Bug Summary

File:lib/Analysis/ScalarEvolution.cpp
Warning:line 6340, column 29
Called C++ object pointer is null

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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 -mframe-pointer=none -fmath-errno -masm-verbose -mconstructor-aliases -munwind-tables -fuse-init-array -target-cpu x86-64 -dwarf-column-info -debugger-tuning=gdb -ffunction-sections -fdata-sections -resource-dir /usr/lib/llvm-10/lib/clang/10.0.0 -D _DEBUG -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I /build/llvm-toolchain-snapshot-10~svn374877/build-llvm/lib/Analysis -I /build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis -I /build/llvm-toolchain-snapshot-10~svn374877/build-llvm/include -I /build/llvm-toolchain-snapshot-10~svn374877/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/local/include -internal-isystem /usr/lib/llvm-10/lib/clang/10.0.0/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++14 -fdeprecated-macro -fdebug-compilation-dir /build/llvm-toolchain-snapshot-10~svn374877/build-llvm/lib/Analysis -fdebug-prefix-map=/build/llvm-toolchain-snapshot-10~svn374877=. -ferror-limit 19 -fmessage-length 0 -fvisibility-inlines-hidden -stack-protector 2 -fgnuc-version=4.2.1 -fobjc-runtime=gcc -fdiagnostics-show-option -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -o /tmp/scan-build-2019-10-15-233810-7101-1 -x c++ /build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp

/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp

1//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// This file contains the implementation of the scalar evolution analysis
10// engine, which is used primarily to analyze expressions involving induction
11// variables in loops.
12//
13// There are several aspects to this library. First is the representation of
14// scalar expressions, which are represented as subclasses of the SCEV class.
15// These classes are used to represent certain types of subexpressions that we
16// can handle. We only create one SCEV of a particular shape, so
17// pointer-comparisons for equality are legal.
18//
19// One important aspect of the SCEV objects is that they are never cyclic, even
20// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
21// the PHI node is one of the idioms that we can represent (e.g., a polynomial
22// recurrence) then we represent it directly as a recurrence node, otherwise we
23// represent it as a SCEVUnknown node.
24//
25// In addition to being able to represent expressions of various types, we also
26// have folders that are used to build the *canonical* representation for a
27// particular expression. These folders are capable of using a variety of
28// rewrite rules to simplify the expressions.
29//
30// Once the folders are defined, we can implement the more interesting
31// higher-level code, such as the code that recognizes PHI nodes of various
32// types, computes the execution count of a loop, etc.
33//
34// TODO: We should use these routines and value representations to implement
35// dependence analysis!
36//
37//===----------------------------------------------------------------------===//
38//
39// There are several good references for the techniques used in this analysis.
40//
41// Chains of recurrences -- a method to expedite the evaluation
42// of closed-form functions
43// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
44//
45// On computational properties of chains of recurrences
46// Eugene V. Zima
47//
48// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
49// Robert A. van Engelen
50//
51// Efficient Symbolic Analysis for Optimizing Compilers
52// Robert A. van Engelen
53//
54// Using the chains of recurrences algebra for data dependence testing and
55// induction variable substitution
56// MS Thesis, Johnie Birch
57//
58//===----------------------------------------------------------------------===//
