Bug Summary

File:lib/Analysis/ScalarEvolution.cpp
Warning:line 8112, column 23
Value stored to 'MultipleInitValues' is never read

Annotated Source Code

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clang -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name ScalarEvolution.cpp -analyzer-store=region -analyzer-opt-analyze-nested-blocks -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=cplusplus -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -mthread-model posix -fmath-errno -masm-verbose -mconstructor-aliases -munwind-tables -fuse-init-array -target-cpu x86-64 -dwarf-column-info -debugger-tuning=gdb -momit-leaf-frame-pointer -ffunction-sections -fdata-sections -resource-dir /usr/lib/llvm-8/lib/clang/8.0.0 -D _DEBUG -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I /build/llvm-toolchain-snapshot-8~svn350071/build-llvm/lib/Analysis -I /build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis -I /build/llvm-toolchain-snapshot-8~svn350071/build-llvm/include -I /build/llvm-toolchain-snapshot-8~svn350071/include -U NDEBUG -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/x86_64-linux-gnu/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/x86_64-linux-gnu/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/c++/6.3.0/backward -internal-isystem /usr/include/clang/8.0.0/include/ -internal-isystem /usr/local/include -internal-isystem /usr/lib/llvm-8/lib/clang/8.0.0/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -O2 -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-maybe-uninitialized -Wno-comment -std=c++11 -fdeprecated-macro -fdebug-compilation-dir /build/llvm-toolchain-snapshot-8~svn350071/build-llvm/lib/Analysis -fdebug-prefix-map=/build/llvm-toolchain-snapshot-8~svn350071=. -ferror-limit 19 -fmessage-length 0 -fvisibility-inlines-hidden -stack-protector 2 -fobjc-runtime=gcc -fdiagnostics-show-option -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -o /tmp/scan-build-2018-12-27-042839-1215-1 -x c++ /build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp -faddrsig
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
2//
3// The LLVM Compiler Infrastructure
4//
5// This file is distributed under the University of Illinois Open Source
6// License. See LICENSE.TXT for details.
7//
8//===----------------------------------------------------------------------===//
9//
10// This file contains the implementation of the scalar evolution analysis
11// engine, which is used primarily to analyze expressions involving induction
12// variables in loops.
13//
14// There are several aspects to this library. First is the representation of
15// scalar expressions, which are represented as subclasses of the SCEV class.
16// These classes are used to represent certain types of subexpressions that we
17// can handle. We only create one SCEV of a particular shape, so
18// pointer-comparisons for equality are legal.
19//
20// One important aspect of the SCEV objects is that they are never cyclic, even
21// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22// the PHI node is one of the idioms that we can represent (e.g., a polynomial
23// recurrence) then we represent it directly as a recurrence node, otherwise we
24// represent it as a SCEVUnknown node.
25//
26// In addition to being able to represent expressions of various types, we also
27// have folders that are used to build the *canonical* representation for a
28// particular expression. These folders are capable of using a variety of
29// rewrite rules to simplify the expressions.
30//
31// Once the folders are defined, we can implement the more interesting
32// higher-level code, such as the code that recognizes PHI nodes of various
33// types, computes the execution count of a loop, etc.
34//
35// TODO: We should use these routines and value representations to implement
36// dependence analysis!
37//
38//===----------------------------------------------------------------------===//
39//
40// There are several good references for the techniques used in this analysis.
41//
42// Chains of recurrences -- a method to expedite the evaluation
43// of closed-form functions
44// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
45//
46// On computational properties of chains of recurrences
47// Eugene V. Zima
48//
49// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50// Robert A. van Engelen
51//
52// Efficient Symbolic Analysis for Optimizing Compilers
53// Robert A. van Engelen
54//
55// Using the chains of recurrences algebra for data dependence testing and
56// induction variable substitution
57// MS Thesis, Johnie Birch
58//
59//===----------------------------------------------------------------------===//
60
61#include "llvm/Analysis/ScalarEvolution.h"
62#include "llvm/ADT/APInt.h"
63#include "llvm/ADT/ArrayRef.h"
64#include "llvm/ADT/DenseMap.h"
65#include "llvm/ADT/DepthFirstIterator.h"
66#include "llvm/ADT/EquivalenceClasses.h"
67#include "llvm/ADT/FoldingSet.h"
68#include "llvm/ADT/None.h"
69#include "llvm/ADT/Optional.h"
70#include "llvm/ADT/STLExtras.h"
71#include "llvm/ADT/ScopeExit.h"
72#include "llvm/ADT/Sequence.h"
73#include "llvm/ADT/SetVector.h"
74#include "llvm/ADT/SmallPtrSet.h"
75#include "llvm/ADT/SmallSet.h"
76#include "llvm/ADT/SmallVector.h"
77#include "llvm/ADT/Statistic.h"
78#include "llvm/ADT/StringRef.h"
79#include "llvm/Analysis/AssumptionCache.h"
80#include "llvm/Analysis/ConstantFolding.h"
81#include "llvm/Analysis/InstructionSimplify.h"
82#include "llvm/Analysis/LoopInfo.h"
83#include "llvm/Analysis/ScalarEvolutionExpressions.h"
84#include "llvm/Analysis/TargetLibraryInfo.h"
85#include "llvm/Analysis/ValueTracking.h"
86#include "llvm/Config/llvm-config.h"
87#include "llvm/IR/Argument.h"
88#include "llvm/IR/BasicBlock.h"
89#include "llvm/IR/CFG.h"
90#include "llvm/IR/CallSite.h"
91#include "llvm/IR/Constant.h"
92#include "llvm/IR/ConstantRange.h"
93#include "llvm/IR/Constants.h"
94#include "llvm/IR/DataLayout.h"
95#include "llvm/IR/DerivedTypes.h"
96#include "llvm/IR/Dominators.h"
97#include "llvm/IR/Function.h"
98#include "llvm/IR/GlobalAlias.h"
99#include "llvm/IR/GlobalValue.h"
100#include "llvm/IR/GlobalVariable.h"
101#include "llvm/IR/InstIterator.h"
102#include "llvm/IR/InstrTypes.h"
103#include "llvm/IR/Instruction.h"
104#include "llvm/IR/Instructions.h"
105#include "llvm/IR/IntrinsicInst.h"
106#include "llvm/IR/Intrinsics.h"
107#include "llvm/IR/LLVMContext.h"
108#include "llvm/IR/Metadata.h"
109#include "llvm/IR/Operator.h"
110#include "llvm/IR/PatternMatch.h"
111#include "llvm/IR/Type.h"
112#include "llvm/IR/Use.h"
113#include "llvm/IR/User.h"
114#include "llvm/IR/Value.h"
115#include "llvm/IR/Verifier.h"
116#include "llvm/Pass.h"
117#include "llvm/Support/Casting.h"
118#include "llvm/Support/CommandLine.h"
119#include "llvm/Support/Compiler.h"
120#include "llvm/Support/Debug.h"
121#include "llvm/Support/ErrorHandling.h"
122#include "llvm/Support/KnownBits.h"
123#include "llvm/Support/SaveAndRestore.h"
124#include "llvm/Support/raw_ostream.h"
125#include <algorithm>
126#include <cassert>
127#include <climits>
128#include <cstddef>
129#include <cstdint>
130#include <cstdlib>
131#include <map>
132#include <memory>
133#include <tuple>
134#include <utility>
135#include <vector>
136
137using namespace llvm;
138
139#define DEBUG_TYPE"scalar-evolution" "scalar-evolution"
140
141STATISTIC(NumArrayLenItCounts,static llvm::Statistic NumArrayLenItCounts = {"scalar-evolution"
, "NumArrayLenItCounts", "Number of trip counts computed with array length"
, {0}, {false}}
142 "Number of trip counts computed with array length")static llvm::Statistic NumArrayLenItCounts = {"scalar-evolution"
, "NumArrayLenItCounts", "Number of trip counts computed with array length"
, {0}, {false}}
;
143STATISTIC(NumTripCountsComputed,static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
, {0}, {false}}
144 "Number of loops with predictable loop counts")static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
, {0}, {false}}
;
145STATISTIC(NumTripCountsNotComputed,static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
, {0}, {false}}
146 "Number of loops without predictable loop counts")static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
, {0}, {false}}
;
147STATISTIC(NumBruteForceTripCountsComputed,static llvm::Statistic NumBruteForceTripCountsComputed = {"scalar-evolution"
, "NumBruteForceTripCountsComputed", "Number of loops with trip counts computed by force"
, {0}, {false}}
148 "Number of loops with trip counts computed by force")static llvm::Statistic NumBruteForceTripCountsComputed = {"scalar-evolution"
, "NumBruteForceTripCountsComputed", "Number of loops with trip counts computed by force"
, {0}, {false}}
;
149
150static cl::opt<unsigned>
151MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
152 cl::desc("Maximum number of iterations SCEV will "
153 "symbolically execute a constant "
154 "derived loop"),
155 cl::init(100));
156
157// FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
158static cl::opt<bool> VerifySCEV(
159 "verify-scev", cl::Hidden,
160 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
161static cl::opt<bool>
162 VerifySCEVMap("verify-scev-maps", cl::Hidden,
163 cl::desc("Verify no dangling value in ScalarEvolution's "
164 "ExprValueMap (slow)"));
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(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(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(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(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(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(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(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(32));
204
205static cl::opt<unsigned>
206 MaxExtDepth("scalar-evolution-max-ext-depth", cl::Hidden,
207 cl::desc("Maximum depth of recursive SExt/ZExt"),
208 cl::init(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(8));
214
215//===----------------------------------------------------------------------===//
216// SCEV class definitions
217//===----------------------------------------------------------------------===//
218
219//===----------------------------------------------------------------------===//
220// Implementation of the SCEV class.
221//
222
223#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
224LLVM_DUMP_METHOD__attribute__((noinline)) __attribute__((__used__)) void SCEV::dump() const {
225 print(dbgs());
226 dbgs() << '\n';
227}
228#endif
229
230void SCEV::print(raw_ostream &OS) const {
231 switch (static_cast<SCEVTypes>(getSCEVType())) {
232 case scConstant:
233 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
234 return;
235 case scTruncate: {
236 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
237 const SCEV *Op = Trunc->getOperand();
238 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
239 << *Trunc->getType() << ")";
240 return;
241 }
242 case scZeroExtend: {
243 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
244 const SCEV *Op = ZExt->getOperand();
245 OS << "(zext " << *Op->getType() << " " << *Op << " to "
246 << *ZExt->getType() << ")";
247 return;
248 }
249 case scSignExtend: {
250 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
251 const SCEV *Op = SExt->getOperand();
252 OS << "(sext " << *Op->getType() << " " << *Op << " to "
253 << *SExt->getType() << ")";
254 return;
255 }
256 case scAddRecExpr: {
257 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
258 OS << "{" << *AR->getOperand(0);
259 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
260 OS << ",+," << *AR->getOperand(i);
261 OS << "}<";
262 if (AR->hasNoUnsignedWrap())
263 OS << "nuw><";
264 if (AR->hasNoSignedWrap())
265 OS << "nsw><";
266 if (AR->hasNoSelfWrap() &&
267 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
268 OS << "nw><";
269 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
270 OS << ">";
271 return;
272 }
273 case scAddExpr:
274 case scMulExpr:
275 case scUMaxExpr:
276 case scSMaxExpr: {
277 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
278 const char *OpStr = nullptr;
279 switch (NAry->getSCEVType()) {
280 case scAddExpr: OpStr = " + "; break;
281 case scMulExpr: OpStr = " * "; break;
282 case scUMaxExpr: OpStr = " umax "; break;
283 case scSMaxExpr: OpStr = " smax "; break;
284 }
285 OS << "(";
286 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
287 I != E; ++I) {
288 OS << **I;
289 if (std::next(I) != E)
290 OS << OpStr;
291 }
292 OS << ")";
293 switch (NAry->getSCEVType()) {
294 case scAddExpr:
295 case scMulExpr:
296 if (NAry->hasNoUnsignedWrap())
297 OS << "<nuw>";
298 if (NAry->hasNoSignedWrap())
299 OS << "<nsw>";
300 }
301 return;
302 }
303 case scUDivExpr: {
304 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
305 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
306 return;
307 }
308 case scUnknown: {
309 const SCEVUnknown *U = cast<SCEVUnknown>(this);
310 Type *AllocTy;
311 if (U->isSizeOf(AllocTy)) {
312 OS << "sizeof(" << *AllocTy << ")";
313 return;
314 }
315 if (U->isAlignOf(AllocTy)) {
316 OS << "alignof(" << *AllocTy << ")";
317 return;
318 }
319
320 Type *CTy;
321 Constant *FieldNo;
322 if (U->isOffsetOf(CTy, FieldNo)) {
323 OS << "offsetof(" << *CTy << ", ";
324 FieldNo->printAsOperand(OS, false);
325 OS << ")";
326 return;
327 }
328
329 // Otherwise just print it normally.
330 U->getValue()->printAsOperand(OS, false);
331 return;
332 }
333 case scCouldNotCompute:
334 OS << "***COULDNOTCOMPUTE***";
335 return;
336 }
337 llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 337)
;
338}
339
340Type *SCEV::getType() const {
341 switch (static_cast<SCEVTypes>(getSCEVType())) {
342 case scConstant:
343 return cast<SCEVConstant>(this)->getType();
344 case scTruncate:
345 case scZeroExtend:
346 case scSignExtend:
347 return cast<SCEVCastExpr>(this)->getType();
348 case scAddRecExpr:
349 case scMulExpr:
350 case scUMaxExpr:
351 case scSMaxExpr:
352 return cast<SCEVNAryExpr>(this)->getType();
353 case scAddExpr:
354 return cast<SCEVAddExpr>(this)->getType();
355 case scUDivExpr:
356 return cast<SCEVUDivExpr>(this)->getType();
357 case scUnknown:
358 return cast<SCEVUnknown>(this)->getType();
359 case scCouldNotCompute:
360 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 360)
;
361 }
362 llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 362)
;
363}
364
365bool SCEV::isZero() const {
366 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
367 return SC->getValue()->isZero();
368 return false;
369}
370
371bool SCEV::isOne() const {
372 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
373 return SC->getValue()->isOne();
374 return false;
375}
376
377bool SCEV::isAllOnesValue() const {
378 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
379 return SC->getValue()->isMinusOne();
380 return false;
381}
382
383bool SCEV::isNonConstantNegative() const {
384 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
385 if (!Mul) return false;
386
387 // If there is a constant factor, it will be first.
388 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
389 if (!SC) return false;
390
391 // Return true if the value is negative, this matches things like (-42 * V).
392 return SC->getAPInt().isNegative();
393}
394
395SCEVCouldNotCompute::SCEVCouldNotCompute() :
396 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
397
398bool SCEVCouldNotCompute::classof(const SCEV *S) {
399 return S->getSCEVType() == scCouldNotCompute;
400}
401
402const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
403 FoldingSetNodeID ID;
404 ID.AddInteger(scConstant);
405 ID.AddPointer(V);
406 void *IP = nullptr;
407 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
408 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
409 UniqueSCEVs.InsertNode(S, IP);
410 return S;
411}
412
413const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
414 return getConstant(ConstantInt::get(getContext(), Val));
415}
416
417const SCEV *
418ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
419 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
420 return getConstant(ConstantInt::get(ITy, V, isSigned));
421}
422
423SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
424 unsigned SCEVTy, const SCEV *op, Type *ty)
425 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
426
427SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
428 const SCEV *op, Type *ty)
429 : SCEVCastExpr(ID, scTruncate, op, ty) {
430 assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy
() && "Cannot truncate non-integer value!") ? static_cast
<void> (0) : __assert_fail ("Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate non-integer value!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 431, __PRETTY_FUNCTION__))
431 "Cannot truncate non-integer value!")((Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy
() && "Cannot truncate non-integer value!") ? static_cast
<void> (0) : __assert_fail ("Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate non-integer value!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 431, __PRETTY_FUNCTION__))
;
432}
433
434SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
435 const SCEV *op, Type *ty)
436 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
437 assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy
() && "Cannot zero extend non-integer value!") ? static_cast
<void> (0) : __assert_fail ("Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot zero extend non-integer value!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 438, __PRETTY_FUNCTION__))
438 "Cannot zero extend non-integer value!")((Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy
() && "Cannot zero extend non-integer value!") ? static_cast
<void> (0) : __assert_fail ("Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot zero extend non-integer value!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 438, __PRETTY_FUNCTION__))
;
439}
440
441SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
442 const SCEV *op, Type *ty)
443 : SCEVCastExpr(ID, scSignExtend, op, ty) {
444 assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy
() && "Cannot sign extend non-integer value!") ? static_cast
<void> (0) : __assert_fail ("Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot sign extend non-integer value!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 445, __PRETTY_FUNCTION__))
445 "Cannot sign extend non-integer value!")((Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy
() && "Cannot sign extend non-integer value!") ? static_cast
<void> (0) : __assert_fail ("Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot sign extend non-integer value!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 445, __PRETTY_FUNCTION__))
;
446}
447
448void SCEVUnknown::deleted() {
449 // Clear this SCEVUnknown from various maps.
450 SE->forgetMemoizedResults(this);
451
452 // Remove this SCEVUnknown from the uniquing map.
453 SE->UniqueSCEVs.RemoveNode(this);
454
455 // Release the value.
456 setValPtr(nullptr);
457}
458
459void SCEVUnknown::allUsesReplacedWith(Value *New) {
460 // Remove this SCEVUnknown from the uniquing map.
461 SE->UniqueSCEVs.RemoveNode(this);
462
463 // Update this SCEVUnknown to point to the new value. This is needed
464 // because there may still be outstanding SCEVs which still point to
465 // this SCEVUnknown.
466 setValPtr(New);
467}
468
469bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
470 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
471 if (VCE->getOpcode() == Instruction::PtrToInt)
472 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
473 if (CE->getOpcode() == Instruction::GetElementPtr &&
474 CE->getOperand(0)->isNullValue() &&
475 CE->getNumOperands() == 2)
476 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
477 if (CI->isOne()) {
478 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
479 ->getElementType();
480 return true;
481 }
482
483 return false;
484}
485
486bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
487 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
488 if (VCE->getOpcode() == Instruction::PtrToInt)
489 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
490 if (CE->getOpcode() == Instruction::GetElementPtr &&
491 CE->getOperand(0)->isNullValue()) {
492 Type *Ty =
493 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
494 if (StructType *STy = dyn_cast<StructType>(Ty))
495 if (!STy->isPacked() &&
496 CE->getNumOperands() == 3 &&
497 CE->getOperand(1)->isNullValue()) {
498 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
499 if (CI->isOne() &&
500 STy->getNumElements() == 2 &&
501 STy->getElementType(0)->isIntegerTy(1)) {
502 AllocTy = STy->getElementType(1);
503 return true;
504 }
505 }
506 }
507
508 return false;
509}
510
511bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
512 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
513 if (VCE->getOpcode() == Instruction::PtrToInt)
514 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
515 if (CE->getOpcode() == Instruction::GetElementPtr &&
516 CE->getNumOperands() == 3 &&
517 CE->getOperand(0)->isNullValue() &&
518 CE->getOperand(1)->isNullValue()) {
519 Type *Ty =
520 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
521 // Ignore vector types here so that ScalarEvolutionExpander doesn't
522 // emit getelementptrs that index into vectors.
523 if (Ty->isStructTy() || Ty->isArrayTy()) {
524 CTy = Ty;
525 FieldNo = CE->getOperand(2);
526 return true;
527 }
528 }
529
530 return false;
531}
532
533//===----------------------------------------------------------------------===//
534// SCEV Utilities
535//===----------------------------------------------------------------------===//
536
537/// Compare the two values \p LV and \p RV in terms of their "complexity" where
538/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
539/// operands in SCEV expressions. \p EqCache is a set of pairs of values that
540/// have been previously deemed to be "equally complex" by this routine. It is
541/// intended to avoid exponential time complexity in cases like:
542///
543/// %a = f(%x, %y)
544/// %b = f(%a, %a)
545/// %c = f(%b, %b)
546///
547/// %d = f(%x, %y)
548/// %e = f(%d, %d)
549/// %f = f(%e, %e)
550///
551/// CompareValueComplexity(%f, %c)
552///
553/// Since we do not continue running this routine on expression trees once we
554/// have seen unequal values, there is no need to track them in the cache.
555static int
556CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
557 const LoopInfo *const LI, Value *LV, Value *RV,
558 unsigned Depth) {
559 if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
560 return 0;
561
562 // Order pointer values after integer values. This helps SCEVExpander form
563 // GEPs.
564 bool LIsPointer = LV->getType()->isPointerTy(),
565 RIsPointer = RV->getType()->isPointerTy();
566 if (LIsPointer != RIsPointer)
567 return (int)LIsPointer - (int)RIsPointer;
568
569 // Compare getValueID values.
570 unsigned LID = LV->getValueID(), RID = RV->getValueID();
571 if (LID != RID)
572 return (int)LID - (int)RID;
573
574 // Sort arguments by their position.
575 if (const auto *LA = dyn_cast<Argument>(LV)) {
576 const auto *RA = cast<Argument>(RV);
577 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
578 return (int)LArgNo - (int)RArgNo;
579 }
580
581 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
582 const auto *RGV = cast<GlobalValue>(RV);
583
584 const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
585 auto LT = GV->getLinkage();
586 return !(GlobalValue::isPrivateLinkage(LT) ||
587 GlobalValue::isInternalLinkage(LT));
588 };
589
590 // Use the names to distinguish the two values, but only if the
591 // names are semantically important.
592 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
593 return LGV->getName().compare(RGV->getName());
594 }
595
596 // For instructions, compare their loop depth, and their operand count. This
597 // is pretty loose.
598 if (const auto *LInst = dyn_cast<Instruction>(LV)) {
599 const auto *RInst = cast<Instruction>(RV);
600
601 // Compare loop depths.
602 const BasicBlock *LParent = LInst->getParent(),
603 *RParent = RInst->getParent();
604 if (LParent != RParent) {
605 unsigned LDepth = LI->getLoopDepth(LParent),
606 RDepth = LI->getLoopDepth(RParent);
607 if (LDepth != RDepth)
608 return (int)LDepth - (int)RDepth;
609 }
610
611 // Compare the number of operands.
612 unsigned LNumOps = LInst->getNumOperands(),
613 RNumOps = RInst->getNumOperands();
614 if (LNumOps != RNumOps)
615 return (int)LNumOps - (int)RNumOps;
616
617 for (unsigned Idx : seq(0u, LNumOps)) {
618 int Result =
619 CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
620 RInst->getOperand(Idx), Depth + 1);
621 if (Result != 0)
622 return Result;
623 }
624 }
625
626 EqCacheValue.unionSets(LV, RV);
627 return 0;
628}
629
630// Return negative, zero, or positive, if LHS is less than, equal to, or greater
631// than RHS, respectively. A three-way result allows recursive comparisons to be
632// more efficient.
633static int CompareSCEVComplexity(
634 EquivalenceClasses<const SCEV *> &EqCacheSCEV,
635 EquivalenceClasses<const Value *> &EqCacheValue,
636 const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
637 DominatorTree &DT, unsigned Depth = 0) {
638 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
639 if (LHS == RHS)
640 return 0;
641
642 // Primarily, sort the SCEVs by their getSCEVType().
643 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
644 if (LType != RType)
645 return (int)LType - (int)RType;
646
647 if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS))
648 return 0;
649 // Aside from the getSCEVType() ordering, the particular ordering
650 // isn't very important except that it's beneficial to be consistent,
651 // so that (a + b) and (b + a) don't end up as different expressions.
652 switch (static_cast<SCEVTypes>(LType)) {
653 case scUnknown: {
654 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
655 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
656
657 int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
658 RU->getValue(), Depth + 1);
659 if (X == 0)
660 EqCacheSCEV.unionSets(LHS, RHS);
661 return X;
662 }
663
664 case scConstant: {
665 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
666 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
667
668 // Compare constant values.
669 const APInt &LA = LC->getAPInt();
670 const APInt &RA = RC->getAPInt();
671 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
672 if (LBitWidth != RBitWidth)
673 return (int)LBitWidth - (int)RBitWidth;
674 return LA.ult(RA) ? -1 : 1;
675 }
676
677 case scAddRecExpr: {
678 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
679 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
680
681 // There is always a dominance between two recs that are used by one SCEV,
682 // so we can safely sort recs by loop header dominance. We require such
683 // order in getAddExpr.
684 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
685 if (LLoop != RLoop) {
686 const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
687 assert(LHead != RHead && "Two loops share the same header?")((LHead != RHead && "Two loops share the same header?"
