
10503 if (!CountDown && !isKnownNonNegative(S: StepWLG))
10504 return getCouldNotCompute();
10505
10506 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(V: Start);
10507 // Handle unitary steps, which cannot wraparound.
10508 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
10509 // N = Distance (as unsigned)
10510 if (StepC &&
10511 (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne())) {
10512 APInt MaxBECount = getUnsignedRangeMax(S: applyLoopGuards(Expr: Distance, Guards));
10513 MaxBECount = APIntOps::umin(A: MaxBECount, B: getUnsignedRangeMax(S: Distance));
10514
10515 // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
10516 // we end up with a loop whose backedge-taken count is n - 1. Detect this
10517 // case, and see if we can improve the bound.
10518 //
10519 // Explicitly handling this here is necessary because getUnsignedRange
10520 // isn't context-sensitive; it doesn't know that we only care about the
10521 // range inside the loop.
10522 const SCEV *Zero = getZero(Ty: Distance->getType());
10523 const SCEV *One = getOne(Ty: Distance->getType());
10524 const SCEV *DistancePlusOne = getAddExpr(LHS: Distance, RHS: One);
10525 if (isLoopEntryGuardedByCond(L, Pred: ICmpInst::ICMP_NE, LHS: DistancePlusOne, RHS: Zero)) {
10526 // If Distance + 1 doesn't overflow, we can compute the maximum distance
10527 // as "unsigned_max(Distance + 1) - 1".
10528 ConstantRange CR = getUnsignedRange(S: DistancePlusOne);
10529 MaxBECount = APIntOps::umin(A: MaxBECount, B: CR.getUnsignedMax() - 1);
10530 }
10531 return ExitLimit(Distance, getConstant(Val: MaxBECount), Distance, false,
10532 Predicates);
10533 }
10534
10535 // If the condition controls loop exit (the loop exits only if the expression
10536 // is true) and the addition is no-wrap we can use unsigned divide to
10537 // compute the backedge count. In this case, the step may not divide the
10538 // distance, but we don't care because if the condition is "missed" the loop
10539 // will have undefined behavior due to wrapping.
10540 if (ControlsOnlyExit && AddRec->hasNoSelfWrap() &&
10541 loopHasNoAbnormalExits(L: AddRec->getLoop())) {
10542
10543 // If the stride is zero, the loop must be infinite. In C++, most loops
10544 // are finite by assumption, in which case the step being zero implies
10545 // UB must execute if the loop is entered.
10546 if (!loopIsFiniteByAssumption(L) && !isKnownNonZero(S: StepWLG))
10547 return getCouldNotCompute();
10548
10549 const SCEV *Exact =
10550 getUDivExpr(LHS: Distance, RHS: CountDown ? getNegativeSCEV(V: Step) : Step);
10551 const SCEV *ConstantMax = getCouldNotCompute();
10552 if (Exact != getCouldNotCompute()) {
10553 APInt MaxInt = getUnsignedRangeMax(S: applyLoopGuards(Expr: Exact, Guards));
10554 ConstantMax =
10555 getConstant(Val: APIntOps::umin(A: MaxInt, B: getUnsignedRangeMax(S: Exact)));
10556 }
10557 const SCEV *SymbolicMax =
10558 isa<SCEVCouldNotCompute>(Val: Exact) ? ConstantMax : Exact;
10559 return ExitLimit(Exact, ConstantMax, SymbolicMax, false, Predicates);
10560 }
10561
10562 // Solve the general equation.
10563 if (!StepC || StepC->getValue()->isZero())
10564 return getCouldNotCompute();
10565 const SCEV *E = SolveLinEquationWithOverflow(A: StepC->getAPInt(),
10566 B: getNegativeSCEV(V: Start), SE&: *this);
10567
10568 const SCEV *M = E;
10569 if (E != getCouldNotCompute()) {
10570 APInt MaxWithGuards = getUnsignedRangeMax(S: applyLoopGuards(Expr: E, Guards));
10571 M = getConstant(Val: APIntOps::umin(A: MaxWithGuards, B: getUnsignedRangeMax(S: E)));
10572 }
10573 auto *S = isa<SCEVCouldNotCompute>(Val: E) ? M : E;
10574 return ExitLimit(E, M, S, false, Predicates);
10575}
10576
10577ScalarEvolution::ExitLimit
10578ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
10579 // Loops that look like: while (X == 0) are very strange indeed. We don't
10580 // handle them yet except for the trivial case. This could be expanded in the
10581 // future as needed.
10582
10583 // If the value is a constant, check to see if it is known to be non-zero
10584 // already. If so, the backedge will execute zero times.
10585 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Val: V)) {
10586 if (!C->getValue()->isZero())
10587 return getZero(Ty: C->getType());
10588 return getCouldNotCompute(); // Otherwise it will loop infinitely.
10589 }
10590
10591 // We could implement others, but I really doubt anyone writes loops like
10592 // this, and if they did, they would already be constant folded.
10593 return getCouldNotCompute();
10594}
10595
10596std::pair<const BasicBlock *, const BasicBlock *>
10597ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(const BasicBlock *BB)
10598 const {
10599 // If the block has a unique predecessor, then there is no path from the
10600 // predecessor to the block that does not go through the direct edge
10601 // from the predecessor to the block.
10602 if (const BasicBlock *Pred = BB->getSinglePredecessor())
10603 return {Pred, BB};
10604
10605 // A loop's header is defined to be a block that dominates the loop.
10606 // If the header has a unique predecessor outside the loop, it must be
10607 // a block that has exactly one successor that can reach the loop.
10608 if (const Loop *L = LI.getLoopFor(BB))
10609 return {L->getLoopPredecessor(), L->getHeader()};
10610
10611 return {nullptr, nullptr};
10612}
10613
10614/// SCEV structural equivalence is usually sufficient for testing whether two
10615/// expressions are equal, however for the purposes of looking for a condition
10616/// guarding a loop, it can be useful to be a little more general, since a
10617/// front-end may have replicated the controlling expression.
10618static bool HasSameValue(const SCEV *A, const SCEV *B) {
10619 // Quick check to see if they are the same SCEV.
10620 if (A == B) return true;
10621
10622 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
10623 // Not all instructions that are "identical" compute the same value. For
10624 // instance, two distinct alloca instructions allocating the same type are
10625 // identical and do not read memory; but compute distinct values.
10626 return A->isIdenticalTo(I: B) && (isa<BinaryOperator>(Val: A) || isa<GetElementPtrInst>(Val: A));
10627 };
10628
10629 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
10630 // two different instructions with the same value. Check for this case.
10631 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(Val: A))
10632 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(Val: B))
10633 if (const Instruction *AI = dyn_cast<Instruction>(Val: AU->getValue()))
10634 if (const Instruction *BI = dyn_cast<Instruction>(Val: BU->getValue()))
10635 if (ComputesEqualValues(AI, BI))
10636 return true;
10637
10638 // Otherwise assume they may have a different value.
10639 return false;
10640}
10641
10642static bool MatchBinarySub(const SCEV *S, const SCEV *&LHS, const SCEV *&RHS) {
10643 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Val: S);
10644 if (!Add || Add->getNumOperands() != 2)
10645 return false;
10646 if (auto *ME = dyn_cast<SCEVMulExpr>(Val: Add->getOperand(i: 0));
10647 ME && ME->getNumOperands() == 2 && ME->getOperand(i: 0)->isAllOnesValue()) {
10648 LHS = Add->getOperand(i: 1);
10649 RHS = ME->getOperand(i: 1);
10650 return true;
10651 }
10652 if (auto *ME = dyn_cast<SCEVMulExpr>(Val: Add->getOperand(i: 1));
10653 ME && ME->getNumOperands() == 2 && ME->getOperand(i: 0)->isAllOnesValue()) {
10654 LHS = Add->getOperand(i: 0);
10655 RHS = ME->getOperand(i: 1);
10656 return true;
10657 }
10658 return false;
10659}
10660
10661bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
10662 const SCEV *&LHS, const SCEV *&RHS,
10663 unsigned Depth) {
10664 bool Changed = false;
10665 // Simplifies ICMP to trivial true or false by turning it into '0 == 0' or
10666 // '0 != 0'.
10667 auto TrivialCase = [&](bool TriviallyTrue) {
10668 LHS = RHS = getConstant(V: ConstantInt::getFalse(Context&: getContext()));
10669 Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE;
10670 return true;
10671 };
10672 // If we hit the max recursion limit bail out.
10673 if (Depth >= 3)
10674 return false;
10675
10676 // Canonicalize a constant to the right side.
10677 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Val: LHS)) {
10678 // Check for both operands constant.
10679 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Val: RHS)) {
10680 if (!ICmpInst::compare(LHS: LHSC->getAPInt(), RHS: RHSC->getAPInt(), Pred))
10681 return TrivialCase(false);
10682 return TrivialCase(true);
10683 }
10684 // Otherwise swap the operands to put the constant on the right.
10685 std::swap(a&: LHS, b&: RHS);
10686 Pred = ICmpInst::getSwappedPredicate(pred: Pred);
10687 Changed = true;
10688 }
10689
10690 // If we're comparing an addrec with a value which is loop-invariant in the
10691 // addrec's loop, put the addrec on the left. Also make a dominance check,
10692 // as both operands could be addrecs loop-invariant in each other's loop.
10693 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Val: RHS)) {
10694 const Loop *L = AR->getLoop();
10695 if (isLoopInvariant(S: LHS, L) && properlyDominates(S: LHS, BB: L->getHeader())) {
10696 std::swap(a&: LHS, b&: RHS);
10697 Pred = ICmpInst::getSwappedPredicate(pred: Pred);
10698 Changed = true;
10699 }
10700 }
10701
10702 // If there's a constant operand, canonicalize comparisons with boundary
10703 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
10704 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(Val: RHS)) {
10705 const APInt &RA = RC->getAPInt();
10706
10707 bool SimplifiedByConstantRange = false;
10708
10709 if (!ICmpInst::isEquality(P: Pred)) {
10710 ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, Other: RA);
10711 if (ExactCR.isFullSet())
10712 return TrivialCase(true);
10713 if (ExactCR.isEmptySet())
10714 return TrivialCase(false);
10715
10716 APInt NewRHS;
10717 CmpInst::Predicate NewPred;
10718 if (ExactCR.getEquivalentICmp(Pred&: NewPred, RHS&: NewRHS) &&
10719 ICmpInst::isEquality(P: NewPred)) {
10720 // We were able to convert an inequality to an equality.
10721 Pred = NewPred;
10722 RHS = getConstant(Val: NewRHS);
10723 Changed = SimplifiedByConstantRange = true;
10724 }
10725 }
10726
10727 if (!SimplifiedByConstantRange) {
10728 switch (Pred) {
10729 default:
10730 break;
10731 case ICmpInst::ICMP_EQ:
10732 case ICmpInst::ICMP_NE:
10733 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
10734 if (RA.isZero() && MatchBinarySub(S: LHS, LHS, RHS))
10735 Changed = true;
10736 break;
10737
10738 // The "Should have been caught earlier!" messages refer to the fact
10739 // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
10740 // should have fired on the corresponding cases, and canonicalized the
10741 // check to trivial case.
10742
10743 case ICmpInst::ICMP_UGE:
10744 assert(!RA.isMinValue() && "Should have been caught earlier!");
10745 Pred = ICmpInst::ICMP_UGT;
10746 RHS = getConstant(Val: RA - 1);
10747 Changed = true;
10748 break;
10749 case ICmpInst::ICMP_ULE:
10750 assert(!RA.isMaxValue() && "Should have been caught earlier!");
10751 Pred = ICmpInst::ICMP_ULT;
10752 RHS = getConstant(Val: RA + 1);
10753 Changed = true;
10754 break;
10755 case ICmpInst::ICMP_SGE:
10756 assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
10757 Pred = ICmpInst::ICMP_SGT;
10758 RHS = getConstant(Val: RA - 1);
10759 Changed = true;
10760 break;
10761 case ICmpInst::ICMP_SLE:
10762 assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
10763 Pred = ICmpInst::ICMP_SLT;
10764 RHS = getConstant(Val: RA + 1);
10765 Changed = true;
10766 break;
10767 }
10768 }
10769 }
10770
10771 // Check for obvious equality.
10772 if (HasSameValue(A: LHS, B: RHS)) {
10773 if (ICmpInst::isTrueWhenEqual(predicate: Pred))
10774 return TrivialCase(true);
10775 if (ICmpInst::isFalseWhenEqual(predicate: Pred))
10776 return TrivialCase(false);
10777 }
10778
10779 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
10780 // adding or subtracting 1 from one of the operands.
10781 switch (Pred) {
10782 case ICmpInst::ICMP_SLE:
10783 if (!getSignedRangeMax(S: RHS).isMaxSignedValue()) {
10784 RHS = getAddExpr(LHS: getConstant(Ty: RHS->getType(), V: 1, isSigned: true), RHS,
10785 Flags: SCEV::FlagNSW);
10786 Pred = ICmpInst::ICMP_SLT;
10787 Changed = true;
10788 } else if (!getSignedRangeMin(S: LHS).isMinSignedValue()) {
10789 LHS = getAddExpr(LHS: getConstant(Ty: RHS->getType(), V: (uint64_t)-1, isSigned: true), RHS: LHS,
10790 Flags: SCEV::FlagNSW);
10791 Pred = ICmpInst::ICMP_SLT;
10792 Changed = true;
10793 }
10794 break;
10795 case ICmpInst::ICMP_SGE:
10796 if (!getSignedRangeMin(S: RHS).isMinSignedValue()) {
10797 RHS = getAddExpr(LHS: getConstant(Ty: RHS->getType(), V: (uint64_t)-1, isSigned: true), RHS,
10798 Flags: SCEV::FlagNSW);
10799 Pred = ICmpInst::ICMP_SGT;
10800 Changed = true;
10801 } else if (!getSignedRangeMax(S: LHS).isMaxSignedValue()) {
10802 LHS = getAddExpr(LHS: getConstant(Ty: RHS->getType(), V: 1, isSigned: true), RHS: LHS,
10803 Flags: SCEV::FlagNSW);
10804 Pred = ICmpInst::ICMP_SGT;
10805 Changed = true;
10806 }
10807 break;
10808 case ICmpInst::ICMP_ULE:
10809 if (!getUnsignedRangeMax(S: RHS).isMaxValue()) {
10810 RHS = getAddExpr(LHS: getConstant(Ty: RHS->getType(), V: 1, isSigned: true), RHS,
10811 Flags: SCEV::FlagNUW);
10812 Pred = ICmpInst::ICMP_ULT;
10813 Changed = true;
10814 } else if (!getUnsignedRangeMin(S: LHS).isMinValue()) {
10815 LHS = getAddExpr(LHS: getConstant(Ty: RHS->getType(), V: (uint64_t)-1, isSigned: true), RHS: LHS);
10816 Pred = ICmpInst::ICMP_ULT;
10817 Changed = true;
10818 }
10819 break;
10820 case ICmpInst::ICMP_UGE:
10821 if (!getUnsignedRangeMin(S: RHS).isMinValue()) {
10822 RHS = getAddExpr(LHS: getConstant(Ty: RHS->getType(), V: (uint64_t)-1, isSigned: true), RHS);
10823 Pred = ICmpInst::ICMP_UGT;
10824 Changed = true;
10825 } else if (!getUnsignedRangeMax(S: LHS).isMaxValue()) {
10826 LHS = getAddExpr(LHS: getConstant(Ty: RHS->getType(), V: 1, isSigned: true), RHS: LHS,
10827 Flags: SCEV::FlagNUW);
10828 Pred = ICmpInst::ICMP_UGT;
10829 Changed = true;
10830 }
10831 break;
10832 default:
10833 break;
10834 }
10835
10836 // TODO: More simplifications are possible here.
10837
10838 // Recursively simplify until we either hit a recursion limit or nothing
10839 // changes.
10840 if (Changed)
10841 return SimplifyICmpOperands(Pred, LHS, RHS, Depth: Depth + 1);
10842
10843 return Changed;
10844}
10845
10846bool ScalarEvolution::isKnownNegative(const SCEV *S) {
10847 return getSignedRangeMax(S).isNegative();
10848}
10849
10850bool ScalarEvolution::isKnownPositive(const SCEV *S) {
10851 return getSignedRangeMin(S).isStrictlyPositive();
10852}
10853
10854bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
10855 return !getSignedRangeMin(S).isNegative();
10856}
10857
10858bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
10859 return !getSignedRangeMax(S).isStrictlyPositive();
10860}
10861
10862bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
10863 // Query push down for cases where the unsigned range is
10864 // less than sufficient.
10865 if (const auto *SExt = dyn_cast<SCEVSignExtendExpr>(Val: S))
10866 return isKnownNonZero(S: SExt->getOperand(i: 0));
10867 return getUnsignedRangeMin(S) != 0;
10868}
10869
10870std::pair<const SCEV *, const SCEV *>
10871ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) {
10872 // Compute SCEV on entry of loop L.
10873 const SCEV *Start = SCEVInitRewriter::rewrite(S, L, SE&: *this);
10874 if (Start == getCouldNotCompute())
10875 return { Start, Start };
10876 // Compute post increment SCEV for loop L.
10877 const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, SE&: *this);
10878 assert(PostInc != getCouldNotCompute() && "Unexpected could not compute");
10879 return { Start, PostInc };
10880}
10881
10882bool ScalarEvolution::isKnownViaInduction(ICmpInst::Predicate Pred,
10883 const SCEV *LHS, const SCEV *RHS) {
10884 // First collect all loops.
10885 SmallPtrSet<const Loop *, 8> LoopsUsed;
10886 getUsedLoops(S: LHS, LoopsUsed);
10887 getUsedLoops(S: RHS, LoopsUsed);
10888
10889 if (LoopsUsed.empty())
10890 return false;
10891
10892 // Domination relationship must be a linear order on collected loops.
10893#ifndef NDEBUG
10894 for (const auto *L1 : LoopsUsed)
10895 for (const auto *L2 : LoopsUsed)
10896 assert((DT.dominates(L1->getHeader(), L2->getHeader()) ||
10897 DT.dominates(L2->getHeader(), L1->getHeader())) &&
10898 "Domination relationship is not a linear order");
10899#endif
10900
10901 const Loop *MDL =
10902 *llvm::max_element(Range&: LoopsUsed, C: [&](const Loop *L1, const Loop *L2) {
10903 return DT.properlyDominates(A: L1->getHeader(), B: L2->getHeader());
10904 });
10905
10906 // Get init and post increment value for LHS.
10907 auto SplitLHS = SplitIntoInitAndPostInc(L: MDL, S: LHS);
10908 // if LHS contains unknown non-invariant SCEV then bail out.
10909 if (SplitLHS.first == getCouldNotCompute())
10910 return false;
10911 assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC");
10912 // Get init and post increment value for RHS.
10913 auto SplitRHS = SplitIntoInitAndPostInc(L: MDL, S: RHS);
10914 // if RHS contains unknown non-invariant SCEV then bail out.
10915 if (SplitRHS.first == getCouldNotCompute())
10916 return false;
10917 assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC");
10918 // It is possible that init SCEV contains an invariant load but it does
10919 // not dominate MDL and is not available at MDL loop entry, so we should
10920 // check it here.
10921 if (!isAvailableAtLoopEntry(S: SplitLHS.first, L: MDL) ||
10922 !isAvailableAtLoopEntry(S: SplitRHS.first, L: MDL))
10923 return false;
10924
10925 // It seems backedge guard check is faster than entry one so in some cases
10926 // it can speed up whole estimation by short circuit
10927 return isLoopBackedgeGuardedByCond(L: MDL, Pred, LHS: SplitLHS.second,
10928 RHS: SplitRHS.second) &&
10929 isLoopEntryGuardedByCond(L: MDL, Pred, LHS: SplitLHS.first, RHS: SplitRHS.first);
10930}
10931
10932bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
10933 const SCEV *LHS, const SCEV *RHS) {
10934 // Canonicalize the inputs first.
10935 (void)SimplifyICmpOperands(Pred, LHS, RHS);
10936
10937 if (isKnownViaInduction(Pred, LHS, RHS))
10938 return true;
10939
10940 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
10941 return true;
10942
10943 // Otherwise see what can be done with some simple reasoning.
10944 return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS);
10945}
10946
10947std::optional<bool> ScalarEvolution::evaluatePredicate(ICmpInst::Predicate Pred,
10948 const SCEV *LHS,
10949 const SCEV *RHS) {
10950 if (isKnownPredicate(Pred, LHS, RHS))
10951 return true;
10952 if (isKnownPredicate(Pred: ICmpInst::getInversePredicate(pred: Pred), LHS, RHS))
10953 return false;
10954 return std::nullopt;
10955}
10956
10957bool ScalarEvolution::isKnownPredicateAt(ICmpInst::Predicate Pred,
10958 const SCEV *LHS, const SCEV *RHS,
10959 const Instruction *CtxI) {
10960 // TODO: Analyze guards and assumes from Context's block.
10961 return isKnownPredicate(Pred, LHS, RHS) ||
10962 isBasicBlockEntryGuardedByCond(BB: CtxI->getParent(), Pred, LHS, RHS);
10963}
10964
10965std::optional<bool>
10966ScalarEvolution::evaluatePredicateAt(ICmpInst::Predicate Pred, const SCEV *LHS,
10967 const SCEV *RHS, const Instruction *CtxI) {
10968 std::optional<bool> KnownWithoutContext = evaluatePredicate(Pred, LHS, RHS);
10969 if (KnownWithoutContext)
10970 return KnownWithoutContext;
10971
10972 if (isBasicBlockEntryGuardedByCond(BB: CtxI->getParent(), Pred, LHS, RHS))
10973 return true;
10974 if (isBasicBlockEntryGuardedByCond(BB: CtxI->getParent(),
10975 Pred: ICmpInst::getInversePredicate(pred: Pred),
10976 LHS, RHS))
10977 return false;
10978 return std::nullopt;
10979}
10980
10981bool ScalarEvolution::isKnownOnEveryIteration(ICmpInst::Predicate Pred,
10982 const SCEVAddRecExpr *LHS,
10983 const SCEV *RHS) {
10984 const Loop *L = LHS->getLoop();
10985 return isLoopEntryGuardedByCond(L, Pred, LHS: LHS->getStart(), RHS) &&
10986 isLoopBackedgeGuardedByCond(L, Pred, LHS: LHS->getPostIncExpr(SE&: *this), RHS);
10987}
10988
10989std::optional<ScalarEvolution::MonotonicPredicateType>
10990ScalarEvolution::getMonotonicPredicateType(const SCEVAddRecExpr *LHS,
10991 ICmpInst::Predicate Pred) {
10992 auto Result = getMonotonicPredicateTypeImpl(LHS, Pred);
10993
10994#ifndef NDEBUG
10995 // Verify an invariant: inverting the predicate should turn a monotonically
10996 // increasing change to a monotonically decreasing one, and vice versa.
10997 if (Result) {
10998 auto ResultSwapped =
10999 getMonotonicPredicateTypeImpl(LHS, ICmpInst::getSwappedPredicate(Pred));
11000
11001 assert(*ResultSwapped != *Result &&
11002 "monotonicity should flip as we flip the predicate");
11003 }
11004#endif
11005
11006 return Result;
11007}
11008
11009std::optional<ScalarEvolution::MonotonicPredicateType>
11010ScalarEvolution::getMonotonicPredicateTypeImpl(const SCEVAddRecExpr *LHS,
11011 ICmpInst::Predicate Pred) {
11012 // A zero step value for LHS means the induction variable is essentially a
11013 // loop invariant value. We don't really depend on the predicate actually
11014 // flipping from false to true (for increasing predicates, and the other way
11015 // around for decreasing predicates), all we care about is that *if* the
11016 // predicate changes then it only changes from false to true.
11017 //
11018 // A zero step value in itself is not very useful, but there may be places
11019 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
11020 // as general as possible.
11021
11022 // Only handle LE/LT/GE/GT predicates.
11023 if (!ICmpInst::isRelational(P: Pred))
11024 return std::nullopt;
11025
11026 bool IsGreater = ICmpInst::isGE(P: Pred) || ICmpInst::isGT(P: Pred);
11027 assert((IsGreater || ICmpInst::isLE(Pred) || ICmpInst::isLT(Pred)) &&
11028 "Should be greater or less!");
11029
11030 // Check that AR does not wrap.
11031 if (ICmpInst::isUnsigned(predicate: Pred)) {
11032 if (!LHS->hasNoUnsignedWrap())
11033 return std::nullopt;
11034 return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
11035 }
11036 assert(ICmpInst::isSigned(Pred) &&
11037 "Relational predicate is either signed or unsigned!");
11038 if (!LHS->hasNoSignedWrap())
11039 return std::nullopt;
11040
11041 const SCEV *Step = LHS->getStepRecurrence(SE&: *this);
11042
11043 if (isKnownNonNegative(S: Step))
11044 return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
11045
11046 if (isKnownNonPositive(S: Step))
11047 return !IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
11048
11049 return std::nullopt;
11050}
11051
11052std::optional<ScalarEvolution::LoopInvariantPredicate>
11053ScalarEvolution::getLoopInvariantPredicate(ICmpInst::Predicate Pred,
11054 const SCEV *LHS, const SCEV *RHS,
11055 const Loop *L,
11056 const Instruction *CtxI) {
11057 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
11058 if (!isLoopInvariant(S: RHS, L)) {
11059 if (!isLoopInvariant(S: LHS, L))
11060 return std::nullopt;
11061
11062 std::swap(a&: LHS, b&: RHS);
11063 Pred = ICmpInst::getSwappedPredicate(pred: Pred);
11064 }
11065
11066 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(Val: LHS);
11067 if (!ArLHS || ArLHS->getLoop() != L)
11068 return std::nullopt;
11069
11070 auto MonotonicType = getMonotonicPredicateType(LHS: ArLHS, Pred);
11071 if (!MonotonicType)
11072 return std::nullopt;
11073 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
11074 // true as the loop iterates, and the backedge is control dependent on
11075 // "ArLHS `Pred` RHS" == true then we can reason as follows:
11076 //
11077 // * if the predicate was false in the first iteration then the predicate
11078 // is never evaluated again, since the loop exits without taking the
11079 // backedge.
11080 // * if the predicate was true in the first iteration then it will
11081 // continue to be true for all future iterations since it is
11082 // monotonically increasing.
11083 //
11084 // For both the above possibilities, we can replace the loop varying
11085 // predicate with its value on the first iteration of the loop (which is
11086 // loop invariant).
11087 //
11088 // A similar reasoning applies for a monotonically decreasing predicate, by
11089 // replacing true with false and false with true in the above two bullets.
11090 bool Increasing = *MonotonicType == ScalarEvolution::MonotonicallyIncreasing;
11091 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(pred: Pred);
11092
11093 if (isLoopBackedgeGuardedByCond(L, Pred: P, LHS, RHS))
11094 return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(),
11095 RHS);
11096
11097 if (!CtxI)
11098 return std::nullopt;
11099 // Try to prove via context.
11100 // TODO: Support other cases.
11101 switch (Pred) {
11102 default:
11103 break;
11104 case ICmpInst::ICMP_ULE:
11105 case ICmpInst::ICMP_ULT: {
11106 assert(ArLHS->hasNoUnsignedWrap() && "Is a requirement of monotonicity!");
11107 // Given preconditions
11108 // (1) ArLHS does not cross the border of positive and negative parts of
11109 // range because of:
11110 // - Positive step; (TODO: lift this limitation)
11111 // - nuw - does not cross zero boundary;
11112 // - nsw - does not cross SINT_MAX boundary;
11113 // (2) ArLHS <s RHS
11114 // (3) RHS >=s 0
11115 // we can replace the loop variant ArLHS <u RHS condition with loop
11116 // invariant Start(ArLHS) <u RHS.
11117 //
11118 // Because of (1) there are two options:
11119 // - ArLHS is always negative. It means that ArLHS <u RHS is always false;
11120 // - ArLHS is always non-negative. Because of (3) RHS is also non-negative.
11121 // It means that ArLHS <s RHS <=> ArLHS <u RHS.
11122 // Because of (2) ArLHS <u RHS is trivially true.
11123 // All together it means that ArLHS <u RHS <=> Start(ArLHS) >=s 0.
11124 // We can strengthen this to Start(ArLHS) <u RHS.
11125 auto SignFlippedPred = ICmpInst::getFlippedSignednessPredicate(pred: Pred);
11126 if (ArLHS->hasNoSignedWrap() && ArLHS->isAffine() &&
11127 isKnownPositive(S: ArLHS->getStepRecurrence(SE&: *this)) &&
11128 isKnownNonNegative(S: RHS) &&
11129 isKnownPredicateAt(Pred: SignFlippedPred, LHS: ArLHS, RHS, CtxI))
11130 return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(),
11131 RHS);
11132 }
11133 }
11134
11135 return std::nullopt;
11136}
11137
11138std::optional<ScalarEvolution::LoopInvariantPredicate>
11139ScalarEvolution::getLoopInvariantExitCondDuringFirstIterations(
11140 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
11141 const Instruction *CtxI, const SCEV *MaxIter) {
11142 if (auto LIP = getLoopInvariantExitCondDuringFirstIterationsImpl(
11143 Pred, LHS, RHS, L, CtxI, MaxIter))
11144 return LIP;
11145 if (auto *UMin = dyn_cast<SCEVUMinExpr>(Val: MaxIter))
11146 // Number of iterations expressed as UMIN isn't always great for expressing
11147 // the value on the last iteration. If the straightforward approach didn't
11148 // work, try the following trick: if the a predicate is invariant for X, it
11149 // is also invariant for umin(X, ...). So try to find something that works
11150 // among subexpressions of MaxIter expressed as umin.