59
60#include "llvm/Analysis/ScalarEvolution.h"
61#include "llvm/ADT/APInt.h"
62#include "llvm/ADT/ArrayRef.h"
63#include "llvm/ADT/DenseMap.h"
64#include "llvm/ADT/DepthFirstIterator.h"
65#include "llvm/ADT/EquivalenceClasses.h"
66#include "llvm/ADT/FoldingSet.h"
67#include "llvm/ADT/None.h"
68#include "llvm/ADT/Optional.h"
69#include "llvm/ADT/STLExtras.h"
70#include "llvm/ADT/ScopeExit.h"
71#include "llvm/ADT/Sequence.h"
72#include "llvm/ADT/SetVector.h"
73#include "llvm/ADT/SmallPtrSet.h"
74#include "llvm/ADT/SmallSet.h"
75#include "llvm/ADT/SmallVector.h"
76#include "llvm/ADT/Statistic.h"
77#include "llvm/ADT/StringRef.h"
78#include "llvm/Analysis/AssumptionCache.h"
79#include "llvm/Analysis/ConstantFolding.h"
80#include "llvm/Analysis/InstructionSimplify.h"
81#include "llvm/Analysis/LoopInfo.h"
82#include "llvm/Analysis/ScalarEvolutionExpressions.h"
83#include "llvm/Analysis/TargetLibraryInfo.h"
84#include "llvm/Analysis/ValueTracking.h"
85#include "llvm/Config/llvm-config.h"
86#include "llvm/IR/Argument.h"
87#include "llvm/IR/BasicBlock.h"
88#include "llvm/IR/CFG.h"
89#include "llvm/IR/CallSite.h"
90#include "llvm/IR/Constant.h"
91#include "llvm/IR/ConstantRange.h"
92#include "llvm/IR/Constants.h"
93#include "llvm/IR/DataLayout.h"
94#include "llvm/IR/DerivedTypes.h"
95#include "llvm/IR/Dominators.h"
96#include "llvm/IR/Function.h"
97#include "llvm/IR/GlobalAlias.h"
98#include "llvm/IR/GlobalValue.h"
99#include "llvm/IR/GlobalVariable.h"
100#include "llvm/IR/InstIterator.h"
101#include "llvm/IR/InstrTypes.h"
102#include "llvm/IR/Instruction.h"
103#include "llvm/IR/Instructions.h"
104#include "llvm/IR/IntrinsicInst.h"
105#include "llvm/IR/Intrinsics.h"
106#include "llvm/IR/LLVMContext.h"
107#include "llvm/IR/Metadata.h"
108#include "llvm/IR/Operator.h"
109#include "llvm/IR/PatternMatch.h"
110#include "llvm/IR/Type.h"
111#include "llvm/IR/Use.h"
112#include "llvm/IR/User.h"
113#include "llvm/IR/Value.h"
114#include "llvm/IR/Verifier.h"
115#include "llvm/Pass.h"
116#include "llvm/Support/Casting.h"
117#include "llvm/Support/CommandLine.h"
118#include "llvm/Support/Compiler.h"
119#include "llvm/Support/Debug.h"
120#include "llvm/Support/ErrorHandling.h"
121#include "llvm/Support/KnownBits.h"
122#include "llvm/Support/SaveAndRestore.h"
123#include "llvm/Support/raw_ostream.h"
124#include <algorithm>
125#include <cassert>
126#include <climits>
127#include <cstddef>
128#include <cstdint>
129#include <cstdlib>
130#include <map>
131#include <memory>
132#include <tuple>
133#include <utility>
134#include <vector>
135
136using namespace llvm;
137
138#define DEBUG_TYPE"scalar-evolution" "scalar-evolution"
139
140STATISTIC(NumArrayLenItCounts,static llvm::Statistic NumArrayLenItCounts = {"scalar-evolution"
, "NumArrayLenItCounts", "Number of trip counts computed with array length"
}
141 "Number of trip counts computed with array length")static llvm::Statistic NumArrayLenItCounts = {"scalar-evolution"
, "NumArrayLenItCounts", "Number of trip counts computed with array length"
}
;
142STATISTIC(NumTripCountsComputed,static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
}
143 "Number of loops with predictable loop counts")static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
}
;
144STATISTIC(NumTripCountsNotComputed,static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
}
145 "Number of loops without predictable loop counts")static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
}
;
146STATISTIC(NumBruteForceTripCountsComputed,static llvm::Statistic NumBruteForceTripCountsComputed = {"scalar-evolution"
, "NumBruteForceTripCountsComputed", "Number of loops with trip counts computed by force"
}
147 "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"
}
;
148
149static cl::opt<unsigned>
150MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
151 cl::ZeroOrMore,