) ? static_cast<void> (0) : __assert_fail ("LHead != RHead && \"Two loops share the same header?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 687, __PRETTY_FUNCTION__))
;
688 if (DT.dominates(LHead, RHead))
689 return 1;
690 else
691 assert(DT.dominates(RHead, LHead) &&((DT.dominates(RHead, LHead) && "No dominance between recurrences used by one SCEV?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates(RHead, LHead) && \"No dominance between recurrences used by one SCEV?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 692, __PRETTY_FUNCTION__))
692 "No dominance between recurrences used by one SCEV?")((DT.dominates(RHead, LHead) && "No dominance between recurrences used by one SCEV?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates(RHead, LHead) && \"No dominance between recurrences used by one SCEV?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 692, __PRETTY_FUNCTION__))
;
693 return -1;
694 }
695
696 // Addrec complexity grows with operand count.
697 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
698 if (LNumOps != RNumOps)
699 return (int)LNumOps - (int)RNumOps;
700
701 // Lexicographically compare.
702 for (unsigned i = 0; i != LNumOps; ++i) {
703 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
704 LA->getOperand(i), RA->getOperand(i), DT,
705 Depth + 1);
706 if (X != 0)
707 return X;
708 }
709 EqCacheSCEV.unionSets(LHS, RHS);
710 return 0;
711 }
712
713 case scAddExpr:
714 case scMulExpr:
715 case scSMaxExpr:
716 case scUMaxExpr: {
717 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
718 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
719
720 // Lexicographically compare n-ary expressions.
721 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
722 if (LNumOps != RNumOps)
723 return (int)LNumOps - (int)RNumOps;
724
725 for (unsigned i = 0; i != LNumOps; ++i) {
726 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
727 LC->getOperand(i), RC->getOperand(i), DT,
728 Depth + 1);
729 if (X != 0)
730 return X;
731 }
732 EqCacheSCEV.unionSets(LHS, RHS);
733 return 0;
734 }
735
736 case scUDivExpr: {
737 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
738 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
739
740 // Lexicographically compare udiv expressions.
741 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
742 RC->getLHS(), DT, Depth + 1);
743 if (X != 0)
744 return X;
745 X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
746 RC->getRHS(), DT, Depth + 1);
747 if (X == 0)
748 EqCacheSCEV.unionSets(LHS, RHS);
749 return X;
750 }
751
752 case scTruncate:
753 case scZeroExtend:
754 case scSignExtend: {
755 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
756 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
757
758 // Compare cast expressions by operand.
759 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
760 LC->getOperand(), RC->getOperand(), DT,
761 Depth + 1);
762 if (X == 0)
763 EqCacheSCEV.unionSets(LHS, RHS);
764 return X;
765 }
766
767 case scCouldNotCompute:
768 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 768)
;
769 }
770 llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 770)
;
771}
772
773/// Given a list of SCEV objects, order them by their complexity, and group
774/// objects of the same complexity together by value. When this routine is
775/// finished, we know that any duplicates in the vector are consecutive and that
776/// complexity is monotonically increasing.
777///
778/// Note that we go take special precautions to ensure that we get deterministic
779/// results from this routine. In other words, we don't want the results of
780/// this to depend on where the addresses of various SCEV objects happened to
781/// land in memory.
782static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
783 LoopInfo *LI, DominatorTree &DT) {
784 if (Ops.size() < 2) return; // Noop
785
786 EquivalenceClasses<const SCEV *> EqCacheSCEV;
787 EquivalenceClasses<const Value *> EqCacheValue;
788 if (Ops.size() == 2) {
789 // This is the common case, which also happens to be trivially simple.
790 // Special case it.
791 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
792 if (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0)
793 std::swap(LHS, RHS);
794 return;
795 }
796
797 // Do the rough sort by complexity.
798 std::stable_sort(Ops.begin(), Ops.end(),
799 [&](const SCEV *LHS, const SCEV *RHS) {
800 return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
801 LHS, RHS, DT) < 0;
802 });
803
804 // Now that we are sorted by complexity, group elements of the same
805 // complexity. Note that this is, at worst, N^2, but the vector is likely to
806 // be extremely short in practice. Note that we take this approach because we
807 // do not want to depend on the addresses of the objects we are grouping.
808 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
809 const SCEV *S = Ops[i];
810 unsigned Complexity = S->getSCEVType();
811
812 // If there are any objects of the same complexity and same value as this
813 // one, group them.
814 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
815 if (Ops[j] == S) { // Found a duplicate.
816 // Move it to immediately after i'th element.
817 std::swap(Ops[i+1], Ops[j]);
818 ++i; // no need to rescan it.
819 if (i == e-2) return; // Done!
820 }
821 }
822 }
823}
824
825// Returns the size of the SCEV S.
826static inline int sizeOfSCEV(const SCEV *S) {
827 struct FindSCEVSize {
828 int Size = 0;
829
830 FindSCEVSize() = default;
831
832 bool follow(const SCEV *S) {
833 ++Size;
834 // Keep looking at all operands of S.
835 return true;
836 }
837
838 bool isDone() const {
839 return false;
840 }
841 };
842
843 FindSCEVSize F;
844 SCEVTraversal<FindSCEVSize> ST(F);
845 ST.visitAll(S);
846 return F.Size;
847}
848
849namespace {
850
851struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
852public:
853 // Computes the Quotient and Remainder of the division of Numerator by
854 // Denominator.
855 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
856 const SCEV *Denominator, const SCEV **Quotient,
857 const SCEV **Remainder) {
858 assert(Numerator && Denominator && "Uninitialized SCEV")((Numerator && Denominator && "Uninitialized SCEV"
) ? static_cast<void> (0) : __assert_fail ("Numerator && Denominator && \"Uninitialized SCEV\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 858, __PRETTY_FUNCTION__))
;
859
860 SCEVDivision D(SE, Numerator, Denominator);
861
862 // Check for the trivial case here to avoid having to check for it in the
863 // rest of the code.
864 if (Numerator == Denominator) {
865 *Quotient = D.One;
866 *Remainder = D.Zero;
867 return;
868 }
869
870 if (Numerator->isZero()) {
871 *Quotient = D.Zero;
872 *Remainder = D.Zero;
873 return;
874 }
875
876 // A simple case when N/1. The quotient is N.
877 if (Denominator->isOne()) {
878 *Quotient = Numerator;
879 *Remainder = D.Zero;
880 return;
881 }
882
883 // Split the Denominator when it is a product.
884 if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
885 const SCEV *Q, *R;
886 *Quotient = Numerator;
887 for (const SCEV *Op : T->operands()) {
888 divide(SE, *Quotient, Op, &Q, &R);
889 *Quotient = Q;
890
891 // Bail out when the Numerator is not divisible by one of the terms of
892 // the Denominator.
893 if (!R->isZero()) {
894 *Quotient = D.Zero;
895 *Remainder = Numerator;
896 return;
897 }
898 }
899 *Remainder = D.Zero;
900 return;
901 }
902
903 D.visit(Numerator);
904 *Quotient = D.Quotient;
905 *Remainder = D.Remainder;
906 }
907
908 // Except in the trivial case described above, we do not know how to divide
909 // Expr by Denominator for the following functions with empty implementation.
910 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
911 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
912 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
913 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
914 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
915 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
916 void visitUnknown(const SCEVUnknown *Numerator) {}
917 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
918
919 void visitConstant(const SCEVConstant *Numerator) {
920 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
921 APInt NumeratorVal = Numerator->getAPInt();
922 APInt DenominatorVal = D->getAPInt();
923 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
924 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
925
926 if (NumeratorBW > DenominatorBW)
927 DenominatorVal = DenominatorVal.sext(NumeratorBW);
928 else if (NumeratorBW < DenominatorBW)
929 NumeratorVal = NumeratorVal.sext(DenominatorBW);
930
931 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
932 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
933 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
934 Quotient = SE.getConstant(QuotientVal);
935 Remainder = SE.getConstant(RemainderVal);
936 return;
937 }
938 }
939
940 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
941 const SCEV *StartQ, *StartR, *StepQ, *StepR;
942 if (!Numerator->isAffine())
943 return cannotDivide(Numerator);
944 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
945 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
946 // Bail out if the types do not match.
947 Type *Ty = Denominator->getType();
948 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
949 Ty != StepQ->getType() || Ty != StepR->getType())
950 return cannotDivide(Numerator);
951 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
952 Numerator->getNoWrapFlags());
953 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
954 Numerator->getNoWrapFlags());
955 }
956
957 void visitAddExpr(const SCEVAddExpr *Numerator) {
958 SmallVector<const SCEV *, 2> Qs, Rs;
959 Type *Ty = Denominator->getType();
960
961 for (const SCEV *Op : Numerator->operands()) {
962 const SCEV *Q, *R;
963 divide(SE, Op, Denominator, &Q, &R);
964
965 // Bail out if types do not match.
966 if (Ty != Q->getType() || Ty != R->getType())
967 return cannotDivide(Numerator);
968
969 Qs.push_back(Q);
970 Rs.push_back(R);
971 }
972
973 if (Qs.size() == 1) {
974 Quotient = Qs[0];
975 Remainder = Rs[0];
976 return;
977 }
978
979 Quotient = SE.getAddExpr(Qs);
980 Remainder = SE.getAddExpr(Rs);
981 }
982
983 void visitMulExpr(const SCEVMulExpr *Numerator) {
984 SmallVector<const SCEV *, 2> Qs;
985 Type *Ty = Denominator->getType();
986
987 bool FoundDenominatorTerm = false;
988 for (const SCEV *Op : Numerator->operands()) {
989 // Bail out if types do not match.
990 if (Ty != Op->getType())
991 return cannotDivide(Numerator);
992
993 if (FoundDenominatorTerm) {
994 Qs.push_back(Op);
995 continue;
996 }
997
998 // Check whether Denominator divides one of the product operands.
999 const SCEV *Q, *R;
1000 divide(SE, Op, Denominator, &Q, &R);
1001 if (!R->isZero()) {
1002 Qs.push_back(Op);
1003 continue;
1004 }
1005
1006 // Bail out if types do not match.
1007 if (Ty != Q->getType())
1008 return cannotDivide(Numerator);
1009
1010 FoundDenominatorTerm = true;
1011 Qs.push_back(Q);
1012 }
1013
1014 if (FoundDenominatorTerm) {
1015 Remainder = Zero;
1016 if (Qs.size() == 1)
1017 Quotient = Qs[0];
1018 else
1019 Quotient = SE.getMulExpr(Qs);
1020 return;
1021 }
1022
1023 if (!isa<SCEVUnknown>(Denominator))
1024 return cannotDivide(Numerator);
1025
1026 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
1027 ValueToValueMap RewriteMap;
1028 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1029 cast<SCEVConstant>(Zero)->getValue();
1030 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1031
1032 if (Remainder->isZero()) {
1033 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
1034 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1035 cast<SCEVConstant>(One)->getValue();
1036 Quotient =
1037 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1038 return;
1039 }
1040
1041 // Quotient is (Numerator - Remainder) divided by Denominator.
1042 const SCEV *Q, *R;
1043 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
1044 // This SCEV does not seem to simplify: fail the division here.
1045 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
1046 return cannotDivide(Numerator);
1047 divide(SE, Diff, Denominator, &Q, &R);
1048 if (R != Zero)
1049 return cannotDivide(Numerator);
1050 Quotient = Q;
1051 }
1052
1053private:
1054 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
1055 const SCEV *Denominator)
1056 : SE(S), Denominator(Denominator) {
1057 Zero = SE.getZero(Denominator->getType());
1058 One = SE.getOne(Denominator->getType());
1059
1060 // We generally do not know how to divide Expr by Denominator. We
1061 // initialize the division to a "cannot divide" state to simplify the rest
1062 // of the code.
1063 cannotDivide(Numerator);
1064 }
1065
1066 // Convenience function for giving up on the division. We set the quotient to
1067 // be equal to zero and the remainder to be equal to the numerator.
1068 void cannotDivide(const SCEV *Numerator) {
1069 Quotient = Zero;
1070 Remainder = Numerator;
1071 }
1072
1073 ScalarEvolution &SE;
1074 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
1075};
1076
1077} // end anonymous namespace
1078
1079//===----------------------------------------------------------------------===//
1080// Simple SCEV method implementations
1081//===----------------------------------------------------------------------===//
1082
1083/// Compute BC(It, K). The result has width W. Assume, K > 0.
1084static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
1085 ScalarEvolution &SE,
1086 Type *ResultTy) {
1087 // Handle the simplest case efficiently.
1088 if (K == 1)
1089 return SE.getTruncateOrZeroExtend(It, ResultTy);
1090
1091 // We are using the following formula for BC(It, K):
1092 //
1093 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
1094 //
1095 // Suppose, W is the bitwidth of the return value. We must be prepared for
1096 // overflow. Hence, we must assure that the result of our computation is
1097 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
1098 // safe in modular arithmetic.
1099 //
1100 // However, this code doesn't use exactly that formula; the formula it uses
1101 // is something like the following, where T is the number of factors of 2 in
1102 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
1103 // exponentiation:
1104 //
1105 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
1106 //
1107 // This formula is trivially equivalent to the previous formula. However,
1108 // this formula can be implemented much more efficiently. The trick is that
1109 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
1110 // arithmetic. To do exact division in modular arithmetic, all we have
1111 // to do is multiply by the inverse. Therefore, this step can be done at
1112 // width W.
1113 //
1114 // The next issue is how to safely do the division by 2^T. The way this
1115 // is done is by doing the multiplication step at a width of at least W + T
1116 // bits. This way, the bottom W+T bits of the product are accurate. Then,
1117 // when we perform the division by 2^T (which is equivalent to a right shift
1118 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
1119 // truncated out after the division by 2^T.
1120 //
1121 // In comparison to just directly using the first formula, this technique
1122 // is much more efficient; using the first formula requires W * K bits,
1123 // but this formula less than W + K bits. Also, the first formula requires
1124 // a division step, whereas this formula only requires multiplies and shifts.
1125 //
1126 // It doesn't matter whether the subtraction step is done in the calculation
1127 // width or the input iteration count's width; if the subtraction overflows,
1128 // the result must be zero anyway. We prefer here to do it in the width of
1129 // the induction variable because it helps a lot for certain cases; CodeGen
1130 // isn't smart enough to ignore the overflow, which leads to much less
1131 // efficient code if the width of the subtraction is wider than the native
1132 // register width.
1133 //
1134 // (It's possible to not widen at all by pulling out factors of 2 before
1135 // the multiplication; for example, K=2 can be calculated as
1136 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1137 // extra arithmetic, so it's not an obvious win, and it gets
1138 // much more complicated for K > 3.)
1139
1140 // Protection from insane SCEVs; this bound is conservative,
1141 // but it probably doesn't matter.
1142 if (K > 1000)
1143 return SE.getCouldNotCompute();
1144
1145 unsigned W = SE.getTypeSizeInBits(ResultTy);
1146
1147 // Calculate K! / 2^T and T; we divide out the factors of two before
1148 // multiplying for calculating K! / 2^T to avoid overflow.
1149 // Other overflow doesn't matter because we only care about the bottom
1150 // W bits of the result.
1151 APInt OddFactorial(W, 1);
1152 unsigned T = 1;
1153 for (unsigned i = 3; i <= K; ++i) {
1154 APInt Mult(W, i);
1155 unsigned TwoFactors = Mult.countTrailingZeros();
1156 T += TwoFactors;
1157 Mult.lshrInPlace(TwoFactors);
1158 OddFactorial *= Mult;
1159 }
1160
1161 // We need at least W + T bits for the multiplication step
1162 unsigned CalculationBits = W + T;
1163
1164 // Calculate 2^T, at width T+W.
1165 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1166
1167 // Calculate the multiplicative inverse of K! / 2^T;
1168 // this multiplication factor will perform the exact division by
1169 // K! / 2^T.
1170 APInt Mod = APInt::getSignedMinValue(W+1);
1171 APInt MultiplyFactor = OddFactorial.zext(W+1);
1172 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1173 MultiplyFactor = MultiplyFactor.trunc(W);
1174
1175 // Calculate the product, at width T+W
1176 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1177 CalculationBits);
1178 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1179 for (unsigned i = 1; i != K; ++i) {
1180 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1181 Dividend = SE.getMulExpr(Dividend,
1182 SE.getTruncateOrZeroExtend(S, CalculationTy));
1183 }
1184
1185 // Divide by 2^T
1186 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1187
1188 // Truncate the result, and divide by K! / 2^T.
1189
1190 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1191 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1192}
1193
1194/// Return the value of this chain of recurrences at the specified iteration
1195/// number. We can evaluate this recurrence by multiplying each element in the
1196/// chain by the binomial coefficient corresponding to it. In other words, we
1197/// can evaluate {A,+,B,+,C,+,D} as:
1198///
1199/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1200///
1201/// where BC(It, k) stands for binomial coefficient.
1202const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1203 ScalarEvolution &SE) const {
1204 const SCEV *Result = getStart();
1205 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1206 // The computation is correct in the face of overflow provided that the
1207 // multiplication is performed _after_ the evaluation of the binomial
1208 // coefficient.
1209 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1210 if (isa<SCEVCouldNotCompute>(Coeff))
1211 return Coeff;
1212
1213 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1214 }
1215 return Result;
1216}
1217
1218//===----------------------------------------------------------------------===//
1219// SCEV Expression folder implementations
1220//===----------------------------------------------------------------------===//
1221
1222const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1223 Type *Ty) {
1224 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&((getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(
Ty) && "This is not a truncating conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && \"This is not a truncating conversion!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1225, __PRETTY_FUNCTION__))
1225 "This is not a truncating conversion!")((getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(
Ty) && "This is not a truncating conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && \"This is not a truncating conversion!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1225, __PRETTY_FUNCTION__))
;
1226 assert(isSCEVable(Ty) &&((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1227, __PRETTY_FUNCTION__))
1227 "This is not a conversion to a SCEVable type!")((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1227, __PRETTY_FUNCTION__))
;
1228 Ty = getEffectiveSCEVType(Ty);
1229
1230 FoldingSetNodeID ID;
1231 ID.AddInteger(scTruncate);
1232 ID.AddPointer(Op);
1233 ID.AddPointer(Ty);
1234 void *IP = nullptr;
1235 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1236
1237 // Fold if the operand is constant.
1238 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1239 return getConstant(
1240 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1241
1242 // trunc(trunc(x)) --> trunc(x)
1243 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1244 return getTruncateExpr(ST->getOperand(), Ty);
1245
1246 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1247 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1248 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1249
1250 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1251 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1252 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1253
1254 // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
1255 // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
1256 // if after transforming we have at most one truncate, not counting truncates
1257 // that replace other casts.
1258 if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
1259 auto *CommOp = cast<SCEVCommutativeExpr>(Op);
1260 SmallVector<const SCEV *, 4> Operands;
1261 unsigned numTruncs = 0;
1262 for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
1263 ++i) {
1264 const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty);
1265 if (!isa<SCEVCastExpr>(CommOp->getOperand(i)) && isa<SCEVTruncateExpr>(S))
1266 numTruncs++;
1267 Operands.push_back(S);
1268 }
1269 if (numTruncs < 2) {
1270 if (isa<SCEVAddExpr>(Op))
1271 return getAddExpr(Operands);
1272 else if (isa<SCEVMulExpr>(Op))
1273 return getMulExpr(Operands);
1274 else
1275 llvm_unreachable("Unexpected SCEV type for Op.")::llvm::llvm_unreachable_internal("Unexpected SCEV type for Op."
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1275)
;
1276 }
1277 // Although we checked in the beginning that ID is not in the cache, it is
1278 // possible that during recursion and different modification ID was inserted
1279 // into the cache. So if we find it, just return it.
1280 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
1281 return S;
1282 }
1283
1284 // If the input value is a chrec scev, truncate the chrec's operands.
1285 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1286 SmallVector<const SCEV *, 4> Operands;
1287 for (const SCEV *Op : AddRec->operands())
1288 Operands.push_back(getTruncateExpr(Op, Ty));
1289 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1290 }
1291
1292 // The cast wasn't folded; create an explicit cast node. We can reuse
1293 // the existing insert position since if we get here, we won't have
1294 // made any changes which would invalidate it.
1295 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1296 Op, Ty);
1297 UniqueSCEVs.InsertNode(S, IP);
1298 addToLoopUseLists(S);
1299 return S;
1300}
1301
1302// Get the limit of a recurrence such that incrementing by Step cannot cause
1303// signed overflow as long as the value of the recurrence within the
1304// loop does not exceed this limit before incrementing.
1305static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1306 ICmpInst::Predicate *Pred,
1307 ScalarEvolution *SE) {
1308 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1309 if (SE->isKnownPositive(Step)) {
1310 *Pred = ICmpInst::ICMP_SLT;
1311 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1312 SE->getSignedRangeMax(Step));
1313 }
1314 if (SE->isKnownNegative(Step)) {
1315 *Pred = ICmpInst::ICMP_SGT;
1316 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1317 SE->getSignedRangeMin(Step));
1318 }
1319 return nullptr;
1320}
1321
1322// Get the limit of a recurrence such that incrementing by Step cannot cause
1323// unsigned overflow as long as the value of the recurrence within the loop does
1324// not exceed this limit before incrementing.
1325static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1326 ICmpInst::Predicate *Pred,
1327 ScalarEvolution *SE) {
1328 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1329 *Pred = ICmpInst::ICMP_ULT;
1330
1331 return SE->getConstant(APInt::getMinValue(BitWidth) -
1332 SE->getUnsignedRangeMax(Step));
1333}
1334
1335namespace {
1336
1337struct ExtendOpTraitsBase {
1338 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
1339 unsigned);
1340};
1341
1342// Used to make code generic over signed and unsigned overflow.
1343template <typename ExtendOp> struct ExtendOpTraits {
1344 // Members present:
1345 //
1346 // static const SCEV::NoWrapFlags WrapType;
1347 //
1348 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1349 //
1350 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1351 // ICmpInst::Predicate *Pred,
1352 // ScalarEvolution *SE);
1353};
1354
1355template <>
1356struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1357 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1358
1359 static const GetExtendExprTy GetExtendExpr;
1360
1361 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1362 ICmpInst::Predicate *Pred,
1363 ScalarEvolution *SE) {
1364 return getSignedOverflowLimitForStep(Step, Pred, SE);
1365 }
1366};
1367
1368const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1369 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1370
1371template <>
1372struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1373 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1374
1375 static const GetExtendExprTy GetExtendExpr;
1376
1377 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1378 ICmpInst::Predicate *Pred,
1379 ScalarEvolution *SE) {
1380 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1381 }
1382};
1383
1384const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1385 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1386
1387} // end anonymous namespace
1388
1389// The recurrence AR has been shown to have no signed/unsigned wrap or something
1390// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1391// easily prove NSW/NUW for its preincrement or postincrement sibling. This
1392// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1393// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1394// expression "Step + sext/zext(PreIncAR)" is congruent with
1395// "sext/zext(PostIncAR)"
1396template <typename ExtendOpTy>
1397static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1398 ScalarEvolution *SE, unsigned Depth) {
1399 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1400 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1401
1402 const Loop *L = AR->getLoop();
1403 const SCEV *Start = AR->getStart();
1404 const SCEV *Step = AR->getStepRecurrence(*SE);
1405
1406 // Check for a simple looking step prior to loop entry.
1407 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1408 if (!SA)
1409 return nullptr;
1410
1411 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1412 // subtraction is expensive. For this purpose, perform a quick and dirty
1413 // difference, by checking for Step in the operand list.
1414 SmallVector<const SCEV *, 4> DiffOps;
1415 for (const SCEV *Op : SA->operands())
1416 if (Op != Step)
1417 DiffOps.push_back(Op);
1418
1419 if (DiffOps.size() == SA->getNumOperands())
1420 return nullptr;
1421
1422 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1423 // `Step`:
1424
1425 // 1. NSW/NUW flags on the step increment.
1426 auto PreStartFlags =
1427 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1428 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1429 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1430 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1431
1432 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1433 // "S+X does not sign/unsign-overflow".
1434 //
1435
1436 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1437 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1438 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1439 return PreStart;
1440
1441 // 2. Direct overflow check on the step operation's expression.
1442 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1443 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1444 const SCEV *OperandExtendedStart =
1445 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
1446 (SE->*GetExtendExpr)(Step, WideTy, Depth));
1447 if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
1448 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1449 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1450 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1451 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1452 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1453 }
1454 return PreStart;
1455 }
1456
1457 // 3. Loop precondition.
1458 ICmpInst::Predicate Pred;
1459 const SCEV *OverflowLimit =
1460 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1461
1462 if (OverflowLimit &&
1463 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1464 return PreStart;
1465
1466 return nullptr;
1467}
1468
1469// Get the normalized zero or sign extended expression for this AddRec's Start.