11151 for (auto *Op : UMin->operands())
11152 if (auto LIP = getLoopInvariantExitCondDuringFirstIterationsImpl(
11153 Pred, LHS, RHS, L, CtxI, MaxIter: Op))
11154 return LIP;
11155 return std::nullopt;
11156}
11157
11158std::optional<ScalarEvolution::LoopInvariantPredicate>
11159ScalarEvolution::getLoopInvariantExitCondDuringFirstIterationsImpl(
11160 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
11161 const Instruction *CtxI, const SCEV *MaxIter) {
11162 // Try to prove the following set of facts:
11163 // - The predicate is monotonic in the iteration space.
11164 // - If the check does not fail on the 1st iteration:
11165 // - No overflow will happen during first MaxIter iterations;
11166 // - It will not fail on the MaxIter'th iteration.
11167 // If the check does fail on the 1st iteration, we leave the loop and no
11168 // other checks matter.
11169
11170 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
11171 if (!isLoopInvariant(S: RHS, L)) {
11172 if (!isLoopInvariant(S: LHS, L))
11173 return std::nullopt;
11174
11175 std::swap(a&: LHS, b&: RHS);
11176 Pred = ICmpInst::getSwappedPredicate(pred: Pred);
11177 }
11178
11179 auto *AR = dyn_cast<SCEVAddRecExpr>(Val: LHS);
11180 if (!AR || AR->getLoop() != L)
11181 return std::nullopt;
11182
11183 // The predicate must be relational (i.e. <, <=, >=, >).
11184 if (!ICmpInst::isRelational(P: Pred))
11185 return std::nullopt;
11186
11187 // TODO: Support steps other than +/- 1.
11188 const SCEV *Step = AR->getStepRecurrence(SE&: *this);
11189 auto *One = getOne(Ty: Step->getType());
11190 auto *MinusOne = getNegativeSCEV(V: One);
11191 if (Step != One && Step != MinusOne)
11192 return std::nullopt;
11193
11194 // Type mismatch here means that MaxIter is potentially larger than max
11195 // unsigned value in start type, which mean we cannot prove no wrap for the
11196 // indvar.
11197 if (AR->getType() != MaxIter->getType())
11198 return std::nullopt;
11199
11200 // Value of IV on suggested last iteration.
11201 const SCEV *Last = AR->evaluateAtIteration(It: MaxIter, SE&: *this);
11202 // Does it still meet the requirement?
11203 if (!isLoopBackedgeGuardedByCond(L, Pred, LHS: Last, RHS))
11204 return std::nullopt;
11205 // Because step is +/- 1 and MaxIter has same type as Start (i.e. it does
11206 // not exceed max unsigned value of this type), this effectively proves
11207 // that there is no wrap during the iteration. To prove that there is no
11208 // signed/unsigned wrap, we need to check that
11209 // Start <= Last for step = 1 or Start >= Last for step = -1.
11210 ICmpInst::Predicate NoOverflowPred =
11211 CmpInst::isSigned(predicate: Pred) ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
11212 if (Step == MinusOne)
11213 NoOverflowPred = CmpInst::getSwappedPredicate(pred: NoOverflowPred);
11214 const SCEV *Start = AR->getStart();
11215 if (!isKnownPredicateAt(Pred: NoOverflowPred, LHS: Start, RHS: Last, CtxI))
11216 return std::nullopt;
11217
11218 // Everything is fine.
11219 return ScalarEvolution::LoopInvariantPredicate(Pred, Start, RHS);
11220}
11221
11222bool ScalarEvolution::isKnownPredicateViaConstantRanges(
11223 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
11224 if (HasSameValue(A: LHS, B: RHS))
11225 return ICmpInst::isTrueWhenEqual(predicate: Pred);
11226
11227 // This code is split out from isKnownPredicate because it is called from
11228 // within isLoopEntryGuardedByCond.
11229
11230 auto CheckRanges = [&](const ConstantRange &RangeLHS,
11231 const ConstantRange &RangeRHS) {
11232 return RangeLHS.icmp(Pred, Other: RangeRHS);
11233 };
11234
11235 // The check at the top of the function catches the case where the values are
11236 // known to be equal.
11237 if (Pred == CmpInst::ICMP_EQ)
11238 return false;
11239
11240 if (Pred == CmpInst::ICMP_NE) {
11241 auto SL = getSignedRange(S: LHS);
11242 auto SR = getSignedRange(S: RHS);
11243 if (CheckRanges(SL, SR))
11244 return true;
11245 auto UL = getUnsignedRange(S: LHS);
11246 auto UR = getUnsignedRange(S: RHS);
11247 if (CheckRanges(UL, UR))
11248 return true;
11249 auto *Diff = getMinusSCEV(LHS, RHS);
11250 return !isa<SCEVCouldNotCompute>(Val: Diff) && isKnownNonZero(S: Diff);
11251 }
11252
11253 if (CmpInst::isSigned(predicate: Pred)) {
11254 auto SL = getSignedRange(S: LHS);
11255 auto SR = getSignedRange(S: RHS);
11256 return CheckRanges(SL, SR);
11257 }
11258
11259 auto UL = getUnsignedRange(S: LHS);
11260 auto UR = getUnsignedRange(S: RHS);
11261 return CheckRanges(UL, UR);
11262}
11263
11264bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
11265 const SCEV *LHS,
11266 const SCEV *RHS) {
11267 // Match X to (A + C1)<ExpectedFlags> and Y to (A + C2)<ExpectedFlags>, where
11268 // C1 and C2 are constant integers. If either X or Y are not add expressions,
11269 // consider them as X + 0 and Y + 0 respectively. C1 and C2 are returned via
11270 // OutC1 and OutC2.
11271 auto MatchBinaryAddToConst = [this](const SCEV *X, const SCEV *Y,
11272 APInt &OutC1, APInt &OutC2,
11273 SCEV::NoWrapFlags ExpectedFlags) {
11274 const SCEV *XNonConstOp, *XConstOp;
11275 const SCEV *YNonConstOp, *YConstOp;
11276 SCEV::NoWrapFlags XFlagsPresent;
11277 SCEV::NoWrapFlags YFlagsPresent;
11278
11279 if (!splitBinaryAdd(Expr: X, L&: XConstOp, R&: XNonConstOp, Flags&: XFlagsPresent)) {
11280 XConstOp = getZero(Ty: X->getType());
11281 XNonConstOp = X;
11282 XFlagsPresent = ExpectedFlags;
11283 }
11284 if (!isa<SCEVConstant>(Val: XConstOp) ||
11285 (XFlagsPresent & ExpectedFlags) != ExpectedFlags)
11286 return false;
11287
11288 if (!splitBinaryAdd(Expr: Y, L&: YConstOp, R&: YNonConstOp, Flags&: YFlagsPresent)) {
11289 YConstOp = getZero(Ty: Y->getType());
11290 YNonConstOp = Y;
11291 YFlagsPresent = ExpectedFlags;
11292 }
11293
11294 if (!isa<SCEVConstant>(Val: YConstOp) ||
11295 (YFlagsPresent & ExpectedFlags) != ExpectedFlags)
11296 return false;
11297
11298 if (YNonConstOp != XNonConstOp)
11299 return false;
11300
11301 OutC1 = cast<SCEVConstant>(Val: XConstOp)->getAPInt();
11302 OutC2 = cast<SCEVConstant>(Val: YConstOp)->getAPInt();
11303
11304 return true;
11305 };
11306
11307 APInt C1;
11308 APInt C2;
11309
11310 switch (Pred) {
11311 default:
11312 break;
11313
11314 case ICmpInst::ICMP_SGE:
11315 std::swap(a&: LHS, b&: RHS);
11316 [[fallthrough]];
11317 case ICmpInst::ICMP_SLE:
11318 // (X + C1)<nsw> s<= (X + C2)<nsw> if C1 s<= C2.
11319 if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.sle(RHS: C2))
11320 return true;
11321
11322 break;
11323
11324 case ICmpInst::ICMP_SGT:
11325 std::swap(a&: LHS, b&: RHS);
11326 [[fallthrough]];
11327 case ICmpInst::ICMP_SLT:
11328 // (X + C1)<nsw> s< (X + C2)<nsw> if C1 s< C2.
11329 if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.slt(RHS: C2))
11330 return true;
11331
11332 break;
11333
11334 case ICmpInst::ICMP_UGE:
11335 std::swap(a&: LHS, b&: RHS);
11336 [[fallthrough]];
11337 case ICmpInst::ICMP_ULE:
11338 // (X + C1)<nuw> u<= (X + C2)<nuw> for C1 u<= C2.
11339 if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNUW) && C1.ule(RHS: C2))
11340 return true;
11341
11342 break;
11343
11344 case ICmpInst::ICMP_UGT:
11345 std::swap(a&: LHS, b&: RHS);
11346 [[fallthrough]];
11347 case ICmpInst::ICMP_ULT:
11348 // (X + C1)<nuw> u< (X + C2)<nuw> if C1 u< C2.
11349 if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNUW) && C1.ult(RHS: C2))
11350 return true;
11351 break;
11352 }
11353
11354 return false;
11355}
11356
11357bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
11358 const SCEV *LHS,
11359 const SCEV *RHS) {
11360 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
11361 return false;
11362
11363 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
11364 // the stack can result in exponential time complexity.
11365 SaveAndRestore Restore(ProvingSplitPredicate, true);
11366
11367 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
11368 //
11369 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
11370 // isKnownPredicate. isKnownPredicate is more powerful, but also more
11371 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
11372 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
11373 // use isKnownPredicate later if needed.
11374 return isKnownNonNegative(S: RHS) &&
11375 isKnownPredicate(Pred: CmpInst::ICMP_SGE, LHS, RHS: getZero(Ty: LHS->getType())) &&
11376 isKnownPredicate(Pred: CmpInst::ICMP_SLT, LHS, RHS);
11377}
11378
11379bool ScalarEvolution::isImpliedViaGuard(const BasicBlock *BB,
11380 ICmpInst::Predicate Pred,
11381 const SCEV *LHS, const SCEV *RHS) {
11382 // No need to even try if we know the module has no guards.
11383 if (!HasGuards)
11384 return false;
11385
11386 return any_of(Range: *BB, P: [&](const Instruction &I) {
11387 using namespace llvm::PatternMatch;
11388
11389 Value *Condition;
11390 return match(V: &I, P: m_Intrinsic<Intrinsic::experimental_guard>(
11391 Op0: m_Value(V&: Condition))) &&
11392 isImpliedCond(Pred, LHS, RHS, FoundCondValue: Condition, Inverse: false);
11393 });
11394}
11395
11396/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
11397/// protected by a conditional between LHS and RHS. This is used to
11398/// to eliminate casts.
11399bool
11400ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
11401 ICmpInst::Predicate Pred,
11402 const SCEV *LHS, const SCEV *RHS) {
11403 // Interpret a null as meaning no loop, where there is obviously no guard
11404 // (interprocedural conditions notwithstanding). Do not bother about
11405 // unreachable loops.
11406 if (!L || !DT.isReachableFromEntry(A: L->getHeader()))
11407 return true;
11408
11409 if (VerifyIR)
11410 assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&
11411 "This cannot be done on broken IR!");
11412
11413
11414 if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
11415 return true;
11416
11417 BasicBlock *Latch = L->getLoopLatch();
11418 if (!Latch)
11419 return false;
11420
11421 BranchInst *LoopContinuePredicate =
11422 dyn_cast<BranchInst>(Val: Latch->getTerminator());
11423 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
11424 isImpliedCond(Pred, LHS, RHS,
11425 FoundCondValue: LoopContinuePredicate->getCondition(),
11426 Inverse: LoopContinuePredicate->getSuccessor(i: 0) != L->getHeader()))
11427 return true;
11428
11429 // We don't want more than one activation of the following loops on the stack
11430 // -- that can lead to O(n!) time complexity.
11431 if (WalkingBEDominatingConds)
11432 return false;
11433
11434 SaveAndRestore ClearOnExit(WalkingBEDominatingConds, true);
11435
11436 // See if we can exploit a trip count to prove the predicate.
11437 const auto &BETakenInfo = getBackedgeTakenInfo(L);
11438 const SCEV *LatchBECount = BETakenInfo.getExact(ExitingBlock: Latch, SE: this);
11439 if (LatchBECount != getCouldNotCompute()) {
11440 // We know that Latch branches back to the loop header exactly
11441 // LatchBECount times. This means the backdege condition at Latch is
11442 // equivalent to "{0,+,1} u< LatchBECount".
11443 Type *Ty = LatchBECount->getType();
11444 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
11445 const SCEV *LoopCounter =
11446 getAddRecExpr(Start: getZero(Ty), Step: getOne(Ty), L, Flags: NoWrapFlags);
11447 if (isImpliedCond(Pred, LHS, RHS, FoundPred: ICmpInst::ICMP_ULT, FoundLHS: LoopCounter,
11448 FoundRHS: LatchBECount))
11449 return true;
11450 }
11451
11452 // Check conditions due to any @llvm.assume intrinsics.
11453 for (auto &AssumeVH : AC.assumptions()) {
11454 if (!AssumeVH)
11455 continue;
11456 auto *CI = cast<CallInst>(Val&: AssumeVH);
11457 if (!DT.dominates(Def: CI, User: Latch->getTerminator()))
11458 continue;
11459
11460 if (isImpliedCond(Pred, LHS, RHS, FoundCondValue: CI->getArgOperand(i: 0), Inverse: false))
11461 return true;
11462 }
11463
11464 if (isImpliedViaGuard(BB: Latch, Pred, LHS, RHS))
11465 return true;
11466
11467 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
11468 DTN != HeaderDTN; DTN = DTN->getIDom()) {
11469 assert(DTN && "should reach the loop header before reaching the root!");
11470
11471 BasicBlock *BB = DTN->getBlock();
11472 if (isImpliedViaGuard(BB, Pred, LHS, RHS))
11473 return true;
11474
11475 BasicBlock *PBB = BB->getSinglePredecessor();
11476 if (!PBB)
11477 continue;
11478
11479 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(Val: PBB->getTerminator());
11480 if (!ContinuePredicate || !ContinuePredicate->isConditional())
11481 continue;
11482
11483 Value *Condition = ContinuePredicate->getCondition();
11484
11485 // If we have an edge `E` within the loop body that dominates the only
11486 // latch, the condition guarding `E` also guards the backedge. This
11487 // reasoning works only for loops with a single latch.
11488
11489 BasicBlockEdge DominatingEdge(PBB, BB);
11490 if (DominatingEdge.isSingleEdge()) {
11491 // We're constructively (and conservatively) enumerating edges within the
11492 // loop body that dominate the latch. The dominator tree better agree
11493 // with us on this:
11494 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
11495
11496 if (isImpliedCond(Pred, LHS, RHS, FoundCondValue: Condition,
11497 Inverse: BB != ContinuePredicate->getSuccessor(i: 0)))
11498 return true;
11499 }
11500 }
11501
11502 return false;
11503}
11504
11505bool ScalarEvolution::isBasicBlockEntryGuardedByCond(const BasicBlock *BB,
11506 ICmpInst::Predicate Pred,
11507 const SCEV *LHS,
11508 const SCEV *RHS) {
11509 // Do not bother proving facts for unreachable code.
11510 if (!DT.isReachableFromEntry(A: BB))
11511 return true;
11512 if (VerifyIR)
11513 assert(!verifyFunction(*BB->getParent(), &dbgs()) &&
11514 "This cannot be done on broken IR!");
11515
11516 // If we cannot prove strict comparison (e.g. a > b), maybe we can prove
11517 // the facts (a >= b && a != b) separately. A typical situation is when the
11518 // non-strict comparison is known from ranges and non-equality is known from
11519 // dominating predicates. If we are proving strict comparison, we always try
11520 // to prove non-equality and non-strict comparison separately.
11521 auto NonStrictPredicate = ICmpInst::getNonStrictPredicate(pred: Pred);
11522 const bool ProvingStrictComparison = (Pred != NonStrictPredicate);
11523 bool ProvedNonStrictComparison = false;
11524 bool ProvedNonEquality = false;
11525
11526 auto SplitAndProve =
11527 [&](std::function<bool(ICmpInst::Predicate)> Fn) -> bool {
11528 if (!ProvedNonStrictComparison)
11529 ProvedNonStrictComparison = Fn(NonStrictPredicate);
11530 if (!ProvedNonEquality)
11531 ProvedNonEquality = Fn(ICmpInst::ICMP_NE);
11532 if (ProvedNonStrictComparison && ProvedNonEquality)
11533 return true;
11534 return false;
11535 };
11536
11537 if (ProvingStrictComparison) {
11538 auto ProofFn = [&](ICmpInst::Predicate P) {
11539 return isKnownViaNonRecursiveReasoning(Pred: P, LHS, RHS);
11540 };
11541 if (SplitAndProve(ProofFn))
11542 return true;
11543 }
11544
11545 // Try to prove (Pred, LHS, RHS) using isImpliedCond.
11546 auto ProveViaCond = [&](const Value *Condition, bool Inverse) {
11547 const Instruction *CtxI = &BB->front();
11548 if (isImpliedCond(Pred, LHS, RHS, FoundCondValue: Condition, Inverse, Context: CtxI))
11549 return true;
11550 if (ProvingStrictComparison) {
11551 auto ProofFn = [&](ICmpInst::Predicate P) {
11552 return isImpliedCond(Pred: P, LHS, RHS, FoundCondValue: Condition, Inverse, Context: CtxI);
11553 };
11554 if (SplitAndProve(ProofFn))
11555 return true;
11556 }
11557 return false;
11558 };
11559
11560 // Starting at the block's predecessor, climb up the predecessor chain, as long
11561 // as there are predecessors that can be found that have unique successors
11562 // leading to the original block.
11563 const Loop *ContainingLoop = LI.getLoopFor(BB);
11564 const BasicBlock *PredBB;
11565 if (ContainingLoop && ContainingLoop->getHeader() == BB)
11566 PredBB = ContainingLoop->getLoopPredecessor();
11567 else
11568 PredBB = BB->getSinglePredecessor();
11569 for (std::pair<const BasicBlock *, const BasicBlock *> Pair(PredBB, BB);
11570 Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(BB: Pair.first)) {
11571 const BranchInst *BlockEntryPredicate =
11572 dyn_cast<BranchInst>(Val: Pair.first->getTerminator());
11573 if (!BlockEntryPredicate || BlockEntryPredicate->isUnconditional())
11574 continue;
11575
11576 if (ProveViaCond(BlockEntryPredicate->getCondition(),
11577 BlockEntryPredicate->getSuccessor(i: 0) != Pair.second))
11578 return true;
11579 }
11580
11581 // Check conditions due to any @llvm.assume intrinsics.
11582 for (auto &AssumeVH : AC.assumptions()) {
11583 if (!AssumeVH)
11584 continue;
11585 auto *CI = cast<CallInst>(Val&: AssumeVH);
11586 if (!DT.dominates(Def: CI, BB))
11587 continue;
11588
11589 if (ProveViaCond(CI->getArgOperand(i: 0), false))
11590 return true;
11591 }
11592
11593 // Check conditions due to any @llvm.experimental.guard intrinsics.
11594 auto *GuardDecl = F.getParent()->getFunction(
11595 Name: Intrinsic::getName(id: Intrinsic::experimental_guard));
11596 if (GuardDecl)
11597 for (const auto *GU : GuardDecl->users())
11598 if (const auto *Guard = dyn_cast<IntrinsicInst>(Val: GU))
11599 if (Guard->getFunction() == BB->getParent() && DT.dominates(Def: Guard, BB))
11600 if (ProveViaCond(Guard->getArgOperand(i: 0), false))
11601 return true;
11602 return false;
11603}
11604
11605bool ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
11606 ICmpInst::Predicate Pred,
11607 const SCEV *LHS,
11608 const SCEV *RHS) {
11609 // Interpret a null as meaning no loop, where there is obviously no guard
11610 // (interprocedural conditions notwithstanding).
11611 if (!L)
11612 return false;
11613
11614 // Both LHS and RHS must be available at loop entry.
11615 assert(isAvailableAtLoopEntry(LHS, L) &&
11616 "LHS is not available at Loop Entry");
11617 assert(isAvailableAtLoopEntry(RHS, L) &&
11618 "RHS is not available at Loop Entry");
11619
11620 if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
11621 return true;
11622
11623 return isBasicBlockEntryGuardedByCond(BB: L->getHeader(), Pred, LHS, RHS);
11624}
11625
11626bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
11627 const SCEV *RHS,
11628 const Value *FoundCondValue, bool Inverse,
11629 const Instruction *CtxI) {
11630 // False conditions implies anything. Do not bother analyzing it further.
11631 if (FoundCondValue ==
11632 ConstantInt::getBool(Context&: FoundCondValue->getContext(), V: Inverse))
11633 return true;
11634
11635 if (!PendingLoopPredicates.insert(Ptr: FoundCondValue).second)
11636 return false;
11637
11638 auto ClearOnExit =
11639 make_scope_exit(F: [&]() { PendingLoopPredicates.erase(Ptr: FoundCondValue); });
11640
11641 // Recursively handle And and Or conditions.
11642 const Value *Op0, *Op1;
11643 if (match(V: FoundCondValue, P: m_LogicalAnd(L: m_Value(V&: Op0), R: m_Value(V&: Op1)))) {
11644 if (!Inverse)
11645 return isImpliedCond(Pred, LHS, RHS, FoundCondValue: Op0, Inverse, CtxI) ||
11646 isImpliedCond(Pred, LHS, RHS, FoundCondValue: Op1, Inverse, CtxI);
11647 } else if (match(V: FoundCondValue, P: m_LogicalOr(L: m_Value(V&: Op0), R: m_Value(V&: Op1)))) {
11648 if (Inverse)
11649 return isImpliedCond(Pred, LHS, RHS, FoundCondValue: Op0, Inverse, CtxI) ||
11650 isImpliedCond(Pred, LHS, RHS, FoundCondValue: Op1, Inverse, CtxI);
11651 }
11652
11653 const ICmpInst *ICI = dyn_cast<ICmpInst>(Val: FoundCondValue);
11654 if (!ICI) return false;
11655
11656 // Now that we found a conditional branch that dominates the loop or controls
11657 // the loop latch. Check to see if it is the comparison we are looking for.
11658 ICmpInst::Predicate FoundPred;
11659 if (Inverse)
11660 FoundPred = ICI->getInversePredicate();
11661 else
11662 FoundPred = ICI->getPredicate();
11663
11664 const SCEV *FoundLHS = getSCEV(V: ICI->getOperand(i_nocapture: 0));
11665 const SCEV *FoundRHS = getSCEV(V: ICI->getOperand(i_nocapture: 1));
11666
11667 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS, Context: CtxI);
11668}
11669
11670bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
11671 const SCEV *RHS,
11672 ICmpInst::Predicate FoundPred,
11673 const SCEV *FoundLHS, const SCEV *FoundRHS,
11674 const Instruction *CtxI) {
11675 // Balance the types.
11676 if (getTypeSizeInBits(Ty: LHS->getType()) <
11677 getTypeSizeInBits(Ty: FoundLHS->getType())) {
11678 // For unsigned and equality predicates, try to prove that both found
11679 // operands fit into narrow unsigned range. If so, try to prove facts in
11680 // narrow types.
11681 if (!CmpInst::isSigned(predicate: FoundPred) && !FoundLHS->getType()->isPointerTy() &&
11682 !FoundRHS->getType()->isPointerTy()) {
11683 auto *NarrowType = LHS->getType();
11684 auto *WideType = FoundLHS->getType();
11685 auto BitWidth = getTypeSizeInBits(Ty: NarrowType);
11686 const SCEV *MaxValue = getZeroExtendExpr(
11687 Op: getConstant(Val: APInt::getMaxValue(numBits: BitWidth)), Ty: WideType);
11688 if (isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_ULE, LHS: FoundLHS,
11689 RHS: MaxValue) &&
11690 isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_ULE, LHS: FoundRHS,
11691 RHS: MaxValue)) {
11692 const SCEV *TruncFoundLHS = getTruncateExpr(Op: FoundLHS, Ty: NarrowType);
11693 const SCEV *TruncFoundRHS = getTruncateExpr(Op: FoundRHS, Ty: NarrowType);
11694 if (isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, FoundLHS: TruncFoundLHS,
11695 FoundRHS: TruncFoundRHS, CtxI))
11696 return true;
11697 }
11698 }
11699
11700 if (LHS->getType()->isPointerTy() || RHS->getType()->isPointerTy())
11701 return false;
11702 if (CmpInst::isSigned(predicate: Pred)) {
11703 LHS = getSignExtendExpr(Op: LHS, Ty: FoundLHS->getType());
11704 RHS = getSignExtendExpr(Op: RHS, Ty: FoundLHS->getType());
11705 } else {
11706 LHS = getZeroExtendExpr(Op: LHS, Ty: FoundLHS->getType());
11707 RHS = getZeroExtendExpr(Op: RHS, Ty: FoundLHS->getType());
11708 }
11709 } else if (getTypeSizeInBits(Ty: LHS->getType()) >
11710 getTypeSizeInBits(Ty: FoundLHS->getType())) {
11711 if (FoundLHS->getType()->isPointerTy() || FoundRHS->getType()->isPointerTy())
11712 return false;
11713 if (CmpInst::isSigned(predicate: FoundPred)) {
11714 FoundLHS = getSignExtendExpr(Op: FoundLHS, Ty: LHS->getType());
11715 FoundRHS = getSignExtendExpr(Op: FoundRHS, Ty: LHS->getType());
11716 } else {
11717 FoundLHS = getZeroExtendExpr(Op: FoundLHS, Ty: LHS->getType());
11718 FoundRHS = getZeroExtendExpr(Op: FoundRHS, Ty: LHS->getType());
11719 }
11720 }
11721 return isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, FoundLHS,
11722 FoundRHS, CtxI);
11723}
11724
11725bool ScalarEvolution::isImpliedCondBalancedTypes(
11726 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
11727 ICmpInst::Predicate FoundPred, const SCEV *FoundLHS, const SCEV *FoundRHS,
11728 const Instruction *CtxI) {
11729 assert(getTypeSizeInBits(LHS->getType()) ==
11730 getTypeSizeInBits(FoundLHS->getType()) &&
11731 "Types should be balanced!");
11732 // Canonicalize the query to match the way instcombine will have
11733 // canonicalized the comparison.
11734 if (SimplifyICmpOperands(Pred, LHS, RHS))
11735 if (LHS == RHS)
11736 return CmpInst::isTrueWhenEqual(predicate: Pred);
11737 if (SimplifyICmpOperands(Pred&: FoundPred, LHS&: FoundLHS, RHS&: FoundRHS))
11738 if (FoundLHS == FoundRHS)
11739 return CmpInst::isFalseWhenEqual(predicate: FoundPred);
11740
11741 // Check to see if we can make the LHS or RHS match.
11742 if (LHS == FoundRHS || RHS == FoundLHS) {
11743 if (isa<SCEVConstant>(Val: RHS)) {
11744 std::swap(a&: FoundLHS, b&: FoundRHS);
11745 FoundPred = ICmpInst::getSwappedPredicate(pred: FoundPred);
11746 } else {
11747 std::swap(a&: LHS, b&: RHS);
11748 Pred = ICmpInst::getSwappedPredicate(pred: Pred);
11749 }
11750 }
11751
11752 // Check whether the found predicate is the same as the desired predicate.
11753 if (FoundPred == Pred)
11754 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context: CtxI);
11755
11756 // Check whether swapping the found predicate makes it the same as the
11757 // desired predicate.
11758 if (ICmpInst::getSwappedPredicate(pred: FoundPred) == Pred) {
11759 // We can write the implication
11760 // 0. LHS Pred RHS <- FoundLHS SwapPred FoundRHS
11761 // using one of the following ways:
11762 // 1. LHS Pred RHS <- FoundRHS Pred FoundLHS
11763 // 2. RHS SwapPred LHS <- FoundLHS SwapPred FoundRHS
11764 // 3. LHS Pred RHS <- ~FoundLHS Pred ~FoundRHS
11765 // 4. ~LHS SwapPred ~RHS <- FoundLHS SwapPred FoundRHS
11766 // Forms 1. and 2. require swapping the operands of one condition. Don't
11767 // do this if it would break canonical constant/addrec ordering.
11768 if (!isa<SCEVConstant>(Val: RHS) && !isa<SCEVAddRecExpr>(Val: LHS))
11769 return isImpliedCondOperands(Pred: FoundPred, LHS: RHS, RHS: LHS, FoundLHS, FoundRHS,
11770 Context: CtxI);
11771 if (!isa<SCEVConstant>(Val: FoundRHS) && !isa<SCEVAddRecExpr>(Val: FoundLHS))
11772 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS: FoundRHS, FoundRHS: FoundLHS, Context: CtxI);
11773
11774 // There's no clear preference between forms 3. and 4., try both. Avoid
11775 // forming getNotSCEV of pointer values as the resulting subtract is
11776 // not legal.