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> VerifySCEVStrict(
162 "verify-scev-strict", cl::Hidden,
163 cl::desc("Enable stricter verification with -verify-scev is passed"));
164static cl::opt<bool>
165 VerifySCEVMap("verify-scev-maps", cl::Hidden,
166 cl::desc("Verify no dangling value in ScalarEvolution's "
167 "ExprValueMap (slow)"));
168
169static cl::opt<bool> VerifyIR(
170 "scev-verify-ir", cl::Hidden,
171 cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
172 cl::init(false));
173
174static cl::opt<unsigned> MulOpsInlineThreshold(
175 "scev-mulops-inline-threshold", cl::Hidden,
176 cl::desc("Threshold for inlining multiplication operands into a SCEV"),
177 cl::init(32));
178
179static cl::opt<unsigned> AddOpsInlineThreshold(
180 "scev-addops-inline-threshold", cl::Hidden,
181 cl::desc("Threshold for inlining addition operands into a SCEV"),
182 cl::init(500));
183
184static cl::opt<unsigned> MaxSCEVCompareDepth(
185 "scalar-evolution-max-scev-compare-depth", cl::Hidden,
186 cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
187 cl::init(32));
188
189static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
190 "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
191 cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
192 cl::init(2));
193
194static cl::opt<unsigned> MaxValueCompareDepth(
195 "scalar-evolution-max-value-compare-depth", cl::Hidden,
196 cl::desc("Maximum depth of recursive value complexity comparisons"),
197 cl::init(2));
198
199static cl::opt<unsigned>
200 MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
201 cl::desc("Maximum depth of recursive arithmetics"),
202 cl::init(32));
203
204static cl::opt<unsigned> MaxConstantEvolvingDepth(
205 "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
206 cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
207
208static cl::opt<unsigned>
209 MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
210 cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
211 cl::init(8));
212
213static cl::opt<unsigned>
214 MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
215 cl::desc("Max coefficients in AddRec during evolving"),
216 cl::init(8));
217
218static cl::opt<unsigned>
219 HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
220 cl::desc("Size of the expression which is considered huge"),
221 cl::init(4096));
222
223//===----------------------------------------------------------------------===//
224// SCEV class definitions
225//===----------------------------------------------------------------------===//
226
227//===----------------------------------------------------------------------===//
228// Implementation of the SCEV class.
229//
230
231#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
232LLVM_DUMP_METHOD__attribute__((noinline)) __attribute__((__used__)) void SCEV::dump() const {
233 print(dbgs());
234 dbgs() << '\n';
235}
236#endif
237
238void SCEV::print(raw_ostream &OS) const {
239 switch (static_cast<SCEVTypes>(getSCEVType())) {
240 case scConstant:
241 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
242 return;
243 case scTruncate: {
244 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
245 const SCEV *Op = Trunc->getOperand();
246 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
247 << *Trunc->getType() << ")";
248 return;
249 }
250 case scZeroExtend: {
251 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
252 const SCEV *Op = ZExt->getOperand();
253 OS << "(zext " << *Op->getType() << " " << *Op << " to "
254 << *ZExt->getType() << ")";
255 return;
256 }
257 case scSignExtend: {
258 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
259 const SCEV *Op = SExt->getOperand();
260 OS << "(sext " << *Op->getType() << " " << *Op << " to "
261 << *SExt->getType() << ")";
262 return;
263 }
264 case scAddRecExpr: {
265 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
266 OS << "{" << *AR->getOperand(0);