1470template <typename ExtendOpTy>
1471static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1472 ScalarEvolution *SE,
1473 unsigned Depth) {
1474 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1475
1476 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
1477 if (!PreStart)
1478 return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
1479
1480 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
1481 Depth),
1482 (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1483}
1484
1485// Try to prove away overflow by looking at "nearby" add recurrences. A
1486// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1487// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1488//
1489// Formally:
1490//
1491// {S,+,X} == {S-T,+,X} + T
1492// => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1493//
1494// If ({S-T,+,X} + T) does not overflow ... (1)
1495//
1496// RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1497//
1498// If {S-T,+,X} does not overflow ... (2)
1499//
1500// RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1501// == {Ext(S-T)+Ext(T),+,Ext(X)}
1502//
1503// If (S-T)+T does not overflow ... (3)
1504//
1505// RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1506// == {Ext(S),+,Ext(X)} == LHS
1507//
1508// Thus, if (1), (2) and (3) are true for some T, then
1509// Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1510//
1511// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1512// does not overflow" restricted to the 0th iteration. Therefore we only need
1513// to check for (1) and (2).
1514//
1515// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1516// is `Delta` (defined below).
1517template <typename ExtendOpTy>
1518bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1519 const SCEV *Step,
1520 const Loop *L) {
1521 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1522
1523 // We restrict `Start` to a constant to prevent SCEV from spending too much
1524 // time here. It is correct (but more expensive) to continue with a
1525 // non-constant `Start` and do a general SCEV subtraction to compute
1526 // `PreStart` below.
1527 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1528 if (!StartC)
1529 return false;
1530
1531 APInt StartAI = StartC->getAPInt();
1532
1533 for (unsigned Delta : {-2, -1, 1, 2}) {
1534 const SCEV *PreStart = getConstant(StartAI - Delta);
1535
1536 FoldingSetNodeID ID;
1537 ID.AddInteger(scAddRecExpr);
1538 ID.AddPointer(PreStart);
1539 ID.AddPointer(Step);
1540 ID.AddPointer(L);
1541 void *IP = nullptr;
1542 const auto *PreAR =
1543 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1544
1545 // Give up if we don't already have the add recurrence we need because
1546 // actually constructing an add recurrence is relatively expensive.
1547 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1548 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1549 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1550 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1551 DeltaS, &Pred, this);
1552 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1553 return true;
1554 }
1555 }
1556
1557 return false;
1558}
1559
1560// Finds an integer D for an expression (C + x + y + ...) such that the top
1561// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
1562// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
1563// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
1564// the (C + x + y + ...) expression is \p WholeAddExpr.
1565static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1566 const SCEVConstant *ConstantTerm,
1567 const SCEVAddExpr *WholeAddExpr) {
1568 const APInt C = ConstantTerm->getAPInt();
1569 const unsigned BitWidth = C.getBitWidth();
1570 // Find number of trailing zeros of (x + y + ...) w/o the C first:
1571 uint32_t TZ = BitWidth;
1572 for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
1573 TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I)));
1574 if (TZ) {
1575 // Set D to be as many least significant bits of C as possible while still
1576 // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
1577 return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
1578 }
1579 return APInt(BitWidth, 0);
1580}
1581
1582// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
1583// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
1584// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
1585// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
1586static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1587 const APInt &ConstantStart,
1588 const SCEV *Step) {
1589 const unsigned BitWidth = ConstantStart.getBitWidth();
1590 const uint32_t TZ = SE.GetMinTrailingZeros(Step);
1591 if (TZ)
1592 return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
1593 : ConstantStart;
1594 return APInt(BitWidth, 0);
1595}
1596
1597const SCEV *
1598ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1599 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1600, __PRETTY_FUNCTION__))
1600 "This is not an extending conversion!")((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1600, __PRETTY_FUNCTION__))
;
1601 assert(isSCEVable(Ty) &&((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1602, __PRETTY_FUNCTION__))
1602 "This is not a conversion to a SCEVable type!")((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1602, __PRETTY_FUNCTION__))
;
1603 Ty = getEffectiveSCEVType(Ty);
1604
1605 // Fold if the operand is constant.
1606 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1607 return getConstant(
1608 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1609
1610 // zext(zext(x)) --> zext(x)
1611 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1612 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1613
1614 // Before doing any expensive analysis, check to see if we've already
1615 // computed a SCEV for this Op and Ty.
1616 FoldingSetNodeID ID;
1617 ID.AddInteger(scZeroExtend);
1618 ID.AddPointer(Op);
1619 ID.AddPointer(Ty);
1620 void *IP = nullptr;
1621 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1622 if (Depth > MaxExtDepth) {
1623 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1624 Op, Ty);
1625 UniqueSCEVs.InsertNode(S, IP);
1626 addToLoopUseLists(S);
1627 return S;
1628 }
1629
1630 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1631 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1632 // It's possible the bits taken off by the truncate were all zero bits. If
1633 // so, we should be able to simplify this further.
1634 const SCEV *X = ST->getOperand();
1635 ConstantRange CR = getUnsignedRange(X);
1636 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1637 unsigned NewBits = getTypeSizeInBits(Ty);
1638 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1639 CR.zextOrTrunc(NewBits)))
1640 return getTruncateOrZeroExtend(X, Ty);
1641 }
1642
1643 // If the input value is a chrec scev, and we can prove that the value
1644 // did not overflow the old, smaller, value, we can zero extend all of the
1645 // operands (often constants). This allows analysis of something like
1646 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1647 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1648 if (AR->isAffine()) {
1649 const SCEV *Start = AR->getStart();
1650 const SCEV *Step = AR->getStepRecurrence(*this);
1651 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1652 const Loop *L = AR->getLoop();
1653
1654 if (!AR->hasNoUnsignedWrap()) {
1655 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1656 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1657 }
1658
1659 // If we have special knowledge that this addrec won't overflow,
1660 // we don't need to do any further analysis.
1661 if (AR->hasNoUnsignedWrap())
1662 return getAddRecExpr(
1663 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1664 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1665
1666 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1667 // Note that this serves two purposes: It filters out loops that are
1668 // simply not analyzable, and it covers the case where this code is
1669 // being called from within backedge-taken count analysis, such that
1670 // attempting to ask for the backedge-taken count would likely result
1671 // in infinite recursion. In the later case, the analysis code will
1672 // cope with a conservative value, and it will take care to purge
1673 // that value once it has finished.
1674 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1675 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1676 // Manually compute the final value for AR, checking for
1677 // overflow.
1678
1679 // Check whether the backedge-taken count can be losslessly casted to
1680 // the addrec's type. The count is always unsigned.
1681 const SCEV *CastedMaxBECount =
1682 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1683 const SCEV *RecastedMaxBECount =
1684 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1685 if (MaxBECount == RecastedMaxBECount) {
1686 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1687 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1688 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
1689 SCEV::FlagAnyWrap, Depth + 1);
1690 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
1691 SCEV::FlagAnyWrap,
1692 Depth + 1),
1693 WideTy, Depth + 1);
1694 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
1695 const SCEV *WideMaxBECount =
1696 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1697 const SCEV *OperandExtendedAdd =
1698 getAddExpr(WideStart,
1699 getMulExpr(WideMaxBECount,
1700 getZeroExtendExpr(Step, WideTy, Depth + 1),
1701 SCEV::FlagAnyWrap, Depth + 1),
1702 SCEV::FlagAnyWrap, Depth + 1);
1703 if (ZAdd == OperandExtendedAdd) {
1704 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1705 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1706 // Return the expression with the addrec on the outside.
1707 return getAddRecExpr(
1708 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1709 Depth + 1),
1710 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1711 AR->getNoWrapFlags());
1712 }
1713 // Similar to above, only this time treat the step value as signed.
1714 // This covers loops that count down.
1715 OperandExtendedAdd =
1716 getAddExpr(WideStart,
1717 getMulExpr(WideMaxBECount,
1718 getSignExtendExpr(Step, WideTy, Depth + 1),
1719 SCEV::FlagAnyWrap, Depth + 1),
1720 SCEV::FlagAnyWrap, Depth + 1);
1721 if (ZAdd == OperandExtendedAdd) {
1722 // Cache knowledge of AR NW, which is propagated to this AddRec.
1723 // Negative step causes unsigned wrap, but it still can't self-wrap.
1724 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1725 // Return the expression with the addrec on the outside.
1726 return getAddRecExpr(
1727 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1728 Depth + 1),
1729 getSignExtendExpr(Step, Ty, Depth + 1), L,
1730 AR->getNoWrapFlags());
1731 }
1732 }
1733 }
1734
1735 // Normally, in the cases we can prove no-overflow via a
1736 // backedge guarding condition, we can also compute a backedge
1737 // taken count for the loop. The exceptions are assumptions and
1738 // guards present in the loop -- SCEV is not great at exploiting
1739 // these to compute max backedge taken counts, but can still use
1740 // these to prove lack of overflow. Use this fact to avoid
1741 // doing extra work that may not pay off.
1742 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1743 !AC.assumptions().empty()) {
1744 // If the backedge is guarded by a comparison with the pre-inc
1745 // value the addrec is safe. Also, if the entry is guarded by
1746 // a comparison with the start value and the backedge is
1747 // guarded by a comparison with the post-inc value, the addrec
1748 // is safe.
1749 if (isKnownPositive(Step)) {
1750 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1751 getUnsignedRangeMax(Step));
1752 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1753 isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
1754 // Cache knowledge of AR NUW, which is propagated to this
1755 // AddRec.
1756 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1757 // Return the expression with the addrec on the outside.
1758 return getAddRecExpr(
1759 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1760 Depth + 1),
1761 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1762 AR->getNoWrapFlags());
1763 }
1764 } else if (isKnownNegative(Step)) {
1765 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1766 getSignedRangeMin(Step));
1767 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1768 isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
1769 // Cache knowledge of AR NW, which is propagated to this
1770 // AddRec. Negative step causes unsigned wrap, but it
1771 // still can't self-wrap.
1772 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1773 // Return the expression with the addrec on the outside.
1774 return getAddRecExpr(
1775 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1776 Depth + 1),
1777 getSignExtendExpr(Step, Ty, Depth + 1), L,
1778 AR->getNoWrapFlags());
1779 }
1780 }
1781 }
1782
1783 // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
1784 // if D + (C - D + Step * n) could be proven to not unsigned wrap
1785 // where D maximizes the number of trailing zeros of (C - D + Step * n)
1786 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
1787 const APInt &C = SC->getAPInt();
1788 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
1789 if (D != 0) {
1790 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1791 const SCEV *SResidual =
1792 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
1793 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1794 return getAddExpr(SZExtD, SZExtR,
1795 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1796 Depth + 1);
1797 }
1798 }
1799
1800 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1801 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1802 return getAddRecExpr(
1803 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1804 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1805 }
1806 }
1807
1808 // zext(A % B) --> zext(A) % zext(B)
1809 {
1810 const SCEV *LHS;
1811 const SCEV *RHS;
1812 if (matchURem(Op, LHS, RHS))
1813 return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
1814 getZeroExtendExpr(RHS, Ty, Depth + 1));
1815 }
1816
1817 // zext(A / B) --> zext(A) / zext(B).
1818 if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
1819 return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
1820 getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
1821
1822 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1823 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1824 if (SA->hasNoUnsignedWrap()) {
1825 // If the addition does not unsign overflow then we can, by definition,
1826 // commute the zero extension with the addition operation.
1827 SmallVector<const SCEV *, 4> Ops;
1828 for (const auto *Op : SA->operands())
1829 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1830 return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
1831 }
1832
1833 // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
1834 // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
1835 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1836 //
1837 // Often address arithmetics contain expressions like
1838 // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
1839 // This transformation is useful while proving that such expressions are
1840 // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
1841 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
1842 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
1843 if (D != 0) {
1844 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1845 const SCEV *SResidual =
1846 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
1847 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1848 return getAddExpr(SZExtD, SZExtR,
1849 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1850 Depth + 1);
1851 }
1852 }
1853 }
1854
1855 if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
1856 // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
1857 if (SM->hasNoUnsignedWrap()) {
1858 // If the multiply does not unsign overflow then we can, by definition,
1859 // commute the zero extension with the multiply operation.
1860 SmallVector<const SCEV *, 4> Ops;
1861 for (const auto *Op : SM->operands())
1862 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1863 return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
1864 }
1865
1866 // zext(2^K * (trunc X to iN)) to iM ->
1867 // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
1868 //
1869 // Proof:
1870 //
1871 // zext(2^K * (trunc X to iN)) to iM
1872 // = zext((trunc X to iN) << K) to iM
1873 // = zext((trunc X to i{N-K}) << K)<nuw> to iM
1874 // (because shl removes the top K bits)
1875 // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
1876 // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
1877 //
1878 if (SM->getNumOperands() == 2)
1879 if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0)))
1880 if (MulLHS->getAPInt().isPowerOf2())
1881 if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) {
1882 int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) -
1883 MulLHS->getAPInt().logBase2();
1884 Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
1885 return getMulExpr(
1886 getZeroExtendExpr(MulLHS, Ty),
1887 getZeroExtendExpr(
1888 getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty),
1889 SCEV::FlagNUW, Depth + 1);
1890 }
1891 }
1892
1893 // The cast wasn't folded; create an explicit cast node.
1894 // Recompute the insert position, as it may have been invalidated.
1895 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1896 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1897 Op, Ty);
1898 UniqueSCEVs.InsertNode(S, IP);
1899 addToLoopUseLists(S);
1900 return S;
1901}
1902
1903const SCEV *
1904ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1905 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1906, __PRETTY_FUNCTION__))
1906 "This is not an extending conversion!")((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1906, __PRETTY_FUNCTION__))
;
1907 assert(isSCEVable(Ty) &&((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1908, __PRETTY_FUNCTION__))
1908 "This is not a conversion to a SCEVable type!")((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 1908, __PRETTY_FUNCTION__))
;
1909 Ty = getEffectiveSCEVType(Ty);
1910
1911 // Fold if the operand is constant.
1912 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1913 return getConstant(
1914 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1915
1916 // sext(sext(x)) --> sext(x)
1917 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1918 return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
1919
1920 // sext(zext(x)) --> zext(x)
1921 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1922 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1923
1924 // Before doing any expensive analysis, check to see if we've already
1925 // computed a SCEV for this Op and Ty.
1926 FoldingSetNodeID ID;
1927 ID.AddInteger(scSignExtend);
1928 ID.AddPointer(Op);
1929 ID.AddPointer(Ty);
1930 void *IP = nullptr;
1931 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1932 // Limit recursion depth.
1933 if (Depth > MaxExtDepth) {
1934 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1935 Op, Ty);
1936 UniqueSCEVs.InsertNode(S, IP);
1937 addToLoopUseLists(S);
1938 return S;
1939 }
1940
1941 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1942 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1943 // It's possible the bits taken off by the truncate were all sign bits. If
1944 // so, we should be able to simplify this further.
1945 const SCEV *X = ST->getOperand();
1946 ConstantRange CR = getSignedRange(X);
1947 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1948 unsigned NewBits = getTypeSizeInBits(Ty);
1949 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1950 CR.sextOrTrunc(NewBits)))
1951 return getTruncateOrSignExtend(X, Ty);
1952 }
1953
1954 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1955 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1956 if (SA->hasNoSignedWrap()) {
1957 // If the addition does not sign overflow then we can, by definition,
1958 // commute the sign extension with the addition operation.
1959 SmallVector<const SCEV *, 4> Ops;
1960 for (const auto *Op : SA->operands())
1961 Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
1962 return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
1963 }
1964
1965 // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
1966 // if D + (C - D + x + y + ...) could be proven to not signed wrap
1967 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1968 //
1969 // For instance, this will bring two seemingly different expressions:
1970 // 1 + sext(5 + 20 * %x + 24 * %y) and
1971 // sext(6 + 20 * %x + 24 * %y)
1972 // to the same form:
1973 // 2 + sext(4 + 20 * %x + 24 * %y)
1974 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
1975 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
1976 if (D != 0) {
1977 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
1978 const SCEV *SResidual =
1979 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
1980 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
1981 return getAddExpr(SSExtD, SSExtR,
1982 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1983 Depth + 1);
1984 }
1985 }
1986 }
1987 // If the input value is a chrec scev, and we can prove that the value
1988 // did not overflow the old, smaller, value, we can sign extend all of the
1989 // operands (often constants). This allows analysis of something like
1990 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1991 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1992 if (AR->isAffine()) {
1993 const SCEV *Start = AR->getStart();
1994 const SCEV *Step = AR->getStepRecurrence(*this);
1995 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1996 const Loop *L = AR->getLoop();
1997
1998 if (!AR->hasNoSignedWrap()) {
1999 auto NewFlags = proveNoWrapViaConstantRanges(AR);
2000 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
2001 }
2002
2003 // If we have special knowledge that this addrec won't overflow,
2004 // we don't need to do any further analysis.
2005 if (AR->hasNoSignedWrap())
2006 return getAddRecExpr(
2007 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2008 getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
2009
2010 // Check whether the backedge-taken count is SCEVCouldNotCompute.
2011 // Note that this serves two purposes: It filters out loops that are
2012 // simply not analyzable, and it covers the case where this code is
2013 // being called from within backedge-taken count analysis, such that
2014 // attempting to ask for the backedge-taken count would likely result
2015 // in infinite recursion. In the later case, the analysis code will
2016 // cope with a conservative value, and it will take care to purge
2017 // that value once it has finished.
2018 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
2019 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
2020 // Manually compute the final value for AR, checking for
2021 // overflow.
2022
2023 // Check whether the backedge-taken count can be losslessly casted to
2024 // the addrec's type. The count is always unsigned.
2025 const SCEV *CastedMaxBECount =
2026 getTruncateOrZeroExtend(MaxBECount, Start->getType());
2027 const SCEV *RecastedMaxBECount =
2028 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
2029 if (MaxBECount == RecastedMaxBECount) {
2030 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
2031 // Check whether Start+Step*MaxBECount has no signed overflow.
2032 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
2033 SCEV::FlagAnyWrap, Depth + 1);
2034 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
2035 SCEV::FlagAnyWrap,
2036 Depth + 1),
2037 WideTy, Depth + 1);
2038 const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
2039 const SCEV *WideMaxBECount =
2040 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
2041 const SCEV *OperandExtendedAdd =
2042 getAddExpr(WideStart,
2043 getMulExpr(WideMaxBECount,
2044 getSignExtendExpr(Step, WideTy, Depth + 1),
2045 SCEV::FlagAnyWrap, Depth + 1),
2046 SCEV::FlagAnyWrap, Depth + 1);
2047 if (SAdd == OperandExtendedAdd) {
2048 // Cache knowledge of AR NSW, which is propagated to this AddRec.
2049 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2050 // Return the expression with the addrec on the outside.
2051 return getAddRecExpr(
2052 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
2053 Depth + 1),
2054 getSignExtendExpr(Step, Ty, Depth + 1), L,
2055 AR->getNoWrapFlags());
2056 }
2057 // Similar to above, only this time treat the step value as unsigned.
2058 // This covers loops that count up with an unsigned step.
2059 OperandExtendedAdd =
2060 getAddExpr(WideStart,
2061 getMulExpr(WideMaxBECount,
2062 getZeroExtendExpr(Step, WideTy, Depth + 1),
2063 SCEV::FlagAnyWrap, Depth + 1),
2064 SCEV::FlagAnyWrap, Depth + 1);
2065 if (SAdd == OperandExtendedAdd) {
2066 // If AR wraps around then
2067 //
2068 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
2069 // => SAdd != OperandExtendedAdd
2070 //
2071 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
2072 // (SAdd == OperandExtendedAdd => AR is NW)
2073
2074 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
2075
2076 // Return the expression with the addrec on the outside.
2077 return getAddRecExpr(
2078 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
2079 Depth + 1),
2080 getZeroExtendExpr(Step, Ty, Depth + 1), L,
2081 AR->getNoWrapFlags());
2082 }
2083 }
2084 }
2085
2086 // Normally, in the cases we can prove no-overflow via a
2087 // backedge guarding condition, we can also compute a backedge
2088 // taken count for the loop. The exceptions are assumptions and
2089 // guards present in the loop -- SCEV is not great at exploiting
2090 // these to compute max backedge taken counts, but can still use
2091 // these to prove lack of overflow. Use this fact to avoid
2092 // doing extra work that may not pay off.
2093
2094 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
2095 !AC.assumptions().empty()) {
2096 // If the backedge is guarded by a comparison with the pre-inc
2097 // value the addrec is safe. Also, if the entry is guarded by
2098 // a comparison with the start value and the backedge is
2099 // guarded by a comparison with the post-inc value, the addrec
2100 // is safe.
2101 ICmpInst::Predicate Pred;
2102 const SCEV *OverflowLimit =
2103 getSignedOverflowLimitForStep(Step, &Pred, this);
2104 if (OverflowLimit &&
2105 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
2106 isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
2107 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
2108 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2109 return getAddRecExpr(
2110 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2111 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2112 }
2113 }
2114
2115 // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
2116 // if D + (C - D + Step * n) could be proven to not signed wrap
2117 // where D maximizes the number of trailing zeros of (C - D + Step * n)
2118 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
2119 const APInt &C = SC->getAPInt();
2120 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
2121 if (D != 0) {
2122 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
2123 const SCEV *SResidual =
2124 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
2125 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
2126 return getAddExpr(SSExtD, SSExtR,
2127 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
2128 Depth + 1);
2129 }
2130 }
2131
2132 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
2133 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2134 return getAddRecExpr(
2135 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2136 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2137 }
2138 }
2139
2140 // If the input value is provably positive and we could not simplify
2141 // away the sext build a zext instead.
2142 if (isKnownNonNegative(Op))
2143 return getZeroExtendExpr(Op, Ty, Depth + 1);
2144
2145 // The cast wasn't folded; create an explicit cast node.
2146 // Recompute the insert position, as it may have been invalidated.
2147 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2148 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
2149 Op, Ty);
2150 UniqueSCEVs.InsertNode(S, IP);
2151 addToLoopUseLists(S);
2152 return S;
2153}
2154
2155/// getAnyExtendExpr - Return a SCEV for the given operand extended with
2156/// unspecified bits out to the given type.
2157const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
2158 Type *Ty) {
2159 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2160, __PRETTY_FUNCTION__))
2160 "This is not an extending conversion!")((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2160, __PRETTY_FUNCTION__))
;
2161 assert(isSCEVable(Ty) &&((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2162, __PRETTY_FUNCTION__))
2162 "This is not a conversion to a SCEVable type!")((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2162, __PRETTY_FUNCTION__))
;
2163 Ty = getEffectiveSCEVType(Ty);
2164
2165 // Sign-extend negative constants.
2166 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
2167 if (SC->getAPInt().isNegative())
2168 return getSignExtendExpr(Op, Ty);
2169
2170 // Peel off a truncate cast.
2171 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
2172 const SCEV *NewOp = T->getOperand();
2173 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
2174 return getAnyExtendExpr(NewOp, Ty);
2175 return getTruncateOrNoop(NewOp, Ty);
2176 }
2177
2178 // Next try a zext cast. If the cast is folded, use it.
2179 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
2180 if (!isa<SCEVZeroExtendExpr>(ZExt))
2181 return ZExt;
2182
2183 // Next try a sext cast. If the cast is folded, use it.
2184 const SCEV *SExt = getSignExtendExpr(Op, Ty);
2185 if (!isa<SCEVSignExtendExpr>(SExt))
2186 return SExt;
2187
2188 // Force the cast to be folded into the operands of an addrec.
2189 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
2190 SmallVector<const SCEV *, 4> Ops;
2191 for (const SCEV *Op : AR->operands())
2192 Ops.push_back(getAnyExtendExpr(Op, Ty));
2193 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
2194 }
2195
2196 // If the expression is obviously signed, use the sext cast value.
2197 if (isa<SCEVSMaxExpr>(Op))
2198 return SExt;
2199
2200 // Absent any other information, use the zext cast value.
2201 return ZExt;
2202}
2203
2204/// Process the given Ops list, which is a list of operands to be added under
2205/// the given scale, update the given map. This is a helper function for
2206/// getAddRecExpr. As an example of what it does, given a sequence of operands
2207/// that would form an add expression like this:
2208///
2209/// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2210///
2211/// where A and B are constants, update the map with these values:
2212///
2213/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2214///
2215/// and add 13 + A*B*29 to AccumulatedConstant.
2216/// This will allow getAddRecExpr to produce this:
2217///
2218/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2219///
2220/// This form often exposes folding opportunities that are hidden in
2221/// the original operand list.
2222///
2223/// Return true iff it appears that any interesting folding opportunities
2224/// may be exposed. This helps getAddRecExpr short-circuit extra work in
2225/// the common case where no interesting opportunities are present, and
2226/// is also used as a check to avoid infinite recursion.