11777 if (!LHS->getType()->isPointerTy() && !RHS->getType()->isPointerTy() &&
11778 isImpliedCondOperands(Pred: FoundPred, LHS: getNotSCEV(V: LHS), RHS: getNotSCEV(V: RHS),
11779 FoundLHS, FoundRHS, Context: CtxI))
11780 return true;
11781
11782 if (!FoundLHS->getType()->isPointerTy() &&
11783 !FoundRHS->getType()->isPointerTy() &&
11784 isImpliedCondOperands(Pred, LHS, RHS, FoundLHS: getNotSCEV(V: FoundLHS),
11785 FoundRHS: getNotSCEV(V: FoundRHS), Context: CtxI))
11786 return true;
11787
11788 return false;
11789 }
11790
11791 auto IsSignFlippedPredicate = [](CmpInst::Predicate P1,
11792 CmpInst::Predicate P2) {
11793 assert(P1 != P2 && "Handled earlier!");
11794 return CmpInst::isRelational(P: P2) &&
11795 P1 == CmpInst::getFlippedSignednessPredicate(pred: P2);
11796 };
11797 if (IsSignFlippedPredicate(Pred, FoundPred)) {
11798 // Unsigned comparison is the same as signed comparison when both the
11799 // operands are non-negative or negative.
11800 if ((isKnownNonNegative(S: FoundLHS) && isKnownNonNegative(S: FoundRHS)) ||
11801 (isKnownNegative(S: FoundLHS) && isKnownNegative(S: FoundRHS)))
11802 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context: CtxI);
11803 // Create local copies that we can freely swap and canonicalize our
11804 // conditions to "le/lt".
11805 ICmpInst::Predicate CanonicalPred = Pred, CanonicalFoundPred = FoundPred;
11806 const SCEV *CanonicalLHS = LHS, *CanonicalRHS = RHS,
11807 *CanonicalFoundLHS = FoundLHS, *CanonicalFoundRHS = FoundRHS;
11808 if (ICmpInst::isGT(P: CanonicalPred) || ICmpInst::isGE(P: CanonicalPred)) {
11809 CanonicalPred = ICmpInst::getSwappedPredicate(pred: CanonicalPred);
11810 CanonicalFoundPred = ICmpInst::getSwappedPredicate(pred: CanonicalFoundPred);
11811 std::swap(a&: CanonicalLHS, b&: CanonicalRHS);
11812 std::swap(a&: CanonicalFoundLHS, b&: CanonicalFoundRHS);
11813 }
11814 assert((ICmpInst::isLT(CanonicalPred) || ICmpInst::isLE(CanonicalPred)) &&
11815 "Must be!");
11816 assert((ICmpInst::isLT(CanonicalFoundPred) ||
11817 ICmpInst::isLE(CanonicalFoundPred)) &&
11818 "Must be!");
11819 if (ICmpInst::isSigned(predicate: CanonicalPred) && isKnownNonNegative(S: CanonicalRHS))
11820 // Use implication:
11821 // x <u y && y >=s 0 --> x <s y.
11822 // If we can prove the left part, the right part is also proven.
11823 return isImpliedCondOperands(Pred: CanonicalFoundPred, LHS: CanonicalLHS,
11824 RHS: CanonicalRHS, FoundLHS: CanonicalFoundLHS,
11825 FoundRHS: CanonicalFoundRHS);
11826 if (ICmpInst::isUnsigned(predicate: CanonicalPred) && isKnownNegative(S: CanonicalRHS))
11827 // Use implication:
11828 // x <s y && y <s 0 --> x <u y.
11829 // If we can prove the left part, the right part is also proven.
11830 return isImpliedCondOperands(Pred: CanonicalFoundPred, LHS: CanonicalLHS,
11831 RHS: CanonicalRHS, FoundLHS: CanonicalFoundLHS,
11832 FoundRHS: CanonicalFoundRHS);
11833 }
11834
11835 // Check if we can make progress by sharpening ranges.
11836 if (FoundPred == ICmpInst::ICMP_NE &&
11837 (isa<SCEVConstant>(Val: FoundLHS) || isa<SCEVConstant>(Val: FoundRHS))) {
11838
11839 const SCEVConstant *C = nullptr;
11840 const SCEV *V = nullptr;
11841
11842 if (isa<SCEVConstant>(Val: FoundLHS)) {
11843 C = cast<SCEVConstant>(Val: FoundLHS);
11844 V = FoundRHS;
11845 } else {
11846 C = cast<SCEVConstant>(Val: FoundRHS);
11847 V = FoundLHS;
11848 }
11849
11850 // The guarding predicate tells us that C != V. If the known range
11851 // of V is [C, t), we can sharpen the range to [C + 1, t). The
11852 // range we consider has to correspond to same signedness as the
11853 // predicate we're interested in folding.
11854
11855 APInt Min = ICmpInst::isSigned(predicate: Pred) ?
11856 getSignedRangeMin(S: V) : getUnsignedRangeMin(S: V);
11857
11858 if (Min == C->getAPInt()) {
11859 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
11860 // This is true even if (Min + 1) wraps around -- in case of
11861 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
11862
11863 APInt SharperMin = Min + 1;
11864
11865 switch (Pred) {
11866 case ICmpInst::ICMP_SGE:
11867 case ICmpInst::ICMP_UGE:
11868 // We know V `Pred` SharperMin. If this implies LHS `Pred`
11869 // RHS, we're done.
11870 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS: V, FoundRHS: getConstant(Val: SharperMin),
11871 Context: CtxI))
11872 return true;
11873 [[fallthrough]];
11874
11875 case ICmpInst::ICMP_SGT:
11876 case ICmpInst::ICMP_UGT:
11877 // We know from the range information that (V `Pred` Min ||
11878 // V == Min). We know from the guarding condition that !(V
11879 // == Min). This gives us
11880 //
11881 // V `Pred` Min || V == Min && !(V == Min)
11882 // => V `Pred` Min
11883 //
11884 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
11885
11886 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS: V, FoundRHS: getConstant(Val: Min), Context: CtxI))
11887 return true;
11888 break;
11889
11890 // `LHS < RHS` and `LHS <= RHS` are handled in the same way as `RHS > LHS` and `RHS >= LHS` respectively.
11891 case ICmpInst::ICMP_SLE:
11892 case ICmpInst::ICMP_ULE:
11893 if (isImpliedCondOperands(Pred: CmpInst::getSwappedPredicate(pred: Pred), LHS: RHS,
11894 RHS: LHS, FoundLHS: V, FoundRHS: getConstant(Val: SharperMin), Context: CtxI))
11895 return true;
11896 [[fallthrough]];
11897
11898 case ICmpInst::ICMP_SLT:
11899 case ICmpInst::ICMP_ULT:
11900 if (isImpliedCondOperands(Pred: CmpInst::getSwappedPredicate(pred: Pred), LHS: RHS,
11901 RHS: LHS, FoundLHS: V, FoundRHS: getConstant(Val: Min), Context: CtxI))
11902 return true;
11903 break;
11904
11905 default:
11906 // No change
11907 break;
11908 }
11909 }
11910 }
11911
11912 // Check whether the actual condition is beyond sufficient.
11913 if (FoundPred == ICmpInst::ICMP_EQ)
11914 if (ICmpInst::isTrueWhenEqual(predicate: Pred))
11915 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context: CtxI))
11916 return true;
11917 if (Pred == ICmpInst::ICMP_NE)
11918 if (!ICmpInst::isTrueWhenEqual(predicate: FoundPred))
11919 if (isImpliedCondOperands(Pred: FoundPred, LHS, RHS, FoundLHS, FoundRHS, Context: CtxI))
11920 return true;
11921
11922 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS))
11923 return true;
11924
11925 // Otherwise assume the worst.
11926 return false;
11927}
11928
11929bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
11930 const SCEV *&L, const SCEV *&R,
11931 SCEV::NoWrapFlags &Flags) {
11932 const auto *AE = dyn_cast<SCEVAddExpr>(Val: Expr);
11933 if (!AE || AE->getNumOperands() != 2)
11934 return false;
11935
11936 L = AE->getOperand(i: 0);
11937 R = AE->getOperand(i: 1);
11938 Flags = AE->getNoWrapFlags();
11939 return true;
11940}
11941
11942std::optional<APInt>
11943ScalarEvolution::computeConstantDifference(const SCEV *More, const SCEV *Less) {
11944 // We avoid subtracting expressions here because this function is usually
11945 // fairly deep in the call stack (i.e. is called many times).
11946
11947 // X - X = 0.
11948 if (More == Less)
11949 return APInt(getTypeSizeInBits(Ty: More->getType()), 0);
11950
11951 if (isa<SCEVAddRecExpr>(Val: Less) && isa<SCEVAddRecExpr>(Val: More)) {
11952 const auto *LAR = cast<SCEVAddRecExpr>(Val: Less);
11953 const auto *MAR = cast<SCEVAddRecExpr>(Val: More);
11954
11955 if (LAR->getLoop() != MAR->getLoop())
11956 return std::nullopt;
11957
11958 // We look at affine expressions only; not for correctness but to keep
11959 // getStepRecurrence cheap.
11960 if (!LAR->isAffine() || !MAR->isAffine())
11961 return std::nullopt;
11962
11963 if (LAR->getStepRecurrence(SE&: *this) != MAR->getStepRecurrence(SE&: *this))
11964 return std::nullopt;
11965
11966 Less = LAR->getStart();
11967 More = MAR->getStart();
11968
11969 // fall through
11970 }
11971
11972 if (isa<SCEVConstant>(Val: Less) && isa<SCEVConstant>(Val: More)) {
11973 const auto &M = cast<SCEVConstant>(Val: More)->getAPInt();
11974 const auto &L = cast<SCEVConstant>(Val: Less)->getAPInt();
11975 return M - L;
11976 }
11977
11978 SCEV::NoWrapFlags Flags;
11979 const SCEV *LLess = nullptr, *RLess = nullptr;
11980 const SCEV *LMore = nullptr, *RMore = nullptr;
11981 const SCEVConstant *C1 = nullptr, *C2 = nullptr;
11982 // Compare (X + C1) vs X.
11983 if (splitBinaryAdd(Expr: Less, L&: LLess, R&: RLess, Flags))
11984 if ((C1 = dyn_cast<SCEVConstant>(Val: LLess)))
11985 if (RLess == More)
11986 return -(C1->getAPInt());
11987
11988 // Compare X vs (X + C2).
11989 if (splitBinaryAdd(Expr: More, L&: LMore, R&: RMore, Flags))
11990 if ((C2 = dyn_cast<SCEVConstant>(Val: LMore)))
11991 if (RMore == Less)
11992 return C2->getAPInt();
11993
11994 // Compare (X + C1) vs (X + C2).
11995 if (C1 && C2 && RLess == RMore)
11996 return C2->getAPInt() - C1->getAPInt();
11997
11998 return std::nullopt;
11999}
12000
12001bool ScalarEvolution::isImpliedCondOperandsViaAddRecStart(
12002 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
12003 const SCEV *FoundLHS, const SCEV *FoundRHS, const Instruction *CtxI) {
12004 // Try to recognize the following pattern:
12005 //
12006 // FoundRHS = ...
12007 // ...
12008 // loop:
12009 // FoundLHS = {Start,+,W}
12010 // context_bb: // Basic block from the same loop
12011 // known(Pred, FoundLHS, FoundRHS)
12012 //
12013 // If some predicate is known in the context of a loop, it is also known on
12014 // each iteration of this loop, including the first iteration. Therefore, in
12015 // this case, `FoundLHS Pred FoundRHS` implies `Start Pred FoundRHS`. Try to
12016 // prove the original pred using this fact.
12017 if (!CtxI)
12018 return false;
12019 const BasicBlock *ContextBB = CtxI->getParent();
12020 // Make sure AR varies in the context block.
12021 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Val: FoundLHS)) {
12022 const Loop *L = AR->getLoop();
12023 // Make sure that context belongs to the loop and executes on 1st iteration
12024 // (if it ever executes at all).
12025 if (!L->contains(BB: ContextBB) || !DT.dominates(A: ContextBB, B: L->getLoopLatch()))
12026 return false;
12027 if (!isAvailableAtLoopEntry(S: FoundRHS, L: AR->getLoop()))
12028 return false;
12029 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS: AR->getStart(), FoundRHS);
12030 }
12031
12032 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Val: FoundRHS)) {
12033 const Loop *L = AR->getLoop();
12034 // Make sure that context belongs to the loop and executes on 1st iteration
12035 // (if it ever executes at all).
12036 if (!L->contains(BB: ContextBB) || !DT.dominates(A: ContextBB, B: L->getLoopLatch()))
12037 return false;
12038 if (!isAvailableAtLoopEntry(S: FoundLHS, L: AR->getLoop()))
12039 return false;
12040 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS: AR->getStart());
12041 }
12042
12043 return false;
12044}
12045
12046bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
12047 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
12048 const SCEV *FoundLHS, const SCEV *FoundRHS) {
12049 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
12050 return false;
12051
12052 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(Val: LHS);
12053 if (!AddRecLHS)
12054 return false;
12055
12056 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(Val: FoundLHS);
12057 if (!AddRecFoundLHS)
12058 return false;
12059
12060 // We'd like to let SCEV reason about control dependencies, so we constrain
12061 // both the inequalities to be about add recurrences on the same loop. This
12062 // way we can use isLoopEntryGuardedByCond later.
12063
12064 const Loop *L = AddRecFoundLHS->getLoop();
12065 if (L != AddRecLHS->getLoop())
12066 return false;
12067
12068 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
12069 //
12070 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
12071 // ... (2)
12072 //
12073 // Informal proof for (2), assuming (1) [*]:
12074 //
12075 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
12076 //
12077 // Then
12078 //
12079 // FoundLHS s< FoundRHS s< INT_MIN - C
12080 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
12081 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
12082 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
12083 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
12084 // <=> FoundLHS + C s< FoundRHS + C
12085 //
12086 // [*]: (1) can be proved by ruling out overflow.
12087 //
12088 // [**]: This can be proved by analyzing all the four possibilities:
12089 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
12090 // (A s>= 0, B s>= 0).
12091 //
12092 // Note:
12093 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
12094 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
12095 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
12096 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
12097 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
12098 // C)".
12099
12100 std::optional<APInt> LDiff = computeConstantDifference(More: LHS, Less: FoundLHS);
12101 std::optional<APInt> RDiff = computeConstantDifference(More: RHS, Less: FoundRHS);
12102 if (!LDiff || !RDiff || *LDiff != *RDiff)
12103 return false;
12104
12105 if (LDiff->isMinValue())
12106 return true;
12107
12108 APInt FoundRHSLimit;
12109
12110 if (Pred == CmpInst::ICMP_ULT) {
12111 FoundRHSLimit = -(*RDiff);
12112 } else {
12113 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
12114 FoundRHSLimit = APInt::getSignedMinValue(numBits: getTypeSizeInBits(Ty: RHS->getType())) - *RDiff;
12115 }
12116
12117 // Try to prove (1) or (2), as needed.
12118 return isAvailableAtLoopEntry(S: FoundRHS, L) &&
12119 isLoopEntryGuardedByCond(L, Pred, LHS: FoundRHS,
12120 RHS: getConstant(Val: FoundRHSLimit));
12121}
12122
12123bool ScalarEvolution::isImpliedViaMerge(ICmpInst::Predicate Pred,
12124 const SCEV *LHS, const SCEV *RHS,
12125 const SCEV *FoundLHS,
12126 const SCEV *FoundRHS, unsigned Depth) {
12127 const PHINode *LPhi = nullptr, *RPhi = nullptr;
12128
12129 auto ClearOnExit = make_scope_exit(F: [&]() {
12130 if (LPhi) {
12131 bool Erased = PendingMerges.erase(Ptr: LPhi);
12132 assert(Erased && "Failed to erase LPhi!");
12133 (void)Erased;
12134 }
12135 if (RPhi) {
12136 bool Erased = PendingMerges.erase(Ptr: RPhi);
12137 assert(Erased && "Failed to erase RPhi!");
12138 (void)Erased;
12139 }
12140 });
12141
12142 // Find respective Phis and check that they are not being pending.
12143 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(Val: LHS))
12144 if (auto *Phi = dyn_cast<PHINode>(Val: LU->getValue())) {
12145 if (!PendingMerges.insert(Ptr: Phi).second)
12146 return false;
12147 LPhi = Phi;
12148 }
12149 if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(Val: RHS))
12150 if (auto *Phi = dyn_cast<PHINode>(Val: RU->getValue())) {
12151 // If we detect a loop of Phi nodes being processed by this method, for
12152 // example:
12153 //
12154 // %a = phi i32 [ %some1, %preheader ], [ %b, %latch ]
12155 // %b = phi i32 [ %some2, %preheader ], [ %a, %latch ]
12156 //
12157 // we don't want to deal with a case that complex, so return conservative
12158 // answer false.
12159 if (!PendingMerges.insert(Ptr: Phi).second)
12160 return false;
12161 RPhi = Phi;
12162 }
12163
12164 // If none of LHS, RHS is a Phi, nothing to do here.
12165 if (!LPhi && !RPhi)
12166 return false;
12167
12168 // If there is a SCEVUnknown Phi we are interested in, make it left.
12169 if (!LPhi) {
12170 std::swap(a&: LHS, b&: RHS);
12171 std::swap(a&: FoundLHS, b&: FoundRHS);
12172 std::swap(a&: LPhi, b&: RPhi);
12173 Pred = ICmpInst::getSwappedPredicate(pred: Pred);
12174 }
12175
12176 assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!");
12177 const BasicBlock *LBB = LPhi->getParent();
12178 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(Val: RHS);
12179
12180 auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) {
12181 return isKnownViaNonRecursiveReasoning(Pred, LHS: S1, RHS: S2) ||
12182 isImpliedCondOperandsViaRanges(Pred, LHS: S1, RHS: S2, FoundPred: Pred, FoundLHS, FoundRHS) ||
12183 isImpliedViaOperations(Pred, LHS: S1, RHS: S2, FoundLHS, FoundRHS, Depth);
12184 };
12185
12186 if (RPhi && RPhi->getParent() == LBB) {
12187 // Case one: RHS is also a SCEVUnknown Phi from the same basic block.
12188 // If we compare two Phis from the same block, and for each entry block
12189 // the predicate is true for incoming values from this block, then the
12190 // predicate is also true for the Phis.
12191 for (const BasicBlock *IncBB : predecessors(BB: LBB)) {
12192 const SCEV *L = getSCEV(V: LPhi->getIncomingValueForBlock(BB: IncBB));
12193 const SCEV *R = getSCEV(V: RPhi->getIncomingValueForBlock(BB: IncBB));
12194 if (!ProvedEasily(L, R))
12195 return false;
12196 }
12197 } else if (RAR && RAR->getLoop()->getHeader() == LBB) {
12198 // Case two: RHS is also a Phi from the same basic block, and it is an
12199 // AddRec. It means that there is a loop which has both AddRec and Unknown
12200 // PHIs, for it we can compare incoming values of AddRec from above the loop
12201 // and latch with their respective incoming values of LPhi.
12202 // TODO: Generalize to handle loops with many inputs in a header.
12203 if (LPhi->getNumIncomingValues() != 2) return false;
12204
12205 auto *RLoop = RAR->getLoop();
12206 auto *Predecessor = RLoop->getLoopPredecessor();
12207 assert(Predecessor && "Loop with AddRec with no predecessor?");
12208 const SCEV *L1 = getSCEV(V: LPhi->getIncomingValueForBlock(BB: Predecessor));
12209 if (!ProvedEasily(L1, RAR->getStart()))
12210 return false;
12211 auto *Latch = RLoop->getLoopLatch();
12212 assert(Latch && "Loop with AddRec with no latch?");
12213 const SCEV *L2 = getSCEV(V: LPhi->getIncomingValueForBlock(BB: Latch));
12214 if (!ProvedEasily(L2, RAR->getPostIncExpr(SE&: *this)))
12215 return false;
12216 } else {
12217 // In all other cases go over inputs of LHS and compare each of them to RHS,
12218 // the predicate is true for (LHS, RHS) if it is true for all such pairs.
12219 // At this point RHS is either a non-Phi, or it is a Phi from some block
12220 // different from LBB.
12221 for (const BasicBlock *IncBB : predecessors(BB: LBB)) {
12222 // Check that RHS is available in this block.
12223 if (!dominates(S: RHS, BB: IncBB))
12224 return false;
12225 const SCEV *L = getSCEV(V: LPhi->getIncomingValueForBlock(BB: IncBB));
12226 // Make sure L does not refer to a value from a potentially previous
12227 // iteration of a loop.
12228 if (!properlyDominates(S: L, BB: LBB))
12229 return false;
12230 if (!ProvedEasily(L, RHS))
12231 return false;
12232 }
12233 }
12234 return true;
12235}
12236
12237bool ScalarEvolution::isImpliedCondOperandsViaShift(ICmpInst::Predicate Pred,
12238 const SCEV *LHS,
12239 const SCEV *RHS,
12240 const SCEV *FoundLHS,
12241 const SCEV *FoundRHS) {
12242 // We want to imply LHS < RHS from LHS < (RHS >> shiftvalue). First, make
12243 // sure that we are dealing with same LHS.
12244 if (RHS == FoundRHS) {
12245 std::swap(a&: LHS, b&: RHS);
12246 std::swap(a&: FoundLHS, b&: FoundRHS);
12247 Pred = ICmpInst::getSwappedPredicate(pred: Pred);
12248 }
12249 if (LHS != FoundLHS)
12250 return false;
12251
12252 auto *SUFoundRHS = dyn_cast<SCEVUnknown>(Val: FoundRHS);
12253 if (!SUFoundRHS)
12254 return false;
12255
12256 Value *Shiftee, *ShiftValue;
12257
12258 using namespace PatternMatch;
12259 if (match(V: SUFoundRHS->getValue(),
12260 P: m_LShr(L: m_Value(V&: Shiftee), R: m_Value(V&: ShiftValue)))) {
12261 auto *ShifteeS = getSCEV(V: Shiftee);
12262 // Prove one of the following:
12263 // LHS <u (shiftee >> shiftvalue) && shiftee <=u RHS ---> LHS <u RHS
12264 // LHS <=u (shiftee >> shiftvalue) && shiftee <=u RHS ---> LHS <=u RHS
12265 // LHS <s (shiftee >> shiftvalue) && shiftee <=s RHS && shiftee >=s 0
12266 // ---> LHS <s RHS
12267 // LHS <=s (shiftee >> shiftvalue) && shiftee <=s RHS && shiftee >=s 0
12268 // ---> LHS <=s RHS
12269 if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_ULE)
12270 return isKnownPredicate(Pred: ICmpInst::ICMP_ULE, LHS: ShifteeS, RHS);
12271 if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE)
12272 if (isKnownNonNegative(S: ShifteeS))
12273 return isKnownPredicate(Pred: ICmpInst::ICMP_SLE, LHS: ShifteeS, RHS);
12274 }
12275
12276 return false;
12277}
12278
12279bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
12280 const SCEV *LHS, const SCEV *RHS,
12281 const SCEV *FoundLHS,
12282 const SCEV *FoundRHS,
12283 const Instruction *CtxI) {
12284 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundPred: Pred, FoundLHS, FoundRHS))
12285 return true;
12286
12287 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
12288 return true;
12289
12290 if (isImpliedCondOperandsViaShift(Pred, LHS, RHS, FoundLHS, FoundRHS))
12291 return true;
12292
12293 if (isImpliedCondOperandsViaAddRecStart(Pred, LHS, RHS, FoundLHS, FoundRHS,
12294 CtxI))
12295 return true;
12296
12297 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
12298 FoundLHS, FoundRHS);
12299}
12300
12301/// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values?
12302template <typename MinMaxExprType>
12303static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr,
12304 const SCEV *Candidate) {
12305 const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr);
12306 if (!MinMaxExpr)
12307 return false;
12308
12309 return is_contained(MinMaxExpr->operands(), Candidate);
12310}
12311
12312static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
12313 ICmpInst::Predicate Pred,
12314 const SCEV *LHS, const SCEV *RHS) {
12315 // If both sides are affine addrecs for the same loop, with equal
12316 // steps, and we know the recurrences don't wrap, then we only
12317 // need to check the predicate on the starting values.
12318
12319 if (!ICmpInst::isRelational(P: Pred))
12320 return false;
12321
12322 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(Val: LHS);
12323 if (!LAR)
12324 return false;
12325 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(Val: RHS);
12326 if (!RAR)
12327 return false;
12328 if (LAR->getLoop() != RAR->getLoop())
12329 return false;
12330 if (!LAR->isAffine() || !RAR->isAffine())
12331 return false;
12332
12333 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
12334 return false;
12335
12336 SCEV::NoWrapFlags NW = ICmpInst::isSigned(predicate: Pred) ?
12337 SCEV::FlagNSW : SCEV::FlagNUW;
12338 if (!LAR->getNoWrapFlags(Mask: NW) || !RAR->getNoWrapFlags(Mask: NW))
12339 return false;
12340
12341 return SE.isKnownPredicate(Pred, LHS: LAR->getStart(), RHS: RAR->getStart());
12342}
12343
12344/// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
12345/// expression?
12346static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
12347 ICmpInst::Predicate Pred,
12348 const SCEV *LHS, const SCEV *RHS) {
12349 switch (Pred) {
12350 default:
12351 return false;
12352
12353 case ICmpInst::ICMP_SGE:
12354 std::swap(a&: LHS, b&: RHS);
12355 [[fallthrough]];
12356 case ICmpInst::ICMP_SLE:
12357 return
12358 // min(A, ...) <= A
12359 IsMinMaxConsistingOf<SCEVSMinExpr>(MaybeMinMaxExpr: LHS, Candidate: RHS) ||
12360 // A <= max(A, ...)
12361 IsMinMaxConsistingOf<SCEVSMaxExpr>(MaybeMinMaxExpr: RHS, Candidate: LHS);
12362
12363 case ICmpInst::ICMP_UGE:
12364 std::swap(a&: LHS, b&: RHS);
12365 [[fallthrough]];
12366 case ICmpInst::ICMP_ULE:
12367 return
12368 // min(A, ...) <= A
12369 // FIXME: what about umin_seq?
12370 IsMinMaxConsistingOf<SCEVUMinExpr>(MaybeMinMaxExpr: LHS, Candidate: RHS) ||
12371 // A <= max(A, ...)
12372 IsMinMaxConsistingOf<SCEVUMaxExpr>(MaybeMinMaxExpr: RHS, Candidate: LHS);
12373 }
12374
12375 llvm_unreachable("covered switch fell through?!");
12376}
12377
12378bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred,
12379 const SCEV *LHS, const SCEV *RHS,
12380 const SCEV *FoundLHS,
12381 const SCEV *FoundRHS,
12382 unsigned Depth) {
12383 assert(getTypeSizeInBits(LHS->getType()) ==
12384 getTypeSizeInBits(RHS->getType()) &&
12385 "LHS and RHS have different sizes?");
12386 assert(getTypeSizeInBits(FoundLHS->getType()) ==
12387 getTypeSizeInBits(FoundRHS->getType()) &&
12388 "FoundLHS and FoundRHS have different sizes?");
12389 // We want to avoid hurting the compile time with analysis of too big trees.
12390 if (Depth > MaxSCEVOperationsImplicationDepth)
12391 return false;
12392
12393 // We only want to work with GT comparison so far.
12394 if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_SLT) {
12395 Pred = CmpInst::getSwappedPredicate(pred: Pred);
12396 std::swap(a&: LHS, b&: RHS);
12397 std::swap(a&: FoundLHS, b&: FoundRHS);
12398 }
12399
12400 // For unsigned, try to reduce it to corresponding signed comparison.
12401 if (Pred == ICmpInst::ICMP_UGT)
12402 // We can replace unsigned predicate with its signed counterpart if all
12403 // involved values are non-negative.
12404 // TODO: We could have better support for unsigned.
12405 if (isKnownNonNegative(S: FoundLHS) && isKnownNonNegative(S: FoundRHS)) {
12406 // Knowing that both FoundLHS and FoundRHS are non-negative, and knowing
12407 // FoundLHS >u FoundRHS, we also know that FoundLHS >s FoundRHS. Let us
12408 // use this fact to prove that LHS and RHS are non-negative.
12409 const SCEV *MinusOne = getMinusOne(Ty: LHS->getType());
12410 if (isImpliedCondOperands(Pred: ICmpInst::ICMP_SGT, LHS, RHS: MinusOne, FoundLHS,
12411 FoundRHS) &&
12412 isImpliedCondOperands(Pred: ICmpInst::ICMP_SGT, LHS: RHS, RHS: MinusOne, FoundLHS,
12413 FoundRHS))
12414 Pred = ICmpInst::ICMP_SGT;
12415 }
12416
12417 if (Pred != ICmpInst::ICMP_SGT)
12418 return false;
12419
12420 auto GetOpFromSExt = [&](const SCEV *S) {
12421 if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(Val: S))
12422 return Ext->getOperand();
12423 // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off
12424 // the constant in some cases.
12425 return S;
12426 };
12427
12428 // Acquire values from extensions.
12429 auto *OrigLHS = LHS;
12430 auto *OrigFoundLHS = FoundLHS;
12431 LHS = GetOpFromSExt(LHS);
12432 FoundLHS = GetOpFromSExt(FoundLHS);
12433
12434 // Is the SGT predicate can be proved trivially or using the found context.