267 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
268 OS << ",+," << *AR->getOperand(i);
269 OS << "}<";
270 if (AR->hasNoUnsignedWrap())
271 OS << "nuw><";
272 if (AR->hasNoSignedWrap())
273 OS << "nsw><";
274 if (AR->hasNoSelfWrap() &&
275 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
276 OS << "nw><";
277 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
278 OS << ">";
279 return;
280 }
281 case scAddExpr:
282 case scMulExpr:
283 case scUMaxExpr:
284 case scSMaxExpr:
285 case scUMinExpr:
286 case scSMinExpr: {
287 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
288 const char *OpStr = nullptr;
289 switch (NAry->getSCEVType()) {
290 case scAddExpr: OpStr = " + "; break;
291 case scMulExpr: OpStr = " * "; break;
292 case scUMaxExpr: OpStr = " umax "; break;
293 case scSMaxExpr: OpStr = " smax "; break;
294 case scUMinExpr:
295 OpStr = " umin ";
296 break;
297 case scSMinExpr:
298 OpStr = " smin ";
299 break;
300 }
301 OS << "(";
302 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
303 I != E; ++I) {
304 OS << **I;
305 if (std::next(I) != E)
306 OS << OpStr;
307 }
308 OS << ")";
309 switch (NAry->getSCEVType()) {
310 case scAddExpr:
311 case scMulExpr:
312 if (NAry->hasNoUnsignedWrap())
313 OS << "<nuw>";
314 if (NAry->hasNoSignedWrap())
315 OS << "<nsw>";
316 }
317 return;
318 }
319 case scUDivExpr: {
320 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
321 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
322 return;
323 }
324 case scUnknown: {
325 const SCEVUnknown *U = cast<SCEVUnknown>(this);
326 Type *AllocTy;
327 if (U->isSizeOf(AllocTy)) {
328 OS << "sizeof(" << *AllocTy << ")";
329 return;
330 }
331 if (U->isAlignOf(AllocTy)) {
332 OS << "alignof(" << *AllocTy << ")";
333 return;
334 }
335
336 Type *CTy;
337 Constant *FieldNo;
338 if (U->isOffsetOf(CTy, FieldNo)) {
339 OS << "offsetof(" << *CTy << ", ";
340 FieldNo->printAsOperand(OS, false);
341 OS << ")";
342 return;
343 }
344
345 // Otherwise just print it normally.
346 U->getValue()->printAsOperand(OS, false);
347 return;
348 }
349 case scCouldNotCompute:
350 OS << "***COULDNOTCOMPUTE***";
351 return;
352 }
353 llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 353)
;
354}
355
356Type *SCEV::getType() const {
357 switch (static_cast<SCEVTypes>(getSCEVType())) {
358 case scConstant:
359 return cast<SCEVConstant>(this)->getType();
360 case scTruncate:
361 case scZeroExtend:
362 case scSignExtend:
363 return cast<SCEVCastExpr>(this)->getType();
364 case scAddRecExpr:
365 case scMulExpr:
366 case scUMaxExpr:
367 case scSMaxExpr:
368 case scUMinExpr:
369 case scSMinExpr:
370 return cast<SCEVNAryExpr>(this)->getType();
371 case scAddExpr:
372 return cast<SCEVAddExpr>(this)->getType();
373 case scUDivExpr:
374 return cast<SCEVUDivExpr>(this)->getType();
375 case scUnknown:
376 return cast<SCEVUnknown>(this)->getType();
377 case scCouldNotCompute:
378 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 378)
;
379 }
380 llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 380)
;
381}
382
383bool SCEV::isZero() const {
384 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
385 return SC->getValue()->isZero();
386 return false;
387}
388
389bool SCEV::isOne() const {
390 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
391 return SC->getValue()->isOne();
392 return false;
393}
394
395bool SCEV::isAllOnesValue() const {
396 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
397 return SC->getValue()->isMinusOne();
398 return false;
399}
400
401bool SCEV::isNonConstantNegative() const {
402 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
403 if (!Mul) return false;
404
405 // If there is a constant factor, it will be first.
406 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
407 if (!SC) return false;
408
409 // Return true if the value is negative, this matches things like (-42 * V).