2227static bool
2228CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
2229 SmallVectorImpl<const SCEV *> &NewOps,
2230 APInt &AccumulatedConstant,
2231 const SCEV *const *Ops, size_t NumOperands,
2232 const APInt &Scale,
2233 ScalarEvolution &SE) {
2234 bool Interesting = false;
2235
2236 // Iterate over the add operands. They are sorted, with constants first.
2237 unsigned i = 0;
2238 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2239 ++i;
2240 // Pull a buried constant out to the outside.
2241 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
2242 Interesting = true;
2243 AccumulatedConstant += Scale * C->getAPInt();
2244 }
2245
2246 // Next comes everything else. We're especially interested in multiplies
2247 // here, but they're in the middle, so just visit the rest with one loop.
2248 for (; i != NumOperands; ++i) {
2249 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
2250 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
2251 APInt NewScale =
2252 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
2253 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
2254 // A multiplication of a constant with another add; recurse.
2255 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2256 Interesting |=
2257 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2258 Add->op_begin(), Add->getNumOperands(),
2259 NewScale, SE);
2260 } else {
2261 // A multiplication of a constant with some other value. Update
2262 // the map.
2263 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
2264 const SCEV *Key = SE.getMulExpr(MulOps);
2265 auto Pair = M.insert({Key, NewScale});
2266 if (Pair.second) {
2267 NewOps.push_back(Pair.first->first);
2268 } else {
2269 Pair.first->second += NewScale;
2270 // The map already had an entry for this value, which may indicate
2271 // a folding opportunity.
2272 Interesting = true;
2273 }
2274 }
2275 } else {
2276 // An ordinary operand. Update the map.
2277 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2278 M.insert({Ops[i], Scale});
2279 if (Pair.second) {
2280 NewOps.push_back(Pair.first->first);
2281 } else {
2282 Pair.first->second += Scale;
2283 // The map already had an entry for this value, which may indicate
2284 // a folding opportunity.
2285 Interesting = true;
2286 }
2287 }
2288 }
2289
2290 return Interesting;
2291}
2292
2293// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2294// `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2295// can't-overflow flags for the operation if possible.
2296static SCEV::NoWrapFlags
2297StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
2298 const SmallVectorImpl<const SCEV *> &Ops,
2299 SCEV::NoWrapFlags Flags) {
2300 using namespace std::placeholders;
2301
2302 using OBO = OverflowingBinaryOperator;
2303
2304 bool CanAnalyze =
2305 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2306 (void)CanAnalyze;
2307 assert(CanAnalyze && "don't call from other places!")((CanAnalyze && "don't call from other places!") ? static_cast
<void> (0) : __assert_fail ("CanAnalyze && \"don't call from other places!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2307, __PRETTY_FUNCTION__))
;
2308
2309 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2310 SCEV::NoWrapFlags SignOrUnsignWrap =
2311 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2312
2313 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2314 auto IsKnownNonNegative = [&](const SCEV *S) {
2315 return SE->isKnownNonNegative(S);
2316 };
2317
2318 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2319 Flags =
2320 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2321
2322 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2323
2324 if (SignOrUnsignWrap != SignOrUnsignMask &&
2325 (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
2326 isa<SCEVConstant>(Ops[0])) {
2327
2328 auto Opcode = [&] {
2329 switch (Type) {
2330 case scAddExpr:
2331 return Instruction::Add;
2332 case scMulExpr:
2333 return Instruction::Mul;
2334 default:
2335 llvm_unreachable("Unexpected SCEV op.")::llvm::llvm_unreachable_internal("Unexpected SCEV op.", "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2335)
;
2336 }
2337 }();
2338
2339 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2340
2341 // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
2342 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2343 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2344 Opcode, C, OBO::NoSignedWrap);
2345 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2346 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2347 }
2348
2349 // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
2350 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2351 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2352 Opcode, C, OBO::NoUnsignedWrap);
2353 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2354 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2355 }
2356 }
2357
2358 return Flags;
2359}
2360
2361bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
2362 return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
2363}
2364
2365/// Get a canonical add expression, or something simpler if possible.
2366const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2367 SCEV::NoWrapFlags Flags,
2368 unsigned Depth) {
2369 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&((!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && "only nuw or nsw allowed"
) ? static_cast<void> (0) : __assert_fail ("!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && \"only nuw or nsw allowed\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2370, __PRETTY_FUNCTION__))
2370 "only nuw or nsw allowed")((!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && "only nuw or nsw allowed"
) ? static_cast<void> (0) : __assert_fail ("!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && \"only nuw or nsw allowed\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2370, __PRETTY_FUNCTION__))
;
2371 assert(!Ops.empty() && "Cannot get empty add!")((!Ops.empty() && "Cannot get empty add!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty add!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2371, __PRETTY_FUNCTION__))
;
2372 if (Ops.size() == 1) return Ops[0];
2373#ifndef NDEBUG
2374 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2375 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2376 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVAddExpr operand types don't match!") ? static_cast<void
> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVAddExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2377, __PRETTY_FUNCTION__))
2377 "SCEVAddExpr operand types don't match!")((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVAddExpr operand types don't match!") ? static_cast<void
> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVAddExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2377, __PRETTY_FUNCTION__))
;
2378#endif
2379
2380 // Sort by complexity, this groups all similar expression types together.
2381 GroupByComplexity(Ops, &LI, DT);
2382
2383 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2384
2385 // If there are any constants, fold them together.
2386 unsigned Idx = 0;
2387 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2388 ++Idx;
2389 assert(Idx < Ops.size())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2389, __PRETTY_FUNCTION__))
;
2390 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2391 // We found two constants, fold them together!
2392 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2393 if (Ops.size() == 2) return Ops[0];
2394 Ops.erase(Ops.begin()+1); // Erase the folded element
2395 LHSC = cast<SCEVConstant>(Ops[0]);
2396 }
2397
2398 // If we are left with a constant zero being added, strip it off.
2399 if (LHSC->getValue()->isZero()) {
2400 Ops.erase(Ops.begin());
2401 --Idx;
2402 }
2403
2404 if (Ops.size() == 1) return Ops[0];
2405 }
2406
2407 // Limit recursion calls depth.
2408 if (Depth > MaxArithDepth)
2409 return getOrCreateAddExpr(Ops, Flags);
2410
2411 // Okay, check to see if the same value occurs in the operand list more than
2412 // once. If so, merge them together into an multiply expression. Since we
2413 // sorted the list, these values are required to be adjacent.
2414 Type *Ty = Ops[0]->getType();
2415 bool FoundMatch = false;
2416 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2417 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2418 // Scan ahead to count how many equal operands there are.
2419 unsigned Count = 2;
2420 while (i+Count != e && Ops[i+Count] == Ops[i])
2421 ++Count;
2422 // Merge the values into a multiply.
2423 const SCEV *Scale = getConstant(Ty, Count);
2424 const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
2425 if (Ops.size() == Count)
2426 return Mul;
2427 Ops[i] = Mul;
2428 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2429 --i; e -= Count - 1;
2430 FoundMatch = true;
2431 }
2432 if (FoundMatch)
2433 return getAddExpr(Ops, Flags, Depth + 1);
2434
2435 // Check for truncates. If all the operands are truncated from the same
2436 // type, see if factoring out the truncate would permit the result to be
2437 // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
2438 // if the contents of the resulting outer trunc fold to something simple.
2439 auto FindTruncSrcType = [&]() -> Type * {
2440 // We're ultimately looking to fold an addrec of truncs and muls of only
2441 // constants and truncs, so if we find any other types of SCEV
2442 // as operands of the addrec then we bail and return nullptr here.
2443 // Otherwise, we return the type of the operand of a trunc that we find.
2444 if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
2445 return T->getOperand()->getType();
2446 if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2447 const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
2448 if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
2449 return T->getOperand()->getType();
2450 }
2451 return nullptr;
2452 };
2453 if (auto *SrcType = FindTruncSrcType()) {
2454 SmallVector<const SCEV *, 8> LargeOps;
2455 bool Ok = true;
2456 // Check all the operands to see if they can be represented in the
2457 // source type of the truncate.
2458 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2459 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2460 if (T->getOperand()->getType() != SrcType) {
2461 Ok = false;
2462 break;
2463 }
2464 LargeOps.push_back(T->getOperand());
2465 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2466 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2467 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2468 SmallVector<const SCEV *, 8> LargeMulOps;
2469 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2470 if (const SCEVTruncateExpr *T =
2471 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2472 if (T->getOperand()->getType() != SrcType) {
2473 Ok = false;
2474 break;
2475 }
2476 LargeMulOps.push_back(T->getOperand());
2477 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2478 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2479 } else {
2480 Ok = false;
2481 break;
2482 }
2483 }
2484 if (Ok)
2485 LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
2486 } else {
2487 Ok = false;
2488 break;
2489 }
2490 }
2491 if (Ok) {
2492 // Evaluate the expression in the larger type.
2493 const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
2494 // If it folds to something simple, use it. Otherwise, don't.
2495 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2496 return getTruncateExpr(Fold, Ty);
2497 }
2498 }
2499
2500 // Skip past any other cast SCEVs.
2501 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2502 ++Idx;
2503
2504 // If there are add operands they would be next.
2505 if (Idx < Ops.size()) {
2506 bool DeletedAdd = false;
2507 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2508 if (Ops.size() > AddOpsInlineThreshold ||
2509 Add->getNumOperands() > AddOpsInlineThreshold)
2510 break;
2511 // If we have an add, expand the add operands onto the end of the operands
2512 // list.
2513 Ops.erase(Ops.begin()+Idx);
2514 Ops.append(Add->op_begin(), Add->op_end());
2515 DeletedAdd = true;
2516 }
2517
2518 // If we deleted at least one add, we added operands to the end of the list,
2519 // and they are not necessarily sorted. Recurse to resort and resimplify
2520 // any operands we just acquired.
2521 if (DeletedAdd)
2522 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2523 }
2524
2525 // Skip over the add expression until we get to a multiply.
2526 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2527 ++Idx;
2528
2529 // Check to see if there are any folding opportunities present with
2530 // operands multiplied by constant values.
2531 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2532 uint64_t BitWidth = getTypeSizeInBits(Ty);
2533 DenseMap<const SCEV *, APInt> M;
2534 SmallVector<const SCEV *, 8> NewOps;
2535 APInt AccumulatedConstant(BitWidth, 0);
2536 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2537 Ops.data(), Ops.size(),
2538 APInt(BitWidth, 1), *this)) {
2539 struct APIntCompare {
2540 bool operator()(const APInt &LHS, const APInt &RHS) const {
2541 return LHS.ult(RHS);
2542 }
2543 };
2544
2545 // Some interesting folding opportunity is present, so its worthwhile to
2546 // re-generate the operands list. Group the operands by constant scale,
2547 // to avoid multiplying by the same constant scale multiple times.
2548 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2549 for (const SCEV *NewOp : NewOps)
2550 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2551 // Re-generate the operands list.
2552 Ops.clear();
2553 if (AccumulatedConstant != 0)
2554 Ops.push_back(getConstant(AccumulatedConstant));
2555 for (auto &MulOp : MulOpLists)
2556 if (MulOp.first != 0)
2557 Ops.push_back(getMulExpr(
2558 getConstant(MulOp.first),
2559 getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
2560 SCEV::FlagAnyWrap, Depth + 1));
2561 if (Ops.empty())
2562 return getZero(Ty);
2563 if (Ops.size() == 1)
2564 return Ops[0];
2565 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2566 }
2567 }
2568
2569 // If we are adding something to a multiply expression, make sure the
2570 // something is not already an operand of the multiply. If so, merge it into
2571 // the multiply.
2572 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2573 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2574 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2575 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2576 if (isa<SCEVConstant>(MulOpSCEV))
2577 continue;
2578 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2579 if (MulOpSCEV == Ops[AddOp]) {
2580 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2581 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2582 if (Mul->getNumOperands() != 2) {
2583 // If the multiply has more than two operands, we must get the
2584 // Y*Z term.
2585 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2586 Mul->op_begin()+MulOp);
2587 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2588 InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2589 }
2590 SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
2591 const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2592 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
2593 SCEV::FlagAnyWrap, Depth + 1);
2594 if (Ops.size() == 2) return OuterMul;
2595 if (AddOp < Idx) {
2596 Ops.erase(Ops.begin()+AddOp);
2597 Ops.erase(Ops.begin()+Idx-1);
2598 } else {
2599 Ops.erase(Ops.begin()+Idx);
2600 Ops.erase(Ops.begin()+AddOp-1);
2601 }
2602 Ops.push_back(OuterMul);
2603 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2604 }
2605
2606 // Check this multiply against other multiplies being added together.
2607 for (unsigned OtherMulIdx = Idx+1;
2608 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2609 ++OtherMulIdx) {
2610 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2611 // If MulOp occurs in OtherMul, we can fold the two multiplies
2612 // together.
2613 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2614 OMulOp != e; ++OMulOp)
2615 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2616 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2617 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2618 if (Mul->getNumOperands() != 2) {
2619 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2620 Mul->op_begin()+MulOp);
2621 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2622 InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2623 }
2624 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2625 if (OtherMul->getNumOperands() != 2) {
2626 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2627 OtherMul->op_begin()+OMulOp);
2628 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2629 InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2630 }
2631 SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
2632 const SCEV *InnerMulSum =
2633 getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2634 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
2635 SCEV::FlagAnyWrap, Depth + 1);
2636 if (Ops.size() == 2) return OuterMul;
2637 Ops.erase(Ops.begin()+Idx);
2638 Ops.erase(Ops.begin()+OtherMulIdx-1);
2639 Ops.push_back(OuterMul);
2640 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2641 }
2642 }
2643 }
2644 }
2645
2646 // If there are any add recurrences in the operands list, see if any other
2647 // added values are loop invariant. If so, we can fold them into the
2648 // recurrence.
2649 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2650 ++Idx;
2651
2652 // Scan over all recurrences, trying to fold loop invariants into them.
2653 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2654 // Scan all of the other operands to this add and add them to the vector if
2655 // they are loop invariant w.r.t. the recurrence.
2656 SmallVector<const SCEV *, 8> LIOps;
2657 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2658 const Loop *AddRecLoop = AddRec->getLoop();
2659 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2660 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2661 LIOps.push_back(Ops[i]);
2662 Ops.erase(Ops.begin()+i);
2663 --i; --e;
2664 }
2665
2666 // If we found some loop invariants, fold them into the recurrence.
2667 if (!LIOps.empty()) {
2668 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2669 LIOps.push_back(AddRec->getStart());
2670
2671 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2672 AddRec->op_end());
2673 // This follows from the fact that the no-wrap flags on the outer add
2674 // expression are applicable on the 0th iteration, when the add recurrence
2675 // will be equal to its start value.
2676 AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
2677
2678 // Build the new addrec. Propagate the NUW and NSW flags if both the
2679 // outer add and the inner addrec are guaranteed to have no overflow.
2680 // Always propagate NW.
2681 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2682 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2683
2684 // If all of the other operands were loop invariant, we are done.
2685 if (Ops.size() == 1) return NewRec;
2686
2687 // Otherwise, add the folded AddRec by the non-invariant parts.
2688 for (unsigned i = 0;; ++i)
2689 if (Ops[i] == AddRec) {
2690 Ops[i] = NewRec;
2691 break;
2692 }
2693 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2694 }
2695
2696 // Okay, if there weren't any loop invariants to be folded, check to see if
2697 // there are multiple AddRec's with the same loop induction variable being
2698 // added together. If so, we can fold them.
2699 for (unsigned OtherIdx = Idx+1;
2700 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2701 ++OtherIdx) {
2702 // We expect the AddRecExpr's to be sorted in reverse dominance order,
2703 // so that the 1st found AddRecExpr is dominated by all others.
2704 assert(DT.dominates(((DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->
getLoop()->getHeader(), AddRec->getLoop()->getHeader
()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2707, __PRETTY_FUNCTION__))
2705 cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),((DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->
getLoop()->getHeader(), AddRec->getLoop()->getHeader
()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2707, __PRETTY_FUNCTION__))
2706 AddRec->getLoop()->getHeader()) &&((DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->
getLoop()->getHeader(), AddRec->getLoop()->getHeader
()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2707, __PRETTY_FUNCTION__))
2707 "AddRecExprs are not sorted in reverse dominance order?")((DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->
getLoop()->getHeader(), AddRec->getLoop()->getHeader
()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2707, __PRETTY_FUNCTION__))
;
2708 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2709 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2710 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2711 AddRec->op_end());
2712 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2713 ++OtherIdx) {
2714 const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2715 if (OtherAddRec->getLoop() == AddRecLoop) {
2716 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2717 i != e; ++i) {
2718 if (i >= AddRecOps.size()) {
2719 AddRecOps.append(OtherAddRec->op_begin()+i,
2720 OtherAddRec->op_end());
2721 break;
2722 }
2723 SmallVector<const SCEV *, 2> TwoOps = {
2724 AddRecOps[i], OtherAddRec->getOperand(i)};
2725 AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2726 }
2727 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2728 }
2729 }
2730 // Step size has changed, so we cannot guarantee no self-wraparound.
2731 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2732 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2733 }
2734 }
2735
2736 // Otherwise couldn't fold anything into this recurrence. Move onto the
2737 // next one.
2738 }
2739
2740 // Okay, it looks like we really DO need an add expr. Check to see if we
2741 // already have one, otherwise create a new one.
2742 return getOrCreateAddExpr(Ops, Flags);
2743}
2744
2745const SCEV *
2746ScalarEvolution::getOrCreateAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2747 SCEV::NoWrapFlags Flags) {
2748 FoldingSetNodeID ID;
2749 ID.AddInteger(scAddExpr);
2750 for (const SCEV *Op : Ops)
2751 ID.AddPointer(Op);
2752 void *IP = nullptr;
2753 SCEVAddExpr *S =
2754 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2755 if (!S) {
2756 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2757 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2758 S = new (SCEVAllocator)
2759 SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
2760 UniqueSCEVs.InsertNode(S, IP);
2761 addToLoopUseLists(S);
2762 }
2763 S->setNoWrapFlags(Flags);
2764 return S;
2765}
2766
2767const SCEV *
2768ScalarEvolution::getOrCreateAddRecExpr(SmallVectorImpl<const SCEV *> &Ops,
2769 const Loop *L, SCEV::NoWrapFlags Flags) {
2770 FoldingSetNodeID ID;
2771 ID.AddInteger(scAddRecExpr);
2772 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2773 ID.AddPointer(Ops[i]);
2774 ID.AddPointer(L);
2775 void *IP = nullptr;
2776 SCEVAddRecExpr *S =
2777 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2778 if (!S) {
2779 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2780 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2781 S = new (SCEVAllocator)
2782 SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
2783 UniqueSCEVs.InsertNode(S, IP);
2784 addToLoopUseLists(S);
2785 }
2786 S->setNoWrapFlags(Flags);
2787 return S;
2788}
2789
2790const SCEV *
2791ScalarEvolution::getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2792 SCEV::NoWrapFlags Flags) {
2793 FoldingSetNodeID ID;
2794 ID.AddInteger(scMulExpr);
2795 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2796 ID.AddPointer(Ops[i]);
2797 void *IP = nullptr;
2798 SCEVMulExpr *S =
2799 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2800 if (!S) {
2801 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2802 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2803 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2804 O, Ops.size());
2805 UniqueSCEVs.InsertNode(S, IP);
2806 addToLoopUseLists(S);
2807 }
2808 S->setNoWrapFlags(Flags);
2809 return S;
2810}
2811
2812static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2813 uint64_t k = i*j;
2814 if (j > 1 && k / j != i) Overflow = true;
2815 return k;
2816}
2817
2818/// Compute the result of "n choose k", the binomial coefficient. If an
2819/// intermediate computation overflows, Overflow will be set and the return will
2820/// be garbage. Overflow is not cleared on absence of overflow.
2821static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2822 // We use the multiplicative formula:
2823 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2824 // At each iteration, we take the n-th term of the numeral and divide by the
2825 // (k-n)th term of the denominator. This division will always produce an
2826 // integral result, and helps reduce the chance of overflow in the
2827 // intermediate computations. However, we can still overflow even when the
2828 // final result would fit.
2829
2830 if (n == 0 || n == k) return 1;
2831 if (k > n) return 0;
2832
2833 if (k > n/2)
2834 k = n-k;
2835
2836 uint64_t r = 1;
2837 for (uint64_t i = 1; i <= k; ++i) {
2838 r = umul_ov(r, n-(i-1), Overflow);
2839 r /= i;
2840 }
2841 return r;
2842}
2843
2844/// Determine if any of the operands in this SCEV are a constant or if
2845/// any of the add or multiply expressions in this SCEV contain a constant.
2846static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
2847 struct FindConstantInAddMulChain {
2848 bool FoundConstant = false;
2849
2850 bool follow(const SCEV *S) {
2851 FoundConstant |= isa<SCEVConstant>(S);
2852 return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
2853 }
2854
2855 bool isDone() const {
2856 return FoundConstant;
2857 }
2858 };
2859
2860 FindConstantInAddMulChain F;
2861 SCEVTraversal<FindConstantInAddMulChain> ST(F);
2862 ST.visitAll(StartExpr);
2863 return F.FoundConstant;
2864}
2865
2866/// Get a canonical multiply expression, or something simpler if possible.
2867const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2868 SCEV::NoWrapFlags Flags,
2869 unsigned Depth) {
2870 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&((Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
"only nuw or nsw allowed") ? static_cast<void> (0) : __assert_fail
("Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && \"only nuw or nsw allowed\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2871, __PRETTY_FUNCTION__))
2871 "only nuw or nsw allowed")((Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
"only nuw or nsw allowed") ? static_cast<void> (0) : __assert_fail
("Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && \"only nuw or nsw allowed\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2871, __PRETTY_FUNCTION__))
;
2872 assert(!Ops.empty() && "Cannot get empty mul!")((!Ops.empty() && "Cannot get empty mul!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty mul!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2872, __PRETTY_FUNCTION__))
;
2873 if (Ops.size() == 1) return Ops[0];
2874#ifndef NDEBUG
2875 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2876 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2877 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVMulExpr operand types don't match!") ? static_cast<void
> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVMulExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2878, __PRETTY_FUNCTION__))
2878 "SCEVMulExpr operand types don't match!")((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVMulExpr operand types don't match!") ? static_cast<void
> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVMulExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 2878, __PRETTY_FUNCTION__))
;
2879#endif
2880
2881 // Sort by complexity, this groups all similar expression types together.
2882 GroupByComplexity(Ops, &LI, DT);
2883
2884 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2885
2886 // Limit recursion calls depth.
2887 if (Depth > MaxArithDepth)
2888 return getOrCreateMulExpr(Ops, Flags);
2889
2890 // If there are any constants, fold them together.
2891 unsigned Idx = 0;
2892 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2893
2894 if (Ops.size() == 2)
2895 // C1*(C2+V) -> C1*C2 + C1*V
2896 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2897 // If any of Add's ops are Adds or Muls with a constant, apply this
2898 // transformation as well.
2899 //
2900 // TODO: There are some cases where this transformation is not
2901 // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
2902 // this transformation should be narrowed down.
2903 if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add))
2904 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
2905 SCEV::FlagAnyWrap, Depth + 1),
2906 getMulExpr(LHSC, Add->getOperand(1),
2907 SCEV::FlagAnyWrap, Depth + 1),
2908 SCEV::FlagAnyWrap, Depth + 1);
2909
2910 ++Idx;
2911 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2912 // We found two constants, fold them together!
2913 ConstantInt *Fold =
2914 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2915 Ops[0] = getConstant(Fold);
2916 Ops.erase(Ops.begin()+1); // Erase the folded element
2917 if (Ops.size() == 1) return Ops[0];
2918 LHSC = cast<SCEVConstant>(Ops[0]);
2919 }
2920
2921 // If we are left with a constant one being multiplied, strip it off.
2922 if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
2923 Ops.erase(Ops.begin());
2924 --Idx;
2925 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2926 // If we have a multiply of zero, it will always be zero.
2927 return Ops[0];
2928 } else if (Ops[0]->isAllOnesValue()) {
2929 // If we have a mul by -1 of an add, try distributing the -1 among the
2930 // add operands.
2931 if (Ops.size() == 2) {
2932 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2933 SmallVector<const SCEV *, 4> NewOps;
2934 bool AnyFolded = false;
2935 for (const SCEV *AddOp : Add->operands()) {
2936 const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
2937 Depth + 1);
2938 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2939 NewOps.push_back(Mul);
2940 }
2941 if (AnyFolded)
2942 return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
2943 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2944 // Negation preserves a recurrence's no self-wrap property.
2945 SmallVector<const SCEV *, 4> Operands;
2946 for (const SCEV *AddRecOp : AddRec->operands())
2947 Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
2948 Depth + 1));
2949
2950 return getAddRecExpr(Operands, AddRec->getLoop(),
2951 AddRec->getNoWrapFlags(SCEV::FlagNW));
2952 }
2953 }
2954 }
2955
2956 if (Ops.size() == 1)
2957 return Ops[0];
2958 }
2959
2960 // Skip over the add expression until we get to a multiply.