12435 auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) {
12436 return isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_SGT, LHS: S1, RHS: S2) ||
12437 isImpliedViaOperations(Pred: ICmpInst::ICMP_SGT, LHS: S1, RHS: S2, FoundLHS: OrigFoundLHS,
12438 FoundRHS, Depth: Depth + 1);
12439 };
12440
12441 if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(Val: LHS)) {
12442 // We want to avoid creation of any new non-constant SCEV. Since we are
12443 // going to compare the operands to RHS, we should be certain that we don't
12444 // need any size extensions for this. So let's decline all cases when the
12445 // sizes of types of LHS and RHS do not match.
12446 // TODO: Maybe try to get RHS from sext to catch more cases?
12447 if (getTypeSizeInBits(Ty: LHS->getType()) != getTypeSizeInBits(Ty: RHS->getType()))
12448 return false;
12449
12450 // Should not overflow.
12451 if (!LHSAddExpr->hasNoSignedWrap())
12452 return false;
12453
12454 auto *LL = LHSAddExpr->getOperand(i: 0);
12455 auto *LR = LHSAddExpr->getOperand(i: 1);
12456 auto *MinusOne = getMinusOne(Ty: RHS->getType());
12457
12458 // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context.
12459 auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) {
12460 return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS);
12461 };
12462 // Try to prove the following rule:
12463 // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS).
12464 // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS).
12465 if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL))
12466 return true;
12467 } else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(Val: LHS)) {
12468 Value *LL, *LR;
12469 // FIXME: Once we have SDiv implemented, we can get rid of this matching.
12470
12471 using namespace llvm::PatternMatch;
12472
12473 if (match(V: LHSUnknownExpr->getValue(), P: m_SDiv(L: m_Value(V&: LL), R: m_Value(V&: LR)))) {
12474 // Rules for division.
12475 // We are going to perform some comparisons with Denominator and its
12476 // derivative expressions. In general case, creating a SCEV for it may
12477 // lead to a complex analysis of the entire graph, and in particular it
12478 // can request trip count recalculation for the same loop. This would
12479 // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid
12480 // this, we only want to create SCEVs that are constants in this section.
12481 // So we bail if Denominator is not a constant.
12482 if (!isa<ConstantInt>(Val: LR))
12483 return false;
12484
12485 auto *Denominator = cast<SCEVConstant>(Val: getSCEV(V: LR));
12486
12487 // We want to make sure that LHS = FoundLHS / Denominator. If it is so,
12488 // then a SCEV for the numerator already exists and matches with FoundLHS.
12489 auto *Numerator = getExistingSCEV(V: LL);
12490 if (!Numerator || Numerator->getType() != FoundLHS->getType())
12491 return false;
12492
12493 // Make sure that the numerator matches with FoundLHS and the denominator
12494 // is positive.
12495 if (!HasSameValue(A: Numerator, B: FoundLHS) || !isKnownPositive(S: Denominator))
12496 return false;
12497
12498 auto *DTy = Denominator->getType();
12499 auto *FRHSTy = FoundRHS->getType();
12500 if (DTy->isPointerTy() != FRHSTy->isPointerTy())
12501 // One of types is a pointer and another one is not. We cannot extend
12502 // them properly to a wider type, so let us just reject this case.
12503 // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help
12504 // to avoid this check.
12505 return false;
12506
12507 // Given that:
12508 // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0.
12509 auto *WTy = getWiderType(T1: DTy, T2: FRHSTy);
12510 auto *DenominatorExt = getNoopOrSignExtend(V: Denominator, Ty: WTy);
12511 auto *FoundRHSExt = getNoopOrSignExtend(V: FoundRHS, Ty: WTy);
12512
12513 // Try to prove the following rule:
12514 // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS).
12515 // For example, given that FoundLHS > 2. It means that FoundLHS is at
12516 // least 3. If we divide it by Denominator < 4, we will have at least 1.
12517 auto *DenomMinusTwo = getMinusSCEV(LHS: DenominatorExt, RHS: getConstant(Ty: WTy, V: 2));
12518 if (isKnownNonPositive(S: RHS) &&
12519 IsSGTViaContext(FoundRHSExt, DenomMinusTwo))
12520 return true;
12521
12522 // Try to prove the following rule:
12523 // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS).
12524 // For example, given that FoundLHS > -3. Then FoundLHS is at least -2.
12525 // If we divide it by Denominator > 2, then:
12526 // 1. If FoundLHS is negative, then the result is 0.
12527 // 2. If FoundLHS is non-negative, then the result is non-negative.
12528 // Anyways, the result is non-negative.
12529 auto *MinusOne = getMinusOne(Ty: WTy);
12530 auto *NegDenomMinusOne = getMinusSCEV(LHS: MinusOne, RHS: DenominatorExt);
12531 if (isKnownNegative(S: RHS) &&
12532 IsSGTViaContext(FoundRHSExt, NegDenomMinusOne))
12533 return true;
12534 }
12535 }
12536
12537 // If our expression contained SCEVUnknown Phis, and we split it down and now
12538 // need to prove something for them, try to prove the predicate for every
12539 // possible incoming values of those Phis.
12540 if (isImpliedViaMerge(Pred, LHS: OrigLHS, RHS, FoundLHS: OrigFoundLHS, FoundRHS, Depth: Depth + 1))
12541 return true;
12542
12543 return false;
12544}
12545
12546static bool isKnownPredicateExtendIdiom(ICmpInst::Predicate Pred,
12547 const SCEV *LHS, const SCEV *RHS) {
12548 // zext x u<= sext x, sext x s<= zext x
12549 switch (Pred) {
12550 case ICmpInst::ICMP_SGE:
12551 std::swap(a&: LHS, b&: RHS);
12552 [[fallthrough]];
12553 case ICmpInst::ICMP_SLE: {
12554 // If operand >=s 0 then ZExt == SExt. If operand <s 0 then SExt <s ZExt.
12555 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Val: LHS);
12556 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Val: RHS);
12557 if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
12558 return true;
12559 break;
12560 }
12561 case ICmpInst::ICMP_UGE:
12562 std::swap(a&: LHS, b&: RHS);
12563 [[fallthrough]];
12564 case ICmpInst::ICMP_ULE: {
12565 // If operand >=s 0 then ZExt == SExt. If operand <s 0 then ZExt <u SExt.
12566 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Val: LHS);
12567 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Val: RHS);
12568 if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
12569 return true;
12570 break;
12571 }
12572 default:
12573 break;
12574 };
12575 return false;
12576}
12577
12578bool
12579ScalarEvolution::isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
12580 const SCEV *LHS, const SCEV *RHS) {
12581 return isKnownPredicateExtendIdiom(Pred, LHS, RHS) ||
12582 isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
12583 IsKnownPredicateViaMinOrMax(SE&: *this, Pred, LHS, RHS) ||
12584 IsKnownPredicateViaAddRecStart(SE&: *this, Pred, LHS, RHS) ||
12585 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
12586}
12587
12588bool
12589ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
12590 const SCEV *LHS, const SCEV *RHS,
12591 const SCEV *FoundLHS,
12592 const SCEV *FoundRHS) {
12593 switch (Pred) {
12594 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
12595 case ICmpInst::ICMP_EQ:
12596 case ICmpInst::ICMP_NE:
12597 if (HasSameValue(A: LHS, B: FoundLHS) && HasSameValue(A: RHS, B: FoundRHS))
12598 return true;
12599 break;
12600 case ICmpInst::ICMP_SLT:
12601 case ICmpInst::ICMP_SLE:
12602 if (isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_SLE, LHS, RHS: FoundLHS) &&
12603 isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_SGE, LHS: RHS, RHS: FoundRHS))
12604 return true;
12605 break;
12606 case ICmpInst::ICMP_SGT:
12607 case ICmpInst::ICMP_SGE:
12608 if (isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_SGE, LHS, RHS: FoundLHS) &&
12609 isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_SLE, LHS: RHS, RHS: FoundRHS))
12610 return true;
12611 break;
12612 case ICmpInst::ICMP_ULT:
12613 case ICmpInst::ICMP_ULE:
12614 if (isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_ULE, LHS, RHS: FoundLHS) &&
12615 isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_UGE, LHS: RHS, RHS: FoundRHS))
12616 return true;
12617 break;
12618 case ICmpInst::ICMP_UGT:
12619 case ICmpInst::ICMP_UGE:
12620 if (isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_UGE, LHS, RHS: FoundLHS) &&
12621 isKnownViaNonRecursiveReasoning(Pred: ICmpInst::ICMP_ULE, LHS: RHS, RHS: FoundRHS))
12622 return true;
12623 break;
12624 }
12625
12626 // Maybe it can be proved via operations?
12627 if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS))
12628 return true;
12629
12630 return false;
12631}
12632
12633bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
12634 const SCEV *LHS,
12635 const SCEV *RHS,
12636 ICmpInst::Predicate FoundPred,
12637 const SCEV *FoundLHS,
12638 const SCEV *FoundRHS) {
12639 if (!isa<SCEVConstant>(Val: RHS) || !isa<SCEVConstant>(Val: FoundRHS))
12640 // The restriction on `FoundRHS` be lifted easily -- it exists only to
12641 // reduce the compile time impact of this optimization.
12642 return false;
12643
12644 std::optional<APInt> Addend = computeConstantDifference(More: LHS, Less: FoundLHS);
12645 if (!Addend)
12646 return false;
12647
12648 const APInt &ConstFoundRHS = cast<SCEVConstant>(Val: FoundRHS)->getAPInt();
12649
12650 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
12651 // antecedent "`FoundLHS` `FoundPred` `FoundRHS`".
12652 ConstantRange FoundLHSRange =
12653 ConstantRange::makeExactICmpRegion(Pred: FoundPred, Other: ConstFoundRHS);
12654
12655 // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
12656 ConstantRange LHSRange = FoundLHSRange.add(Other: ConstantRange(*Addend));
12657
12658 // We can also compute the range of values for `LHS` that satisfy the
12659 // consequent, "`LHS` `Pred` `RHS`":
12660 const APInt &ConstRHS = cast<SCEVConstant>(Val: RHS)->getAPInt();
12661 // The antecedent implies the consequent if every value of `LHS` that
12662 // satisfies the antecedent also satisfies the consequent.
12663 return LHSRange.icmp(Pred, Other: ConstRHS);
12664}
12665
12666bool ScalarEvolution::canIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
12667 bool IsSigned) {
12668 assert(isKnownPositive(Stride) && "Positive stride expected!");
12669
12670 unsigned BitWidth = getTypeSizeInBits(Ty: RHS->getType());
12671 const SCEV *One = getOne(Ty: Stride->getType());
12672
12673 if (IsSigned) {
12674 APInt MaxRHS = getSignedRangeMax(S: RHS);
12675 APInt MaxValue = APInt::getSignedMaxValue(numBits: BitWidth);
12676 APInt MaxStrideMinusOne = getSignedRangeMax(S: getMinusSCEV(LHS: Stride, RHS: One));
12677
12678 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
12679 return (std::move(MaxValue) - MaxStrideMinusOne).slt(RHS: MaxRHS);
12680 }
12681
12682 APInt MaxRHS = getUnsignedRangeMax(S: RHS);
12683 APInt MaxValue = APInt::getMaxValue(numBits: BitWidth);
12684 APInt MaxStrideMinusOne = getUnsignedRangeMax(S: getMinusSCEV(LHS: Stride, RHS: One));
12685
12686 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
12687 return (std::move(MaxValue) - MaxStrideMinusOne).ult(RHS: MaxRHS);
12688}
12689
12690bool ScalarEvolution::canIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
12691 bool IsSigned) {
12692
12693 unsigned BitWidth = getTypeSizeInBits(Ty: RHS->getType());
12694 const SCEV *One = getOne(Ty: Stride->getType());
12695
12696 if (IsSigned) {
12697 APInt MinRHS = getSignedRangeMin(S: RHS);
12698 APInt MinValue = APInt::getSignedMinValue(numBits: BitWidth);
12699 APInt MaxStrideMinusOne = getSignedRangeMax(S: getMinusSCEV(LHS: Stride, RHS: One));
12700
12701 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
12702 return (std::move(MinValue) + MaxStrideMinusOne).sgt(RHS: MinRHS);
12703 }
12704
12705 APInt MinRHS = getUnsignedRangeMin(S: RHS);
12706 APInt MinValue = APInt::getMinValue(numBits: BitWidth);
12707 APInt MaxStrideMinusOne = getUnsignedRangeMax(S: getMinusSCEV(LHS: Stride, RHS: One));
12708
12709 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
12710 return (std::move(MinValue) + MaxStrideMinusOne).ugt(RHS: MinRHS);
12711}
12712
12713const SCEV *ScalarEvolution::getUDivCeilSCEV(const SCEV *N, const SCEV *D) {
12714 // umin(N, 1) + floor((N - umin(N, 1)) / D)
12715 // This is equivalent to "1 + floor((N - 1) / D)" for N != 0. The umin
12716 // expression fixes the case of N=0.
12717 const SCEV *MinNOne = getUMinExpr(LHS: N, RHS: getOne(Ty: N->getType()));
12718 const SCEV *NMinusOne = getMinusSCEV(LHS: N, RHS: MinNOne);
12719 return getAddExpr(LHS: MinNOne, RHS: getUDivExpr(LHS: NMinusOne, RHS: D));
12720}
12721
12722const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
12723 const SCEV *Stride,
12724 const SCEV *End,
12725 unsigned BitWidth,
12726 bool IsSigned) {
12727 // The logic in this function assumes we can represent a positive stride.
12728 // If we can't, the backedge-taken count must be zero.
12729 if (IsSigned && BitWidth == 1)
12730 return getZero(Ty: Stride->getType());
12731
12732 // This code below only been closely audited for negative strides in the
12733 // unsigned comparison case, it may be correct for signed comparison, but
12734 // that needs to be established.
12735 if (IsSigned && isKnownNegative(S: Stride))
12736 return getCouldNotCompute();
12737
12738 // Calculate the maximum backedge count based on the range of values
12739 // permitted by Start, End, and Stride.
12740 APInt MinStart =
12741 IsSigned ? getSignedRangeMin(S: Start) : getUnsignedRangeMin(S: Start);
12742
12743 APInt MinStride =
12744 IsSigned ? getSignedRangeMin(S: Stride) : getUnsignedRangeMin(S: Stride);
12745
12746 // We assume either the stride is positive, or the backedge-taken count
12747 // is zero. So force StrideForMaxBECount to be at least one.
12748 APInt One(BitWidth, 1);
12749 APInt StrideForMaxBECount = IsSigned ? APIntOps::smax(A: One, B: MinStride)
12750 : APIntOps::umax(A: One, B: MinStride);
12751
12752 APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(numBits: BitWidth)
12753 : APInt::getMaxValue(numBits: BitWidth);
12754 APInt Limit = MaxValue - (StrideForMaxBECount - 1);
12755
12756 // Although End can be a MAX expression we estimate MaxEnd considering only
12757 // the case End = RHS of the loop termination condition. This is safe because
12758 // in the other case (End - Start) is zero, leading to a zero maximum backedge
12759 // taken count.
12760 APInt MaxEnd = IsSigned ? APIntOps::smin(A: getSignedRangeMax(S: End), B: Limit)
12761 : APIntOps::umin(A: getUnsignedRangeMax(S: End), B: Limit);
12762
12763 // MaxBECount = ceil((max(MaxEnd, MinStart) - MinStart) / Stride)
12764 MaxEnd = IsSigned ? APIntOps::smax(A: MaxEnd, B: MinStart)
12765 : APIntOps::umax(A: MaxEnd, B: MinStart);
12766
12767 return getUDivCeilSCEV(N: getConstant(Val: MaxEnd - MinStart) /* Delta */,
12768 D: getConstant(Val: StrideForMaxBECount) /* Step */);
12769}
12770
12771ScalarEvolution::ExitLimit
12772ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
12773 const Loop *L, bool IsSigned,
12774 bool ControlsOnlyExit, bool AllowPredicates) {
12775 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
12776
12777 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(Val: LHS);
12778 bool PredicatedIV = false;
12779
12780 auto canAssumeNoSelfWrap = [&](const SCEVAddRecExpr *AR) {
12781 // Can we prove this loop *must* be UB if overflow of IV occurs?
12782 // Reasoning goes as follows:
12783 // * Suppose the IV did self wrap.
12784 // * If Stride evenly divides the iteration space, then once wrap
12785 // occurs, the loop must revisit the same values.
12786 // * We know that RHS is invariant, and that none of those values
12787 // caused this exit to be taken previously. Thus, this exit is
12788 // dynamically dead.
12789 // * If this is the sole exit, then a dead exit implies the loop
12790 // must be infinite if there are no abnormal exits.
12791 // * If the loop were infinite, then it must either not be mustprogress
12792 // or have side effects. Otherwise, it must be UB.
12793 // * It can't (by assumption), be UB so we have contradicted our
12794 // premise and can conclude the IV did not in fact self-wrap.
12795 if (!isLoopInvariant(S: RHS, L))
12796 return false;
12797
12798 auto *StrideC = dyn_cast<SCEVConstant>(Val: AR->getStepRecurrence(SE&: *this));
12799 if (!StrideC || !StrideC->getAPInt().isPowerOf2())
12800 return false;
12801
12802 if (!ControlsOnlyExit || !loopHasNoAbnormalExits(L))
12803 return false;
12804
12805 return loopIsFiniteByAssumption(L);
12806 };
12807
12808 if (!IV) {
12809 if (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(Val: LHS)) {
12810 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Val: ZExt->getOperand());
12811 if (AR && AR->getLoop() == L && AR->isAffine()) {
12812 auto canProveNUW = [&]() {
12813 // We can use the comparison to infer no-wrap flags only if it fully
12814 // controls the loop exit.
12815 if (!ControlsOnlyExit)
12816 return false;
12817
12818 if (!isLoopInvariant(S: RHS, L))
12819 return false;
12820
12821 if (!isKnownNonZero(S: AR->getStepRecurrence(SE&: *this)))
12822 // We need the sequence defined by AR to strictly increase in the
12823 // unsigned integer domain for the logic below to hold.
12824 return false;
12825
12826 const unsigned InnerBitWidth = getTypeSizeInBits(Ty: AR->getType());
12827 const unsigned OuterBitWidth = getTypeSizeInBits(Ty: RHS->getType());
12828 // If RHS <=u Limit, then there must exist a value V in the sequence
12829 // defined by AR (e.g. {Start,+,Step}) such that V >u RHS, and
12830 // V <=u UINT_MAX. Thus, we must exit the loop before unsigned
12831 // overflow occurs. This limit also implies that a signed comparison
12832 // (in the wide bitwidth) is equivalent to an unsigned comparison as
12833 // the high bits on both sides must be zero.
12834 APInt StrideMax = getUnsignedRangeMax(S: AR->getStepRecurrence(SE&: *this));
12835 APInt Limit = APInt::getMaxValue(numBits: InnerBitWidth) - (StrideMax - 1);
12836 Limit = Limit.zext(width: OuterBitWidth);
12837 return getUnsignedRangeMax(S: applyLoopGuards(Expr: RHS, L)).ule(RHS: Limit);
12838 };
12839 auto Flags = AR->getNoWrapFlags();
12840 if (!hasFlags(Flags, TestFlags: SCEV::FlagNUW) && canProveNUW())
12841 Flags = setFlags(Flags, OnFlags: SCEV::FlagNUW);
12842
12843 setNoWrapFlags(AddRec: const_cast<SCEVAddRecExpr *>(AR), Flags);
12844 if (AR->hasNoUnsignedWrap()) {
12845 // Emulate what getZeroExtendExpr would have done during construction
12846 // if we'd been able to infer the fact just above at that time.
12847 const SCEV *Step = AR->getStepRecurrence(SE&: *this);
12848 Type *Ty = ZExt->getType();
12849 auto *S = getAddRecExpr(
12850 Start: getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, SE: this, Depth: 0),
12851 Step: getZeroExtendExpr(Op: Step, Ty, Depth: 0), L, Flags: AR->getNoWrapFlags());
12852 IV = dyn_cast<SCEVAddRecExpr>(Val: S);
12853 }
12854 }
12855 }
12856 }
12857
12858
12859 if (!IV && AllowPredicates) {
12860 // Try to make this an AddRec using runtime tests, in the first X
12861 // iterations of this loop, where X is the SCEV expression found by the
12862 // algorithm below.
12863 IV = convertSCEVToAddRecWithPredicates(S: LHS, L, Preds&: Predicates);
12864 PredicatedIV = true;
12865 }
12866
12867 // Avoid weird loops
12868 if (!IV || IV->getLoop() != L || !IV->isAffine())
12869 return getCouldNotCompute();
12870
12871 // A precondition of this method is that the condition being analyzed
12872 // reaches an exiting branch which dominates the latch. Given that, we can
12873 // assume that an increment which violates the nowrap specification and
12874 // produces poison must cause undefined behavior when the resulting poison
12875 // value is branched upon and thus we can conclude that the backedge is
12876 // taken no more often than would be required to produce that poison value.
12877 // Note that a well defined loop can exit on the iteration which violates
12878 // the nowrap specification if there is another exit (either explicit or
12879 // implicit/exceptional) which causes the loop to execute before the
12880 // exiting instruction we're analyzing would trigger UB.
12881 auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
12882 bool NoWrap = ControlsOnlyExit && IV->getNoWrapFlags(Mask: WrapType);
12883 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT;
12884
12885 const SCEV *Stride = IV->getStepRecurrence(SE&: *this);
12886
12887 bool PositiveStride = isKnownPositive(S: Stride);
12888
12889 // Avoid negative or zero stride values.
12890 if (!PositiveStride) {
12891 // We can compute the correct backedge taken count for loops with unknown
12892 // strides if we can prove that the loop is not an infinite loop with side
12893 // effects. Here's the loop structure we are trying to handle -
12894 //
12895 // i = start
12896 // do {
12897 // A[i] = i;
12898 // i += s;
12899 // } while (i < end);
12900 //
12901 // The backedge taken count for such loops is evaluated as -
12902 // (max(end, start + stride) - start - 1) /u stride
12903 //
12904 // The additional preconditions that we need to check to prove correctness
12905 // of the above formula is as follows -
12906 //
12907 // a) IV is either nuw or nsw depending upon signedness (indicated by the
12908 // NoWrap flag).
12909 // b) the loop is guaranteed to be finite (e.g. is mustprogress and has
12910 // no side effects within the loop)
12911 // c) loop has a single static exit (with no abnormal exits)
12912 //
12913 // Precondition a) implies that if the stride is negative, this is a single
12914 // trip loop. The backedge taken count formula reduces to zero in this case.
12915 //
12916 // Precondition b) and c) combine to imply that if rhs is invariant in L,
12917 // then a zero stride means the backedge can't be taken without executing
12918 // undefined behavior.
12919 //
12920 // The positive stride case is the same as isKnownPositive(Stride) returning
12921 // true (original behavior of the function).
12922 //
12923 if (PredicatedIV || !NoWrap || !loopIsFiniteByAssumption(L) ||
12924 !loopHasNoAbnormalExits(L))
12925 return getCouldNotCompute();
12926
12927 if (!isKnownNonZero(S: Stride)) {
12928 // If we have a step of zero, and RHS isn't invariant in L, we don't know
12929 // if it might eventually be greater than start and if so, on which
12930 // iteration. We can't even produce a useful upper bound.
12931 if (!isLoopInvariant(S: RHS, L))
12932 return getCouldNotCompute();
12933
12934 // We allow a potentially zero stride, but we need to divide by stride
12935 // below. Since the loop can't be infinite and this check must control
12936 // the sole exit, we can infer the exit must be taken on the first
12937 // iteration (e.g. backedge count = 0) if the stride is zero. Given that,
12938 // we know the numerator in the divides below must be zero, so we can
12939 // pick an arbitrary non-zero value for the denominator (e.g. stride)
12940 // and produce the right result.
12941 // FIXME: Handle the case where Stride is poison?
12942 auto wouldZeroStrideBeUB = [&]() {
12943 // Proof by contradiction. Suppose the stride were zero. If we can
12944 // prove that the backedge *is* taken on the first iteration, then since
12945 // we know this condition controls the sole exit, we must have an
12946 // infinite loop. We can't have a (well defined) infinite loop per
12947 // check just above.
12948 // Note: The (Start - Stride) term is used to get the start' term from
12949 // (start' + stride,+,stride). Remember that we only care about the
12950 // result of this expression when stride == 0 at runtime.
12951 auto *StartIfZero = getMinusSCEV(LHS: IV->getStart(), RHS: Stride);
12952 return isLoopEntryGuardedByCond(L, Pred: Cond, LHS: StartIfZero, RHS);
12953 };
12954 if (!wouldZeroStrideBeUB()) {
12955 Stride = getUMaxExpr(LHS: Stride, RHS: getOne(Ty: Stride->getType()));
12956 }
12957 }
12958 } else if (!Stride->isOne() && !NoWrap) {
12959 auto isUBOnWrap = [&]() {
12960 // From no-self-wrap, we need to then prove no-(un)signed-wrap. This
12961 // follows trivially from the fact that every (un)signed-wrapped, but
12962 // not self-wrapped value must be LT than the last value before
12963 // (un)signed wrap. Since we know that last value didn't exit, nor
12964 // will any smaller one.
12965 return canAssumeNoSelfWrap(IV);
12966 };
12967
12968 // Avoid proven overflow cases: this will ensure that the backedge taken
12969 // count will not generate any unsigned overflow. Relaxed no-overflow
12970 // conditions exploit NoWrapFlags, allowing to optimize in presence of
12971 // undefined behaviors like the case of C language.
12972 if (canIVOverflowOnLT(RHS, Stride, IsSigned) && !isUBOnWrap())
12973 return getCouldNotCompute();
12974 }
12975
12976 // On all paths just preceeding, we established the following invariant:
12977 // IV can be assumed not to overflow up to and including the exiting
12978 // iteration. We proved this in one of two ways:
12979 // 1) We can show overflow doesn't occur before the exiting iteration
12980 // 1a) canIVOverflowOnLT, and b) step of one
12981 // 2) We can show that if overflow occurs, the loop must execute UB
12982 // before any possible exit.
12983 // Note that we have not yet proved RHS invariant (in general).
12984
12985 const SCEV *Start = IV->getStart();
12986
12987 // Preserve pointer-typed Start/RHS to pass to isLoopEntryGuardedByCond.
12988 // If we convert to integers, isLoopEntryGuardedByCond will miss some cases.
12989 // Use integer-typed versions for actual computation; we can't subtract
12990 // pointers in general.
12991 const SCEV *OrigStart = Start;
12992 const SCEV *OrigRHS = RHS;
12993 if (Start->getType()->isPointerTy()) {
12994 Start = getLosslessPtrToIntExpr(Op: Start);
12995 if (isa<SCEVCouldNotCompute>(Val: Start))
12996 return Start;
12997 }
12998 if (RHS->getType()->isPointerTy()) {
12999 RHS = getLosslessPtrToIntExpr(Op: RHS);
13000 if (isa<SCEVCouldNotCompute>(Val: RHS))
13001 return RHS;
13002 }
13003
13004 const SCEV *End = nullptr, *BECount = nullptr,
13005 *BECountIfBackedgeTaken = nullptr;
13006 if (!isLoopInvariant(S: RHS, L)) {
13007 const auto *RHSAddRec = dyn_cast<SCEVAddRecExpr>(Val: RHS);
13008 if (PositiveStride && RHSAddRec != nullptr && RHSAddRec->getLoop() == L &&
13009 RHSAddRec->getNoWrapFlags()) {
13010 // The structure of loop we are trying to calculate backedge count of:
13011 //
13012 // left = left_start
13013 // right = right_start
13014 //
13015 // while(left < right){
13016 // ... do something here ...
13017 // left += s1; // stride of left is s1 (s1 > 0)
13018 // right += s2; // stride of right is s2 (s2 < 0)
13019 // }
13020 //
13021
13022 const SCEV *RHSStart = RHSAddRec->getStart();
13023 const SCEV *RHSStride = RHSAddRec->getStepRecurrence(SE&: *this);
13024
13025 // If Stride - RHSStride is positive and does not overflow, we can write
13026 // backedge count as ->
13027 // ceil((End - Start) /u (Stride - RHSStride))
13028 // Where, End = max(RHSStart, Start)
13029
13030 // Check if RHSStride < 0 and Stride - RHSStride will not overflow.
13031 if (isKnownNegative(S: RHSStride) &&
13032 willNotOverflow(BinOp: Instruction::Sub, /*Signed=*/true, LHS: Stride,
13033 RHS: RHSStride)) {
13034
13035 const SCEV *Denominator = getMinusSCEV(LHS: Stride, RHS: RHSStride);
13036 if (isKnownPositive(S: Denominator)) {
13037 End = IsSigned ? getSMaxExpr(LHS: RHSStart, RHS: Start)
13038 : getUMaxExpr(LHS: RHSStart, RHS: Start);
13039
13040 // We can do this because End >= Start, as End = max(RHSStart, Start)
13041 const SCEV *Delta = getMinusSCEV(LHS: End, RHS: Start);
13042
13043 BECount = getUDivCeilSCEV(N: Delta, D: Denominator);
13044 BECountIfBackedgeTaken =
13045 getUDivCeilSCEV(N: getMinusSCEV(LHS: RHSStart, RHS: Start), D: Denominator);
13046 }
13047 }
13048 }
13049 if (BECount == nullptr) {
13050 // If we cannot calculate ExactBECount, we can calculate the MaxBECount,
13051 // given the start, stride and max value for the end bound of the
13052 // loop (RHS), and the fact that IV does not overflow (which is
13053 // checked above).