410 return SC->getAPInt().isNegative();
411}
412
413SCEVCouldNotCompute::SCEVCouldNotCompute() :
414 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {}
415
416bool SCEVCouldNotCompute::classof(const SCEV *S) {
417 return S->getSCEVType() == scCouldNotCompute;
418}
419
420const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
421 FoldingSetNodeID ID;
422 ID.AddInteger(scConstant);
423 ID.AddPointer(V);
424 void *IP = nullptr;
425 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
426 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
427 UniqueSCEVs.InsertNode(S, IP);
428 return S;
429}
430
431const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
432 return getConstant(ConstantInt::get(getContext(), Val));
433}
434
435const SCEV *
436ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
437 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
438 return getConstant(ConstantInt::get(ITy, V, isSigned));
439}
440
441SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
442 unsigned SCEVTy, const SCEV *op, Type *ty)
443 : SCEV(ID, SCEVTy, computeExpressionSize(op)), Op(op), Ty(ty) {}
444
445SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
446 const SCEV *op, Type *ty)
447 : SCEVCastExpr(ID, scTruncate, op, ty) {
448 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 449, __PRETTY_FUNCTION__))
449 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 449, __PRETTY_FUNCTION__))
;
450}
451
452SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
453 const SCEV *op, Type *ty)
454 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
455 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 456, __PRETTY_FUNCTION__))
456 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 456, __PRETTY_FUNCTION__))
;
457}
458
459SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
460 const SCEV *op, Type *ty)
461 : SCEVCastExpr(ID, scSignExtend, op, ty) {
462 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 463, __PRETTY_FUNCTION__))
463 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 463, __PRETTY_FUNCTION__))
;
464}
465
466void SCEVUnknown::deleted() {
467 // Clear this SCEVUnknown from various maps.
468 SE->forgetMemoizedResults(this);
469
470 // Remove this SCEVUnknown from the uniquing map.
471 SE->UniqueSCEVs.RemoveNode(this);
472
473 // Release the value.
474 setValPtr(nullptr);
475}
476
477void SCEVUnknown::allUsesReplacedWith(Value *New) {
478 // Remove this SCEVUnknown from the uniquing map.
479 SE->UniqueSCEVs.RemoveNode(this);
480
481 // Update this SCEVUnknown to point to the new value. This is needed
482 // because there may still be outstanding SCEVs which still point to
483 // this SCEVUnknown.
484 setValPtr(New);
485}
486
487bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
488 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
489 if (VCE->getOpcode() == Instruction::PtrToInt)
490 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
491 if (CE->getOpcode() == Instruction::GetElementPtr &&
492 CE->getOperand(0)->isNullValue() &&
493 CE->getNumOperands() == 2)
494 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
495 if (CI->isOne()) {
496 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
497 ->getElementType();
498 return true;
499 }
500
501 return false;
502}
503
504bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
505 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
506 if (VCE->getOpcode() == Instruction::PtrToInt)
507 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
508 if (CE->getOpcode() == Instruction::GetElementPtr &&
509 CE->getOperand(0)->isNullValue()) {
510 Type *Ty =
511 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
512 if (StructType *STy = dyn_cast<StructType>(Ty))
513 if (!STy->isPacked() &&
514 CE->getNumOperands() == 3 &&
515 CE->getOperand(1)->isNullValue()) {
516 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
517 if (CI->isOne() &&
518 STy->getNumElements() == 2 &&
519 STy->getElementType(0)->isIntegerTy(1)) {
520 AllocTy = STy->getElementType(1);
521 return true;
522 }
523 }
524 }
525
526 return false;
527}
528
529bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
530 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
531 if (VCE->getOpcode() == Instruction::PtrToInt)
532 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
533 if (CE->getOpcode() == Instruction::GetElementPtr &&
534 CE->getNumOperands() == 3 &&
535 CE->getOperand(0)->isNullValue() &&
536 CE->getOperand(1)->isNullValue()) {
537 Type *Ty =
538 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
539 // Ignore vector types here so that ScalarEvolutionExpander doesn't
540 // emit getelementptrs that index into vectors.