2961 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2962 ++Idx;
2963
2964 // If there are mul operands inline them all into this expression.
2965 if (Idx < Ops.size()) {
2966 bool DeletedMul = false;
2967 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2968 if (Ops.size() > MulOpsInlineThreshold)
2969 break;
2970 // If we have an mul, expand the mul operands onto the end of the
2971 // operands list.
2972 Ops.erase(Ops.begin()+Idx);
2973 Ops.append(Mul->op_begin(), Mul->op_end());
2974 DeletedMul = true;
2975 }
2976
2977 // If we deleted at least one mul, we added operands to the end of the
2978 // list, and they are not necessarily sorted. Recurse to resort and
2979 // resimplify any operands we just acquired.
2980 if (DeletedMul)
2981 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2982 }
2983
2984 // If there are any add recurrences in the operands list, see if any other
2985 // added values are loop invariant. If so, we can fold them into the
2986 // recurrence.
2987 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2988 ++Idx;
2989
2990 // Scan over all recurrences, trying to fold loop invariants into them.
2991 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2992 // Scan all of the other operands to this mul and add them to the vector
2993 // if they are loop invariant w.r.t. the recurrence.
2994 SmallVector<const SCEV *, 8> LIOps;
2995 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2996 const Loop *AddRecLoop = AddRec->getLoop();
2997 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2998 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2999 LIOps.push_back(Ops[i]);
3000 Ops.erase(Ops.begin()+i);
3001 --i; --e;
3002 }
3003
3004 // If we found some loop invariants, fold them into the recurrence.
3005 if (!LIOps.empty()) {
3006 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
3007 SmallVector<const SCEV *, 4> NewOps;
3008 NewOps.reserve(AddRec->getNumOperands());
3009 const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
3010 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
3011 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
3012 SCEV::FlagAnyWrap, Depth + 1));
3013
3014 // Build the new addrec. Propagate the NUW and NSW flags if both the
3015 // outer mul and the inner addrec are guaranteed to have no overflow.
3016 //
3017 // No self-wrap cannot be guaranteed after changing the step size, but
3018 // will be inferred if either NUW or NSW is true.
3019 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
3020 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
3021
3022 // If all of the other operands were loop invariant, we are done.
3023 if (Ops.size() == 1) return NewRec;
3024
3025 // Otherwise, multiply the folded AddRec by the non-invariant parts.
3026 for (unsigned i = 0;; ++i)
3027 if (Ops[i] == AddRec) {
3028 Ops[i] = NewRec;
3029 break;
3030 }
3031 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3032 }
3033
3034 // Okay, if there weren't any loop invariants to be folded, check to see
3035 // if there are multiple AddRec's with the same loop induction variable
3036 // being multiplied together. If so, we can fold them.
3037
3038 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
3039 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
3040 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
3041 // ]]],+,...up to x=2n}.
3042 // Note that the arguments to choose() are always integers with values
3043 // known at compile time, never SCEV objects.
3044 //
3045 // The implementation avoids pointless extra computations when the two
3046 // addrec's are of different length (mathematically, it's equivalent to
3047 // an infinite stream of zeros on the right).
3048 bool OpsModified = false;
3049 for (unsigned OtherIdx = Idx+1;
3050 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
3051 ++OtherIdx) {
3052 const SCEVAddRecExpr *OtherAddRec =
3053 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
3054 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
3055 continue;
3056
3057 // Limit max number of arguments to avoid creation of unreasonably big
3058 // SCEVAddRecs with very complex operands.
3059 if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
3060 MaxAddRecSize)
3061 continue;
3062
3063 bool Overflow = false;
3064 Type *Ty = AddRec->getType();
3065 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
3066 SmallVector<const SCEV*, 7> AddRecOps;
3067 for (int x = 0, xe = AddRec->getNumOperands() +
3068 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
3069 SmallVector <const SCEV *, 7> SumOps;
3070 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
3071 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
3072 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
3073 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
3074 z < ze && !Overflow; ++z) {
3075 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
3076 uint64_t Coeff;
3077 if (LargerThan64Bits)
3078 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
3079 else
3080 Coeff = Coeff1*Coeff2;
3081 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
3082 const SCEV *Term1 = AddRec->getOperand(y-z);
3083 const SCEV *Term2 = OtherAddRec->getOperand(z);
3084 SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
3085 SCEV::FlagAnyWrap, Depth + 1));
3086 }
3087 }
3088 if (SumOps.empty())
3089 SumOps.push_back(getZero(Ty));
3090 AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
3091 }
3092 if (!Overflow) {
3093 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
3094 SCEV::FlagAnyWrap);
3095 if (Ops.size() == 2) return NewAddRec;
3096 Ops[Idx] = NewAddRec;
3097 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
3098 OpsModified = true;
3099 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
3100 if (!AddRec)
3101 break;
3102 }
3103 }
3104 if (OpsModified)
3105 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3106
3107 // Otherwise couldn't fold anything into this recurrence. Move onto the
3108 // next one.
3109 }
3110
3111 // Okay, it looks like we really DO need an mul expr. Check to see if we
3112 // already have one, otherwise create a new one.
3113 return getOrCreateMulExpr(Ops, Flags);
3114}
3115
3116/// Represents an unsigned remainder expression based on unsigned division.
3117const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
3118 const SCEV *RHS) {
3119 assert(getEffectiveSCEVType(LHS->getType()) ==((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVURemExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVURemExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3121, __PRETTY_FUNCTION__))
3120 getEffectiveSCEVType(RHS->getType()) &&((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVURemExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVURemExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3121, __PRETTY_FUNCTION__))
3121 "SCEVURemExpr operand types don't match!")((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVURemExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVURemExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3121, __PRETTY_FUNCTION__))
;
3122
3123 // Short-circuit easy cases
3124 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3125 // If constant is one, the result is trivial
3126 if (RHSC->getValue()->isOne())
3127 return getZero(LHS->getType()); // X urem 1 --> 0
3128
3129 // If constant is a power of two, fold into a zext(trunc(LHS)).
3130 if (RHSC->getAPInt().isPowerOf2()) {
3131 Type *FullTy = LHS->getType();
3132 Type *TruncTy =
3133 IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
3134 return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
3135 }
3136 }
3137
3138 // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
3139 const SCEV *UDiv = getUDivExpr(LHS, RHS);
3140 const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
3141 return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
3142}
3143
3144/// Get a canonical unsigned division expression, or something simpler if
3145/// possible.
3146const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
3147 const SCEV *RHS) {
3148 assert(getEffectiveSCEVType(LHS->getType()) ==((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVUDivExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVUDivExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3150, __PRETTY_FUNCTION__))
3149 getEffectiveSCEVType(RHS->getType()) &&((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVUDivExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVUDivExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3150, __PRETTY_FUNCTION__))
3150 "SCEVUDivExpr operand types don't match!")((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVUDivExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVUDivExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3150, __PRETTY_FUNCTION__))
;
3151
3152 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3153 if (RHSC->getValue()->isOne())
3154 return LHS; // X udiv 1 --> x
3155 // If the denominator is zero, the result of the udiv is undefined. Don't
3156 // try to analyze it, because the resolution chosen here may differ from
3157 // the resolution chosen in other parts of the compiler.
3158 if (!RHSC->getValue()->isZero()) {
3159 // Determine if the division can be folded into the operands of
3160 // its operands.
3161 // TODO: Generalize this to non-constants by using known-bits information.
3162 Type *Ty = LHS->getType();
3163 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
3164 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
3165 // For non-power-of-two values, effectively round the value up to the
3166 // nearest power of two.
3167 if (!RHSC->getAPInt().isPowerOf2())
3168 ++MaxShiftAmt;
3169 IntegerType *ExtTy =
3170 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
3171 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
3172 if (const SCEVConstant *Step =
3173 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
3174 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
3175 const APInt &StepInt = Step->getAPInt();
3176 const APInt &DivInt = RHSC->getAPInt();
3177 if (!StepInt.urem(DivInt) &&
3178 getZeroExtendExpr(AR, ExtTy) ==
3179 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3180 getZeroExtendExpr(Step, ExtTy),
3181 AR->getLoop(), SCEV::FlagAnyWrap)) {
3182 SmallVector<const SCEV *, 4> Operands;
3183 for (const SCEV *Op : AR->operands())
3184 Operands.push_back(getUDivExpr(Op, RHS));
3185 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
3186 }
3187 /// Get a canonical UDivExpr for a recurrence.
3188 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
3189 // We can currently only fold X%N if X is constant.
3190 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
3191 if (StartC && !DivInt.urem(StepInt) &&
3192 getZeroExtendExpr(AR, ExtTy) ==
3193 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3194 getZeroExtendExpr(Step, ExtTy),
3195 AR->getLoop(), SCEV::FlagAnyWrap)) {
3196 const APInt &StartInt = StartC->getAPInt();
3197 const APInt &StartRem = StartInt.urem(StepInt);
3198 if (StartRem != 0)
3199 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
3200 AR->getLoop(), SCEV::FlagNW);
3201 }
3202 }
3203 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
3204 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
3205 SmallVector<const SCEV *, 4> Operands;
3206 for (const SCEV *Op : M->operands())
3207 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3208 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
3209 // Find an operand that's safely divisible.
3210 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
3211 const SCEV *Op = M->getOperand(i);
3212 const SCEV *Div = getUDivExpr(Op, RHSC);
3213 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
3214 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
3215 M->op_end());
3216 Operands[i] = Div;
3217 return getMulExpr(Operands);
3218 }
3219 }
3220 }
3221
3222 // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
3223 if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
3224 if (auto *DivisorConstant =
3225 dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
3226 bool Overflow = false;
3227 APInt NewRHS =
3228 DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
3229 if (Overflow) {
3230 return getConstant(RHSC->getType(), 0, false);
3231 }
3232 return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
3233 }
3234 }
3235
3236 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
3237 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
3238 SmallVector<const SCEV *, 4> Operands;
3239 for (const SCEV *Op : A->operands())
3240 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3241 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
3242 Operands.clear();
3243 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
3244 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
3245 if (isa<SCEVUDivExpr>(Op) ||
3246 getMulExpr(Op, RHS) != A->getOperand(i))
3247 break;
3248 Operands.push_back(Op);
3249 }
3250 if (Operands.size() == A->getNumOperands())
3251 return getAddExpr(Operands);
3252 }
3253 }
3254
3255 // Fold if both operands are constant.
3256 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
3257 Constant *LHSCV = LHSC->getValue();
3258 Constant *RHSCV = RHSC->getValue();
3259 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
3260 RHSCV)));
3261 }
3262 }
3263 }
3264
3265 FoldingSetNodeID ID;
3266 ID.AddInteger(scUDivExpr);
3267 ID.AddPointer(LHS);
3268 ID.AddPointer(RHS);
3269 void *IP = nullptr;
3270 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3271 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
3272 LHS, RHS);
3273 UniqueSCEVs.InsertNode(S, IP);
3274 addToLoopUseLists(S);
3275 return S;
3276}
3277
3278static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
3279 APInt A = C1->getAPInt().abs();
3280 APInt B = C2->getAPInt().abs();
3281 uint32_t ABW = A.getBitWidth();
3282 uint32_t BBW = B.getBitWidth();
3283
3284 if (ABW > BBW)
3285 B = B.zext(ABW);
3286 else if (ABW < BBW)
3287 A = A.zext(BBW);
3288
3289 return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
3290}
3291
3292/// Get a canonical unsigned division expression, or something simpler if
3293/// possible. There is no representation for an exact udiv in SCEV IR, but we
3294/// can attempt to remove factors from the LHS and RHS. We can't do this when
3295/// it's not exact because the udiv may be clearing bits.
3296const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
3297 const SCEV *RHS) {
3298 // TODO: we could try to find factors in all sorts of things, but for now we
3299 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
3300 // end of this file for inspiration.
3301
3302 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
3303 if (!Mul || !Mul->hasNoUnsignedWrap())
3304 return getUDivExpr(LHS, RHS);
3305
3306 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
3307 // If the mulexpr multiplies by a constant, then that constant must be the
3308 // first element of the mulexpr.
3309 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
3310 if (LHSCst == RHSCst) {
3311 SmallVector<const SCEV *, 2> Operands;
3312 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3313 return getMulExpr(Operands);
3314 }
3315
3316 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
3317 // that there's a factor provided by one of the other terms. We need to
3318 // check.
3319 APInt Factor = gcd(LHSCst, RHSCst);
3320 if (!Factor.isIntN(1)) {
3321 LHSCst =
3322 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
3323 RHSCst =
3324 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
3325 SmallVector<const SCEV *, 2> Operands;
3326 Operands.push_back(LHSCst);
3327 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3328 LHS = getMulExpr(Operands);
3329 RHS = RHSCst;
3330 Mul = dyn_cast<SCEVMulExpr>(LHS);
3331 if (!Mul)
3332 return getUDivExactExpr(LHS, RHS);
3333 }
3334 }
3335 }
3336
3337 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
3338 if (Mul->getOperand(i) == RHS) {
3339 SmallVector<const SCEV *, 2> Operands;
3340 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
3341 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
3342 return getMulExpr(Operands);
3343 }
3344 }
3345
3346 return getUDivExpr(LHS, RHS);
3347}
3348
3349/// Get an add recurrence expression for the specified loop. Simplify the
3350/// expression as much as possible.
3351const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
3352 const Loop *L,
3353 SCEV::NoWrapFlags Flags) {
3354 SmallVector<const SCEV *, 4> Operands;
3355 Operands.push_back(Start);
3356 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
3357 if (StepChrec->getLoop() == L) {
3358 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
3359 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
3360 }
3361
3362 Operands.push_back(Step);
3363 return getAddRecExpr(Operands, L, Flags);
3364}
3365
3366/// Get an add recurrence expression for the specified loop. Simplify the
3367/// expression as much as possible.
3368const SCEV *
3369ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
3370 const Loop *L, SCEV::NoWrapFlags Flags) {
3371 if (Operands.size() == 1) return Operands[0];
3372#ifndef NDEBUG
3373 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
3374 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
3375 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&((getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
"SCEVAddRecExpr operand types don't match!") ? static_cast<
void> (0) : __assert_fail ("getEffectiveSCEVType(Operands[i]->getType()) == ETy && \"SCEVAddRecExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3376, __PRETTY_FUNCTION__))
3376 "SCEVAddRecExpr operand types don't match!")((getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
"SCEVAddRecExpr operand types don't match!") ? static_cast<
void> (0) : __assert_fail ("getEffectiveSCEVType(Operands[i]->getType()) == ETy && \"SCEVAddRecExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3376, __PRETTY_FUNCTION__))
;
3377 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3378 assert(isLoopInvariant(Operands[i], L) &&((isLoopInvariant(Operands[i], L) && "SCEVAddRecExpr operand is not loop-invariant!"
) ? static_cast<void> (0) : __assert_fail ("isLoopInvariant(Operands[i], L) && \"SCEVAddRecExpr operand is not loop-invariant!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3379, __PRETTY_FUNCTION__))
3379 "SCEVAddRecExpr operand is not loop-invariant!")((isLoopInvariant(Operands[i], L) && "SCEVAddRecExpr operand is not loop-invariant!"
) ? static_cast<void> (0) : __assert_fail ("isLoopInvariant(Operands[i], L) && \"SCEVAddRecExpr operand is not loop-invariant!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3379, __PRETTY_FUNCTION__))
;
3380#endif
3381
3382 if (Operands.back()->isZero()) {
3383 Operands.pop_back();
3384 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
3385 }
3386
3387 // It's tempting to want to call getMaxBackedgeTakenCount count here and
3388 // use that information to infer NUW and NSW flags. However, computing a
3389 // BE count requires calling getAddRecExpr, so we may not yet have a
3390 // meaningful BE count at this point (and if we don't, we'd be stuck
3391 // with a SCEVCouldNotCompute as the cached BE count).
3392
3393 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
3394
3395 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
3396 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
3397 const Loop *NestedLoop = NestedAR->getLoop();
3398 if (L->contains(NestedLoop)
3399 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
3400 : (!NestedLoop->contains(L) &&
3401 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
3402 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
3403 NestedAR->op_end());
3404 Operands[0] = NestedAR->getStart();
3405 // AddRecs require their operands be loop-invariant with respect to their
3406 // loops. Don't perform this transformation if it would break this
3407 // requirement.
3408 bool AllInvariant = all_of(
3409 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
3410
3411 if (AllInvariant) {
3412 // Create a recurrence for the outer loop with the same step size.
3413 //
3414 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3415 // inner recurrence has the same property.
3416 SCEV::NoWrapFlags OuterFlags =
3417 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3418
3419 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3420 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3421 return isLoopInvariant(Op, NestedLoop);
3422 });
3423
3424 if (AllInvariant) {
3425 // Ok, both add recurrences are valid after the transformation.
3426 //
3427 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3428 // the outer recurrence has the same property.
3429 SCEV::NoWrapFlags InnerFlags =
3430 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3431 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3432 }
3433 }
3434 // Reset Operands to its original state.
3435 Operands[0] = NestedAR;
3436 }
3437 }
3438
3439 // Okay, it looks like we really DO need an addrec expr. Check to see if we
3440 // already have one, otherwise create a new one.
3441 return getOrCreateAddRecExpr(Operands, L, Flags);
3442}
3443
3444const SCEV *
3445ScalarEvolution::getGEPExpr(GEPOperator *GEP,
3446 const SmallVectorImpl<const SCEV *> &IndexExprs) {
3447 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3448 // getSCEV(Base)->getType() has the same address space as Base->getType()
3449 // because SCEV::getType() preserves the address space.
3450 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
3451 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3452 // instruction to its SCEV, because the Instruction may be guarded by control
3453 // flow and the no-overflow bits may not be valid for the expression in any
3454 // context. This can be fixed similarly to how these flags are handled for
3455 // adds.
3456 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
3457 : SCEV::FlagAnyWrap;
3458
3459 const SCEV *TotalOffset = getZero(IntPtrTy);
3460 // The array size is unimportant. The first thing we do on CurTy is getting
3461 // its element type.
3462 Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
3463 for (const SCEV *IndexExpr : IndexExprs) {
3464 // Compute the (potentially symbolic) offset in bytes for this index.
3465 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3466 // For a struct, add the member offset.
3467 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3468 unsigned FieldNo = Index->getZExtValue();
3469 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3470
3471 // Add the field offset to the running total offset.
3472 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3473
3474 // Update CurTy to the type of the field at Index.
3475 CurTy = STy->getTypeAtIndex(Index);
3476 } else {
3477 // Update CurTy to its element type.
3478 CurTy = cast<SequentialType>(CurTy)->getElementType();
3479 // For an array, add the element offset, explicitly scaled.
3480 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3481 // Getelementptr indices are signed.
3482 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3483
3484 // Multiply the index by the element size to compute the element offset.
3485 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3486
3487 // Add the element offset to the running total offset.
3488 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3489 }
3490 }
3491
3492 // Add the total offset from all the GEP indices to the base.
3493 return getAddExpr(BaseExpr, TotalOffset, Wrap);
3494}
3495
3496const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
3497 const SCEV *RHS) {
3498 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3499 return getSMaxExpr(Ops);
3500}
3501
3502const SCEV *
3503ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3504 assert(!Ops.empty() && "Cannot get empty smax!")((!Ops.empty() && "Cannot get empty smax!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty smax!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3504, __PRETTY_FUNCTION__))
;
3505 if (Ops.size() == 1) return Ops[0];
3506#ifndef NDEBUG
3507 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3508 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3509 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVSMaxExpr operand types don't match!") ? static_cast<
void> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVSMaxExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3510, __PRETTY_FUNCTION__))
3510 "SCEVSMaxExpr operand types don't match!")((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVSMaxExpr operand types don't match!") ? static_cast<
void> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVSMaxExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3510, __PRETTY_FUNCTION__))
;
3511#endif
3512
3513 // Sort by complexity, this groups all similar expression types together.
3514 GroupByComplexity(Ops, &LI, DT);
3515
3516 // If there are any constants, fold them together.
3517 unsigned Idx = 0;
3518 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3519 ++Idx;
3520 assert(Idx < Ops.size())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3520, __PRETTY_FUNCTION__))
;
3521 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3522 // We found two constants, fold them together!
3523 ConstantInt *Fold = ConstantInt::get(
3524 getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3525 Ops[0] = getConstant(Fold);
3526 Ops.erase(Ops.begin()+1); // Erase the folded element
3527 if (Ops.size() == 1) return Ops[0];
3528 LHSC = cast<SCEVConstant>(Ops[0]);
3529 }
3530
3531 // If we are left with a constant minimum-int, strip it off.
3532 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3533 Ops.erase(Ops.begin());
3534 --Idx;
3535 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3536 // If we have an smax with a constant maximum-int, it will always be
3537 // maximum-int.
3538 return Ops[0];
3539 }
3540
3541 if (Ops.size() == 1) return Ops[0];
3542 }
3543
3544 // Find the first SMax
3545 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3546 ++Idx;
3547
3548 // Check to see if one of the operands is an SMax. If so, expand its operands
3549 // onto our operand list, and recurse to simplify.
3550 if (Idx < Ops.size()) {
3551 bool DeletedSMax = false;
3552 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3553 Ops.erase(Ops.begin()+Idx);
3554 Ops.append(SMax->op_begin(), SMax->op_end());
3555 DeletedSMax = true;
3556 }
3557
3558 if (DeletedSMax)
3559 return getSMaxExpr(Ops);
3560 }
3561
3562 // Okay, check to see if the same value occurs in the operand list twice. If
3563 // so, delete one. Since we sorted the list, these values are required to
3564 // be adjacent.
3565 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3566 // X smax Y smax Y --> X smax Y
3567 // X smax Y --> X, if X is always greater than Y
3568 if (Ops[i] == Ops[i+1] ||
3569 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3570 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3571 --i; --e;
3572 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3573 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3574 --i; --e;
3575 }
3576
3577 if (Ops.size() == 1) return Ops[0];
3578
3579 assert(!Ops.empty() && "Reduced smax down to nothing!")((!Ops.empty() && "Reduced smax down to nothing!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"Reduced smax down to nothing!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3579, __PRETTY_FUNCTION__))
;
3580
3581 // Okay, it looks like we really DO need an smax expr. Check to see if we
3582 // already have one, otherwise create a new one.
3583 FoldingSetNodeID ID;
3584 ID.AddInteger(scSMaxExpr);
3585 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3586 ID.AddPointer(Ops[i]);
3587 void *IP = nullptr;
3588 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3589 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3590 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3591 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3592 O, Ops.size());
3593 UniqueSCEVs.InsertNode(S, IP);
3594 addToLoopUseLists(S);
3595 return S;
3596}
3597
3598const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3599 const SCEV *RHS) {
3600 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3601 return getUMaxExpr(Ops);
3602}
3603
3604const SCEV *
3605ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3606 assert(!Ops.empty() && "Cannot get empty umax!")((!Ops.empty() && "Cannot get empty umax!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty umax!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3606, __PRETTY_FUNCTION__))
;
3607 if (Ops.size() == 1) return Ops[0];
3608#ifndef NDEBUG
3609 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3610 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3611 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVUMaxExpr operand types don't match!") ? static_cast<
void> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVUMaxExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3612, __PRETTY_FUNCTION__))
3612 "SCEVUMaxExpr operand types don't match!")((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVUMaxExpr operand types don't match!") ? static_cast<
void> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVUMaxExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3612, __PRETTY_FUNCTION__))
;
3613#endif
3614
3615 // Sort by complexity, this groups all similar expression types together.
3616 GroupByComplexity(Ops, &LI, DT);
3617
3618 // If there are any constants, fold them together.
3619 unsigned Idx = 0;
3620 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3621 ++Idx;
3622 assert(Idx < Ops.size())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3622, __PRETTY_FUNCTION__))
;
3623 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3624 // We found two constants, fold them together!
3625 ConstantInt *Fold = ConstantInt::get(
3626 getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3627 Ops[0] = getConstant(Fold);
3628 Ops.erase(Ops.begin()+1); // Erase the folded element
3629 if (Ops.size() == 1) return Ops[0];
3630 LHSC = cast<SCEVConstant>(Ops[0]);
3631 }
3632
3633 // If we are left with a constant minimum-int, strip it off.
3634 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3635 Ops.erase(Ops.begin());
3636 --Idx;
3637 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3638 // If we have an umax with a constant maximum-int, it will always be
3639 // maximum-int.
3640 return Ops[0];
3641 }
3642
3643 if (Ops.size() == 1) return Ops[0];
3644 }
3645
3646 // Find the first UMax
3647 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3648 ++Idx;
3649
3650 // Check to see if one of the operands is a UMax. If so, expand its operands
3651 // onto our operand list, and recurse to simplify.