13054 const SCEV *MaxBECount = computeMaxBECountForLT(
13055 Start, Stride, End: RHS, BitWidth: getTypeSizeInBits(Ty: LHS->getType()), IsSigned);
13056 return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
13057 MaxBECount, false /*MaxOrZero*/, Predicates);
13058 }
13059 } else {
13060 // We use the expression (max(End,Start)-Start)/Stride to describe the
13061 // backedge count, as if the backedge is taken at least once
13062 // max(End,Start) is End and so the result is as above, and if not
13063 // max(End,Start) is Start so we get a backedge count of zero.
13064 auto *OrigStartMinusStride = getMinusSCEV(LHS: OrigStart, RHS: Stride);
13065 assert(isAvailableAtLoopEntry(OrigStartMinusStride, L) && "Must be!");
13066 assert(isAvailableAtLoopEntry(OrigStart, L) && "Must be!");
13067 assert(isAvailableAtLoopEntry(OrigRHS, L) && "Must be!");
13068 // Can we prove (max(RHS,Start) > Start - Stride?
13069 if (isLoopEntryGuardedByCond(L, Pred: Cond, LHS: OrigStartMinusStride, RHS: OrigStart) &&
13070 isLoopEntryGuardedByCond(L, Pred: Cond, LHS: OrigStartMinusStride, RHS: OrigRHS)) {
13071 // In this case, we can use a refined formula for computing backedge
13072 // taken count. The general formula remains:
13073 // "End-Start /uceiling Stride" where "End = max(RHS,Start)"
13074 // We want to use the alternate formula:
13075 // "((End - 1) - (Start - Stride)) /u Stride"
13076 // Let's do a quick case analysis to show these are equivalent under
13077 // our precondition that max(RHS,Start) > Start - Stride.
13078 // * For RHS <= Start, the backedge-taken count must be zero.
13079 // "((End - 1) - (Start - Stride)) /u Stride" reduces to
13080 // "((Start - 1) - (Start - Stride)) /u Stride" which simplies to
13081 // "Stride - 1 /u Stride" which is indeed zero for all non-zero values
13082 // of Stride. For 0 stride, we've use umin(1,Stride) above,
13083 // reducing this to the stride of 1 case.
13084 // * For RHS >= Start, the backedge count must be "RHS-Start /uceil
13085 // Stride".
13086 // "((End - 1) - (Start - Stride)) /u Stride" reduces to
13087 // "((RHS - 1) - (Start - Stride)) /u Stride" reassociates to
13088 // "((RHS - (Start - Stride) - 1) /u Stride".
13089 // Our preconditions trivially imply no overflow in that form.
13090 const SCEV *MinusOne = getMinusOne(Ty: Stride->getType());
13091 const SCEV *Numerator =
13092 getMinusSCEV(LHS: getAddExpr(LHS: RHS, RHS: MinusOne), RHS: getMinusSCEV(LHS: Start, RHS: Stride));
13093 BECount = getUDivExpr(LHS: Numerator, RHS: Stride);
13094 }
13095
13096 if (!BECount) {
13097 auto canProveRHSGreaterThanEqualStart = [&]() {
13098 auto CondGE = IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
13099 const SCEV *GuardedRHS = applyLoopGuards(Expr: OrigRHS, L);
13100 const SCEV *GuardedStart = applyLoopGuards(Expr: OrigStart, L);
13101
13102 if (isLoopEntryGuardedByCond(L, Pred: CondGE, LHS: OrigRHS, RHS: OrigStart) ||
13103 isKnownPredicate(Pred: CondGE, LHS: GuardedRHS, RHS: GuardedStart))
13104 return true;
13105
13106 // (RHS > Start - 1) implies RHS >= Start.
13107 // * "RHS >= Start" is trivially equivalent to "RHS > Start - 1" if
13108 // "Start - 1" doesn't overflow.
13109 // * For signed comparison, if Start - 1 does overflow, it's equal
13110 // to INT_MAX, and "RHS >s INT_MAX" is trivially false.
13111 // * For unsigned comparison, if Start - 1 does overflow, it's equal
13112 // to UINT_MAX, and "RHS >u UINT_MAX" is trivially false.
13113 //
13114 // FIXME: Should isLoopEntryGuardedByCond do this for us?
13115 auto CondGT = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
13116 auto *StartMinusOne =
13117 getAddExpr(LHS: OrigStart, RHS: getMinusOne(Ty: OrigStart->getType()));
13118 return isLoopEntryGuardedByCond(L, Pred: CondGT, LHS: OrigRHS, RHS: StartMinusOne);
13119 };
13120
13121 // If we know that RHS >= Start in the context of loop, then we know
13122 // that max(RHS, Start) = RHS at this point.
13123 if (canProveRHSGreaterThanEqualStart()) {
13124 End = RHS;
13125 } else {
13126 // If RHS < Start, the backedge will be taken zero times. So in
13127 // general, we can write the backedge-taken count as:
13128 //
13129 // RHS >= Start ? ceil(RHS - Start) / Stride : 0
13130 //
13131 // We convert it to the following to make it more convenient for SCEV:
13132 //
13133 // ceil(max(RHS, Start) - Start) / Stride
13134 End = IsSigned ? getSMaxExpr(LHS: RHS, RHS: Start) : getUMaxExpr(LHS: RHS, RHS: Start);
13135
13136 // See what would happen if we assume the backedge is taken. This is
13137 // used to compute MaxBECount.
13138 BECountIfBackedgeTaken =
13139 getUDivCeilSCEV(N: getMinusSCEV(LHS: RHS, RHS: Start), D: Stride);
13140 }
13141
13142 // At this point, we know:
13143 //
13144 // 1. If IsSigned, Start <=s End; otherwise, Start <=u End
13145 // 2. The index variable doesn't overflow.
13146 //
13147 // Therefore, we know N exists such that
13148 // (Start + Stride * N) >= End, and computing "(Start + Stride * N)"
13149 // doesn't overflow.
13150 //
13151 // Using this information, try to prove whether the addition in
13152 // "(Start - End) + (Stride - 1)" has unsigned overflow.
13153 const SCEV *One = getOne(Ty: Stride->getType());
13154 bool MayAddOverflow = [&] {
13155 if (auto *StrideC = dyn_cast<SCEVConstant>(Val: Stride)) {
13156 if (StrideC->getAPInt().isPowerOf2()) {
13157 // Suppose Stride is a power of two, and Start/End are unsigned
13158 // integers. Let UMAX be the largest representable unsigned
13159 // integer.
13160 //
13161 // By the preconditions of this function, we know
13162 // "(Start + Stride * N) >= End", and this doesn't overflow.
13163 // As a formula:
13164 //
13165 // End <= (Start + Stride * N) <= UMAX
13166 //
13167 // Subtracting Start from all the terms:
13168 //
13169 // End - Start <= Stride * N <= UMAX - Start
13170 //
13171 // Since Start is unsigned, UMAX - Start <= UMAX. Therefore:
13172 //
13173 // End - Start <= Stride * N <= UMAX
13174 //
13175 // Stride * N is a multiple of Stride. Therefore,
13176 //
13177 // End - Start <= Stride * N <= UMAX - (UMAX mod Stride)
13178 //
13179 // Since Stride is a power of two, UMAX + 1 is divisible by
13180 // Stride. Therefore, UMAX mod Stride == Stride - 1. So we can
13181 // write:
13182 //
13183 // End - Start <= Stride * N <= UMAX - Stride - 1
13184 //
13185 // Dropping the middle term:
13186 //
13187 // End - Start <= UMAX - Stride - 1
13188 //
13189 // Adding Stride - 1 to both sides:
13190 //
13191 // (End - Start) + (Stride - 1) <= UMAX
13192 //
13193 // In other words, the addition doesn't have unsigned overflow.
13194 //
13195 // A similar proof works if we treat Start/End as signed values.
13196 // Just rewrite steps before "End - Start <= Stride * N <= UMAX"
13197 // to use signed max instead of unsigned max. Note that we're
13198 // trying to prove a lack of unsigned overflow in either case.
13199 return false;
13200 }
13201 }
13202 if (Start == Stride || Start == getMinusSCEV(LHS: Stride, RHS: One)) {
13203 // If Start is equal to Stride, (End - Start) + (Stride - 1) == End
13204 // - 1. If !IsSigned, 0 <u Stride == Start <=u End; so 0 <u End - 1
13205 // <u End. If IsSigned, 0 <s Stride == Start <=s End; so 0 <s End -
13206 // 1 <s End.
13207 //
13208 // If Start is equal to Stride - 1, (End - Start) + Stride - 1 ==
13209 // End.
13210 return false;
13211 }
13212 return true;
13213 }();
13214
13215 const SCEV *Delta = getMinusSCEV(LHS: End, RHS: Start);
13216 if (!MayAddOverflow) {
13217 // floor((D + (S - 1)) / S)
13218 // We prefer this formulation if it's legal because it's fewer
13219 // operations.
13220 BECount =
13221 getUDivExpr(LHS: getAddExpr(LHS: Delta, RHS: getMinusSCEV(LHS: Stride, RHS: One)), RHS: Stride);
13222 } else {
13223 BECount = getUDivCeilSCEV(N: Delta, D: Stride);
13224 }
13225 }
13226 }
13227
13228 const SCEV *ConstantMaxBECount;
13229 bool MaxOrZero = false;
13230 if (isa<SCEVConstant>(Val: BECount)) {
13231 ConstantMaxBECount = BECount;
13232 } else if (BECountIfBackedgeTaken &&
13233 isa<SCEVConstant>(Val: BECountIfBackedgeTaken)) {
13234 // If we know exactly how many times the backedge will be taken if it's
13235 // taken at least once, then the backedge count will either be that or
13236 // zero.
13237 ConstantMaxBECount = BECountIfBackedgeTaken;
13238 MaxOrZero = true;
13239 } else {
13240 ConstantMaxBECount = computeMaxBECountForLT(
13241 Start, Stride, End: RHS, BitWidth: getTypeSizeInBits(Ty: LHS->getType()), IsSigned);
13242 }
13243
13244 if (isa<SCEVCouldNotCompute>(Val: ConstantMaxBECount) &&
13245 !isa<SCEVCouldNotCompute>(Val: BECount))
13246 ConstantMaxBECount = getConstant(Val: getUnsignedRangeMax(S: BECount));
13247
13248 const SCEV *SymbolicMaxBECount =
13249 isa<SCEVCouldNotCompute>(Val: BECount) ? ConstantMaxBECount : BECount;
13250 return ExitLimit(BECount, ConstantMaxBECount, SymbolicMaxBECount, MaxOrZero,
13251 Predicates);
13252}
13253
13254ScalarEvolution::ExitLimit ScalarEvolution::howManyGreaterThans(
13255 const SCEV *LHS, const SCEV *RHS, const Loop *L, bool IsSigned,
13256 bool ControlsOnlyExit, bool AllowPredicates) {
13257 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
13258 // We handle only IV > Invariant
13259 if (!isLoopInvariant(S: RHS, L))
13260 return getCouldNotCompute();
13261
13262 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(Val: LHS);
13263 if (!IV && AllowPredicates)
13264 // Try to make this an AddRec using runtime tests, in the first X
13265 // iterations of this loop, where X is the SCEV expression found by the
13266 // algorithm below.
13267 IV = convertSCEVToAddRecWithPredicates(S: LHS, L, Preds&: Predicates);
13268
13269 // Avoid weird loops
13270 if (!IV || IV->getLoop() != L || !IV->isAffine())
13271 return getCouldNotCompute();
13272
13273 auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
13274 bool NoWrap = ControlsOnlyExit && IV->getNoWrapFlags(Mask: WrapType);
13275 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
13276
13277 const SCEV *Stride = getNegativeSCEV(V: IV->getStepRecurrence(SE&: *this));
13278
13279 // Avoid negative or zero stride values
13280 if (!isKnownPositive(S: Stride))
13281 return getCouldNotCompute();
13282
13283 // Avoid proven overflow cases: this will ensure that the backedge taken count
13284 // will not generate any unsigned overflow. Relaxed no-overflow conditions
13285 // exploit NoWrapFlags, allowing to optimize in presence of undefined
13286 // behaviors like the case of C language.
13287 if (!Stride->isOne() && !NoWrap)
13288 if (canIVOverflowOnGT(RHS, Stride, IsSigned))
13289 return getCouldNotCompute();
13290
13291 const SCEV *Start = IV->getStart();
13292 const SCEV *End = RHS;
13293 if (!isLoopEntryGuardedByCond(L, Pred: Cond, LHS: getAddExpr(LHS: Start, RHS: Stride), RHS)) {
13294 // If we know that Start >= RHS in the context of loop, then we know that
13295 // min(RHS, Start) = RHS at this point.
13296 if (isLoopEntryGuardedByCond(
13297 L, Pred: IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, LHS: Start, RHS))
13298 End = RHS;
13299 else
13300 End = IsSigned ? getSMinExpr(LHS: RHS, RHS: Start) : getUMinExpr(LHS: RHS, RHS: Start);
13301 }
13302
13303 if (Start->getType()->isPointerTy()) {
13304 Start = getLosslessPtrToIntExpr(Op: Start);
13305 if (isa<SCEVCouldNotCompute>(Val: Start))
13306 return Start;
13307 }
13308 if (End->getType()->isPointerTy()) {
13309 End = getLosslessPtrToIntExpr(Op: End);
13310 if (isa<SCEVCouldNotCompute>(Val: End))
13311 return End;
13312 }
13313
13314 // Compute ((Start - End) + (Stride - 1)) / Stride.
13315 // FIXME: This can overflow. Holding off on fixing this for now;
13316 // howManyGreaterThans will hopefully be gone soon.
13317 const SCEV *One = getOne(Ty: Stride->getType());
13318 const SCEV *BECount = getUDivExpr(
13319 LHS: getAddExpr(LHS: getMinusSCEV(LHS: Start, RHS: End), RHS: getMinusSCEV(LHS: Stride, RHS: One)), RHS: Stride);
13320
13321 APInt MaxStart = IsSigned ? getSignedRangeMax(S: Start)
13322 : getUnsignedRangeMax(S: Start);
13323
13324 APInt MinStride = IsSigned ? getSignedRangeMin(S: Stride)
13325 : getUnsignedRangeMin(S: Stride);
13326
13327 unsigned BitWidth = getTypeSizeInBits(Ty: LHS->getType());
13328 APInt Limit = IsSigned ? APInt::getSignedMinValue(numBits: BitWidth) + (MinStride - 1)
13329 : APInt::getMinValue(numBits: BitWidth) + (MinStride - 1);
13330
13331 // Although End can be a MIN expression we estimate MinEnd considering only
13332 // the case End = RHS. This is safe because in the other case (Start - End)
13333 // is zero, leading to a zero maximum backedge taken count.
13334 APInt MinEnd =
13335 IsSigned ? APIntOps::smax(A: getSignedRangeMin(S: RHS), B: Limit)
13336 : APIntOps::umax(A: getUnsignedRangeMin(S: RHS), B: Limit);
13337
13338 const SCEV *ConstantMaxBECount =
13339 isa<SCEVConstant>(Val: BECount)
13340 ? BECount
13341 : getUDivCeilSCEV(N: getConstant(Val: MaxStart - MinEnd),
13342 D: getConstant(Val: MinStride));
13343
13344 if (isa<SCEVCouldNotCompute>(Val: ConstantMaxBECount))
13345 ConstantMaxBECount = BECount;
13346 const SCEV *SymbolicMaxBECount =
13347 isa<SCEVCouldNotCompute>(Val: BECount) ? ConstantMaxBECount : BECount;
13348
13349 return ExitLimit(BECount, ConstantMaxBECount, SymbolicMaxBECount, false,
13350 Predicates);
13351}
13352
13353const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
13354 ScalarEvolution &SE) const {
13355 if (Range.isFullSet()) // Infinite loop.
13356 return SE.getCouldNotCompute();
13357
13358 // If the start is a non-zero constant, shift the range to simplify things.
13359 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Val: getStart()))
13360 if (!SC->getValue()->isZero()) {
13361 SmallVector<const SCEV *, 4> Operands(operands());
13362 Operands[0] = SE.getZero(Ty: SC->getType());
13363 const SCEV *Shifted = SE.getAddRecExpr(Operands, L: getLoop(),
13364 Flags: getNoWrapFlags(Mask: FlagNW));
13365 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Val: Shifted))
13366 return ShiftedAddRec->getNumIterationsInRange(
13367 Range: Range.subtract(CI: SC->getAPInt()), SE);
13368 // This is strange and shouldn't happen.
13369 return SE.getCouldNotCompute();
13370 }
13371
13372 // The only time we can solve this is when we have all constant indices.
13373 // Otherwise, we cannot determine the overflow conditions.
13374 if (any_of(Range: operands(), P: [](const SCEV *Op) { return !isa<SCEVConstant>(Val: Op); }))
13375 return SE.getCouldNotCompute();
13376
13377 // Okay at this point we know that all elements of the chrec are constants and
13378 // that the start element is zero.
13379
13380 // First check to see if the range contains zero. If not, the first
13381 // iteration exits.
13382 unsigned BitWidth = SE.getTypeSizeInBits(Ty: getType());
13383 if (!Range.contains(Val: APInt(BitWidth, 0)))
13384 return SE.getZero(Ty: getType());
13385
13386 if (isAffine()) {
13387 // If this is an affine expression then we have this situation:
13388 // Solve {0,+,A} in Range === Ax in Range
13389
13390 // We know that zero is in the range. If A is positive then we know that
13391 // the upper value of the range must be the first possible exit value.
13392 // If A is negative then the lower of the range is the last possible loop
13393 // value. Also note that we already checked for a full range.
13394 APInt A = cast<SCEVConstant>(Val: getOperand(i: 1))->getAPInt();
13395 APInt End = A.sge(RHS: 1) ? (Range.getUpper() - 1) : Range.getLower();
13396
13397 // The exit value should be (End+A)/A.
13398 APInt ExitVal = (End + A).udiv(RHS: A);
13399 ConstantInt *ExitValue = ConstantInt::get(Context&: SE.getContext(), V: ExitVal);
13400
13401 // Evaluate at the exit value. If we really did fall out of the valid
13402 // range, then we computed our trip count, otherwise wrap around or other
13403 // things must have happened.
13404 ConstantInt *Val = EvaluateConstantChrecAtConstant(AddRec: this, C: ExitValue, SE);
13405 if (Range.contains(Val: Val->getValue()))
13406 return SE.getCouldNotCompute(); // Something strange happened
13407
13408 // Ensure that the previous value is in the range.
13409 assert(Range.contains(
13410 EvaluateConstantChrecAtConstant(this,
13411 ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) &&
13412 "Linear scev computation is off in a bad way!");
13413 return SE.getConstant(V: ExitValue);
13414 }
13415
13416 if (isQuadratic()) {
13417 if (auto S = SolveQuadraticAddRecRange(AddRec: this, Range, SE))
13418 return SE.getConstant(Val: *S);
13419 }
13420
13421 return SE.getCouldNotCompute();
13422}
13423
13424const SCEVAddRecExpr *
13425SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const {
13426 assert(getNumOperands() > 1 && "AddRec with zero step?");
13427 // There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)),
13428 // but in this case we cannot guarantee that the value returned will be an
13429 // AddRec because SCEV does not have a fixed point where it stops
13430 // simplification: it is legal to return ({rec1} + {rec2}). For example, it
13431 // may happen if we reach arithmetic depth limit while simplifying. So we
13432 // construct the returned value explicitly.
13433 SmallVector<const SCEV *, 3> Ops;
13434 // If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and
13435 // (this + Step) is {A+B,+,B+C,+...,+,N}.
13436 for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i)
13437 Ops.push_back(Elt: SE.getAddExpr(LHS: getOperand(i), RHS: getOperand(i: i + 1)));
13438 // We know that the last operand is not a constant zero (otherwise it would
13439 // have been popped out earlier). This guarantees us that if the result has
13440 // the same last operand, then it will also not be popped out, meaning that
13441 // the returned value will be an AddRec.
13442 const SCEV *Last = getOperand(i: getNumOperands() - 1);
13443 assert(!Last->isZero() && "Recurrency with zero step?");
13444 Ops.push_back(Elt: Last);
13445 return cast<SCEVAddRecExpr>(Val: SE.getAddRecExpr(Operands&: Ops, L: getLoop(),
13446 Flags: SCEV::FlagAnyWrap));
13447}
13448
13449// Return true when S contains at least an undef value.
13450bool ScalarEvolution::containsUndefs(const SCEV *S) const {
13451 return SCEVExprContains(Root: S, Pred: [](const SCEV *S) {
13452 if (const auto *SU = dyn_cast<SCEVUnknown>(Val: S))
13453 return isa<UndefValue>(Val: SU->getValue());
13454 return false;
13455 });
13456}
13457
13458// Return true when S contains a value that is a nullptr.
13459bool ScalarEvolution::containsErasedValue(const SCEV *S) const {
13460 return SCEVExprContains(Root: S, Pred: [](const SCEV *S) {
13461 if (const auto *SU = dyn_cast<SCEVUnknown>(Val: S))
13462 return SU->getValue() == nullptr;
13463 return false;
13464 });
13465}
13466
13467/// Return the size of an element read or written by Inst.
13468const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
13469 Type *Ty;
13470 if (StoreInst *Store = dyn_cast<StoreInst>(Val: Inst))
13471 Ty = Store->getValueOperand()->getType();
13472 else if (LoadInst *Load = dyn_cast<LoadInst>(Val: Inst))
13473 Ty = Load->getType();
13474 else
13475 return nullptr;
13476
13477 Type *ETy = getEffectiveSCEVType(Ty: PointerType::getUnqual(ElementType: Ty));
13478 return getSizeOfExpr(IntTy: ETy, AllocTy: Ty);
13479}
13480
13481//===----------------------------------------------------------------------===//
13482// SCEVCallbackVH Class Implementation
13483//===----------------------------------------------------------------------===//
13484
13485void ScalarEvolution::SCEVCallbackVH::deleted() {
13486 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
13487 if (PHINode *PN = dyn_cast<PHINode>(Val: getValPtr()))
13488 SE->ConstantEvolutionLoopExitValue.erase(Val: PN);
13489 SE->eraseValueFromMap(V: getValPtr());
13490 // this now dangles!
13491}
13492
13493void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
13494 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
13495
13496 // Forget all the expressions associated with users of the old value,
13497 // so that future queries will recompute the expressions using the new
13498 // value.
13499 SE->forgetValue(V: getValPtr());
13500 // this now dangles!
13501}
13502
13503ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
13504 : CallbackVH(V), SE(se) {}
13505
13506//===----------------------------------------------------------------------===//
13507// ScalarEvolution Class Implementation
13508//===----------------------------------------------------------------------===//
13509
13510ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
13511 AssumptionCache &AC, DominatorTree &DT,
13512 LoopInfo &LI)
13513 : F(F), DL(F.getDataLayout()), TLI(TLI), AC(AC), DT(DT), LI(LI),
13514 CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64),
13515 LoopDispositions(64), BlockDispositions(64) {
13516 // To use guards for proving predicates, we need to scan every instruction in
13517 // relevant basic blocks, and not just terminators. Doing this is a waste of
13518 // time if the IR does not actually contain any calls to
13519 // @llvm.experimental.guard, so do a quick check and remember this beforehand.
13520 //
13521 // This pessimizes the case where a pass that preserves ScalarEvolution wants
13522 // to _add_ guards to the module when there weren't any before, and wants
13523 // ScalarEvolution to optimize based on those guards. For now we prefer to be
13524 // efficient in lieu of being smart in that rather obscure case.
13525
13526 auto *GuardDecl = F.getParent()->getFunction(
13527 Name: Intrinsic::getName(id: Intrinsic::experimental_guard));
13528 HasGuards = GuardDecl && !GuardDecl->use_empty();
13529}
13530
13531ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
13532 : F(Arg.F), DL(Arg.DL), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC),
13533 DT(Arg.DT), LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
13534 ValueExprMap(std::move(Arg.ValueExprMap)),
13535 PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
13536 PendingPhiRanges(std::move(Arg.PendingPhiRanges)),
13537 PendingMerges(std::move(Arg.PendingMerges)),
13538 ConstantMultipleCache(std::move(Arg.ConstantMultipleCache)),
13539 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
13540 PredicatedBackedgeTakenCounts(
13541 std::move(Arg.PredicatedBackedgeTakenCounts)),
13542 BECountUsers(std::move(Arg.BECountUsers)),
13543 ConstantEvolutionLoopExitValue(
13544 std::move(Arg.ConstantEvolutionLoopExitValue)),
13545 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
13546 ValuesAtScopesUsers(std::move(Arg.ValuesAtScopesUsers)),
13547 LoopDispositions(std::move(Arg.LoopDispositions)),
13548 LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
13549 BlockDispositions(std::move(Arg.BlockDispositions)),
13550 SCEVUsers(std::move(Arg.SCEVUsers)),
13551 UnsignedRanges(std::move(Arg.UnsignedRanges)),
13552 SignedRanges(std::move(Arg.SignedRanges)),
13553 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
13554 UniquePreds(std::move(Arg.UniquePreds)),
13555 SCEVAllocator(std::move(Arg.SCEVAllocator)),
13556 LoopUsers(std::move(Arg.LoopUsers)),
13557 PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
13558 FirstUnknown(Arg.FirstUnknown) {
13559 Arg.FirstUnknown = nullptr;
13560}
13561
13562ScalarEvolution::~ScalarEvolution() {
13563 // Iterate through all the SCEVUnknown instances and call their
13564 // destructors, so that they release their references to their values.
13565 for (SCEVUnknown *U = FirstUnknown; U;) {
13566 SCEVUnknown *Tmp = U;
13567 U = U->Next;
13568 Tmp->~SCEVUnknown();
13569 }
13570 FirstUnknown = nullptr;
13571
13572 ExprValueMap.clear();
13573 ValueExprMap.clear();
13574 HasRecMap.clear();
13575 BackedgeTakenCounts.clear();
13576 PredicatedBackedgeTakenCounts.clear();
13577
13578 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
13579 assert(PendingPhiRanges.empty() && "getRangeRef garbage");
13580 assert(PendingMerges.empty() && "isImpliedViaMerge garbage");
13581 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
13582 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
13583}
13584
13585bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
13586 return !isa<SCEVCouldNotCompute>(Val: getBackedgeTakenCount(L));
13587}
13588
13589/// When printing a top-level SCEV for trip counts, it's helpful to include
13590/// a type for constants which are otherwise hard to disambiguate.