541 if (Ty->isStructTy() || Ty->isArrayTy()) {
542 CTy = Ty;
543 FieldNo = CE->getOperand(2);
544 return true;
545 }
546 }
547
548 return false;
549}
550
551//===----------------------------------------------------------------------===//
552// SCEV Utilities
553//===----------------------------------------------------------------------===//
554
555/// Compare the two values \p LV and \p RV in terms of their "complexity" where
556/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
557/// operands in SCEV expressions. \p EqCache is a set of pairs of values that
558/// have been previously deemed to be "equally complex" by this routine. It is
559/// intended to avoid exponential time complexity in cases like:
560///
561/// %a = f(%x, %y)
562/// %b = f(%a, %a)
563/// %c = f(%b, %b)
564///
565/// %d = f(%x, %y)
566/// %e = f(%d, %d)
567/// %f = f(%e, %e)
568///
569/// CompareValueComplexity(%f, %c)
570///
571/// Since we do not continue running this routine on expression trees once we
572/// have seen unequal values, there is no need to track them in the cache.
573static int
574CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
575 const LoopInfo *const LI, Value *LV, Value *RV,
576 unsigned Depth) {
577 if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
578 return 0;
579
580 // Order pointer values after integer values. This helps SCEVExpander form
581 // GEPs.
582 bool LIsPointer = LV->getType()->isPointerTy(),
583 RIsPointer = RV->getType()->isPointerTy();
584 if (LIsPointer != RIsPointer)
585 return (int)LIsPointer - (int)RIsPointer;
586
587 // Compare getValueID values.
588 unsigned LID = LV->getValueID(), RID = RV->getValueID();
589 if (LID != RID)
590 return (int)LID - (int)RID;
591
592 // Sort arguments by their position.
593 if (const auto *LA = dyn_cast<Argument>(LV)) {
594 const auto *RA = cast<Argument>(RV);
595 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
596 return (int)LArgNo - (int)RArgNo;
597 }
598
599 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
600 const auto *RGV = cast<GlobalValue>(RV);
601
602 const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
603 auto LT = GV->getLinkage();
604 return !(GlobalValue::isPrivateLinkage(LT) ||
605 GlobalValue::isInternalLinkage(LT));
606 };
607
608 // Use the names to distinguish the two values, but only if the
609 // names are semantically important.
610 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
611 return LGV->getName().compare(RGV->getName());
612 }
613
614 // For instructions, compare their loop depth, and their operand count. This
615 // is pretty loose.
616 if (const auto *LInst = dyn_cast<Instruction>(LV)) {
617 const auto *RInst = cast<Instruction>(RV);
618
619 // Compare loop depths.
620 const BasicBlock *LParent = LInst->getParent(),
621 *RParent = RInst->getParent();
622 if (LParent != RParent) {
623 unsigned LDepth = LI->getLoopDepth(LParent),
624 RDepth = LI->getLoopDepth(RParent);
625 if (LDepth != RDepth)
626 return (int)LDepth - (int)RDepth;
627 }
628
629 // Compare the number of operands.
630 unsigned LNumOps = LInst->getNumOperands(),
631 RNumOps = RInst->getNumOperands();
632 if (LNumOps != RNumOps)
633 return (int)LNumOps - (int)RNumOps;
634
635 for (unsigned Idx : seq(0u, LNumOps)) {
636 int Result =
637 CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
638 RInst->getOperand(Idx), Depth + 1);
639 if (Result != 0)
640 return Result;
641 }
642 }
643
644 EqCacheValue.unionSets(LV, RV);
645 return 0;
646}
647
648// Return negative, zero, or positive, if LHS is less than, equal to, or greater
649// than RHS, respectively. A three-way result allows recursive comparisons to be
650// more efficient.
651static int CompareSCEVComplexity(
652 EquivalenceClasses<const SCEV *> &EqCacheSCEV,
653 EquivalenceClasses<const Value *> &EqCacheValue,
654 const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
655 DominatorTree &DT, unsigned Depth = 0) {
656 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
657 if (LHS == RHS)
658 return 0;
659
660 // Primarily, sort the SCEVs by their getSCEVType().