3652 if (Idx < Ops.size()) {
3653 bool DeletedUMax = false;
3654 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3655 Ops.erase(Ops.begin()+Idx);
3656 Ops.append(UMax->op_begin(), UMax->op_end());
3657 DeletedUMax = true;
3658 }
3659
3660 if (DeletedUMax)
3661 return getUMaxExpr(Ops);
3662 }
3663
3664 // Okay, check to see if the same value occurs in the operand list twice. If
3665 // so, delete one. Since we sorted the list, these values are required to
3666 // be adjacent.
3667 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3668 // X umax Y umax Y --> X umax Y
3669 // X umax Y --> X, if X is always greater than Y
3670 if (Ops[i] == Ops[i + 1] || isKnownViaNonRecursiveReasoning(
3671 ICmpInst::ICMP_UGE, Ops[i], Ops[i + 1])) {
3672 Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
3673 --i; --e;
3674 } else if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, Ops[i],
3675 Ops[i + 1])) {
3676 Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
3677 --i; --e;
3678 }
3679
3680 if (Ops.size() == 1) return Ops[0];
3681
3682 assert(!Ops.empty() && "Reduced umax down to nothing!")((!Ops.empty() && "Reduced umax down to nothing!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"Reduced umax down to nothing!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3682, __PRETTY_FUNCTION__))
;
3683
3684 // Okay, it looks like we really DO need a umax expr. Check to see if we
3685 // already have one, otherwise create a new one.
3686 FoldingSetNodeID ID;
3687 ID.AddInteger(scUMaxExpr);
3688 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3689 ID.AddPointer(Ops[i]);
3690 void *IP = nullptr;
3691 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3692 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3693 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3694 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3695 O, Ops.size());
3696 UniqueSCEVs.InsertNode(S, IP);
3697 addToLoopUseLists(S);
3698 return S;
3699}
3700
3701const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3702 const SCEV *RHS) {
3703 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3704 return getSMinExpr(Ops);
3705}
3706
3707const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3708 // ~smax(~x, ~y, ~z) == smin(x, y, z).
3709 SmallVector<const SCEV *, 2> NotOps;
3710 for (auto *S : Ops)
3711 NotOps.push_back(getNotSCEV(S));
3712 return getNotSCEV(getSMaxExpr(NotOps));
3713}
3714
3715const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3716 const SCEV *RHS) {
3717 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3718 return getUMinExpr(Ops);
3719}
3720
3721const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3722 assert(!Ops.empty() && "At least one operand must be!")((!Ops.empty() && "At least one operand must be!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"At least one operand must be!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3722, __PRETTY_FUNCTION__))
;
3723 // Trivial case.
3724 if (Ops.size() == 1)
3725 return Ops[0];
3726
3727 // ~umax(~x, ~y, ~z) == umin(x, y, z).
3728 SmallVector<const SCEV *, 2> NotOps;
3729 for (auto *S : Ops)
3730 NotOps.push_back(getNotSCEV(S));
3731 return getNotSCEV(getUMaxExpr(NotOps));
3732}
3733
3734const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3735 // We can bypass creating a target-independent
3736 // constant expression and then folding it back into a ConstantInt.
3737 // This is just a compile-time optimization.
3738 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3739}
3740
3741const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3742 StructType *STy,
3743 unsigned FieldNo) {
3744 // We can bypass creating a target-independent
3745 // constant expression and then folding it back into a ConstantInt.
3746 // This is just a compile-time optimization.
3747 return getConstant(
3748 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3749}
3750
3751const SCEV *ScalarEvolution::getUnknown(Value *V) {
3752 // Don't attempt to do anything other than create a SCEVUnknown object
3753 // here. createSCEV only calls getUnknown after checking for all other
3754 // interesting possibilities, and any other code that calls getUnknown
3755 // is doing so in order to hide a value from SCEV canonicalization.
3756
3757 FoldingSetNodeID ID;
3758 ID.AddInteger(scUnknown);
3759 ID.AddPointer(V);
3760 void *IP = nullptr;
3761 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3762 assert(cast<SCEVUnknown>(S)->getValue() == V &&((cast<SCEVUnknown>(S)->getValue() == V && "Stale SCEVUnknown in uniquing map!"
) ? static_cast<void> (0) : __assert_fail ("cast<SCEVUnknown>(S)->getValue() == V && \"Stale SCEVUnknown in uniquing map!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3763, __PRETTY_FUNCTION__))
3763 "Stale SCEVUnknown in uniquing map!")((cast<SCEVUnknown>(S)->getValue() == V && "Stale SCEVUnknown in uniquing map!"
) ? static_cast<void> (0) : __assert_fail ("cast<SCEVUnknown>(S)->getValue() == V && \"Stale SCEVUnknown in uniquing map!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3763, __PRETTY_FUNCTION__))
;
3764 return S;
3765 }
3766 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3767 FirstUnknown);
3768 FirstUnknown = cast<SCEVUnknown>(S);
3769 UniqueSCEVs.InsertNode(S, IP);
3770 return S;
3771}
3772
3773//===----------------------------------------------------------------------===//
3774// Basic SCEV Analysis and PHI Idiom Recognition Code
3775//
3776
3777/// Test if values of the given type are analyzable within the SCEV
3778/// framework. This primarily includes integer types, and it can optionally
3779/// include pointer types if the ScalarEvolution class has access to
3780/// target-specific information.
3781bool ScalarEvolution::isSCEVable(Type *Ty) const {
3782 // Integers and pointers are always SCEVable.
3783 return Ty->isIntOrPtrTy();
3784}
3785
3786/// Return the size in bits of the specified type, for which isSCEVable must
3787/// return true.
3788uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3789 assert(isSCEVable(Ty) && "Type is not SCEVable!")((isSCEVable(Ty) && "Type is not SCEVable!") ? static_cast
<void> (0) : __assert_fail ("isSCEVable(Ty) && \"Type is not SCEVable!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3789, __PRETTY_FUNCTION__))
;
3790 if (Ty->isPointerTy())
3791 return getDataLayout().getIndexTypeSizeInBits(Ty);
3792 return getDataLayout().getTypeSizeInBits(Ty);
3793}
3794
3795/// Return a type with the same bitwidth as the given type and which represents
3796/// how SCEV will treat the given type, for which isSCEVable must return
3797/// true. For pointer types, this is the pointer-sized integer type.
3798Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3799 assert(isSCEVable(Ty) && "Type is not SCEVable!")((isSCEVable(Ty) && "Type is not SCEVable!") ? static_cast
<void> (0) : __assert_fail ("isSCEVable(Ty) && \"Type is not SCEVable!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3799, __PRETTY_FUNCTION__))
;
3800
3801 if (Ty->isIntegerTy())
3802 return Ty;
3803
3804 // The only other support type is pointer.
3805 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!")((Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"
) ? static_cast<void> (0) : __assert_fail ("Ty->isPointerTy() && \"Unexpected non-pointer non-integer type!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3805, __PRETTY_FUNCTION__))
;
3806 return getDataLayout().getIntPtrType(Ty);
3807}
3808
3809Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
3810 return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
3811}
3812
3813const SCEV *ScalarEvolution::getCouldNotCompute() {
3814 return CouldNotCompute.get();
3815}
3816
3817bool ScalarEvolution::checkValidity(const SCEV *S) const {
3818 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3819 auto *SU = dyn_cast<SCEVUnknown>(S);
3820 return SU && SU->getValue() == nullptr;
3821 });
3822
3823 return !ContainsNulls;
3824}
3825
3826bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3827 HasRecMapType::iterator I = HasRecMap.find(S);
3828 if (I != HasRecMap.end())
3829 return I->second;
3830
3831 bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
3832 HasRecMap.insert({S, FoundAddRec});
3833 return FoundAddRec;
3834}
3835
3836/// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3837/// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3838/// offset I, then return {S', I}, else return {\p S, nullptr}.
3839static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3840 const auto *Add = dyn_cast<SCEVAddExpr>(S);
3841 if (!Add)
3842 return {S, nullptr};
3843
3844 if (Add->getNumOperands() != 2)
3845 return {S, nullptr};
3846
3847 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3848 if (!ConstOp)
3849 return {S, nullptr};
3850
3851 return {Add->getOperand(1), ConstOp->getValue()};
3852}
3853
3854/// Return the ValueOffsetPair set for \p S. \p S can be represented
3855/// by the value and offset from any ValueOffsetPair in the set.
3856SetVector<ScalarEvolution::ValueOffsetPair> *
3857ScalarEvolution::getSCEVValues(const SCEV *S) {
3858 ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3859 if (SI == ExprValueMap.end())
3860 return nullptr;
3861#ifndef NDEBUG
3862 if (VerifySCEVMap) {
3863 // Check there is no dangling Value in the set returned.
3864 for (const auto &VE : SI->second)
3865 assert(ValueExprMap.count(VE.first))((ValueExprMap.count(VE.first)) ? static_cast<void> (0)
: __assert_fail ("ValueExprMap.count(VE.first)", "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3865, __PRETTY_FUNCTION__))
;
3866 }
3867#endif
3868 return &SI->second;
3869}
3870
3871/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3872/// cannot be used separately. eraseValueFromMap should be used to remove
3873/// V from ValueExprMap and ExprValueMap at the same time.
3874void ScalarEvolution::eraseValueFromMap(Value *V) {
3875 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3876 if (I != ValueExprMap.end()) {
3877 const SCEV *S = I->second;
3878 // Remove {V, 0} from the set of ExprValueMap[S]
3879 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
3880 SV->remove({V, nullptr});
3881
3882 // Remove {V, Offset} from the set of ExprValueMap[Stripped]
3883 const SCEV *Stripped;
3884 ConstantInt *Offset;
3885 std::tie(Stripped, Offset) = splitAddExpr(S);
3886 if (Offset != nullptr) {
3887 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
3888 SV->remove({V, Offset});
3889 }
3890 ValueExprMap.erase(V);
3891 }
3892}
3893
3894/// Check whether value has nuw/nsw/exact set but SCEV does not.
3895/// TODO: In reality it is better to check the poison recursevely
3896/// but this is better than nothing.
3897static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) {
3898 if (auto *I = dyn_cast<Instruction>(V)) {
3899 if (isa<OverflowingBinaryOperator>(I)) {
3900 if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) {
3901 if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap())
3902 return true;
3903 if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap())
3904 return true;
3905 }
3906 } else if (isa<PossiblyExactOperator>(I) && I->isExact())
3907 return true;
3908 }
3909 return false;
3910}
3911
3912/// Return an existing SCEV if it exists, otherwise analyze the expression and
3913/// create a new one.
3914const SCEV *ScalarEvolution::getSCEV(Value *V) {
3915 assert(isSCEVable(V->getType()) && "Value is not SCEVable!")((isSCEVable(V->getType()) && "Value is not SCEVable!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(V->getType()) && \"Value is not SCEVable!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3915, __PRETTY_FUNCTION__))
;
3916
3917 const SCEV *S = getExistingSCEV(V);
3918 if (S == nullptr) {
3919 S = createSCEV(V);
3920 // During PHI resolution, it is possible to create two SCEVs for the same
3921 // V, so it is needed to double check whether V->S is inserted into
3922 // ValueExprMap before insert S->{V, 0} into ExprValueMap.
3923 std::pair<ValueExprMapType::iterator, bool> Pair =
3924 ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3925 if (Pair.second && !SCEVLostPoisonFlags(S, V)) {
3926 ExprValueMap[S].insert({V, nullptr});
3927
3928 // If S == Stripped + Offset, add Stripped -> {V, Offset} into
3929 // ExprValueMap.
3930 const SCEV *Stripped = S;
3931 ConstantInt *Offset = nullptr;
3932 std::tie(Stripped, Offset) = splitAddExpr(S);
3933 // If stripped is SCEVUnknown, don't bother to save
3934 // Stripped -> {V, offset}. It doesn't simplify and sometimes even
3935 // increase the complexity of the expansion code.
3936 // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
3937 // because it may generate add/sub instead of GEP in SCEV expansion.
3938 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
3939 !isa<GetElementPtrInst>(V))
3940 ExprValueMap[Stripped].insert({V, Offset});
3941 }
3942 }
3943 return S;
3944}
3945
3946const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3947 assert(isSCEVable(V->getType()) && "Value is not SCEVable!")((isSCEVable(V->getType()) && "Value is not SCEVable!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(V->getType()) && \"Value is not SCEVable!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 3947, __PRETTY_FUNCTION__))
;
3948
3949 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3950 if (I != ValueExprMap.end()) {
3951 const SCEV *S = I->second;
3952 if (checkValidity(S))
3953 return S;
3954 eraseValueFromMap(V);
3955 forgetMemoizedResults(S);
3956 }
3957 return nullptr;
3958}
3959
3960/// Return a SCEV corresponding to -V = -1*V
3961const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3962 SCEV::NoWrapFlags Flags) {
3963 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3964 return getConstant(
3965 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3966
3967 Type *Ty = V->getType();
3968 Ty = getEffectiveSCEVType(Ty);
3969 return getMulExpr(
3970 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3971}
3972
3973/// Return a SCEV corresponding to ~V = -1-V
3974const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3975 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3976 return getConstant(
3977 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3978
3979 Type *Ty = V->getType();
3980 Ty = getEffectiveSCEVType(Ty);
3981 const SCEV *AllOnes =
3982 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3983 return getMinusSCEV(AllOnes, V);
3984}
3985
3986const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3987 SCEV::NoWrapFlags Flags,
3988 unsigned Depth) {
3989 // Fast path: X - X --> 0.
3990 if (LHS == RHS)
3991 return getZero(LHS->getType());
3992
3993 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3994 // makes it so that we cannot make much use of NUW.
3995 auto AddFlags = SCEV::FlagAnyWrap;
3996 const bool RHSIsNotMinSigned =
3997 !getSignedRangeMin(RHS).isMinSignedValue();
3998 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3999 // Let M be the minimum representable signed value. Then (-1)*RHS
4000 // signed-wraps if and only if RHS is M. That can happen even for
4001 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
4002 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
4003 // (-1)*RHS, we need to prove that RHS != M.
4004 //
4005 // If LHS is non-negative and we know that LHS - RHS does not
4006 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
4007 // either by proving that RHS > M or that LHS >= 0.
4008 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
4009 AddFlags = SCEV::FlagNSW;
4010 }
4011 }
4012
4013 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
4014 // RHS is NSW and LHS >= 0.
4015 //
4016 // The difficulty here is that the NSW flag may have been proven
4017 // relative to a loop that is to be found in a recurrence in LHS and
4018 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
4019 // larger scope than intended.
4020 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
4021
4022 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
4023}
4024
4025const SCEV *
4026ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
4027 Type *SrcTy = V->getType();
4028 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or zero extend with non-integer arguments!"
) ? static_cast<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4029, __PRETTY_FUNCTION__))
4029 "Cannot truncate or zero extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or zero extend with non-integer arguments!"
) ? static_cast<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4029, __PRETTY_FUNCTION__))
;
4030 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4031 return V; // No conversion
4032 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
4033 return getTruncateExpr(V, Ty);
4034 return getZeroExtendExpr(V, Ty);
4035}
4036
4037const SCEV *
4038ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
4039 Type *Ty) {
4040 Type *SrcTy = V->getType();
4041 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or zero extend with non-integer arguments!"
) ? static_cast<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4042, __PRETTY_FUNCTION__))
4042 "Cannot truncate or zero extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or zero extend with non-integer arguments!"
) ? static_cast<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4042, __PRETTY_FUNCTION__))
;
4043 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4044 return V; // No conversion
4045 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
4046 return getTruncateExpr(V, Ty);
4047 return getSignExtendExpr(V, Ty);
4048}
4049
4050const SCEV *
4051ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
4052 Type *SrcTy = V->getType();
4053 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or zero extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4054, __PRETTY_FUNCTION__))
4054 "Cannot noop or zero extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or zero extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4054, __PRETTY_FUNCTION__))
;
4055 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrZeroExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrZeroExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4056, __PRETTY_FUNCTION__))
4056 "getNoopOrZeroExtend cannot truncate!")((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrZeroExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrZeroExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4056, __PRETTY_FUNCTION__))
;
4057 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4058 return V; // No conversion
4059 return getZeroExtendExpr(V, Ty);
4060}
4061
4062const SCEV *
4063ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
4064 Type *SrcTy = V->getType();
4065 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or sign extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or sign extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4066, __PRETTY_FUNCTION__))
4066 "Cannot noop or sign extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or sign extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or sign extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4066, __PRETTY_FUNCTION__))
;
4067 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrSignExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrSignExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4068, __PRETTY_FUNCTION__))
4068 "getNoopOrSignExtend cannot truncate!")((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrSignExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrSignExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4068, __PRETTY_FUNCTION__))
;
4069 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4070 return V; // No conversion
4071 return getSignExtendExpr(V, Ty);
4072}
4073
4074const SCEV *
4075ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
4076 Type *SrcTy = V->getType();
4077 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or any extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or any extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4078, __PRETTY_FUNCTION__))
4078 "Cannot noop or any extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or any extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or any extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4078, __PRETTY_FUNCTION__))
;
4079 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrAnyExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrAnyExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4080, __PRETTY_FUNCTION__))
4080 "getNoopOrAnyExtend cannot truncate!")((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrAnyExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrAnyExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4080, __PRETTY_FUNCTION__))
;
4081 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4082 return V; // No conversion
4083 return getAnyExtendExpr(V, Ty);
4084}
4085
4086const SCEV *
4087ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
4088 Type *SrcTy = V->getType();
4089 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or noop with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or noop with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4090, __PRETTY_FUNCTION__))
4090 "Cannot truncate or noop with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or noop with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or noop with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4090, __PRETTY_FUNCTION__))
;
4091 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&((getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
"getTruncateOrNoop cannot extend!") ? static_cast<void>
(0) : __assert_fail ("getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && \"getTruncateOrNoop cannot extend!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4092, __PRETTY_FUNCTION__))
4092 "getTruncateOrNoop cannot extend!")((getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
"getTruncateOrNoop cannot extend!") ? static_cast<void>
(0) : __assert_fail ("getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && \"getTruncateOrNoop cannot extend!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4092, __PRETTY_FUNCTION__))
;
4093 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4094 return V; // No conversion
4095 return getTruncateExpr(V, Ty);
4096}
4097
4098const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
4099 const SCEV *RHS) {
4100 const SCEV *PromotedLHS = LHS;
4101 const SCEV *PromotedRHS = RHS;
4102
4103 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
4104 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
4105 else
4106 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
4107
4108 return getUMaxExpr(PromotedLHS, PromotedRHS);
4109}
4110
4111const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
4112 const SCEV *RHS) {
4113 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
4114 return getUMinFromMismatchedTypes(Ops);
4115}
4116
4117const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(
4118 SmallVectorImpl<const SCEV *> &Ops) {
4119 assert(!Ops.empty() && "At least one operand must be!")((!Ops.empty() && "At least one operand must be!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"At least one operand must be!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4119, __PRETTY_FUNCTION__))
;
4120 // Trivial case.
4121 if (Ops.size() == 1)
4122 return Ops[0];
4123
4124 // Find the max type first.
4125 Type *MaxType = nullptr;
4126 for (auto *S : Ops)
4127 if (MaxType)
4128 MaxType = getWiderType(MaxType, S->getType());
4129 else
4130 MaxType = S->getType();
4131
4132 // Extend all ops to max type.
4133 SmallVector<const SCEV *, 2> PromotedOps;
4134 for (auto *S : Ops)
4135 PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
4136
4137 // Generate umin.
4138 return getUMinExpr(PromotedOps);
4139}
4140
4141const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
4142 // A pointer operand may evaluate to a nonpointer expression, such as null.
4143 if (!V->getType()->isPointerTy())
4144 return V;
4145
4146 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
4147 return getPointerBase(Cast->getOperand());
4148 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
4149 const SCEV *PtrOp = nullptr;
4150 for (const SCEV *NAryOp : NAry->operands()) {
4151 if (NAryOp->getType()->isPointerTy()) {
4152 // Cannot find the base of an expression with multiple pointer operands.
4153 if (PtrOp)
4154 return V;
4155 PtrOp = NAryOp;
4156 }
4157 }
4158 if (!PtrOp)
4159 return V;
4160 return getPointerBase(PtrOp);
4161 }
4162 return V;
4163}
4164
4165/// Push users of the given Instruction onto the given Worklist.
4166static void
4167PushDefUseChildren(Instruction *I,
4168 SmallVectorImpl<Instruction *> &Worklist) {
4169 // Push the def-use children onto the Worklist stack.
4170 for (User *U : I->users())
4171 Worklist.push_back(cast<Instruction>(U));
4172}
4173
4174void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
4175 SmallVector<Instruction *, 16> Worklist;
4176 PushDefUseChildren(PN, Worklist);
4177
4178 SmallPtrSet<Instruction *, 8> Visited;
4179 Visited.insert(PN);
4180 while (!Worklist.empty()) {
4181 Instruction *I = Worklist.pop_back_val();
4182 if (!Visited.insert(I).second)
4183 continue;
4184
4185 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
4186 if (It != ValueExprMap.end()) {
4187 const SCEV *Old = It->second;
4188
4189 // Short-circuit the def-use traversal if the symbolic name
4190 // ceases to appear in expressions.
4191 if (Old != SymName && !hasOperand(Old, SymName))
4192 continue;
4193
4194 // SCEVUnknown for a PHI either means that it has an unrecognized
4195 // structure, it's a PHI that's in the progress of being computed
4196 // by createNodeForPHI, or it's a single-value PHI. In the first case,
4197 // additional loop trip count information isn't going to change anything.
4198 // In the second case, createNodeForPHI will perform the necessary
4199 // updates on its own when it gets to that point. In the third, we do
4200 // want to forget the SCEVUnknown.
4201 if (!isa<PHINode>(I) ||
4202 !isa<SCEVUnknown>(Old) ||
4203 (I != PN && Old == SymName)) {
4204 eraseValueFromMap(It->first);
4205 forgetMemoizedResults(Old);
4206 }
4207 }
4208
4209 PushDefUseChildren(I, Worklist);
4210 }
4211}
4212
4213namespace {
4214
4215/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
4216/// expression in case its Loop is L. If it is not L then
4217/// if IgnoreOtherLoops is true then use AddRec itself
4218/// otherwise rewrite cannot be done.
4219/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4220class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4221public:
4222 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
4223 bool IgnoreOtherLoops = true) {
4224 SCEVInitRewriter Rewriter(L, SE);
4225 const SCEV *Result = Rewriter.visit(S);
4226 if (Rewriter.hasSeenLoopVariantSCEVUnknown())
4227 return SE.getCouldNotCompute();
4228 return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
4229 ? SE.getCouldNotCompute()
4230 : Result;
4231 }
4232
4233 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4234 if (!SE.isLoopInvariant(Expr, L))
4235 SeenLoopVariantSCEVUnknown = true;
4236 return Expr;
4237 }
4238
4239 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4240 // Only re-write AddRecExprs for this loop.
4241 if (Expr->getLoop() == L)
4242 return Expr->getStart();
4243 SeenOtherLoops = true;
4244 return Expr;
4245 }
4246
4247 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4248
4249 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4250
4251private:
4252 explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
4253 : SCEVRewriteVisitor(SE), L(L) {}
4254
4255 const Loop *L;
4256 bool SeenLoopVariantSCEVUnknown = false;
4257 bool SeenOtherLoops = false;
4258};
4259
4260/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
4261/// increment expression in case its Loop is L. If it is not L then
4262/// use AddRec itself.
4263/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4264class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
4265public:
4266 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
4267 SCEVPostIncRewriter Rewriter(L, SE);
4268 const SCEV *Result = Rewriter.visit(S);
4269 return Rewriter.hasSeenLoopVariantSCEVUnknown()
4270 ? SE.getCouldNotCompute()
4271 : Result;
4272 }
4273
4274 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4275 if (!SE.isLoopInvariant(Expr, L))
4276 SeenLoopVariantSCEVUnknown = true;
4277 return Expr;
4278 }
4279
4280 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4281 // Only re-write AddRecExprs for this loop.
4282 if (Expr->getLoop() == L)
4283 return Expr->getPostIncExpr(SE);
4284 SeenOtherLoops = true;
4285 return Expr;
4286 }
4287
4288 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4289
4290 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4291
4292private:
4293 explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
4294 : SCEVRewriteVisitor(SE), L(L) {}
4295
4296 const Loop *L;
4297 bool SeenLoopVariantSCEVUnknown = false;
4298 bool SeenOtherLoops = false;
4299};
4300
4301/// This class evaluates the compare condition by matching it against the
4302/// condition of loop latch. If there is a match we assume a true value
4303/// for the condition while building SCEV nodes.