13591static void PrintSCEVWithTypeHint(raw_ostream &OS, const SCEV* S) {
13592 if (isa<SCEVConstant>(Val: S))
13593 OS << *S->getType() << " ";
13594 OS << *S;
13595}
13596
13597static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
13598 const Loop *L) {
13599 // Print all inner loops first
13600 for (Loop *I : *L)
13601 PrintLoopInfo(OS, SE, L: I);
13602
13603 OS << "Loop ";
13604 L->getHeader()->printAsOperand(O&: OS, /*PrintType=*/false);
13605 OS << ": ";
13606
13607 SmallVector<BasicBlock *, 8> ExitingBlocks;
13608 L->getExitingBlocks(ExitingBlocks);
13609 if (ExitingBlocks.size() != 1)
13610 OS << "<multiple exits> ";
13611
13612 auto *BTC = SE->getBackedgeTakenCount(L);
13613 if (!isa<SCEVCouldNotCompute>(Val: BTC)) {
13614 OS << "backedge-taken count is ";
13615 PrintSCEVWithTypeHint(OS, S: BTC);
13616 } else
13617 OS << "Unpredictable backedge-taken count.";
13618 OS << "\n";
13619
13620 if (ExitingBlocks.size() > 1)
13621 for (BasicBlock *ExitingBlock : ExitingBlocks) {
13622 OS << " exit count for " << ExitingBlock->getName() << ": ";
13623 PrintSCEVWithTypeHint(OS, S: SE->getExitCount(L, ExitingBlock));
13624 OS << "\n";
13625 }
13626
13627 OS << "Loop ";
13628 L->getHeader()->printAsOperand(O&: OS, /*PrintType=*/false);
13629 OS << ": ";
13630
13631 auto *ConstantBTC = SE->getConstantMaxBackedgeTakenCount(L);
13632 if (!isa<SCEVCouldNotCompute>(Val: ConstantBTC)) {
13633 OS << "constant max backedge-taken count is ";
13634 PrintSCEVWithTypeHint(OS, S: ConstantBTC);
13635 if (SE->isBackedgeTakenCountMaxOrZero(L))
13636 OS << ", actual taken count either this or zero.";
13637 } else {
13638 OS << "Unpredictable constant max backedge-taken count. ";
13639 }
13640
13641 OS << "\n"
13642 "Loop ";
13643 L->getHeader()->printAsOperand(O&: OS, /*PrintType=*/false);
13644 OS << ": ";
13645
13646 auto *SymbolicBTC = SE->getSymbolicMaxBackedgeTakenCount(L);
13647 if (!isa<SCEVCouldNotCompute>(Val: SymbolicBTC)) {
13648 OS << "symbolic max backedge-taken count is ";
13649 PrintSCEVWithTypeHint(OS, S: SymbolicBTC);
13650 if (SE->isBackedgeTakenCountMaxOrZero(L))
13651 OS << ", actual taken count either this or zero.";
13652 } else {
13653 OS << "Unpredictable symbolic max backedge-taken count. ";
13654 }
13655 OS << "\n";
13656
13657 if (ExitingBlocks.size() > 1)
13658 for (BasicBlock *ExitingBlock : ExitingBlocks) {
13659 OS << " symbolic max exit count for " << ExitingBlock->getName() << ": ";
13660 auto *ExitBTC = SE->getExitCount(L, ExitingBlock,
13661 Kind: ScalarEvolution::SymbolicMaximum);
13662 PrintSCEVWithTypeHint(OS, S: ExitBTC);
13663 OS << "\n";
13664 }
13665
13666 SmallVector<const SCEVPredicate *, 4> Preds;
13667 auto *PBT = SE->getPredicatedBackedgeTakenCount(L, Preds);
13668 if (PBT != BTC || !Preds.empty()) {
13669 OS << "Loop ";
13670 L->getHeader()->printAsOperand(O&: OS, /*PrintType=*/false);
13671 OS << ": ";
13672 if (!isa<SCEVCouldNotCompute>(Val: PBT)) {
13673 OS << "Predicated backedge-taken count is ";
13674 PrintSCEVWithTypeHint(OS, S: PBT);
13675 } else
13676 OS << "Unpredictable predicated backedge-taken count.";
13677 OS << "\n";
13678 OS << " Predicates:\n";
13679 for (const auto *P : Preds)
13680 P->print(OS, Depth: 4);
13681 }
13682
13683 Preds.clear();
13684 auto *PredSymbolicMax =
13685 SE->getPredicatedSymbolicMaxBackedgeTakenCount(L, Preds);
13686 if (SymbolicBTC != PredSymbolicMax) {
13687 OS << "Loop ";
13688 L->getHeader()->printAsOperand(O&: OS, /*PrintType=*/false);
13689 OS << ": ";
13690 if (!isa<SCEVCouldNotCompute>(Val: PredSymbolicMax)) {
13691 OS << "Predicated symbolic max backedge-taken count is ";
13692 PrintSCEVWithTypeHint(OS, S: PredSymbolicMax);
13693 } else
13694 OS << "Unpredictable predicated symbolic max backedge-taken count.";
13695 OS << "\n";
13696 OS << " Predicates:\n";
13697 for (const auto *P : Preds)
13698 P->print(OS, Depth: 4);
13699 }
13700
13701 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
13702 OS << "Loop ";
13703 L->getHeader()->printAsOperand(O&: OS, /*PrintType=*/false);
13704 OS << ": ";
13705 OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n";
13706 }
13707}
13708
13709namespace llvm {
13710raw_ostream &operator<<(raw_ostream &OS, ScalarEvolution::LoopDisposition LD) {
13711 switch (LD) {
13712 case ScalarEvolution::LoopVariant:
13713 OS << "Variant";
13714 break;
13715 case ScalarEvolution::LoopInvariant:
13716 OS << "Invariant";
13717 break;
13718 case ScalarEvolution::LoopComputable:
13719 OS << "Computable";
13720 break;
13721 }
13722 return OS;
13723}
13724
13725raw_ostream &operator<<(raw_ostream &OS, ScalarEvolution::BlockDisposition BD) {
13726 switch (BD) {
13727 case ScalarEvolution::DoesNotDominateBlock:
13728 OS << "DoesNotDominate";
13729 break;
13730 case ScalarEvolution::DominatesBlock:
13731 OS << "Dominates";
13732 break;
13733 case ScalarEvolution::ProperlyDominatesBlock:
13734 OS << "ProperlyDominates";
13735 break;
13736 }
13737 return OS;
13738}
13739} // namespace llvm
13740
13741void ScalarEvolution::print(raw_ostream &OS) const {
13742 // ScalarEvolution's implementation of the print method is to print
13743 // out SCEV values of all instructions that are interesting. Doing
13744 // this potentially causes it to create new SCEV objects though,
13745 // which technically conflicts with the const qualifier. This isn't
13746 // observable from outside the class though, so casting away the
13747 // const isn't dangerous.
13748 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
13749
13750 if (ClassifyExpressions) {
13751 OS << "Classifying expressions for: ";
13752 F.printAsOperand(O&: OS, /*PrintType=*/false);
13753 OS << "\n";
13754 for (Instruction &I : instructions(F))
13755 if (isSCEVable(Ty: I.getType()) && !isa<CmpInst>(Val: I)) {
13756 OS << I << '\n';
13757 OS << " --> ";
13758 const SCEV *SV = SE.getSCEV(V: &I);
13759 SV->print(OS);
13760 if (!isa<SCEVCouldNotCompute>(Val: SV)) {
13761 OS << " U: ";
13762 SE.getUnsignedRange(S: SV).print(OS);
13763 OS << " S: ";
13764 SE.getSignedRange(S: SV).print(OS);
13765 }
13766
13767 const Loop *L = LI.getLoopFor(BB: I.getParent());
13768
13769 const SCEV *AtUse = SE.getSCEVAtScope(V: SV, L);
13770 if (AtUse != SV) {
13771 OS << " --> ";
13772 AtUse->print(OS);
13773 if (!isa<SCEVCouldNotCompute>(Val: AtUse)) {
13774 OS << " U: ";
13775 SE.getUnsignedRange(S: AtUse).print(OS);
13776 OS << " S: ";
13777 SE.getSignedRange(S: AtUse).print(OS);
13778 }
13779 }
13780
13781 if (L) {
13782 OS << "\t\t" "Exits: ";
13783 const SCEV *ExitValue = SE.getSCEVAtScope(V: SV, L: L->getParentLoop());
13784 if (!SE.isLoopInvariant(S: ExitValue, L)) {
13785 OS << "<<Unknown>>";
13786 } else {
13787 OS << *ExitValue;
13788 }
13789
13790 bool First = true;
13791 for (const auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
13792 if (First) {
13793 OS << "\t\t" "LoopDispositions: { ";
13794 First = false;
13795 } else {
13796 OS << ", ";
13797 }
13798
13799 Iter->getHeader()->printAsOperand(O&: OS, /*PrintType=*/false);
13800 OS << ": " << SE.getLoopDisposition(S: SV, L: Iter);
13801 }
13802
13803 for (const auto *InnerL : depth_first(G: L)) {
13804 if (InnerL == L)
13805 continue;
13806 if (First) {
13807 OS << "\t\t" "LoopDispositions: { ";
13808 First = false;
13809 } else {
13810 OS << ", ";
13811 }
13812
13813 InnerL->getHeader()->printAsOperand(O&: OS, /*PrintType=*/false);
13814 OS << ": " << SE.getLoopDisposition(S: SV, L: InnerL);
13815 }
13816
13817 OS << " }";
13818 }
13819
13820 OS << "\n";
13821 }
13822 }
13823
13824 OS << "Determining loop execution counts for: ";
13825 F.printAsOperand(O&: OS, /*PrintType=*/false);
13826 OS << "\n";
13827 for (Loop *I : LI)
13828 PrintLoopInfo(OS, SE: &SE, L: I);
13829}
13830
13831ScalarEvolution::LoopDisposition
13832ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
13833 auto &Values = LoopDispositions[S];
13834 for (auto &V : Values) {
13835 if (V.getPointer() == L)
13836 return V.getInt();
13837 }
13838 Values.emplace_back(Args&: L, Args: LoopVariant);
13839 LoopDisposition D = computeLoopDisposition(S, L);
13840 auto &Values2 = LoopDispositions[S];
13841 for (auto &V : llvm::reverse(C&: Values2)) {
13842 if (V.getPointer() == L) {
13843 V.setInt(D);
13844 break;
13845 }
13846 }
13847 return D;
13848}
13849
13850ScalarEvolution::LoopDisposition
13851ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
13852 switch (S->getSCEVType()) {
13853 case scConstant:
13854 case scVScale:
13855 return LoopInvariant;
13856 case scAddRecExpr: {
13857 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(Val: S);
13858
13859 // If L is the addrec's loop, it's computable.
13860 if (AR->getLoop() == L)
13861 return LoopComputable;
13862
13863 // Add recurrences are never invariant in the function-body (null loop).
13864 if (!L)
13865 return LoopVariant;
13866
13867 // Everything that is not defined at loop entry is variant.
13868 if (DT.dominates(A: L->getHeader(), B: AR->getLoop()->getHeader()))
13869 return LoopVariant;
13870 assert(!L->contains(AR->getLoop()) && "Containing loop's header does not"
13871 " dominate the contained loop's header?");
13872
13873 // This recurrence is invariant w.r.t. L if AR's loop contains L.
13874 if (AR->getLoop()->contains(L))
13875 return LoopInvariant;
13876
13877 // This recurrence is variant w.r.t. L if any of its operands
13878 // are variant.
13879 for (const auto *Op : AR->operands())
13880 if (!isLoopInvariant(S: Op, L))
13881 return LoopVariant;
13882
13883 // Otherwise it's loop-invariant.
13884 return LoopInvariant;
13885 }
13886 case scTruncate:
13887 case scZeroExtend:
13888 case scSignExtend:
13889 case scPtrToInt:
13890 case scAddExpr:
13891 case scMulExpr:
13892 case scUDivExpr:
13893 case scUMaxExpr:
13894 case scSMaxExpr:
13895 case scUMinExpr:
13896 case scSMinExpr:
13897 case scSequentialUMinExpr: {
13898 bool HasVarying = false;
13899 for (const auto *Op : S->operands()) {
13900 LoopDisposition D = getLoopDisposition(S: Op, L);
13901 if (D == LoopVariant)
13902 return LoopVariant;
13903 if (D == LoopComputable)
13904 HasVarying = true;
13905 }
13906 return HasVarying ? LoopComputable : LoopInvariant;
13907 }
13908 case scUnknown:
13909 // All non-instruction values are loop invariant. All instructions are loop
13910 // invariant if they are not contained in the specified loop.
13911 // Instructions are never considered invariant in the function body
13912 // (null loop) because they are defined within the "loop".
13913 if (auto *I = dyn_cast<Instruction>(Val: cast<SCEVUnknown>(Val: S)->getValue()))
13914 return (L && !L->contains(Inst: I)) ? LoopInvariant : LoopVariant;
13915 return LoopInvariant;
13916 case scCouldNotCompute:
13917 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
13918 }
13919 llvm_unreachable("Unknown SCEV kind!");
13920}
13921
13922bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
13923 return getLoopDisposition(S, L) == LoopInvariant;
13924}
13925
13926bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
13927 return getLoopDisposition(S, L) == LoopComputable;
13928}
13929
13930ScalarEvolution::BlockDisposition
13931ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
13932 auto &Values = BlockDispositions[S];
13933 for (auto &V : Values) {
13934 if (V.getPointer() == BB)
13935 return V.getInt();
13936 }
13937 Values.emplace_back(Args&: BB, Args: DoesNotDominateBlock);
13938 BlockDisposition D = computeBlockDisposition(S, BB);
13939 auto &Values2 = BlockDispositions[S];
13940 for (auto &V : llvm::reverse(C&: Values2)) {
13941 if (V.getPointer() == BB) {
13942 V.setInt(D);
13943 break;
13944 }
13945 }
13946 return D;
13947}
13948
13949ScalarEvolution::BlockDisposition
13950ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
13951 switch (S->getSCEVType()) {
13952 case scConstant:
13953 case scVScale:
13954 return ProperlyDominatesBlock;
13955 case scAddRecExpr: {
13956 // This uses a "dominates" query instead of "properly dominates" query
13957 // to test for proper dominance too, because the instruction which
13958 // produces the addrec's value is a PHI, and a PHI effectively properly
13959 // dominates its entire containing block.
13960 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(Val: S);
13961 if (!DT.dominates(A: AR->getLoop()->getHeader(), B: BB))
13962 return DoesNotDominateBlock;
13963
13964 // Fall through into SCEVNAryExpr handling.
13965 [[fallthrough]];
13966 }
13967 case scTruncate:
13968 case scZeroExtend:
13969 case scSignExtend:
13970 case scPtrToInt:
13971 case scAddExpr:
13972 case scMulExpr:
13973 case scUDivExpr:
13974 case scUMaxExpr:
13975 case scSMaxExpr:
13976 case scUMinExpr:
13977 case scSMinExpr:
13978 case scSequentialUMinExpr: {
13979 bool Proper = true;
13980 for (const SCEV *NAryOp : S->operands()) {
13981 BlockDisposition D = getBlockDisposition(S: NAryOp, BB);
13982 if (D == DoesNotDominateBlock)
13983 return DoesNotDominateBlock;
13984 if (D == DominatesBlock)
13985 Proper = false;
13986 }
13987 return Proper ? ProperlyDominatesBlock : DominatesBlock;
13988 }
13989 case scUnknown:
13990 if (Instruction *I =
13991 dyn_cast<Instruction>(Val: cast<SCEVUnknown>(Val: S)->getValue())) {
13992 if (I->getParent() == BB)
13993 return DominatesBlock;
13994 if (DT.properlyDominates(A: I->getParent(), B: BB))
13995 return ProperlyDominatesBlock;
13996 return DoesNotDominateBlock;
13997 }
13998 return ProperlyDominatesBlock;
13999 case scCouldNotCompute:
14000 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
14001 }
14002 llvm_unreachable("Unknown SCEV kind!");
14003}
14004
14005bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
14006 return getBlockDisposition(S, BB) >= DominatesBlock;
14007}
14008
14009bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
14010 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
14011}
14012
14013bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
14014 return SCEVExprContains(Root: S, Pred: [&](const SCEV *Expr) { return Expr == Op; });
14015}
14016
14017void ScalarEvolution::forgetBackedgeTakenCounts(const Loop *L,
14018 bool Predicated) {
14019 auto &BECounts =
14020 Predicated ? PredicatedBackedgeTakenCounts : BackedgeTakenCounts;
14021 auto It = BECounts.find(Val: L);
14022 if (It != BECounts.end()) {
14023 for (const ExitNotTakenInfo &ENT : It->second.ExitNotTaken) {
14024 for (const SCEV *S : {ENT.ExactNotTaken, ENT.SymbolicMaxNotTaken}) {
14025 if (!isa<SCEVConstant>(Val: S)) {
14026 auto UserIt = BECountUsers.find(Val: S);
14027 assert(UserIt != BECountUsers.end());
14028 UserIt->second.erase(Ptr: {L, Predicated});
14029 }
14030 }
14031 }
14032 BECounts.erase(I: It);
14033 }
14034}
14035
14036void ScalarEvolution::forgetMemoizedResults(ArrayRef<const SCEV *> SCEVs) {
14037 SmallPtrSet<const SCEV *, 8> ToForget(SCEVs.begin(), SCEVs.end());
14038 SmallVector<const SCEV *, 8> Worklist(ToForget.begin(), ToForget.end());
14039
14040 while (!Worklist.empty()) {
14041 const SCEV *Curr = Worklist.pop_back_val();
14042 auto Users = SCEVUsers.find(Val: Curr);
14043 if (Users != SCEVUsers.end())
14044 for (const auto *User : Users->second)
14045 if (ToForget.insert(Ptr: User).second)
14046 Worklist.push_back(Elt: User);
14047 }
14048
14049 for (const auto *S : ToForget)
14050 forgetMemoizedResultsImpl(S);
14051
14052 for (auto I = PredicatedSCEVRewrites.begin();
14053 I != PredicatedSCEVRewrites.end();) {
14054 std::pair<const SCEV *, const Loop *> Entry = I->first;
14055 if (ToForget.count(Ptr: Entry.first))
14056 PredicatedSCEVRewrites.erase(I: I++);
14057 else
14058 ++I;
14059 }
14060}
14061
14062void ScalarEvolution::forgetMemoizedResultsImpl(const SCEV *S) {
14063 LoopDispositions.erase(Val: S);
14064 BlockDispositions.erase(Val: S);
14065 UnsignedRanges.erase(Val: S);
14066 SignedRanges.erase(Val: S);
14067 HasRecMap.erase(Val: S);
14068 ConstantMultipleCache.erase(Val: S);
14069
14070 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Val: S)) {
14071 UnsignedWrapViaInductionTried.erase(Ptr: AR);
14072 SignedWrapViaInductionTried.erase(Ptr: AR);
14073 }
14074
14075 auto ExprIt = ExprValueMap.find(Val: S);
14076 if (ExprIt != ExprValueMap.end()) {
14077 for (Value *V : ExprIt->second) {
14078 auto ValueIt = ValueExprMap.find_as(Val: V);
14079 if (ValueIt != ValueExprMap.end())
14080 ValueExprMap.erase(I: ValueIt);
14081 }
14082 ExprValueMap.erase(I: ExprIt);
14083 }
14084
14085 auto ScopeIt = ValuesAtScopes.find(Val: S);
14086 if (ScopeIt != ValuesAtScopes.end()) {
14087 for (const auto &Pair : ScopeIt->second)
14088 if (!isa_and_nonnull<SCEVConstant>(Val: Pair.second))
14089 llvm::erase(C&: ValuesAtScopesUsers[Pair.second],
14090 V: std::make_pair(x: Pair.first, y&: S));
14091 ValuesAtScopes.erase(I: ScopeIt);
14092 }
14093
14094 auto ScopeUserIt = ValuesAtScopesUsers.find(Val: S);
14095 if (ScopeUserIt != ValuesAtScopesUsers.end()) {
14096 for (const auto &Pair : ScopeUserIt->second)
14097 llvm::erase(C&: ValuesAtScopes[Pair.second], V: std::make_pair(x: Pair.first, y&: S));
14098 ValuesAtScopesUsers.erase(I: ScopeUserIt);
14099 }
14100
14101 auto BEUsersIt = BECountUsers.find(Val: S);
14102 if (BEUsersIt != BECountUsers.end()) {
14103 // Work on a copy, as forgetBackedgeTakenCounts() will modify the original.
14104 auto Copy = BEUsersIt->second;
14105 for (const auto &Pair : Copy)
14106 forgetBackedgeTakenCounts(L: Pair.getPointer(), Predicated: Pair.getInt());
14107 BECountUsers.erase(I: BEUsersIt);
14108 }
14109
14110 auto FoldUser = FoldCacheUser.find(Val: S);
14111 if (FoldUser != FoldCacheUser.end())
14112 for (auto &KV : FoldUser->second)
14113 FoldCache.erase(Val: KV);
14114 FoldCacheUser.erase(Val: S);
14115}
14116
14117void
14118ScalarEvolution::getUsedLoops(const SCEV *S,
14119 SmallPtrSetImpl<const Loop *> &LoopsUsed) {
14120 struct FindUsedLoops {
14121 FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed)
14122 : LoopsUsed(LoopsUsed) {}
14123 SmallPtrSetImpl<const Loop *> &LoopsUsed;
14124 bool follow(const SCEV *S) {
14125 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Val: S))
14126 LoopsUsed.insert(Ptr: AR->getLoop());
14127 return true;
14128 }
14129
14130 bool isDone() const { return false; }
14131 };
14132
14133 FindUsedLoops F(LoopsUsed);
14134 SCEVTraversal<FindUsedLoops>(F).visitAll(Root: S);
14135}
14136
14137void ScalarEvolution::getReachableBlocks(
14138 SmallPtrSetImpl<BasicBlock *> &Reachable, Function &F) {
14139 SmallVector<BasicBlock *> Worklist;
14140 Worklist.push_back(Elt: &F.getEntryBlock());
14141 while (!Worklist.empty()) {
14142 BasicBlock *BB = Worklist.pop_back_val();
14143 if (!Reachable.insert(Ptr: BB).second)
14144 continue;
14145
14146 Value *Cond;
14147 BasicBlock *TrueBB, *FalseBB;
14148 if (match(V: BB->getTerminator(), P: m_Br(C: m_Value(V&: Cond), T: m_BasicBlock(V&: TrueBB),
14149 F: m_BasicBlock(V&: FalseBB)))) {
14150 if (auto *C = dyn_cast<ConstantInt>(Val: Cond)) {
14151 Worklist.push_back(Elt: C->isOne() ? TrueBB : FalseBB);
14152 continue;
14153 }
14154
14155 if (auto *Cmp = dyn_cast<ICmpInst>(Val: Cond)) {
14156 const SCEV *L = getSCEV(V: Cmp->getOperand(i_nocapture: 0));
14157 const SCEV *R = getSCEV(V: Cmp->getOperand(i_nocapture: 1));
14158 if (isKnownPredicateViaConstantRanges(Pred: Cmp->getPredicate(), LHS: L, RHS: R)) {
14159 Worklist.push_back(Elt: TrueBB);
14160 continue;
14161 }
14162 if (isKnownPredicateViaConstantRanges(Pred: Cmp->getInversePredicate(), LHS: L,
14163 RHS: R)) {
14164 Worklist.push_back(Elt: FalseBB);
14165 continue;
14166 }
14167 }
14168 }
14169
14170 append_range(C&: Worklist, R: successors(BB));
14171 }
14172}
14173
14174void ScalarEvolution::verify() const {
14175 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
14176 ScalarEvolution SE2(F, TLI, AC, DT, LI);
14177
14178 SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end());
14179
14180 // Map's SCEV expressions from one ScalarEvolution "universe" to another.
14181 struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> {
14182 SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {}
14183
14184 const SCEV *visitConstant(const SCEVConstant *Constant) {
14185 return SE.getConstant(Val: Constant->getAPInt());
14186 }
14187
14188 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
14189 return SE.getUnknown(V: Expr->getValue());
14190 }
14191
14192 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
14193 return SE.getCouldNotCompute();
14194 }
14195 };
14196
14197 SCEVMapper SCM(SE2);
14198 SmallPtrSet<BasicBlock *, 16> ReachableBlocks;
14199 SE2.getReachableBlocks(Reachable&: ReachableBlocks, F);
14200
14201 auto GetDelta = [&](const SCEV *Old, const SCEV *New) -> const SCEV * {
14202 if (containsUndefs(S: Old) || containsUndefs(S: New)) {
14203 // SCEV treats "undef" as an unknown but consistent value (i.e. it does
14204 // not propagate undef aggressively). This means we can (and do) fail
14205 // verification in cases where a transform makes a value go from "undef"
14206 // to "undef+1" (say). The transform is fine, since in both cases the
14207 // result is "undef", but SCEV thinks the value increased by 1.
14208 return nullptr;
14209 }
14210
14211 // Unless VerifySCEVStrict is set, we only compare constant deltas.
14212 const SCEV *Delta = SE2.getMinusSCEV(LHS: Old, RHS: New);
14213 if (!VerifySCEVStrict && !isa<SCEVConstant>(Val: Delta))
14214 return nullptr;
14215
14216 return Delta;
14217 };
14218
14219 while (!LoopStack.empty()) {
14220 auto *L = LoopStack.pop_back_val();
14221 llvm::append_range(C&: LoopStack, R&: *L);
14222
14223 // Only verify BECounts in reachable loops. For an unreachable loop,
14224 // any BECount is legal.
14225 if (!ReachableBlocks.contains(Ptr: L->getHeader()))
14226 continue;
14227
14228 // Only verify cached BECounts. Computing new BECounts may change the
14229 // results of subsequent SCEV uses.
14230 auto It = BackedgeTakenCounts.find(Val: L);
14231 if (It == BackedgeTakenCounts.end())
14232 continue;
14233
14234 auto *CurBECount =
14235 SCM.visit(S: It->second.getExact(L, SE: const_cast<ScalarEvolution *>(this)));
14236 auto *NewBECount = SE2.getBackedgeTakenCount(L);
14237
14238 if (CurBECount == SE2.getCouldNotCompute() ||
14239 NewBECount == SE2.getCouldNotCompute()) {
14240 // NB! This situation is legal, but is very suspicious -- whatever pass
14241 // change the loop to make a trip count go from could not compute to
14242 // computable or vice-versa *should have* invalidated SCEV. However, we
14243 // choose not to assert here (for now) since we don't want false
14244 // positives.
14245 continue;
14246 }
14247
14248 if (SE.getTypeSizeInBits(Ty: CurBECount->getType()) >
14249 SE.getTypeSizeInBits(Ty: NewBECount->getType()))
14250 NewBECount = SE2.getZeroExtendExpr(Op: NewBECount, Ty: CurBECount->getType());
14251 else if (SE.getTypeSizeInBits(Ty: CurBECount->getType()) <
14252 SE.getTypeSizeInBits(Ty: NewBECount->getType()))
14253 CurBECount = SE2.getZeroExtendExpr(Op: CurBECount, Ty: NewBECount->getType());
14254
14255 const SCEV *Delta = GetDelta(CurBECount, NewBECount);
14256 if (Delta && !Delta->isZero()) {
14257 dbgs() << "Trip Count for " << *L << " Changed!\n";
14258 dbgs() << "Old: " << *CurBECount << "\n";
14259 dbgs() << "New: " << *NewBECount << "\n";
14260 dbgs() << "Delta: " << *Delta << "\n";
14261 std::abort();
14262 }
14263 }
14264
14265 // Collect all valid loops currently in LoopInfo.
14266 SmallPtrSet<Loop *, 32> ValidLoops;
14267 SmallVector<Loop *, 32> Worklist(LI.begin(), LI.end());
14268 while (!Worklist.empty()) {
14269 Loop *L = Worklist.pop_back_val();
14270 if (ValidLoops.insert(Ptr: L).second)
14271 Worklist.append(in_start: L->begin(), in_end: L->end());
14272 }
14273 for (const auto &KV : ValueExprMap) {
14274#ifndef NDEBUG
14275 // Check for SCEV expressions referencing invalid/deleted loops.
14276 if (auto *AR = dyn_cast<SCEVAddRecExpr>(KV.second)) {
14277 assert(ValidLoops.contains(AR->getLoop()) &&
14278 "AddRec references invalid loop");
14279 }
14280#endif
14281
14282 // Check that the value is also part of the reverse map.
14283 auto It = ExprValueMap.find(Val: KV.second);
14284 if (It == ExprValueMap.end() || !It->second.contains(key: KV.first)) {
14285 dbgs() << "Value " << *KV.first
14286 << " is in ValueExprMap but not in ExprValueMap\n";
14287 std::abort();
14288 }
14289
14290 if (auto *I = dyn_cast<Instruction>(Val: &*KV.first)) {
14291 if (!ReachableBlocks.contains(Ptr: I->getParent()))
14292 continue;
14293 const SCEV *OldSCEV = SCM.visit(S: KV.second);
14294 const SCEV *NewSCEV = SE2.getSCEV(V: I);
14295 const SCEV *Delta = GetDelta(OldSCEV, NewSCEV);
14296 if (Delta && !Delta->isZero()) {
14297 dbgs() << "SCEV for value " << *I << " changed!\n"
14298 << "Old: " << *OldSCEV << "\n"
14299 << "New: " << *NewSCEV << "\n"
14300 << "Delta: " << *Delta << "\n";
14301 std::abort();
14302 }
14303 }
14304 }
14305
14306 for (const auto &KV : ExprValueMap) {
14307 for (Value *V : KV.second) {
14308 auto It = ValueExprMap.find_as(Val: V);
14309 if (It == ValueExprMap.end()) {
14310 dbgs() << "Value " << *V
14311 << " is in ExprValueMap but not in ValueExprMap\n";
14312 std::abort();
14313 }
14314 if (It->second != KV.first) {
14315 dbgs() << "Value " << *V << " mapped to " << *It->second
14316 << " rather than " << *KV.first << "\n";
14317 std::abort();
14318 }
14319 }
14320 }
14321
14322 // Verify integrity of SCEV users.
14323 for (const auto &S : UniqueSCEVs) {
14324 for (const auto *Op : S.operands()) {
14325 // We do not store dependencies of constants.
14326 if (isa<SCEVConstant>(Val: Op))
14327 continue;
14328 auto It = SCEVUsers.find(Val: Op);
14329 if (It != SCEVUsers.end() && It->second.count(Ptr: &S))
14330 continue;
14331 dbgs() << "Use of operand " << *Op << " by user " << S
14332 << " is not being tracked!\n";
14333 std::abort();
14334 }
14335 }
14336
14337 // Verify integrity of ValuesAtScopes users.
14338 for (const auto &ValueAndVec : ValuesAtScopes) {
14339 const SCEV *Value = ValueAndVec.first;
14340 for (const auto &LoopAndValueAtScope : ValueAndVec.second) {
14341 const Loop *L = LoopAndValueAtScope.first;
14342 const SCEV *ValueAtScope = LoopAndValueAtScope.second;
14343 if (!isa<SCEVConstant>(Val: ValueAtScope)) {
14344 auto It = ValuesAtScopesUsers.find(Val: ValueAtScope);
14345 if (It != ValuesAtScopesUsers.end() &&
14346 is_contained(Range: It->second, Element: std::make_pair(x&: L, y&: Value)))
14347 continue;
14348 dbgs() << "Value: " << *Value << ", Loop: " << *L << ", ValueAtScope: "
14349 << *ValueAtScope << " missing in ValuesAtScopesUsers\n";
14350 std::abort();
14351 }
14352 }
14353 }
14354
14355 for (const auto &ValueAtScopeAndVec : ValuesAtScopesUsers) {
14356 const SCEV *ValueAtScope = ValueAtScopeAndVec.first;
14357 for (const auto &LoopAndValue : ValueAtScopeAndVec.second) {
14358 const Loop *L = LoopAndValue.first;
14359 const SCEV *Value = LoopAndValue.second;
14360 assert(!isa<SCEVConstant>(Value));
14361 auto It = ValuesAtScopes.find(Val: Value);
14362 if (It != ValuesAtScopes.end() &&
14363 is_contained(Range: It->second, Element: std::make_pair(x&: L, y&: ValueAtScope)))
14364 continue;
14365 dbgs() << "Value: " << *Value << ", Loop: " << *L << ", ValueAtScope: "
14366 << *ValueAtScope << " missing in ValuesAtScopes\n";
14367 std::abort();
14368 }
14369 }
14370
14371 // Verify integrity of BECountUsers.