4304class SCEVBackedgeConditionFolder
4305 : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4306public:
4307 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4308 ScalarEvolution &SE) {
4309 bool IsPosBECond = false;
4310 Value *BECond = nullptr;
4311 if (BasicBlock *Latch = L->getLoopLatch()) {
4312 BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
4313 if (BI && BI->isConditional()) {
4314 assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&((BI->getSuccessor(0) != BI->getSuccessor(1) &&
"Both outgoing branches should not target same header!") ? static_cast
<void> (0) : __assert_fail ("BI->getSuccessor(0) != BI->getSuccessor(1) && \"Both outgoing branches should not target same header!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4315, __PRETTY_FUNCTION__))
4315 "Both outgoing branches should not target same header!")((BI->getSuccessor(0) != BI->getSuccessor(1) &&
"Both outgoing branches should not target same header!") ? static_cast
<void> (0) : __assert_fail ("BI->getSuccessor(0) != BI->getSuccessor(1) && \"Both outgoing branches should not target same header!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4315, __PRETTY_FUNCTION__))
;
4316 BECond = BI->getCondition();
4317 IsPosBECond = BI->getSuccessor(0) == L->getHeader();
4318 } else {
4319 return S;
4320 }
4321 }
4322 SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
4323 return Rewriter.visit(S);
4324 }
4325
4326 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4327 const SCEV *Result = Expr;
4328 bool InvariantF = SE.isLoopInvariant(Expr, L);
4329
4330 if (!InvariantF) {
4331 Instruction *I = cast<Instruction>(Expr->getValue());
4332 switch (I->getOpcode()) {
4333 case Instruction::Select: {
4334 SelectInst *SI = cast<SelectInst>(I);
4335 Optional<const SCEV *> Res =
4336 compareWithBackedgeCondition(SI->getCondition());
4337 if (Res.hasValue()) {
4338 bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
4339 Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
4340 }
4341 break;
4342 }
4343 default: {
4344 Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
4345 if (Res.hasValue())
4346 Result = Res.getValue();
4347 break;
4348 }
4349 }
4350 }
4351 return Result;
4352 }
4353
4354private:
4355 explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
4356 bool IsPosBECond, ScalarEvolution &SE)
4357 : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
4358 IsPositiveBECond(IsPosBECond) {}
4359
4360 Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
4361
4362 const Loop *L;
4363 /// Loop back condition.
4364 Value *BackedgeCond = nullptr;
4365 /// Set to true if loop back is on positive branch condition.
4366 bool IsPositiveBECond;
4367};
4368
4369Optional<const SCEV *>
4370SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
4371
4372 // If value matches the backedge condition for loop latch,
4373 // then return a constant evolution node based on loopback
4374 // branch taken.
4375 if (BackedgeCond == IC)
4376 return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
4377 : SE.getZero(Type::getInt1Ty(SE.getContext()));
4378 return None;
4379}
4380
4381class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4382public:
4383 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4384 ScalarEvolution &SE) {
4385 SCEVShiftRewriter Rewriter(L, SE);
4386 const SCEV *Result = Rewriter.visit(S);
4387 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4388 }
4389
4390 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4391 // Only allow AddRecExprs for this loop.
4392 if (!SE.isLoopInvariant(Expr, L))
4393 Valid = false;
4394 return Expr;
4395 }
4396
4397 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4398 if (Expr->getLoop() == L && Expr->isAffine())
4399 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
4400 Valid = false;
4401 return Expr;
4402 }
4403
4404 bool isValid() { return Valid; }
4405
4406private:
4407 explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
4408 : SCEVRewriteVisitor(SE), L(L) {}
4409
4410 const Loop *L;
4411 bool Valid = true;
4412};
4413
4414} // end anonymous namespace
4415
4416SCEV::NoWrapFlags
4417ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
4418 if (!AR->isAffine())
4419 return SCEV::FlagAnyWrap;
4420
4421 using OBO = OverflowingBinaryOperator;
4422
4423 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
4424
4425 if (!AR->hasNoSignedWrap()) {
4426 ConstantRange AddRecRange = getSignedRange(AR);
4427 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
4428
4429 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4430 Instruction::Add, IncRange, OBO::NoSignedWrap);
4431 if (NSWRegion.contains(AddRecRange))
4432 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
4433 }
4434
4435 if (!AR->hasNoUnsignedWrap()) {
4436 ConstantRange AddRecRange = getUnsignedRange(AR);
4437 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
4438
4439 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4440 Instruction::Add, IncRange, OBO::NoUnsignedWrap);
4441 if (NUWRegion.contains(AddRecRange))
4442 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
4443 }
4444
4445 return Result;
4446}
4447
4448namespace {
4449
4450/// Represents an abstract binary operation. This may exist as a
4451/// normal instruction or constant expression, or may have been
4452/// derived from an expression tree.
4453struct BinaryOp {
4454 unsigned Opcode;
4455 Value *LHS;
4456 Value *RHS;
4457 bool IsNSW = false;
4458 bool IsNUW = false;
4459
4460 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
4461 /// constant expression.
4462 Operator *Op = nullptr;
4463
4464 explicit BinaryOp(Operator *Op)
4465 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
4466 Op(Op) {
4467 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
4468 IsNSW = OBO->hasNoSignedWrap();
4469 IsNUW = OBO->hasNoUnsignedWrap();
4470 }
4471 }
4472
4473 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
4474 bool IsNUW = false)
4475 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
4476};
4477
4478} // end anonymous namespace
4479
4480/// Try to map \p V into a BinaryOp, and return \c None on failure.
4481static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
4482 auto *Op = dyn_cast<Operator>(V);
4483 if (!Op)
4484 return None;
4485
4486 // Implementation detail: all the cleverness here should happen without
4487 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
4488 // SCEV expressions when possible, and we should not break that.
4489
4490 switch (Op->getOpcode()) {
4491 case Instruction::Add:
4492 case Instruction::Sub:
4493 case Instruction::Mul:
4494 case Instruction::UDiv:
4495 case Instruction::URem:
4496 case Instruction::And:
4497 case Instruction::Or:
4498 case Instruction::AShr:
4499 case Instruction::Shl:
4500 return BinaryOp(Op);
4501
4502 case Instruction::Xor:
4503 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
4504 // If the RHS of the xor is a signmask, then this is just an add.
4505 // Instcombine turns add of signmask into xor as a strength reduction step.
4506 if (RHSC->getValue().isSignMask())
4507 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
4508 return BinaryOp(Op);
4509
4510 case Instruction::LShr:
4511 // Turn logical shift right of a constant into a unsigned divide.
4512 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
4513 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
4514
4515 // If the shift count is not less than the bitwidth, the result of
4516 // the shift is undefined. Don't try to analyze it, because the
4517 // resolution chosen here may differ from the resolution chosen in
4518 // other parts of the compiler.
4519 if (SA->getValue().ult(BitWidth)) {
4520 Constant *X =
4521 ConstantInt::get(SA->getContext(),
4522 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4523 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
4524 }
4525 }
4526 return BinaryOp(Op);
4527
4528 case Instruction::ExtractValue: {
4529 auto *EVI = cast<ExtractValueInst>(Op);
4530 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
4531 break;
4532
4533 auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
4534 if (!CI)
4535 break;
4536
4537 if (auto *F = CI->getCalledFunction())
4538 switch (F->getIntrinsicID()) {
4539 case Intrinsic::sadd_with_overflow:
4540 case Intrinsic::uadd_with_overflow:
4541 if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
4542 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4543 CI->getArgOperand(1));
4544
4545 // Now that we know that all uses of the arithmetic-result component of
4546 // CI are guarded by the overflow check, we can go ahead and pretend
4547 // that the arithmetic is non-overflowing.
4548 if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
4549 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4550 CI->getArgOperand(1), /* IsNSW = */ true,
4551 /* IsNUW = */ false);
4552 else
4553 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4554 CI->getArgOperand(1), /* IsNSW = */ false,
4555 /* IsNUW*/ true);
4556 case Intrinsic::ssub_with_overflow:
4557 case Intrinsic::usub_with_overflow:
4558 if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
4559 return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4560 CI->getArgOperand(1));
4561
4562 // The same reasoning as sadd/uadd above.
4563 if (F->getIntrinsicID() == Intrinsic::ssub_with_overflow)
4564 return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4565 CI->getArgOperand(1), /* IsNSW = */ true,
4566 /* IsNUW = */ false);
4567 else
4568 return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4569 CI->getArgOperand(1), /* IsNSW = */ false,
4570 /* IsNUW = */ true);
4571 case Intrinsic::smul_with_overflow:
4572 case Intrinsic::umul_with_overflow:
4573 return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
4574 CI->getArgOperand(1));
4575 default:
4576 break;
4577 }
4578 break;
4579 }
4580
4581 default:
4582 break;
4583 }
4584
4585 return None;
4586}
4587
4588/// Helper function to createAddRecFromPHIWithCasts. We have a phi
4589/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
4590/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
4591/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
4592/// follows one of the following patterns:
4593/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4594/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4595/// If the SCEV expression of \p Op conforms with one of the expected patterns
4596/// we return the type of the truncation operation, and indicate whether the
4597/// truncated type should be treated as signed/unsigned by setting
4598/// \p Signed to true/false, respectively.
4599static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
4600 bool &Signed, ScalarEvolution &SE) {
4601 // The case where Op == SymbolicPHI (that is, with no type conversions on
4602 // the way) is handled by the regular add recurrence creating logic and
4603 // would have already been triggered in createAddRecForPHI. Reaching it here
4604 // means that createAddRecFromPHI had failed for this PHI before (e.g.,
4605 // because one of the other operands of the SCEVAddExpr updating this PHI is
4606 // not invariant).
4607 //
4608 // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
4609 // this case predicates that allow us to prove that Op == SymbolicPHI will
4610 // be added.
4611 if (Op == SymbolicPHI)
4612 return nullptr;
4613
4614 unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
4615 unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
4616 if (SourceBits != NewBits)
4617 return nullptr;
4618
4619 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
4620 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
4621 if (!SExt && !ZExt)
4622 return nullptr;
4623 const SCEVTruncateExpr *Trunc =
4624 SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
4625 : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
4626 if (!Trunc)
4627 return nullptr;
4628 const SCEV *X = Trunc->getOperand();
4629 if (X != SymbolicPHI)
4630 return nullptr;
4631 Signed = SExt != nullptr;
4632 return Trunc->getType();
4633}
4634
4635static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
4636 if (!PN->getType()->isIntegerTy())
4637 return nullptr;
4638 const Loop *L = LI.getLoopFor(PN->getParent());
4639 if (!L || L->getHeader() != PN->getParent())
4640 return nullptr;
4641 return L;
4642}
4643
4644// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
4645// computation that updates the phi follows the following pattern:
4646// (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
4647// which correspond to a phi->trunc->sext/zext->add->phi update chain.
4648// If so, try to see if it can be rewritten as an AddRecExpr under some
4649// Predicates. If successful, return them as a pair. Also cache the results
4650// of the analysis.
4651//
4652// Example usage scenario:
4653// Say the Rewriter is called for the following SCEV:
4654// 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4655// where:
4656// %X = phi i64 (%Start, %BEValue)
4657// It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
4658// and call this function with %SymbolicPHI = %X.
4659//
4660// The analysis will find that the value coming around the backedge has
4661// the following SCEV:
4662// BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4663// Upon concluding that this matches the desired pattern, the function
4664// will return the pair {NewAddRec, SmallPredsVec} where:
4665// NewAddRec = {%Start,+,%Step}
4666// SmallPredsVec = {P1, P2, P3} as follows:
4667// P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
4668// P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
4669// P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
4670// The returned pair means that SymbolicPHI can be rewritten into NewAddRec
4671// under the predicates {P1,P2,P3}.
4672// This predicated rewrite will be cached in PredicatedSCEVRewrites:
4673// PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
4674//
4675// TODO's:
4676//
4677// 1) Extend the Induction descriptor to also support inductions that involve
4678// casts: When needed (namely, when we are called in the context of the
4679// vectorizer induction analysis), a Set of cast instructions will be
4680// populated by this method, and provided back to isInductionPHI. This is
4681// needed to allow the vectorizer to properly record them to be ignored by
4682// the cost model and to avoid vectorizing them (otherwise these casts,
4683// which are redundant under the runtime overflow checks, will be
4684// vectorized, which can be costly).
4685//
4686// 2) Support additional induction/PHISCEV patterns: We also want to support
4687// inductions where the sext-trunc / zext-trunc operations (partly) occur
4688// after the induction update operation (the induction increment):
4689//
4690// (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
4691// which correspond to a phi->add->trunc->sext/zext->phi update chain.
4692//
4693// (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
4694// which correspond to a phi->trunc->add->sext/zext->phi update chain.
4695//
4696// 3) Outline common code with createAddRecFromPHI to avoid duplication.
4697Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4698ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
4699 SmallVector<const SCEVPredicate *, 3> Predicates;
4700
4701 // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
4702 // return an AddRec expression under some predicate.
4703
4704 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4705 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4706 assert(L && "Expecting an integer loop header phi")((L && "Expecting an integer loop header phi") ? static_cast
<void> (0) : __assert_fail ("L && \"Expecting an integer loop header phi\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4706, __PRETTY_FUNCTION__))
;
4707
4708 // The loop may have multiple entrances or multiple exits; we can analyze
4709 // this phi as an addrec if it has a unique entry value and a unique
4710 // backedge value.
4711 Value *BEValueV = nullptr, *StartValueV = nullptr;
4712 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4713 Value *V = PN->getIncomingValue(i);
4714 if (L->contains(PN->getIncomingBlock(i))) {
4715 if (!BEValueV) {
4716 BEValueV = V;
4717 } else if (BEValueV != V) {
4718 BEValueV = nullptr;
4719 break;
4720 }
4721 } else if (!StartValueV) {
4722 StartValueV = V;
4723 } else if (StartValueV != V) {
4724 StartValueV = nullptr;
4725 break;
4726 }
4727 }
4728 if (!BEValueV || !StartValueV)
4729 return None;
4730
4731 const SCEV *BEValue = getSCEV(BEValueV);
4732
4733 // If the value coming around the backedge is an add with the symbolic
4734 // value we just inserted, possibly with casts that we can ignore under
4735 // an appropriate runtime guard, then we found a simple induction variable!
4736 const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
4737 if (!Add)
4738 return None;
4739
4740 // If there is a single occurrence of the symbolic value, possibly
4741 // casted, replace it with a recurrence.
4742 unsigned FoundIndex = Add->getNumOperands();
4743 Type *TruncTy = nullptr;
4744 bool Signed;
4745 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4746 if ((TruncTy =
4747 isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
4748 if (FoundIndex == e) {
4749 FoundIndex = i;
4750 break;
4751 }
4752
4753 if (FoundIndex == Add->getNumOperands())
4754 return None;
4755
4756 // Create an add with everything but the specified operand.
4757 SmallVector<const SCEV *, 8> Ops;
4758 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4759 if (i != FoundIndex)
4760 Ops.push_back(Add->getOperand(i));
4761 const SCEV *Accum = getAddExpr(Ops);
4762
4763 // The runtime checks will not be valid if the step amount is
4764 // varying inside the loop.
4765 if (!isLoopInvariant(Accum, L))
4766 return None;
4767
4768 // *** Part2: Create the predicates
4769
4770 // Analysis was successful: we have a phi-with-cast pattern for which we
4771 // can return an AddRec expression under the following predicates:
4772 //
4773 // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
4774 // fits within the truncated type (does not overflow) for i = 0 to n-1.
4775 // P2: An Equal predicate that guarantees that
4776 // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
4777 // P3: An Equal predicate that guarantees that
4778 // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
4779 //
4780 // As we next prove, the above predicates guarantee that:
4781 // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
4782 //
4783 //
4784 // More formally, we want to prove that:
4785 // Expr(i+1) = Start + (i+1) * Accum
4786 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4787 //
4788 // Given that:
4789 // 1) Expr(0) = Start
4790 // 2) Expr(1) = Start + Accum
4791 // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
4792 // 3) Induction hypothesis (step i):
4793 // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
4794 //
4795 // Proof:
4796 // Expr(i+1) =
4797 // = Start + (i+1)*Accum
4798 // = (Start + i*Accum) + Accum
4799 // = Expr(i) + Accum
4800 // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
4801 // :: from step i
4802 //
4803 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
4804 //
4805 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
4806 // + (Ext ix (Trunc iy (Accum) to ix) to iy)
4807 // + Accum :: from P3
4808 //
4809 // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
4810 // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
4811 //
4812 // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
4813 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4814 //
4815 // By induction, the same applies to all iterations 1<=i<n:
4816 //
4817
4818 // Create a truncated addrec for which we will add a no overflow check (P1).
4819 const SCEV *StartVal = getSCEV(StartValueV);
4820 const SCEV *PHISCEV =
4821 getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
4822 getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
4823
4824 // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
4825 // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
4826 // will be constant.
4827 //
4828 // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
4829 // add P1.
4830 if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
4831 SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
4832 Signed ? SCEVWrapPredicate::IncrementNSSW
4833 : SCEVWrapPredicate::IncrementNUSW;
4834 const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
4835 Predicates.push_back(AddRecPred);
4836 }
4837
4838 // Create the Equal Predicates P2,P3:
4839
4840 // It is possible that the predicates P2 and/or P3 are computable at
4841 // compile time due to StartVal and/or Accum being constants.
4842 // If either one is, then we can check that now and escape if either P2
4843 // or P3 is false.
4844
4845 // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
4846 // for each of StartVal and Accum
4847 auto getExtendedExpr = [&](const SCEV *Expr,
4848 bool CreateSignExtend) -> const SCEV * {
4849 assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant")((isLoopInvariant(Expr, L) && "Expr is expected to be invariant"
) ? static_cast<void> (0) : __assert_fail ("isLoopInvariant(Expr, L) && \"Expr is expected to be invariant\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4849, __PRETTY_FUNCTION__))
;
4850 const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
4851 const SCEV *ExtendedExpr =
4852 CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
4853 : getZeroExtendExpr(TruncatedExpr, Expr->getType());
4854 return ExtendedExpr;
4855 };
4856
4857 // Given:
4858 // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
4859 // = getExtendedExpr(Expr)
4860 // Determine whether the predicate P: Expr == ExtendedExpr
4861 // is known to be false at compile time
4862 auto PredIsKnownFalse = [&](const SCEV *Expr,
4863 const SCEV *ExtendedExpr) -> bool {
4864 return Expr != ExtendedExpr &&
4865 isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
4866 };
4867
4868 const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
4869 if (PredIsKnownFalse(StartVal, StartExtended)) {
4870 LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";)do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "P2 is compile-time false\n"
;; } } while (false)
;
4871 return None;
4872 }
4873
4874 // The Step is always Signed (because the overflow checks are either
4875 // NSSW or NUSW)
4876 const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
4877 if (PredIsKnownFalse(Accum, AccumExtended)) {
4878 LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";)do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "P3 is compile-time false\n"
;; } } while (false)
;
4879 return None;
4880 }
4881
4882 auto AppendPredicate = [&](const SCEV *Expr,
4883 const SCEV *ExtendedExpr) -> void {
4884 if (Expr != ExtendedExpr &&
4885 !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
4886 const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
4887 LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred)do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "Added Predicate: " <<
*Pred; } } while (false)
;
4888 Predicates.push_back(Pred);
4889 }
4890 };
4891
4892 AppendPredicate(StartVal, StartExtended);
4893 AppendPredicate(Accum, AccumExtended);
4894
4895 // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
4896 // which the casts had been folded away. The caller can rewrite SymbolicPHI
4897 // into NewAR if it will also add the runtime overflow checks specified in
4898 // Predicates.
4899 auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
4900
4901 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
4902 std::make_pair(NewAR, Predicates);
4903 // Remember the result of the analysis for this SCEV at this locayyytion.
4904 PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
4905 return PredRewrite;
4906}
4907
4908Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4909ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
4910 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4911 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4912 if (!L)
4913 return None;
4914
4915 // Check to see if we already analyzed this PHI.
4916 auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
4917 if (I != PredicatedSCEVRewrites.end()) {
4918 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
4919 I->second;
4920 // Analysis was done before and failed to create an AddRec:
4921 if (Rewrite.first == SymbolicPHI)
4922 return None;
4923 // Analysis was done before and succeeded to create an AddRec under
4924 // a predicate:
4925 assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec")((isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec"
) ? static_cast<void> (0) : __assert_fail ("isa<SCEVAddRecExpr>(Rewrite.first) && \"Expected an AddRec\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4925, __PRETTY_FUNCTION__))
;
4926 assert(!(Rewrite.second).empty() && "Expected to find Predicates")((!(Rewrite.second).empty() && "Expected to find Predicates"
) ? static_cast<void> (0) : __assert_fail ("!(Rewrite.second).empty() && \"Expected to find Predicates\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4926, __PRETTY_FUNCTION__))
;
4927 return Rewrite;
4928 }
4929
4930 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4931 Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
4932
4933 // Record in the cache that the analysis failed
4934 if (!Rewrite) {
4935 SmallVector<const SCEVPredicate *, 3> Predicates;
4936 PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
4937 return None;
4938 }
4939
4940 return Rewrite;
4941}
4942
4943// FIXME: This utility is currently required because the Rewriter currently
4944// does not rewrite this expression:
4945// {0, +, (sext ix (trunc iy to ix) to iy)}
4946// into {0, +, %step},
4947// even when the following Equal predicate exists:
4948// "%step == (sext ix (trunc iy to ix) to iy)".
4949bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
4950 const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
4951 if (AR1 == AR2)
4952 return true;
4953
4954 auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
4955 if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
4956 !Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
4957 return false;
4958 return true;
4959 };
4960
4961 if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
4962 !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
4963 return false;
4964 return true;
4965}
4966
4967/// A helper function for createAddRecFromPHI to handle simple cases.
4968///
4969/// This function tries to find an AddRec expression for the simplest (yet most
4970/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
4971/// If it fails, createAddRecFromPHI will use a more general, but slow,
4972/// technique for finding the AddRec expression.
4973const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
4974 Value *BEValueV,
4975 Value *StartValueV) {
4976 const Loop *L = LI.getLoopFor(PN->getParent());
4977 assert(L && L->getHeader() == PN->getParent())((L && L->getHeader() == PN->getParent()) ? static_cast
<void> (0) : __assert_fail ("L && L->getHeader() == PN->getParent()"
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4977, __PRETTY_FUNCTION__))
;
4978 assert(BEValueV && StartValueV)((BEValueV && StartValueV) ? static_cast<void> (
0) : __assert_fail ("BEValueV && StartValueV", "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 4978, __PRETTY_FUNCTION__))
;
4979
4980 auto BO = MatchBinaryOp(BEValueV, DT);
4981 if (!BO)
4982 return nullptr;
4983
4984 if (BO->Opcode != Instruction::Add)
4985 return nullptr;
4986
4987 const SCEV *Accum = nullptr;
4988 if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
4989 Accum = getSCEV(BO->RHS);
4990 else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
4991 Accum = getSCEV(BO->LHS);
4992
4993 if (!Accum)
4994 return nullptr;
4995
4996 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4997 if (BO->IsNUW)
4998 Flags = setFlags(Flags, SCEV::FlagNUW);
4999 if (BO->IsNSW)
5000 Flags = setFlags(Flags, SCEV::FlagNSW);
5001
5002 const SCEV *StartVal = getSCEV(StartValueV);
5003 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
5004
5005 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
5006
5007 // We can add Flags to the post-inc expression only if we
5008 // know that it is *undefined behavior* for BEValueV to
5009 // overflow.
5010 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
5011 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
5012 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
5013
5014 return PHISCEV;
5015}
5016
5017const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
5018 const Loop *L = LI.getLoopFor(PN->getParent());
5019 if (!L || L->getHeader() != PN->getParent())
5020 return nullptr;
5021
5022 // The loop may have multiple entrances or multiple exits; we can analyze
5023 // this phi as an addrec if it has a unique entry value and a unique
5024 // backedge value.
5025 Value *BEValueV = nullptr, *StartValueV = nullptr;
5026 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5027 Value *V = PN->getIncomingValue(i);
5028 if (L->contains(PN->getIncomingBlock(i))) {
5029 if (!BEValueV) {
5030 BEValueV = V;
5031 } else if (BEValueV != V) {
5032 BEValueV = nullptr;
5033 break;
5034 }
5035 } else if (!StartValueV) {
5036 StartValueV = V;
5037 } else if (StartValueV != V) {
5038 StartValueV = nullptr;
5039 break;
5040 }
5041 }
5042 if (!BEValueV || !StartValueV)
5043 return nullptr;
5044
5045 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&((ValueExprMap.find_as(PN) == ValueExprMap.end() && "PHI node already processed?"
) ? static_cast<void> (0) : __assert_fail ("ValueExprMap.find_as(PN) == ValueExprMap.end() && \"PHI node already processed?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 5046, __PRETTY_FUNCTION__))
5046 "PHI node already processed?")((ValueExprMap.find_as(PN) == ValueExprMap.end() && "PHI node already processed?"
) ? static_cast<void> (0) : __assert_fail ("ValueExprMap.find_as(PN) == ValueExprMap.end() && \"PHI node already processed?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 5046, __PRETTY_FUNCTION__))
;
5047
5048 // First, try to find AddRec expression without creating a fictituos symbolic
5049 // value for PN.
5050 if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
5051 return S;
5052
5053 // Handle PHI node value symbolically.
5054 const SCEV *SymbolicName = getUnknown(PN);
5055 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
5056
5057 // Using this symbolic name for the PHI, analyze the value coming around
5058 // the back-edge.
5059 const SCEV *BEValue = getSCEV(BEValueV);
5060
5061 // NOTE: If BEValue is loop invariant, we know that the PHI node just
5062 // has a special value for the first iteration of the loop.
5063
5064 // If the value coming around the backedge is an add with the symbolic
5065 // value we just inserted, then we found a simple induction variable!
5066 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
5067 // If there is a single occurrence of the symbolic value, replace it
5068 // with a recurrence.
5069 unsigned FoundIndex = Add->getNumOperands();
5070 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5071 if (Add->getOperand(i) == SymbolicName)
5072 if (FoundIndex == e) {
5073 FoundIndex = i;
5074 break;
5075 }
5076
5077 if (FoundIndex != Add->getNumOperands()) {
5078 // Create an add with everything but the specified operand.
5079 SmallVector<const SCEV *, 8> Ops;
5080 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5081 if (i != FoundIndex)
5082 Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
5083 L, *this));
5084 const SCEV *Accum = getAddExpr(Ops);
5085
5086 // This is not a valid addrec if the step amount is varying each
5087 // loop iteration, but is not itself an addrec in this loop.
5088 if (isLoopInvariant(Accum, L) ||
5089 (isa<SCEVAddRecExpr>(Accum) &&
5090 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
5091 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5092
5093 if (auto BO = MatchBinaryOp(BEValueV, DT)) {
5094 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
5095 if (BO->IsNUW)
5096 Flags = setFlags(Flags, SCEV::FlagNUW);
5097 if (BO->IsNSW)
5098 Flags = setFlags(Flags, SCEV::FlagNSW);
5099 }
5100 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
5101 // If the increment is an inbounds GEP, then we know the address
5102 // space cannot be wrapped around. We cannot make any guarantee
5103 // about signed or unsigned overflow because pointers are
5104 // unsigned but we may have a negative index from the base
5105 // pointer. We can guarantee that no unsigned wrap occurs if the
5106 // indices form a positive value.
5107 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
5108 Flags = setFlags(Flags, SCEV::FlagNW);
5109
5110 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
5111 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
5112 Flags = setFlags(Flags, SCEV::FlagNUW);
5113 }
5114
5115 // We cannot transfer nuw and nsw flags from subtraction
5116 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
5117 // for instance.
5118 }
5119
5120 const SCEV *StartVal = getSCEV(StartValueV);
5121 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
5122
5123 // Okay, for the entire analysis of this edge we assumed the PHI
5124 // to be symbolic. We now need to go back and purge all of the
5125 // entries for the scalars that use the symbolic expression.
5126 forgetSymbolicName(PN, SymbolicName);
5127 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
5128
5129 // We can add Flags to the post-inc expression only if we
5130 // know that it is *undefined behavior* for BEValueV to
5131 // overflow.
5132 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
5133 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
5134 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
5135
5136 return PHISCEV;
5137 }
5138 }
5139 } else {
5140 // Otherwise, this could be a loop like this:
5141 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
5142 // In this case, j = {1,+,1} and BEValue is j.
5143 // Because the other in-value of i (0) fits the evolution of BEValue
5144 // i really is an addrec evolution.
5145 //
5146 // We can generalize this saying that i is the shifted value of BEValue
5147 // by one iteration:
5148 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
5149 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
5150 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
5151 if (Shifted != getCouldNotCompute() &&
5152 Start != getCouldNotCompute()) {
5153 const SCEV *StartVal = getSCEV(StartValueV);
5154 if (Start == StartVal) {
5155 // Okay, for the entire analysis of this edge we assumed the PHI
5156 // to be symbolic. We now need to go back and purge all of the
5157 // entries for the scalars that use the symbolic expression.
5158 forgetSymbolicName(PN, SymbolicName);
5159 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
5160 return Shifted;
5161 }
5162 }
5163 }
5164
5165 // Remove the temporary PHI node SCEV that has been inserted while intending
5166 // to create an AddRecExpr for this PHI node. We can not keep this temporary
5167 // as it will prevent later (possibly simpler) SCEV expressions to be added
5168 // to the ValueExprMap.
5169 eraseValueFromMap(PN);
5170
5171 return nullptr;
5172}
5173
5174// Checks if the SCEV S is available at BB. S is considered available at BB
5175// if S can be materialized at BB without introducing a fault.
5176static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
5177 BasicBlock *BB) {
5178 struct CheckAvailable {
5179 bool TraversalDone = false;
5180 bool Available = true;
5181
5182 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
5183 BasicBlock *BB = nullptr;
5184 DominatorTree &DT;
5185
5186 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
5187 : L(L), BB(BB), DT(DT) {}
5188
5189 bool setUnavailable() {
5190 TraversalDone = true;
5191 Available = false;
5192 return false;
5193 }
5194
5195 bool follow(const SCEV *S) {
5196 switch (S->getSCEVType()) {
5197 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
5198 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
5199 // These expressions are available if their operand(s) is/are.
5200 return true;
5201
5202 case scAddRecExpr: {
5203 // We allow add recurrences that are on the loop BB is in, or some
5204 // outer loop. This guarantees availability because the value of the
5205 // add recurrence at BB is simply the "current" value of the induction
5206 // variable. We can relax this in the future; for instance an add
5207 // recurrence on a sibling dominating loop is also available at BB.
5208 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
5209 if (L && (ARLoop == L || ARLoop->contains(L)))
5210 return true;
5211
5212 return setUnavailable();
5213 }
5214
5215 case scUnknown: {
5216 // For SCEVUnknown, we check for simple dominance.
5217 const auto *SU = cast<SCEVUnknown>(S);
5218 Value *V = SU->getValue();
5219
5220 if (isa<Argument>(V))
5221 return false;
5222
5223 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
5224 return false;
5225
5226 return setUnavailable();
5227 }
5228
5229 case scUDivExpr:
5230 case scCouldNotCompute:
5231 // We do not try to smart about these at all.
5232 return setUnavailable();
5233 }
5234 llvm_unreachable("switch should be fully covered!")::llvm::llvm_unreachable_internal("switch should be fully covered!"
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 5234)
;
5235 }
5236
5237 bool isDone() { return TraversalDone; }
5238 };
5239
5240 CheckAvailable CA(L, BB, DT);
5241 SCEVTraversal<CheckAvailable> ST(CA);
5242
5243 ST.visitAll(S);
5244 return CA.Available;
5245}
5246
5247// Try to match a control flow sequence that branches out at BI and merges back
5248// at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
5249// match.
5250static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
5251 Value *&C, Value *&LHS, Value *&RHS) {
5252 C = BI->getCondition();
5253
5254 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
5255 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
5256
5257 if (!LeftEdge.isSingleEdge())
5258 return false;
5259
5260 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()")((RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()"
) ? static_cast<void> (0) : __assert_fail ("RightEdge.isSingleEdge() && \"Follows from LeftEdge.isSingleEdge()\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 5260, __PRETTY_FUNCTION__))
;
5261
5262 Use &LeftUse = Merge->getOperandUse(0);
5263 Use &RightUse = Merge->getOperandUse(1);
5264
5265 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
5266 LHS = LeftUse;
5267 RHS = RightUse;
5268 return true;
5269 }
5270
5271 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
5272 LHS = RightUse;
5273 RHS = LeftUse;
5274 return true;
5275 }
5276
5277 return false;
5278}
5279
5280const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
5281 auto IsReachable =
5282 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
5283 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
5284 const Loop *L = LI.getLoopFor(PN->getParent());
5285
5286 // We don't want to break LCSSA, even in a SCEV expression tree.
5287 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
5288 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
5289 return nullptr;
5290
5291 // Try to match
5292 //
5293 // br %cond, label %left, label %right
5294 // left:
5295 // br label %merge
5296 // right:
5297 // br label %merge
5298 // merge:
5299 // V = phi [ %x, %left ], [ %y, %right ]
5300 //
5301 // as "select %cond, %x, %y"
5302
5303 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
5304 assert(IDom && "At least the entry block should dominate PN")((IDom && "At least the entry block should dominate PN"
) ? static_cast<void> (0) : __assert_fail ("IDom && \"At least the entry block should dominate PN\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 5304, __PRETTY_FUNCTION__))
;
5305
5306 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
5307 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
5308
5309 if (BI && BI->isConditional() &&
5310 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
5311 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
5312 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
5313 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
5314 }
5315
5316 return nullptr;
5317}
5318
5319const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
5320 if (const SCEV *S = createAddRecFromPHI(PN))
5321 return S;
5322
5323 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
5324 return S;
5325
5326 // If the PHI has a single incoming value, follow that value, unless the
5327 // PHI's incoming blocks are in a different loop, in which case doing so
5328 // risks breaking LCSSA form. Instcombine would normally zap these, but
5329 // it doesn't have DominatorTree information, so it may miss cases.
5330 if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
5331 if (LI.replacementPreservesLCSSAForm(PN, V))
5332 return getSCEV(V);
5333
5334 // If it's not a loop phi, we can't handle it yet.
5335 return getUnknown(PN);
5336}
5337
5338const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
5339 Value *Cond,
5340 Value *TrueVal,
5341 Value *FalseVal) {
5342 // Handle "constant" branch or select. This can occur for instance when a
5343 // loop pass transforms an inner loop and moves on to process the outer loop.
5344 if (auto *CI = dyn_cast<ConstantInt>(Cond))
5345 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
5346
5347 // Try to match some simple smax or umax patterns.
5348 auto *ICI = dyn_cast<ICmpInst>(Cond);
5349 if (!ICI)
5350 return getUnknown(I);
5351
5352 Value *LHS = ICI->getOperand(0);
5353 Value *RHS = ICI->getOperand(1);
5354
5355 switch (ICI->getPredicate()) {
5356 case ICmpInst::ICMP_SLT:
5357 case ICmpInst::ICMP_SLE:
5358 std::swap(LHS, RHS);
5359 LLVM_FALLTHROUGH[[clang::fallthrough]];
5360 case ICmpInst::ICMP_SGT:
5361 case ICmpInst::ICMP_SGE:
5362 // a >s b ? a+x : b+x -> smax(a, b)+x
5363 // a >s b ? b+x : a+x -> smin(a, b)+x
5364 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5365 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
5366 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
5367 const SCEV *LA = getSCEV(TrueVal);
5368 const SCEV *RA = getSCEV(FalseVal);
5369 const SCEV *LDiff = getMinusSCEV(LA, LS);
5370 const SCEV *RDiff = getMinusSCEV(RA, RS);
5371 if (LDiff == RDiff)
5372 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
5373 LDiff = getMinusSCEV(LA, RS);
5374 RDiff = getMinusSCEV(RA, LS);
5375 if (LDiff == RDiff)
5376 return getAddExpr(getSMinExpr(LS, RS), LDiff);
5377 }
5378 break;
5379 case ICmpInst::ICMP_ULT:
5380 case ICmpInst::ICMP_ULE:
5381 std::swap(LHS, RHS);
5382 LLVM_FALLTHROUGH[[clang::fallthrough]];
5383 case ICmpInst::ICMP_UGT:
5384 case ICmpInst::ICMP_UGE:
5385 // a >u b ? a+x : b+x -> umax(a, b)+x
5386 // a >u b ? b+x : a+x -> umin(a, b)+x
5387 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5388 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5389 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
5390 const SCEV *LA = getSCEV(TrueVal);
5391 const SCEV *RA = getSCEV(FalseVal);
5392 const SCEV *LDiff = getMinusSCEV(LA, LS);
5393 const SCEV *RDiff = getMinusSCEV(RA, RS);
5394 if (LDiff == RDiff)
5395 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
5396 LDiff = getMinusSCEV(LA, RS);
5397 RDiff = getMinusSCEV(RA, LS);
5398 if (LDiff == RDiff)
5399 return getAddExpr(getUMinExpr(LS, RS), LDiff);
5400 }
5401 break;
5402 case ICmpInst::ICMP_NE:
5403 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
5404 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5405 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5406 const SCEV *One = getOne(I->getType());
5407 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5408 const SCEV *LA = getSCEV(TrueVal);
5409 const SCEV *RA = getSCEV(FalseVal);
5410 const SCEV *LDiff = getMinusSCEV(LA, LS);
5411 const SCEV *RDiff = getMinusSCEV(RA, One);
5412 if (LDiff == RDiff)
5413 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5414 }
5415 break;
5416 case ICmpInst::ICMP_EQ:
5417 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
5418 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5419 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5420 const SCEV *One = getOne(I->getType());
5421 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5422 const SCEV *LA = getSCEV(TrueVal);
5423 const SCEV *RA = getSCEV(FalseVal);
5424 const SCEV *LDiff = getMinusSCEV(LA, One);
5425 const SCEV *RDiff = getMinusSCEV(RA, LS);
5426 if (LDiff == RDiff)
5427 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5428 }
5429 break;
5430 default:
5431 break;
5432 }
5433
5434 return getUnknown(I);
5435}
5436
5437/// Expand GEP instructions into add and multiply operations. This allows them
5438/// to be analyzed by regular SCEV code.
5439const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
5440 // Don't attempt to analyze GEPs over unsized objects.
5441 if (!GEP->getSourceElementType()->isSized())
5442 return getUnknown(GEP);
5443
5444 SmallVector<const SCEV *, 4> IndexExprs;
5445 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
5446 IndexExprs.push_back(getSCEV(*Index));
5447 return getGEPExpr(GEP, IndexExprs);
5448}
5449
5450uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
5451 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5452 return C->getAPInt().countTrailingZeros();
5453
5454 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
5455 return std::min(GetMinTrailingZeros(T->getOperand()),
5456 (uint32_t)getTypeSizeInBits(T->getType()));
5457
5458 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
5459 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5460 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5461 ? getTypeSizeInBits(E->getType())
5462 : OpRes;
5463 }
5464
5465 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
5466 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5467 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5468 ? getTypeSizeInBits(E->getType())
5469 : OpRes;
5470 }
5471
5472 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
5473 // The result is the min of all operands results.
5474 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5475 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5476 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5477 return MinOpRes;
5478 }
5479
5480 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
5481 // The result is the sum of all operands results.
5482 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
5483 uint32_t BitWidth = getTypeSizeInBits(M->getType());
5484 for (unsigned i = 1, e = M->getNumOperands();
5485 SumOpRes != BitWidth && i != e; ++i)
5486 SumOpRes =
5487 std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
5488 return SumOpRes;
5489 }
5490
5491 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
5492 // The result is the min of all operands results.
5493 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5494 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5495 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5496 return MinOpRes;
5497 }
5498
5499 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
5500 // The result is the min of all operands results.
5501 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5502 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5503 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5504 return MinOpRes;
5505 }
5506
5507 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
5508 // The result is the min of all operands results.
5509 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5510 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5511 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5512 return MinOpRes;
5513 }
5514
5515 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5516 // For a SCEVUnknown, ask ValueTracking.
5517 KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
5518 return Known.countMinTrailingZeros();
5519 }
5520
5521 // SCEVUDivExpr
5522 return 0;
5523}
5524
5525uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
5526 auto I = MinTrailingZerosCache.find(S);
5527 if (I != MinTrailingZerosCache.end())
5528 return I->second;
5529
5530 uint32_t Result = GetMinTrailingZerosImpl(S);
5531 auto InsertPair = MinTrailingZerosCache.insert({S, Result});
5532 assert(InsertPair.second && "Should insert a new key")((InsertPair.second && "Should insert a new key") ? static_cast
<void> (0) : __assert_fail ("InsertPair.second && \"Should insert a new key\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 5532, __PRETTY_FUNCTION__))
;
5533 return InsertPair.first->second;
5534}
5535
5536/// Helper method to assign a range to V from metadata present in the IR.
5537static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
5538 if (Instruction *I = dyn_cast<Instruction>(V))
5539 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
5540 return getConstantRangeFromMetadata(*MD);
5541
5542 return None;
5543}
5544
5545/// Determine the range for a particular SCEV. If SignHint is
5546/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
5547/// with a "cleaner" unsigned (resp. signed) representation.
5548const ConstantRange &
5549ScalarEvolution::getRangeRef(const SCEV *S,
5550 ScalarEvolution::RangeSignHint SignHint) {
5551 DenseMap<const SCEV *, ConstantRange> &Cache =
5552 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
5553 : SignedRanges;
5554
5555 // See if we've computed this range already.
5556 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
5557 if (I != Cache.end())
5558 return I->second;
5559
5560 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5561 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
5562
5563 unsigned BitWidth = getTypeSizeInBits(S->getType());
5564 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
5565
5566 // If the value has known zeros, the maximum value will have those known zeros
5567 // as well.
5568 uint32_t TZ = GetMinTrailingZeros(S);
5569 if (TZ != 0) {
5570 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
5571 ConservativeResult =
5572 ConstantRange(APInt::getMinValue(BitWidth),
5573 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
5574 else
5575 ConservativeResult = ConstantRange(
5576 APInt::getSignedMinValue(BitWidth),
5577 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
5578 }
5579
5580 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
5581 ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
5582 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
5583 X = X.add(getRangeRef(Add->getOperand(i), SignHint));
5584 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
5585 }
5586
5587 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
5588 ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
5589 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
5590 X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
5591 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
5592 }
5593
5594 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
5595 ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
5596 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
5597 X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
5598 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
5599 }
5600
5601 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
5602 ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
5603 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
5604 X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
5605 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
5606 }
5607
5608 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
5609 ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
5610 ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
5611 return setRange(UDiv, SignHint,
5612 ConservativeResult.intersectWith(X.udiv(Y)));
5613 }
5614
5615 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
5616 ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
5617 return setRange(ZExt, SignHint,
5618 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
5619 }
5620
5621 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
5622 ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
5623 return setRange(SExt, SignHint,
5624 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
5625 }
5626
5627 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
5628 ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
5629 return setRange(Trunc, SignHint,
5630 ConservativeResult.intersectWith(X.truncate(BitWidth)));
5631 }
5632
5633 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
5634 // If there's no unsigned wrap, the value will never be less than its
5635 // initial value.
5636 if (AddRec->hasNoUnsignedWrap())
5637 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
5638 if (!C->getValue()->isZero())
5639 ConservativeResult = ConservativeResult.intersectWith(
5640 ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
5641
5642 // If there's no signed wrap, and all the operands have the same sign or
5643 // zero, the value won't ever change sign.
5644 if (AddRec->hasNoSignedWrap()) {
5645 bool AllNonNeg = true;
5646 bool AllNonPos = true;
5647 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5648 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
5649 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
5650 }
5651 if (AllNonNeg)
5652 ConservativeResult = ConservativeResult.intersectWith(
5653 ConstantRange(APInt(BitWidth, 0),
5654 APInt::getSignedMinValue(BitWidth)));
5655 else if (AllNonPos)
5656 ConservativeResult = ConservativeResult.intersectWith(
5657 ConstantRange(APInt::getSignedMinValue(BitWidth),
5658 APInt(BitWidth, 1)));
5659 }
5660
5661 // TODO: non-affine addrec
5662 if (AddRec->isAffine()) {
5663 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
5664 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
5665 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
5666 auto RangeFromAffine = getRangeForAffineAR(
5667 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5668 BitWidth);
5669 if (!RangeFromAffine.isFullSet())
5670 ConservativeResult =
5671 ConservativeResult.intersectWith(RangeFromAffine);
5672
5673 auto RangeFromFactoring = getRangeViaFactoring(
5674 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5675 BitWidth);
5676 if (!RangeFromFactoring.isFullSet())
5677 ConservativeResult =
5678 ConservativeResult.intersectWith(RangeFromFactoring);
5679 }
5680 }
5681
5682 return setRange(AddRec, SignHint, std::move(ConservativeResult));
5683 }
5684
5685 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5686 // Check if the IR explicitly contains !range metadata.
5687 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
5688 if (MDRange.hasValue())
5689 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
5690
5691 // Split here to avoid paying the compile-time cost of calling both
5692 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
5693 // if needed.
5694 const DataLayout &DL = getDataLayout();
5695 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
5696 // For a SCEVUnknown, ask ValueTracking.
5697 KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5698 if (Known.One != ~Known.Zero + 1)
5699 ConservativeResult =
5700 ConservativeResult.intersectWith(ConstantRange(Known.One,
5701 ~Known.Zero + 1));
5702 } else {
5703 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&((SignHint == ScalarEvolution::HINT_RANGE_SIGNED && "generalize as needed!"
) ? static_cast<void> (0) : __assert_fail ("SignHint == ScalarEvolution::HINT_RANGE_SIGNED && \"generalize as needed!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 5704, __PRETTY_FUNCTION__))
5704 "generalize as needed!")((SignHint == ScalarEvolution::HINT_RANGE_SIGNED && "generalize as needed!"
) ? static_cast<void> (0) : __assert_fail ("SignHint == ScalarEvolution::HINT_RANGE_SIGNED && \"generalize as needed!\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 5704, __PRETTY_FUNCTION__))
;
5705 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5706 if (NS > 1)
5707 ConservativeResult = ConservativeResult.intersectWith(
5708 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
5709 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
5710 }
5711
5712 // A range of Phi is a subset of union of all ranges of its input.
5713 if (const PHINode *Phi = dyn_cast<PHINode>(U->getValue())) {
5714 // Make sure that we do not run over cycled Phis.
5715 if (PendingPhiRanges.insert(Phi).second) {
5716 ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
5717 for (auto &Op : Phi->operands()) {
5718 auto OpRange = getRangeRef(getSCEV(Op), SignHint);
5719 RangeFromOps = RangeFromOps.unionWith(OpRange);
5720 // No point to continue if we already have a full set.
5721 if (RangeFromOps.isFullSet())
5722 break;
5723 }
5724 ConservativeResult = ConservativeResult.intersectWith(RangeFromOps);
5725 bool Erased = PendingPhiRanges.erase(Phi);
5726 assert(Erased && "Failed to erase Phi properly?")((Erased && "Failed to erase Phi properly?") ? static_cast
<void> (0) : __assert_fail ("Erased && \"Failed to erase Phi properly?\""
, "/build/llvm-toolchain-snapshot-8~svn350071/lib/Analysis/ScalarEvolution.cpp"
, 5726, __PRETTY_FUNCTION__))
;
5727 (void) Erased;
5728 }
5729 }
5730
5731 return setRange(U, SignHint, std::move(ConservativeResult));
5732 }
5733
5734 return setRange(S, SignHint, std::move(ConservativeResult));
5735}
5736
5737// Given a StartRange, Step and MaxBECount for an expression compute a range of
5738// values that the expression can take. Initially, the expression has a value
5739// from StartRange and then is changed by Step up to MaxBECount times. Signed
5740// argument defines if we treat Step as signed or unsigned.
5741static ConstantRange getRangeForAffineARHelper(APInt Step,
5742 const ConstantRange &StartRange,
5743 const APInt &MaxBECount,
5744 unsigned BitWidth, bool Signed) {
5745 // If either Step or MaxBECount is 0, then the expression won't change, and we
5746 // just need to return the initial range.
5747 if (Step == 0 || MaxBECount == 0)
5748 return StartRange;
5749
5750 // If we don't know anything about the initial value (i.e. StartRange is
5751 // FullRange), then we don't know anything about the final range either.
5752 // Return FullRange.
5753 if (StartRange.isFullSet())
5754 return ConstantRange(BitWidth, /* isFullSet = */ true);
5755
5756 // If Step is signed and negative, then we use its absolute value, but we also
5757 // note that we're moving in the opposite direction.
5758 bool Descending = Signed && Step.isNegative();
5759
5760 if (Signed)
5761 // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
5762 // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
5763 // This equations hold true due to the well-defined wrap-around behavior of
5764 // APInt.
5765 Step = Step.abs();
5766
5767 // Check if Offset is more than full span of BitWidth. If it is, the
5768 // expression is guaranteed to overflow.
5769 if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
5770 return ConstantRange(BitWidth, /* isFullSet = */ true);
5771
5772 // Offset is by how much the expression can change. Checks above guarantee no
5773 // overflow here.
5774 APInt Offset = Step * MaxBECount;
5775
5776