14372 auto VerifyBECountUsers = [&](bool Predicated) {
14373 auto &BECounts =
14374 Predicated ? PredicatedBackedgeTakenCounts : BackedgeTakenCounts;
14375 for (const auto &LoopAndBEInfo : BECounts) {
14376 for (const ExitNotTakenInfo &ENT : LoopAndBEInfo.second.ExitNotTaken) {
14377 for (const SCEV *S : {ENT.ExactNotTaken, ENT.SymbolicMaxNotTaken}) {
14378 if (!isa<SCEVConstant>(Val: S)) {
14379 auto UserIt = BECountUsers.find(Val: S);
14380 if (UserIt != BECountUsers.end() &&
14381 UserIt->second.contains(Ptr: { LoopAndBEInfo.first, Predicated }))
14382 continue;
14383 dbgs() << "Value " << *S << " for loop " << *LoopAndBEInfo.first
14384 << " missing from BECountUsers\n";
14385 std::abort();
14386 }
14387 }
14388 }
14389 }
14390 };
14391 VerifyBECountUsers(/* Predicated */ false);
14392 VerifyBECountUsers(/* Predicated */ true);
14393
14394 // Verify intergity of loop disposition cache.
14395 for (auto &[S, Values] : LoopDispositions) {
14396 for (auto [Loop, CachedDisposition] : Values) {
14397 const auto RecomputedDisposition = SE2.getLoopDisposition(S, L: Loop);
14398 if (CachedDisposition != RecomputedDisposition) {
14399 dbgs() << "Cached disposition of " << *S << " for loop " << *Loop
14400 << " is incorrect: cached " << CachedDisposition << ", actual "
14401 << RecomputedDisposition << "\n";
14402 std::abort();
14403 }
14404 }
14405 }
14406
14407 // Verify integrity of the block disposition cache.
14408 for (auto &[S, Values] : BlockDispositions) {
14409 for (auto [BB, CachedDisposition] : Values) {
14410 const auto RecomputedDisposition = SE2.getBlockDisposition(S, BB);
14411 if (CachedDisposition != RecomputedDisposition) {
14412 dbgs() << "Cached disposition of " << *S << " for block %"
14413 << BB->getName() << " is incorrect: cached " << CachedDisposition
14414 << ", actual " << RecomputedDisposition << "\n";
14415 std::abort();
14416 }
14417 }
14418 }
14419
14420 // Verify FoldCache/FoldCacheUser caches.
14421 for (auto [FoldID, Expr] : FoldCache) {
14422 auto I = FoldCacheUser.find(Val: Expr);
14423 if (I == FoldCacheUser.end()) {
14424 dbgs() << "Missing entry in FoldCacheUser for cached expression " << *Expr
14425 << "!\n";
14426 std::abort();
14427 }
14428 if (!is_contained(Range: I->second, Element: FoldID)) {
14429 dbgs() << "Missing FoldID in cached users of " << *Expr << "!\n";
14430 std::abort();
14431 }
14432 }
14433 for (auto [Expr, IDs] : FoldCacheUser) {
14434 for (auto &FoldID : IDs) {
14435 auto I = FoldCache.find(Val: FoldID);
14436 if (I == FoldCache.end()) {
14437 dbgs() << "Missing entry in FoldCache for expression " << *Expr
14438 << "!\n";
14439 std::abort();
14440 }
14441 if (I->second != Expr) {
14442 dbgs() << "Entry in FoldCache doesn't match FoldCacheUser: "
14443 << *I->second << " != " << *Expr << "!\n";
14444 std::abort();
14445 }
14446 }
14447 }
14448
14449 // Verify that ConstantMultipleCache computations are correct. We check that
14450 // cached multiples and recomputed multiples are multiples of each other to
14451 // verify correctness. It is possible that a recomputed multiple is different
14452 // from the cached multiple due to strengthened no wrap flags or changes in
14453 // KnownBits computations.
14454 for (auto [S, Multiple] : ConstantMultipleCache) {
14455 APInt RecomputedMultiple = SE2.getConstantMultiple(S);
14456 if ((Multiple != 0 && RecomputedMultiple != 0 &&
14457 Multiple.urem(RHS: RecomputedMultiple) != 0 &&
14458 RecomputedMultiple.urem(RHS: Multiple) != 0)) {
14459 dbgs() << "Incorrect cached computation in ConstantMultipleCache for "
14460 << *S << " : Computed " << RecomputedMultiple
14461 << " but cache contains " << Multiple << "!\n";
14462 std::abort();
14463 }
14464 }
14465}
14466
14467bool ScalarEvolution::invalidate(
14468 Function &F, const PreservedAnalyses &PA,
14469 FunctionAnalysisManager::Invalidator &Inv) {
14470 // Invalidate the ScalarEvolution object whenever it isn't preserved or one
14471 // of its dependencies is invalidated.
14472 auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
14473 return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
14474 Inv.invalidate<AssumptionAnalysis>(IR&: F, PA) ||
14475 Inv.invalidate<DominatorTreeAnalysis>(IR&: F, PA) ||
14476 Inv.invalidate<LoopAnalysis>(IR&: F, PA);
14477}
14478
14479AnalysisKey ScalarEvolutionAnalysis::Key;
14480
14481ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
14482 FunctionAnalysisManager &AM) {
14483 auto &TLI = AM.getResult<TargetLibraryAnalysis>(IR&: F);
14484 auto &AC = AM.getResult<AssumptionAnalysis>(IR&: F);
14485 auto &DT = AM.getResult<DominatorTreeAnalysis>(IR&: F);
14486 auto &LI = AM.getResult<LoopAnalysis>(IR&: F);
14487 return ScalarEvolution(F, TLI, AC, DT, LI);
14488}
14489
14490PreservedAnalyses
14491ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) {
14492 AM.getResult<ScalarEvolutionAnalysis>(IR&: F).verify();
14493 return PreservedAnalyses::all();
14494}
14495
14496PreservedAnalyses
14497ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
14498 // For compatibility with opt's -analyze feature under legacy pass manager
14499 // which was not ported to NPM. This keeps tests using
14500 // update_analyze_test_checks.py working.
14501 OS << "Printing analysis 'Scalar Evolution Analysis' for function '"
14502 << F.getName() << "':\n";
14503 AM.getResult<ScalarEvolutionAnalysis>(IR&: F).print(OS);
14504 return PreservedAnalyses::all();
14505}
14506
14507INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
14508 "Scalar Evolution Analysis", false, true)
14509INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
14510INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
14511INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
14512INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
14513INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
14514 "Scalar Evolution Analysis", false, true)
14515
14516char ScalarEvolutionWrapperPass::ID = 0;
14517
14518ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
14519 initializeScalarEvolutionWrapperPassPass(Registry&: *PassRegistry::getPassRegistry());
14520}
14521
14522bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
14523 SE.reset(p: new ScalarEvolution(
14524 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F),
14525 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
14526 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
14527 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
14528 return false;
14529}
14530
14531void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
14532
14533void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
14534 SE->print(OS);
14535}
14536
14537void ScalarEvolutionWrapperPass::verifyAnalysis() const {
14538 if (!VerifySCEV)
14539 return;
14540
14541 SE->verify();
14542}
14543
14544void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
14545 AU.setPreservesAll();
14546 AU.addRequiredTransitive<AssumptionCacheTracker>();
14547 AU.addRequiredTransitive<LoopInfoWrapperPass>();
14548 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
14549 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
14550}
14551
14552const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS,
14553 const SCEV *RHS) {
14554 return getComparePredicate(Pred: ICmpInst::ICMP_EQ, LHS, RHS);
14555}
14556
14557const SCEVPredicate *
14558ScalarEvolution::getComparePredicate(const ICmpInst::Predicate Pred,
14559 const SCEV *LHS, const SCEV *RHS) {
14560 FoldingSetNodeID ID;
14561 assert(LHS->getType() == RHS->getType() &&
14562 "Type mismatch between LHS and RHS");
14563 // Unique this node based on the arguments
14564 ID.AddInteger(I: SCEVPredicate::P_Compare);
14565 ID.AddInteger(I: Pred);
14566 ID.AddPointer(Ptr: LHS);
14567 ID.AddPointer(Ptr: RHS);
14568 void *IP = nullptr;
14569 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, InsertPos&: IP))
14570 return S;
14571 SCEVComparePredicate *Eq = new (SCEVAllocator)
14572 SCEVComparePredicate(ID.Intern(Allocator&: SCEVAllocator), Pred, LHS, RHS);
14573 UniquePreds.InsertNode(N: Eq, InsertPos: IP);
14574 return Eq;
14575}
14576
14577const SCEVPredicate *ScalarEvolution::getWrapPredicate(
14578 const SCEVAddRecExpr *AR,
14579 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
14580 FoldingSetNodeID ID;
14581 // Unique this node based on the arguments
14582 ID.AddInteger(I: SCEVPredicate::P_Wrap);
14583 ID.AddPointer(Ptr: AR);
14584 ID.AddInteger(I: AddedFlags);
14585 void *IP = nullptr;
14586 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, InsertPos&: IP))
14587 return S;
14588 auto *OF = new (SCEVAllocator)
14589 SCEVWrapPredicate(ID.Intern(Allocator&: SCEVAllocator), AR, AddedFlags);
14590 UniquePreds.InsertNode(N: OF, InsertPos: IP);
14591 return OF;
14592}
14593
14594namespace {
14595
14596class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
14597public:
14598
14599 /// Rewrites \p S in the context of a loop L and the SCEV predication
14600 /// infrastructure.
14601 ///
14602 /// If \p Pred is non-null, the SCEV expression is rewritten to respect the
14603 /// equivalences present in \p Pred.
14604 ///
14605 /// If \p NewPreds is non-null, rewrite is free to add further predicates to
14606 /// \p NewPreds such that the result will be an AddRecExpr.
14607 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
14608 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
14609 const SCEVPredicate *Pred) {
14610 SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
14611 return Rewriter.visit(S);
14612 }
14613
14614 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
14615 if (Pred) {
14616 if (auto *U = dyn_cast<SCEVUnionPredicate>(Val: Pred)) {
14617 for (const auto *Pred : U->getPredicates())
14618 if (const auto *IPred = dyn_cast<SCEVComparePredicate>(Val: Pred))
14619 if (IPred->getLHS() == Expr &&
14620 IPred->getPredicate() == ICmpInst::ICMP_EQ)
14621 return IPred->getRHS();
14622 } else if (const auto *IPred = dyn_cast<SCEVComparePredicate>(Val: Pred)) {
14623 if (IPred->getLHS() == Expr &&
14624 IPred->getPredicate() == ICmpInst::ICMP_EQ)
14625 return IPred->getRHS();
14626 }
14627 }
14628 return convertToAddRecWithPreds(Expr);
14629 }
14630
14631 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
14632 const SCEV *Operand = visit(S: Expr->getOperand());
14633 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Val: Operand);
14634 if (AR && AR->getLoop() == L && AR->isAffine()) {
14635 // This couldn't be folded because the operand didn't have the nuw
14636 // flag. Add the nusw flag as an assumption that we could make.
14637 const SCEV *Step = AR->getStepRecurrence(SE);
14638 Type *Ty = Expr->getType();
14639 if (addOverflowAssumption(AR, AddedFlags: SCEVWrapPredicate::IncrementNUSW))
14640 return SE.getAddRecExpr(Start: SE.getZeroExtendExpr(Op: AR->getStart(), Ty),
14641 Step: SE.getSignExtendExpr(Op: Step, Ty), L,
14642 Flags: AR->getNoWrapFlags());
14643 }
14644 return SE.getZeroExtendExpr(Op: Operand, Ty: Expr->getType());
14645 }
14646
14647 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
14648 const SCEV *Operand = visit(S: Expr->getOperand());
14649 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Val: Operand);
14650 if (AR && AR->getLoop() == L && AR->isAffine()) {
14651 // This couldn't be folded because the operand didn't have the nsw
14652 // flag. Add the nssw flag as an assumption that we could make.
14653 const SCEV *Step = AR->getStepRecurrence(SE);
14654 Type *Ty = Expr->getType();
14655 if (addOverflowAssumption(AR, AddedFlags: SCEVWrapPredicate::IncrementNSSW))
14656 return SE.getAddRecExpr(Start: SE.getSignExtendExpr(Op: AR->getStart(), Ty),
14657 Step: SE.getSignExtendExpr(Op: Step, Ty), L,
14658 Flags: AR->getNoWrapFlags());
14659 }
14660 return SE.getSignExtendExpr(Op: Operand, Ty: Expr->getType());
14661 }
14662
14663private:
14664 explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
14665 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
14666 const SCEVPredicate *Pred)
14667 : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
14668
14669 bool addOverflowAssumption(const SCEVPredicate *P) {
14670 if (!NewPreds) {
14671 // Check if we've already made this assumption.
14672 return Pred && Pred->implies(N: P);
14673 }
14674 NewPreds->insert(Ptr: P);
14675 return true;
14676 }
14677
14678 bool addOverflowAssumption(const SCEVAddRecExpr *AR,
14679 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
14680 auto *A = SE.getWrapPredicate(AR, AddedFlags);
14681 return addOverflowAssumption(P: A);
14682 }
14683
14684 // If \p Expr represents a PHINode, we try to see if it can be represented
14685 // as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible
14686 // to add this predicate as a runtime overflow check, we return the AddRec.
14687 // If \p Expr does not meet these conditions (is not a PHI node, or we
14688 // couldn't create an AddRec for it, or couldn't add the predicate), we just
14689 // return \p Expr.
14690 const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) {
14691 if (!isa<PHINode>(Val: Expr->getValue()))
14692 return Expr;
14693 std::optional<
14694 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
14695 PredicatedRewrite = SE.createAddRecFromPHIWithCasts(SymbolicPHI: Expr);
14696 if (!PredicatedRewrite)
14697 return Expr;
14698 for (const auto *P : PredicatedRewrite->second){
14699 // Wrap predicates from outer loops are not supported.
14700 if (auto *WP = dyn_cast<const SCEVWrapPredicate>(Val: P)) {
14701 if (L != WP->getExpr()->getLoop())
14702 return Expr;
14703 }
14704 if (!addOverflowAssumption(P))
14705 return Expr;
14706 }
14707 return PredicatedRewrite->first;
14708 }
14709
14710 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds;
14711 const SCEVPredicate *Pred;
14712 const Loop *L;
14713};
14714
14715} // end anonymous namespace
14716
14717const SCEV *
14718ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
14719 const SCEVPredicate &Preds) {
14720 return SCEVPredicateRewriter::rewrite(S, L, SE&: *this, NewPreds: nullptr, Pred: &Preds);
14721}
14722
14723const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
14724 const SCEV *S, const Loop *L,
14725 SmallPtrSetImpl<const SCEVPredicate *> &Preds) {
14726 SmallPtrSet<const SCEVPredicate *, 4> TransformPreds;
14727 S = SCEVPredicateRewriter::rewrite(S, L, SE&: *this, NewPreds: &TransformPreds, Pred: nullptr);
14728 auto *AddRec = dyn_cast<SCEVAddRecExpr>(Val: S);
14729
14730 if (!AddRec)
14731 return nullptr;
14732
14733 // Since the transformation was successful, we can now transfer the SCEV
14734 // predicates.
14735 for (const auto *P : TransformPreds)
14736 Preds.insert(Ptr: P);
14737
14738 return AddRec;
14739}
14740
14741/// SCEV predicates
14742SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
14743 SCEVPredicateKind Kind)
14744 : FastID(ID), Kind(Kind) {}
14745
14746SCEVComparePredicate::SCEVComparePredicate(const FoldingSetNodeIDRef ID,
14747 const ICmpInst::Predicate Pred,
14748 const SCEV *LHS, const SCEV *RHS)
14749 : SCEVPredicate(ID, P_Compare), Pred(Pred), LHS(LHS), RHS(RHS) {
14750 assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match");
14751 assert(LHS != RHS && "LHS and RHS are the same SCEV");
14752}
14753
14754bool SCEVComparePredicate::implies(const SCEVPredicate *N) const {
14755 const auto *Op = dyn_cast<SCEVComparePredicate>(Val: N);
14756
14757 if (!Op)
14758 return false;
14759
14760 if (Pred != ICmpInst::ICMP_EQ)
14761 return false;
14762
14763 return Op->LHS == LHS && Op->RHS == RHS;
14764}
14765
14766bool SCEVComparePredicate::isAlwaysTrue() const { return false; }
14767
14768void SCEVComparePredicate::print(raw_ostream &OS, unsigned Depth) const {
14769 if (Pred == ICmpInst::ICMP_EQ)
14770 OS.indent(NumSpaces: Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
14771 else
14772 OS.indent(NumSpaces: Depth) << "Compare predicate: " << *LHS << " " << Pred << ") "
14773 << *RHS << "\n";
14774
14775}
14776
14777SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
14778 const SCEVAddRecExpr *AR,
14779 IncrementWrapFlags Flags)
14780 : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
14781
14782const SCEVAddRecExpr *SCEVWrapPredicate::getExpr() const { return AR; }
14783
14784bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
14785 const auto *Op = dyn_cast<SCEVWrapPredicate>(Val: N);
14786
14787 return Op && Op->AR == AR && setFlags(Flags, OnFlags: Op->Flags) == Flags;
14788}
14789
14790bool SCEVWrapPredicate::isAlwaysTrue() const {
14791 SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
14792 IncrementWrapFlags IFlags = Flags;
14793
14794 if (ScalarEvolution::setFlags(Flags: ScevFlags, OnFlags: SCEV::FlagNSW) == ScevFlags)
14795 IFlags = clearFlags(Flags: IFlags, OffFlags: IncrementNSSW);
14796
14797 return IFlags == IncrementAnyWrap;
14798}
14799
14800void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
14801 OS.indent(NumSpaces: Depth) << *getExpr() << " Added Flags: ";
14802 if (SCEVWrapPredicate::IncrementNUSW & getFlags())
14803 OS << "<nusw>";
14804 if (SCEVWrapPredicate::IncrementNSSW & getFlags())
14805 OS << "<nssw>";
14806 OS << "\n";
14807}
14808
14809SCEVWrapPredicate::IncrementWrapFlags
14810SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
14811 ScalarEvolution &SE) {
14812 IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
14813 SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
14814
14815 // We can safely transfer the NSW flag as NSSW.
14816 if (ScalarEvolution::setFlags(Flags: StaticFlags, OnFlags: SCEV::FlagNSW) == StaticFlags)
14817 ImpliedFlags = IncrementNSSW;
14818
14819 if (ScalarEvolution::setFlags(Flags: StaticFlags, OnFlags: SCEV::FlagNUW) == StaticFlags) {
14820 // If the increment is positive, the SCEV NUW flag will also imply the
14821 // WrapPredicate NUSW flag.
14822 if (const auto *Step = dyn_cast<SCEVConstant>(Val: AR->getStepRecurrence(SE)))
14823 if (Step->getValue()->getValue().isNonNegative())
14824 ImpliedFlags = setFlags(Flags: ImpliedFlags, OnFlags: IncrementNUSW);
14825 }
14826
14827 return ImpliedFlags;
14828}
14829
14830/// Union predicates don't get cached so create a dummy set ID for it.
14831SCEVUnionPredicate::SCEVUnionPredicate(ArrayRef<const SCEVPredicate *> Preds)
14832 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {
14833 for (const auto *P : Preds)
14834 add(N: P);
14835}
14836
14837bool SCEVUnionPredicate::isAlwaysTrue() const {
14838 return all_of(Range: Preds,
14839 P: [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
14840}
14841
14842bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
14843 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(Val: N))
14844 return all_of(Range: Set->Preds,
14845 P: [this](const SCEVPredicate *I) { return this->implies(N: I); });
14846
14847 return any_of(Range: Preds,
14848 P: [N](const SCEVPredicate *I) { return I->implies(N); });
14849}
14850
14851void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
14852 for (const auto *Pred : Preds)
14853 Pred->print(OS, Depth);
14854}
14855
14856void SCEVUnionPredicate::add(const SCEVPredicate *N) {
14857 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(Val: N)) {
14858 for (const auto *Pred : Set->Preds)
14859 add(N: Pred);
14860 return;
14861 }
14862
14863 // Only add predicate if it is not already implied by this union predicate.
14864 if (!implies(N))
14865 Preds.push_back(Elt: N);
14866}
14867
14868PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
14869 Loop &L)
14870 : SE(SE), L(L) {
14871 SmallVector<const SCEVPredicate*, 4> Empty;
14872 Preds = std::make_unique<SCEVUnionPredicate>(args&: Empty);
14873}
14874
14875void ScalarEvolution::registerUser(const SCEV *User,
14876 ArrayRef<const SCEV *> Ops) {
14877 for (const auto *Op : Ops)
14878 // We do not expect that forgetting cached data for SCEVConstants will ever
14879 // open any prospects for sharpening or introduce any correctness issues,
14880 // so we don't bother storing their dependencies.
14881 if (!isa<SCEVConstant>(Val: Op))
14882 SCEVUsers[Op].insert(Ptr: User);
14883}
14884
14885const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
14886 const SCEV *Expr = SE.getSCEV(V);
14887 RewriteEntry &Entry = RewriteMap[Expr];
14888
14889 // If we already have an entry and the version matches, return it.
14890 if (Entry.second && Generation == Entry.first)
14891 return Entry.second;
14892
14893 // We found an entry but it's stale. Rewrite the stale entry
14894 // according to the current predicate.
14895 if (Entry.second)
14896 Expr = Entry.second;
14897
14898 const SCEV *NewSCEV = SE.rewriteUsingPredicate(S: Expr, L: &L, Preds: *Preds);
14899 Entry = {Generation, NewSCEV};
14900
14901 return NewSCEV;
14902}
14903
14904const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
14905 if (!BackedgeCount) {
14906 SmallVector<const SCEVPredicate *, 4> Preds;
14907 BackedgeCount = SE.getPredicatedBackedgeTakenCount(L: &L, Preds);
14908 for (const auto *P : Preds)
14909 addPredicate(Pred: *P);
14910 }
14911 return BackedgeCount;
14912}
14913
14914const SCEV *PredicatedScalarEvolution::getSymbolicMaxBackedgeTakenCount() {
14915 if (!SymbolicMaxBackedgeCount) {
14916 SmallVector<const SCEVPredicate *, 4> Preds;
14917 SymbolicMaxBackedgeCount =
14918 SE.getPredicatedSymbolicMaxBackedgeTakenCount(L: &L, Preds);
14919 for (const auto *P : Preds)
14920 addPredicate(Pred: *P);
14921 }
14922 return SymbolicMaxBackedgeCount;
14923}
14924
14925void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
14926 if (Preds->implies(N: &Pred))
14927 return;
14928
14929 auto &OldPreds = Preds->getPredicates();
14930 SmallVector<const SCEVPredicate*, 4> NewPreds(OldPreds.begin(), OldPreds.end());
14931 NewPreds.push_back(Elt: &Pred);
14932 Preds = std::make_unique<SCEVUnionPredicate>(args&: NewPreds);
14933 updateGeneration();
14934}
14935
14936const SCEVPredicate &PredicatedScalarEvolution::getPredicate() const {
14937 return *Preds;
14938}
14939
14940void PredicatedScalarEvolution::updateGeneration() {
14941 // If the generation number wrapped recompute everything.
14942 if (++Generation == 0) {
14943 for (auto &II : RewriteMap) {
14944 const SCEV *Rewritten = II.second.second;
14945 II.second = {Generation, SE.rewriteUsingPredicate(S: Rewritten, L: &L, Preds: *Preds)};
14946 }
14947 }
14948}
14949
14950void PredicatedScalarEvolution::setNoOverflow(
14951 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
14952 const SCEV *Expr = getSCEV(V);
14953 const auto *AR = cast<SCEVAddRecExpr>(Val: Expr);
14954
14955 auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
14956
14957 // Clear the statically implied flags.
14958 Flags = SCEVWrapPredicate::clearFlags(Flags, OffFlags: ImpliedFlags);
14959 addPredicate(Pred: *SE.getWrapPredicate(AR, AddedFlags: Flags));
14960
14961 auto II = FlagsMap.insert(KV: {V, Flags});
14962 if (!II.second)
14963 II.first->second = SCEVWrapPredicate::setFlags(Flags, OnFlags: II.first->second);
14964}
14965
14966bool PredicatedScalarEvolution::hasNoOverflow(
14967 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
14968 const SCEV *Expr = getSCEV(V);
14969 const auto *AR = cast<SCEVAddRecExpr>(Val: Expr);
14970
14971 Flags = SCEVWrapPredicate::clearFlags(
14972 Flags, OffFlags: SCEVWrapPredicate::getImpliedFlags(AR, SE));
14973
14974 auto II = FlagsMap.find(Val: V);
14975
14976 if (II != FlagsMap.end())
14977 Flags = SCEVWrapPredicate::clearFlags(Flags, OffFlags: II->second);
14978
14979 return Flags == SCEVWrapPredicate::IncrementAnyWrap;
14980}
14981
14982const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
14983 const SCEV *Expr = this->getSCEV(V);
14984 SmallPtrSet<const SCEVPredicate *, 4> NewPreds;
14985 auto *New = SE.convertSCEVToAddRecWithPredicates(S: Expr, L: &L, Preds&: NewPreds);
14986
14987 if (!New)
14988 return nullptr;
14989
14990 for (const auto *P : NewPreds)
14991 addPredicate(Pred: *P);
14992
14993 RewriteMap[SE.getSCEV(V)] = {Generation, New};
14994 return New;
14995}
14996
14997PredicatedScalarEvolution::PredicatedScalarEvolution(
14998 const PredicatedScalarEvolution &Init)
14999 : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L),
15000 Preds(std::make_unique<SCEVUnionPredicate>(args: Init.Preds->getPredicates())),
15001 Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
15002 for (auto I : Init.FlagsMap)
15003 FlagsMap.insert(KV: I);
15004}
15005
15006void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
15007 // For each block.
15008 for (auto *BB : L.getBlocks())
15009 for (auto &I : *BB) {
15010 if (!SE.isSCEVable(Ty: I.getType()))
15011 continue;
15012
15013 auto *Expr = SE.getSCEV(V: &I);
15014 auto II = RewriteMap.find(Val: Expr);
15015
15016 if (II == RewriteMap.end())
15017 continue;
15018
15019 // Don't print things that are not interesting.
15020 if (II->second.second == Expr)
15021 continue;
15022
15023 OS.indent(NumSpaces: Depth) << "[PSE]" << I << ":\n";
15024 OS.indent(NumSpaces: Depth + 2) << *Expr << "\n";
15025 OS.indent(NumSpaces: Depth + 2) << "--> " << *II->second.second << "\n";
15026 }
15027}
15028
15029// Match the mathematical pattern A - (A / B) * B, where A and B can be
15030// arbitrary expressions. Also match zext (trunc A to iB) to iY, which is used
15031// for URem with constant power-of-2 second operands.
15032// It's not always easy, as A and B can be folded (imagine A is X / 2, and B is
15033// 4, A / B becomes X / 8).
15034bool ScalarEvolution::matchURem(const SCEV *Expr, const SCEV *&LHS,
15035 const SCEV *&RHS) {
15036 if (Expr->getType()->isPointerTy())
15037 return false;
15038
15039 // Try to match 'zext (trunc A to iB) to iY', which is used
15040 // for URem with constant power-of-2 second operands. Make sure the size of
15041 // the operand A matches the size of the whole expressions.
15042 if (const auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(Val: Expr))
15043 if (const auto *Trunc = dyn_cast<SCEVTruncateExpr>(Val: ZExt->getOperand(i: 0))) {
15044 LHS = Trunc->getOperand();
15045 // Bail out if the type of the LHS is larger than the type of the
15046 // expression for now.
15047 if (getTypeSizeInBits(Ty: LHS->getType()) >
15048 getTypeSizeInBits(Ty: Expr->getType()))
15049 return false;
15050 if (LHS->getType() != Expr->getType())
15051 LHS = getZeroExtendExpr(Op: LHS, Ty: Expr->getType());
15052 RHS = getConstant(Val: APInt(getTypeSizeInBits(Ty: Expr->getType()), 1)
15053 << getTypeSizeInBits(Ty: Trunc->getType()));
15054 return true;
15055 }
15056 const auto *Add = dyn_cast<SCEVAddExpr>(Val: Expr);
15057 if (Add == nullptr || Add->getNumOperands() != 2)
15058 return false;
15059
15060 const SCEV *A = Add->getOperand(i: 1);
15061 const auto *Mul = dyn_cast<SCEVMulExpr>(Val: Add->getOperand(i: 0));
15062
15063 if (Mul == nullptr)
15064 return false;
15065
15066 const auto MatchURemWithDivisor = [&](const SCEV *B) {
15067 // (SomeExpr + (-(SomeExpr / B) * B)).
15068 if (Expr == getURemExpr(LHS: A, RHS: B)) {
15069 LHS = A;
15070 RHS = B;
15071 return true;
15072 }
15073 return false;
15074 };
15075
15076 // (SomeExpr + (-1 * (SomeExpr / B) * B)).
15077 if (Mul->getNumOperands() == 3 && isa<SCEVConstant>(Val: Mul->getOperand(i: 0)))
15078 return MatchURemWithDivisor(Mul->getOperand(i: 1)) ||
15079 MatchURemWithDivisor(Mul->getOperand(i: 2));
15080
15081 // (SomeExpr + ((-SomeExpr / B) * B)) or (SomeExpr + ((SomeExpr / B) * -B)).
15082 if (Mul->getNumOperands() == 2)
15083 return MatchURemWithDivisor(Mul->getOperand(i: 1)) ||
15084 MatchURemWithDivisor(Mul->getOperand(i: 0)) ||
15085 MatchURemWithDivisor(getNegativeSCEV(V: Mul->getOperand(i: 1))) ||
15086 MatchURemWithDivisor(getNegativeSCEV(V: Mul->getOperand(i: 0)));
15087 return false;
15088}
15089
15090ScalarEvolution::LoopGuards
15091ScalarEvolution::LoopGuards::collect(const Loop *L, ScalarEvolution &SE) {
15092 LoopGuards Guards(SE);
15093 SmallVector<const SCEV *> ExprsToRewrite;
15094 auto CollectCondition = [&](ICmpInst::Predicate Predicate, const SCEV *LHS,
15095 const SCEV *RHS,
15096 DenseMap<const SCEV *, const SCEV *>
15097 &RewriteMap) {
15098 // WARNING: It is generally unsound to apply any wrap flags to the proposed
15099 // replacement SCEV which isn't directly implied by the structure of that
15100 // SCEV. In particular, using contextual facts to imply flags is *NOT*
15101 // legal. See the scoping rules for flags in the header to understand why.
15102
15103 // If LHS is a constant, apply information to the other expression.
15104 if (isa<SCEVConstant>(Val: LHS)) {
15105 std::swap(a&: LHS, b&: RHS);
15106 Predicate = CmpInst::getSwappedPredicate(pred: Predicate);
15107 }
15108
15109 // Check for a condition of the form (-C1 + X < C2). InstCombine will
15110 // create this form when combining two checks of the form (X u< C2 + C1) and
15111 // (X >=u C1).
15112 auto MatchRangeCheckIdiom = [&SE, Predicate, LHS, RHS, &RewriteMap,
15113 &ExprsToRewrite]() {
15114 auto *AddExpr = dyn_cast<SCEVAddExpr>(Val: LHS);
15115 if (!AddExpr || AddExpr->getNumOperands() != 2)
15116 return false;
15117
15118 auto *C1 = dyn_cast<SCEVConstant>(Val: AddExpr->getOperand(i: 0));
15119 auto *LHSUnknown = dyn_cast<SCEVUnknown>(Val: AddExpr->getOperand(i: 1));
15120 auto *C2 = dyn_cast<SCEVConstant>(Val: RHS);
15121 if (!C1 || !C2 || !LHSUnknown)
15122 return false;
15123
15124 auto ExactRegion =
15125 ConstantRange::makeExactICmpRegion(Pred: Predicate, Other: C2->getAPInt())
15126 .sub(Other: C1->getAPInt());
15127
15128 // Bail out, unless we have a non-wrapping, monotonic range.
15129 if (ExactRegion.isWrappedSet() || ExactRegion.isFullSet())
15130 return false;
15131 auto I = RewriteMap.find(Val: LHSUnknown);
15132 const SCEV *RewrittenLHS = I != RewriteMap.end() ? I->second : LHSUnknown;
15133 RewriteMap[LHSUnknown] = SE.getUMaxExpr(
15134 LHS: SE.getConstant(Val: ExactRegion.getUnsignedMin()),
15135 RHS: SE.getUMinExpr(LHS: RewrittenLHS,
15136 RHS: SE.getConstant(Val: ExactRegion.getUnsignedMax())));
15137 ExprsToRewrite.push_back(Elt: LHSUnknown);
15138 return true;
15139 };
15140 if (MatchRangeCheckIdiom())
15141 return;
15142
15143 // Return true if \p Expr is a MinMax SCEV expression with a non-negative
15144 // constant operand. If so, return in \p SCTy the SCEV type and in \p RHS
15145 // the non-constant operand and in \p LHS the constant operand.
15146 auto IsMinMaxSCEVWithNonNegativeConstant =
15147 [&](const SCEV *Expr, SCEVTypes &SCTy, const SCEV *&LHS,
15148 const SCEV *&RHS) {
15149 if (auto *MinMax = dyn_cast<SCEVMinMaxExpr>(Val: Expr)) {
15150 if (MinMax->getNumOperands() != 2)
15151 return false;
15152 if (auto *C = dyn_cast<SCEVConstant>(Val: MinMax->getOperand(i: 0))) {
15153 if (C->getAPInt().isNegative())
15154 return false;
15155 SCTy = MinMax->getSCEVType();
15156 LHS = MinMax->getOperand(i: 0);
15157 RHS = MinMax->getOperand(i: 1);
15158 return true;
15159 }
15160 }
15161 return false;
15162 };
15163
15164 // Checks whether Expr is a non-negative constant, and Divisor is a positive
15165 // constant, and returns their APInt in ExprVal and in DivisorVal.
15166 auto GetNonNegExprAndPosDivisor = [&](const SCEV *Expr, const SCEV *Divisor,
15167 APInt &ExprVal, APInt &DivisorVal) {
15168 auto *ConstExpr = dyn_cast<SCEVConstant>(Val: Expr);
15169 auto *ConstDivisor = dyn_cast<SCEVConstant>(Val: Divisor);
15170 if (!ConstExpr || !ConstDivisor)
15171 return false;
15172 ExprVal = ConstExpr->getAPInt();
15173 DivisorVal = ConstDivisor->getAPInt();
15174 return ExprVal.isNonNegative() && !DivisorVal.isNonPositive();
15175 };
15176
15177 // Return a new SCEV that modifies \p Expr to the closest number divides by
15178 // \p Divisor and greater or equal than Expr.
15179 // For now, only handle constant Expr and Divisor.
15180 auto GetNextSCEVDividesByDivisor = [&](const SCEV *Expr,
15181 const SCEV *Divisor) {
15182 APInt ExprVal;
15183 APInt DivisorVal;
15184 if (!GetNonNegExprAndPosDivisor(Expr, Divisor, ExprVal, DivisorVal))
15185 return Expr;
15186 APInt Rem = ExprVal.urem(RHS: DivisorVal);
15187 if (!Rem.isZero())
15188 // return the SCEV: Expr + Divisor - Expr % Divisor
15189 return SE.getConstant(Val: ExprVal + DivisorVal - Rem);
15190 return Expr;
15191 };
15192
15193 // Return a new SCEV that modifies \p Expr to the closest number divides by
15194 // \p Divisor and less or equal than Expr.
15195 // For now, only handle constant Expr and Divisor.
15196 auto GetPreviousSCEVDividesByDivisor = [&](const SCEV *Expr,
15197 const SCEV *Divisor) {
15198 APInt ExprVal;
15199 APInt DivisorVal;
15200 if (!GetNonNegExprAndPosDivisor(Expr, Divisor, ExprVal, DivisorVal))
15201 return Expr;
15202 APInt Rem = ExprVal.urem(RHS: DivisorVal);
15203 // return the SCEV: Expr - Expr % Divisor
15204 return SE.getConstant(Val: ExprVal - Rem);
15205 };
15206
15207 // Apply divisibilty by \p Divisor on MinMaxExpr with constant values,
15208 // recursively. This is done by aligning up/down the constant value to the
15209 // Divisor.
15210 std::function<const SCEV *(const SCEV *, const SCEV *)>
15211 ApplyDivisibiltyOnMinMaxExpr = [&](const SCEV *MinMaxExpr,
15212 const SCEV *Divisor) {
15213 const SCEV *MinMaxLHS = nullptr, *MinMaxRHS = nullptr;
15214 SCEVTypes SCTy;
15215 if (!IsMinMaxSCEVWithNonNegativeConstant(MinMaxExpr, SCTy, MinMaxLHS,
15216 MinMaxRHS))
15217 return MinMaxExpr;
15218 auto IsMin =
15219 isa<SCEVSMinExpr>(Val: MinMaxExpr) || isa<SCEVUMinExpr>(Val: MinMaxExpr);
15220 assert(SE.isKnownNonNegative(MinMaxLHS) &&
15221 "Expected non-negative operand!");
15222 auto *DivisibleExpr =
15223 IsMin ? GetPreviousSCEVDividesByDivisor(MinMaxLHS, Divisor)
15224 : GetNextSCEVDividesByDivisor(MinMaxLHS, Divisor);
15225 SmallVector<const SCEV *> Ops = {
15226 ApplyDivisibiltyOnMinMaxExpr(MinMaxRHS, Divisor), DivisibleExpr};
15227 return SE.getMinMaxExpr(Kind: SCTy, Ops);
15228 };
15229
15230 // If we have LHS == 0, check if LHS is computing a property of some unknown
15231 // SCEV %v which we can rewrite %v to express explicitly.
15232 const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Val: RHS);
15233 if (Predicate == CmpInst::ICMP_EQ && RHSC &&
15234 RHSC->getValue()->isNullValue()) {
15235 // If LHS is A % B, i.e. A % B == 0, rewrite A to (A /u B) * B to
15236 // explicitly express that.
15237 const SCEV *URemLHS = nullptr;
15238 const SCEV *URemRHS = nullptr;
15239 if (SE.matchURem(Expr: LHS, LHS&: URemLHS, RHS&: URemRHS)) {
15240 if (const SCEVUnknown *LHSUnknown = dyn_cast<SCEVUnknown>(Val: URemLHS)) {
15241 auto I = RewriteMap.find(Val: LHSUnknown);
15242 const SCEV *RewrittenLHS =
15243 I != RewriteMap.end() ? I->second : LHSUnknown;
15244 RewrittenLHS = ApplyDivisibiltyOnMinMaxExpr(RewrittenLHS, URemRHS);
15245 const auto *Multiple =
15246 SE.getMulExpr(LHS: SE.getUDivExpr(LHS: RewrittenLHS, RHS: URemRHS), RHS: URemRHS);
15247 RewriteMap[LHSUnknown] = Multiple;
15248 ExprsToRewrite.push_back(Elt: LHSUnknown);
15249 return;
15250 }
15251 }
15252 }
15253
15254 // Do not apply information for constants or if RHS contains an AddRec.
15255 if (isa<SCEVConstant>(Val: LHS) || SE.containsAddRecurrence(S: RHS))
15256 return;
15257
15258 // If RHS is SCEVUnknown, make sure the information is applied to it.
15259 if (!isa<SCEVUnknown>(Val: LHS) && isa<SCEVUnknown>(Val: RHS)) {
15260 std::swap(a&: LHS, b&: RHS);
15261 Predicate = CmpInst::getSwappedPredicate(pred: Predicate);
15262 }
15263
15264 // Puts rewrite rule \p From -> \p To into the rewrite map. Also if \p From
15265 // and \p FromRewritten are the same (i.e. there has been no rewrite
15266 // registered for \p From), then puts this value in the list of rewritten
15267 // expressions.
15268 auto AddRewrite = [&](const SCEV *From, const SCEV *FromRewritten,
15269 const SCEV *To) {
15270 if (From == FromRewritten)
15271 ExprsToRewrite.push_back(Elt: From);
15272 RewriteMap[From] = To;
15273 };
15274
15275 // Checks whether \p S has already been rewritten. In that case returns the
15276 // existing rewrite because we want to chain further rewrites onto the
15277 // already rewritten value. Otherwise returns \p S.
15278 auto GetMaybeRewritten = [&](const SCEV *S) {
15279 auto I = RewriteMap.find(Val: S);
15280 return I != RewriteMap.end() ? I->second : S;
15281 };
15282
15283 // Check for the SCEV expression (A /u B) * B while B is a constant, inside
15284 // \p Expr. The check is done recuresively on \p Expr, which is assumed to
15285 // be a composition of Min/Max SCEVs. Return whether the SCEV expression (A
15286 // /u B) * B was found, and return the divisor B in \p DividesBy. For
15287 // example, if Expr = umin (umax ((A /u 8) * 8, 16), 64), return true since
15288 // (A /u 8) * 8 matched the pattern, and return the constant SCEV 8 in \p
15289 // DividesBy.
15290 std::function<bool(const SCEV *, const SCEV *&)> HasDivisibiltyInfo =
15291 [&](const SCEV *Expr, const SCEV *&DividesBy) {
15292 if (auto *Mul = dyn_cast<SCEVMulExpr>(Val: Expr)) {
15293 if (Mul->getNumOperands() != 2)
15294 return false;
15295 auto *MulLHS = Mul->getOperand(i: 0);
15296 auto *MulRHS = Mul->getOperand(i: 1);
15297 if (isa<SCEVConstant>(Val: MulLHS))
15298 std::swap(a&: MulLHS, b&: MulRHS);
15299 if (auto *Div = dyn_cast<SCEVUDivExpr>(Val: MulLHS))
15300 if (Div->getOperand(i: 1) == MulRHS) {
15301 DividesBy = MulRHS;
15302 return true;
15303 }
15304 }
15305 if (auto *MinMax = dyn_cast<SCEVMinMaxExpr>(Val: Expr))
15306 return HasDivisibiltyInfo(MinMax->getOperand(i: 0), DividesBy) ||
15307 HasDivisibiltyInfo(MinMax->getOperand(i: 1), DividesBy);
15308 return false;
15309 };
15310
15311 // Return true if Expr known to divide by \p DividesBy.
15312 std::function<bool(const SCEV *, const SCEV *&)> IsKnownToDivideBy =
15313 [&](const SCEV *Expr, const SCEV *DividesBy) {
15314 if (SE.getURemExpr(LHS: Expr, RHS: DividesBy)->isZero())
15315 return true;
15316 if (auto *MinMax = dyn_cast<SCEVMinMaxExpr>(Val: Expr))
15317 return IsKnownToDivideBy(MinMax->getOperand(i: 0), DividesBy) &&
15318 IsKnownToDivideBy(MinMax->getOperand(i: 1), DividesBy);
15319 return false;
15320 };
15321
15322 const SCEV *RewrittenLHS = GetMaybeRewritten(LHS);
15323 const SCEV *DividesBy = nullptr;
15324 if (HasDivisibiltyInfo(RewrittenLHS, DividesBy))
15325 // Check that the whole expression is divided by DividesBy
15326 DividesBy =
15327 IsKnownToDivideBy(RewrittenLHS, DividesBy) ? DividesBy : nullptr;
15328
15329 // Collect rewrites for LHS and its transitive operands based on the
15330 // condition.
15331 // For min/max expressions, also apply the guard to its operands:
15332 // 'min(a, b) >= c' -> '(a >= c) and (b >= c)',
15333 // 'min(a, b) > c' -> '(a > c) and (b > c)',
15334 // 'max(a, b) <= c' -> '(a <= c) and (b <= c)',
15335 // 'max(a, b) < c' -> '(a < c) and (b < c)'.
15336
15337 // We cannot express strict predicates in SCEV, so instead we replace them
15338 // with non-strict ones against plus or minus one of RHS depending on the
15339 // predicate.
15340 const SCEV *One = SE.getOne(Ty: RHS->getType());
15341 switch (Predicate) {
15342 case CmpInst::ICMP_ULT:
15343 if (RHS->getType()->isPointerTy())
15344 return;
15345 RHS = SE.getUMaxExpr(LHS: RHS, RHS: One);
15346 [[fallthrough]];
15347 case CmpInst::ICMP_SLT: {
15348 RHS = SE.getMinusSCEV(LHS: RHS, RHS: One);
15349 RHS = DividesBy ? GetPreviousSCEVDividesByDivisor(RHS, DividesBy) : RHS;
15350 break;
15351 }
15352 case CmpInst::ICMP_UGT:
15353 case CmpInst::ICMP_SGT:
15354 RHS = SE.getAddExpr(LHS: RHS, RHS: One);
15355 RHS = DividesBy ? GetNextSCEVDividesByDivisor(RHS, DividesBy) : RHS;
15356 break;
15357 case CmpInst::ICMP_ULE:
15358 case CmpInst::ICMP_SLE:
15359 RHS = DividesBy ? GetPreviousSCEVDividesByDivisor(RHS, DividesBy) : RHS;
15360 break;
15361 case CmpInst::ICMP_UGE:
15362 case CmpInst::ICMP_SGE:
15363 RHS = DividesBy ? GetNextSCEVDividesByDivisor(RHS, DividesBy) : RHS;
15364 break;
15365 default:
15366 break;
15367 }
15368
15369 SmallVector<const SCEV *, 16> Worklist(1, LHS);
15370 SmallPtrSet<const SCEV *, 16> Visited;
15371
15372 auto EnqueueOperands = [&Worklist](const SCEVNAryExpr *S) {
15373 append_range(C&: Worklist, R: S->operands());
15374 };
15375
15376 while (!Worklist.empty()) {
15377 const SCEV *From = Worklist.pop_back_val();
15378 if (isa<SCEVConstant>(Val: From))
15379 continue;
15380 if (!Visited.insert(Ptr: From).second)
15381 continue;
15382 const SCEV *FromRewritten = GetMaybeRewritten(From);
15383 const SCEV *To = nullptr;
15384
15385 switch (Predicate) {
15386 case CmpInst::ICMP_ULT:
15387 case CmpInst::ICMP_ULE:
15388 To = SE.getUMinExpr(LHS: FromRewritten, RHS);
15389 if (auto *UMax = dyn_cast<SCEVUMaxExpr>(Val: FromRewritten))
15390 EnqueueOperands(UMax);
15391 break;
15392 case CmpInst::ICMP_SLT:
15393 case CmpInst::ICMP_SLE:
15394 To = SE.getSMinExpr(LHS: FromRewritten, RHS);
15395 if (auto *SMax = dyn_cast<SCEVSMaxExpr>(Val: FromRewritten))
15396 EnqueueOperands(SMax);
15397 break;
15398 case CmpInst::ICMP_UGT:
15399 case CmpInst::ICMP_UGE:
15400 To = SE.getUMaxExpr(LHS: FromRewritten, RHS);
15401 if (auto *UMin = dyn_cast<SCEVUMinExpr>(Val: FromRewritten))
15402 EnqueueOperands(UMin);
15403 break;
15404 case CmpInst::ICMP_SGT:
15405 case CmpInst::ICMP_SGE:
15406 To = SE.getSMaxExpr(LHS: FromRewritten, RHS);
15407 if (auto *SMin = dyn_cast<SCEVSMinExpr>(Val: FromRewritten))
15408 EnqueueOperands(SMin);
15409 break;
15410 case CmpInst::ICMP_EQ:
15411 if (isa<SCEVConstant>(Val: RHS))
15412 To = RHS;
15413 break;
15414 case CmpInst::ICMP_NE:
15415 if (isa<SCEVConstant>(Val: RHS) &&
15416 cast<SCEVConstant>(Val: RHS)->getValue()->isNullValue()) {
15417 const SCEV *OneAlignedUp =
15418 DividesBy ? GetNextSCEVDividesByDivisor(One, DividesBy) : One;
15419 To = SE.getUMaxExpr(LHS: FromRewritten, RHS: OneAlignedUp);
15420 }
15421 break;
15422 default:
15423 break;
15424 }
15425
15426 if (To)
15427 AddRewrite(From, FromRewritten, To);
15428 }
15429 };
15430
15431 BasicBlock *Header = L->getHeader();
15432 SmallVector<PointerIntPair<Value *, 1, bool>> Terms;
15433 // First, collect information from assumptions dominating the loop.
15434 for (auto &AssumeVH : SE.AC.assumptions()) {
15435 if (!AssumeVH)
15436 continue;
15437 auto *AssumeI = cast<CallInst>(Val&: AssumeVH);
15438 if (!SE.DT.dominates(Def: AssumeI, BB: Header))
15439 continue;
15440 Terms.emplace_back(Args: AssumeI->getOperand(i_nocapture: 0), Args: true);
15441 }
15442
15443 // Second, collect information from llvm.experimental.guards dominating the loop.
15444 auto *GuardDecl = SE.F.getParent()->getFunction(
15445 Name: Intrinsic::getName(id: Intrinsic::experimental_guard));
15446 if (GuardDecl)
15447 for (const auto *GU : GuardDecl->users())
15448 if (const auto *Guard = dyn_cast<IntrinsicInst>(Val: GU))
15449 if (Guard->getFunction() == Header->getParent() &&
15450 SE.DT.dominates(Def: Guard, BB: Header))
15451 Terms.emplace_back(Args: Guard->getArgOperand(i: 0), Args: true);
15452
15453 // Third, collect conditions from dominating branches. Starting at the loop
15454 // predecessor, climb up the predecessor chain, as long as there are
15455 // predecessors that can be found that have unique successors leading to the
15456 // original header.
15457 // TODO: share this logic with isLoopEntryGuardedByCond.
15458 for (std::pair<const BasicBlock *, const BasicBlock *> Pair(
15459 L->getLoopPredecessor(), Header);
15460 Pair.first;
15461 Pair = SE.getPredecessorWithUniqueSuccessorForBB(BB: Pair.first)) {
15462
15463 const BranchInst *LoopEntryPredicate =
15464 dyn_cast<BranchInst>(Val: Pair.first->getTerminator());
15465 if (!LoopEntryPredicate || LoopEntryPredicate->isUnconditional())
15466 continue;
15467
15468 Terms.emplace_back(Args: LoopEntryPredicate->getCondition(),
15469 Args: LoopEntryPredicate->getSuccessor(i: 0) == Pair.second);
15470 }
15471
15472 // Now apply the information from the collected conditions to
15473 // Guards.RewriteMap. Conditions are processed in reverse order, so the
15474 // earliest conditions is processed first. This ensures the SCEVs with the
15475 // shortest dependency chains are constructed first.
15476 for (auto [Term, EnterIfTrue] : reverse(C&: Terms)) {
15477 SmallVector<Value *, 8> Worklist;
15478 SmallPtrSet<Value *, 8> Visited;
15479 Worklist.push_back(Elt: Term);
15480 while (!Worklist.empty()) {
15481 Value *Cond = Worklist.pop_back_val();
15482 if (!Visited.insert(Ptr: Cond).second)
15483 continue;
15484
15485 if (auto *Cmp = dyn_cast<ICmpInst>(Val: Cond)) {
15486 auto Predicate =
15487 EnterIfTrue ? Cmp->getPredicate() : Cmp->getInversePredicate();
15488 const auto *LHS = SE.getSCEV(V: Cmp->getOperand(i_nocapture: 0));
15489 const auto *RHS = SE.getSCEV(V: Cmp->getOperand(i_nocapture: 1));
15490 CollectCondition(Predicate, LHS, RHS, Guards.RewriteMap);
15491 continue;
15492 }
15493
15494 Value *L, *R;
15495 if (EnterIfTrue ? match(V: Cond, P: m_LogicalAnd(L: m_Value(V&: L), R: m_Value(V&: R)))
15496 : match(V: Cond, P: m_LogicalOr(L: m_Value(V&: L), R: m_Value(V&: R)))) {
15497 Worklist.push_back(Elt: L);
15498 Worklist.push_back(Elt: R);
15499 }
15500 }
15501 }
15502
15503 // Let the rewriter preserve NUW/NSW flags if the unsigned/signed ranges of
15504 // the replacement expressions are contained in the ranges of the replaced
15505 // expressions.
15506 Guards.PreserveNUW = true;
15507 Guards.PreserveNSW = true;
15508 for (const SCEV *Expr : ExprsToRewrite) {
15509 const SCEV *RewriteTo = Guards.RewriteMap[Expr];
15510 Guards.PreserveNUW &=
15511 SE.getUnsignedRange(S: Expr).contains(CR: SE.getUnsignedRange(S: RewriteTo));
15512 Guards.PreserveNSW &=
15513 SE.getSignedRange(S: Expr).contains(CR: SE.getSignedRange(S: RewriteTo));
15514 }
15515
15516 // Now that all rewrite information is collect, rewrite the collected
15517 // expressions with the information in the map. This applies information to
15518 // sub-expressions.
15519 if (ExprsToRewrite.size() > 1) {
15520 for (const SCEV *Expr : ExprsToRewrite) {
15521 const SCEV *RewriteTo = Guards.RewriteMap[Expr];
15522 Guards.RewriteMap.erase(Val: Expr);
15523 Guards.RewriteMap.insert(KV: {Expr, Guards.rewrite(Expr: RewriteTo)});
15524 }
15525 }
15526 return Guards;
15527}
15528
15529const SCEV *ScalarEvolution::LoopGuards::rewrite(const SCEV *Expr) const {
15530 /// A rewriter to replace SCEV expressions in Map with the corresponding entry
15531 /// in the map. It skips AddRecExpr because we cannot guarantee that the
15532 /// replacement is loop invariant in the loop of the AddRec.
15533 class SCEVLoopGuardRewriter
15534 : public SCEVRewriteVisitor<SCEVLoopGuardRewriter> {
15535 const DenseMap<const SCEV *, const SCEV *> &Map;
15536
15537 SCEV::NoWrapFlags FlagMask = SCEV::FlagAnyWrap;
15538
15539 public:
15540 SCEVLoopGuardRewriter(ScalarEvolution &SE,
15541 const ScalarEvolution::LoopGuards &Guards)
15542 : SCEVRewriteVisitor(SE), Map(Guards.RewriteMap) {
15543 if (Guards.PreserveNUW)
15544 FlagMask = ScalarEvolution::setFlags(Flags: FlagMask, OnFlags: SCEV::FlagNUW);
15545 if (Guards.PreserveNSW)
15546 FlagMask = ScalarEvolution::setFlags(Flags: FlagMask, OnFlags: SCEV::FlagNSW);
15547 }
15548
15549 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; }
15550
15551 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
15552 auto I = Map.find(Val: Expr);
15553 if (I == Map.end())
15554 return Expr;
15555 return I->second;
15556 }
15557
15558 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
15559 auto I = Map.find(Val: Expr);
15560 if (I == Map.end()) {
15561 // If we didn't find the extact ZExt expr in the map, check if there's
15562 // an entry for a smaller ZExt we can use instead.
15563 Type *Ty = Expr->getType();
15564 const SCEV *Op = Expr->getOperand(i: 0);
15565 unsigned Bitwidth = Ty->getScalarSizeInBits() / 2;
15566 while (Bitwidth % 8 == 0 && Bitwidth >= 8 &&
15567 Bitwidth > Op->getType()->getScalarSizeInBits()) {
15568 Type *NarrowTy = IntegerType::get(C&: SE.getContext(), NumBits: Bitwidth);
15569 auto *NarrowExt = SE.getZeroExtendExpr(Op, Ty: NarrowTy);
15570 auto I = Map.find(Val: NarrowExt);
15571 if (I != Map.end())
15572 return SE.getZeroExtendExpr(Op: I->second, Ty);
15573 Bitwidth = Bitwidth / 2;
15574 }
15575
15576 return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitZeroExtendExpr(
15577 Expr);
15578 }
15579 return I->second;
15580 }
15581
15582 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
15583 auto I = Map.find(Val: Expr);
15584 if (I == Map.end())
15585 return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitSignExtendExpr(
15586 Expr);
15587 return I->second;
15588 }
15589
15590 const SCEV *visitUMinExpr(const SCEVUMinExpr *Expr) {
15591 auto I = Map.find(Val: Expr);
15592 if (I == Map.end())
15593 return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitUMinExpr(Expr);
15594 return I->second;
15595 }
15596
15597 const SCEV *visitSMinExpr(const SCEVSMinExpr *Expr) {
15598 auto I = Map.find(Val: Expr);
15599 if (I == Map.end())
15600 return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitSMinExpr(Expr);
15601 return I->second;
15602 }
15603
15604 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
15605 SmallVector<const SCEV *, 2> Operands;
15606 bool Changed = false;
15607 for (const auto *Op : Expr->operands()) {
15608 Operands.push_back(
15609 Elt: SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visit(S: Op));
15610 Changed |= Op != Operands.back();
15611 }
15612 // We are only replacing operands with equivalent values, so transfer the
15613 // flags from the original expression.
15614 return !Changed ? Expr
15615 : SE.getAddExpr(Ops&: Operands,
15616 OrigFlags: ScalarEvolution::maskFlags(
15617 Flags: Expr->getNoWrapFlags(), Mask: FlagMask));
15618 }
15619
15620 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
15621 SmallVector<const SCEV *, 2> Operands;
15622 bool Changed = false;
15623 for (const auto *Op : Expr->operands()) {
15624 Operands.push_back(
15625 Elt: SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visit(S: Op));
15626 Changed |= Op != Operands.back();
15627 }
15628 // We are only replacing operands with equivalent values, so transfer the
15629 // flags from the original expression.
15630 return !Changed ? Expr
15631 : SE.getMulExpr(Ops&: Operands,
15632 OrigFlags: ScalarEvolution::maskFlags(
15633 Flags: Expr->getNoWrapFlags(), Mask: FlagMask));
15634 }
15635 };
15636
15637 if (RewriteMap.empty())
15638 return Expr;
15639
15640 SCEVLoopGuardRewriter Rewriter(SE, *this);
15641 return Rewriter.visit(S: Expr);
15642}
15643
15644const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr, const Loop *L) {
15645 return applyLoopGuards(Expr, Guards: LoopGuards::collect(L, SE&: *this));
15646}
15647
15648const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr,
15649 const LoopGuards &Guards) {
15650 return Guards.rewrite(Expr);
15651}
15652