661 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
662 if (LType != RType)
663 return (int)LType - (int)RType;
664
665 if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS))
666 return 0;
667 // Aside from the getSCEVType() ordering, the particular ordering
668 // isn't very important except that it's beneficial to be consistent,
669 // so that (a + b) and (b + a) don't end up as different expressions.
670 switch (static_cast<SCEVTypes>(LType)) {
671 case scUnknown: {
672 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
673 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
674
675 int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
676 RU->getValue(), Depth + 1);
677 if (X == 0)
678 EqCacheSCEV.unionSets(LHS, RHS);
679 return X;
680 }
681
682 case scConstant: {
683 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
684 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
685
686 // Compare constant values.
687 const APInt &LA = LC->getAPInt();
688 const APInt &RA = RC->getAPInt();
689 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
690 if (LBitWidth != RBitWidth)
691 return (int)LBitWidth - (int)RBitWidth;
692 return LA.ult(RA) ? -1 : 1;
693 }
694
695 case scAddRecExpr: {
696 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
697 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
698
699 // There is always a dominance between two recs that are used by one SCEV,
700 // so we can safely sort recs by loop header dominance. We require such
701 // order in getAddExpr.
702 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
703 if (LLoop != RLoop) {
704 const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
705 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 705, __PRETTY_FUNCTION__))
;
706 if (DT.dominates(LHead, RHead))
707 return 1;
708 else
709 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 710, __PRETTY_FUNCTION__))
710 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 710, __PRETTY_FUNCTION__))
;
711 return -1;
712 }
713
714 // Addrec complexity grows with operand count.
715 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
716 if (LNumOps != RNumOps)
717 return (int)LNumOps - (int)RNumOps;
718
719 // Lexicographically compare.
720 for (unsigned i = 0; i != LNumOps; ++i) {
721 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
722 LA->getOperand(i), RA->getOperand(i), DT,
723 Depth + 1);
724 if (X != 0)
725 return X;
726 }
727 EqCacheSCEV.unionSets(LHS, RHS);
728 return 0;
729 }
730
731 case scAddExpr:
732 case scMulExpr:
733 case scSMaxExpr:
734 case scUMaxExpr:
735 case scSMinExpr:
736 case scUMinExpr: {
737 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
738 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
739
740 // Lexicographically compare n-ary expressions.
741 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
742 if (LNumOps != RNumOps)
743 return (int)LNumOps - (int)RNumOps;
744
745 for (unsigned i = 0; i != LNumOps; ++i) {
746 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
747 LC->getOperand(i), RC->getOperand(i), DT,
748 Depth + 1);
749 if (X != 0)
750 return X;
751 }
752 EqCacheSCEV.unionSets(LHS, RHS);
753 return 0;
754 }
755
756 case scUDivExpr: {
757 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
758 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
759
760 // Lexicographically compare udiv expressions.
761 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
762 RC->getLHS(), DT, Depth + 1);
763 if (X != 0)
764 return X;
765 X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
766 RC->getRHS(), DT, Depth + 1);
767 if (X == 0)
768 EqCacheSCEV.unionSets(LHS, RHS);
769 return X;
770 }
771
772 case scTruncate:
773 case scZeroExtend:
774 case scSignExtend: {
775 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
776 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
777
778 // Compare cast expressions by operand.
779 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
780 LC->getOperand(), RC->getOperand(), DT,
781 Depth + 1);
782 if (X == 0)
783 EqCacheSCEV.unionSets(LHS, RHS);
784 return X;
785 }
786
787 case scCouldNotCompute:
788 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 788)
;
789 }
790 llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 790)
;
791}
792
793/// Given a list of SCEV objects, order them by their complexity, and group
794/// objects of the same complexity together by value. When this routine is
795/// finished, we know that any duplicates in the vector are consecutive and that
796/// complexity is monotonically increasing.
797///
798/// Note that we go take special precautions to ensure that we get deterministic
799/// results from this routine. In other words, we don't want the results of
800/// this to depend on where the addresses of various SCEV objects happened to
801/// land in memory.
802static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
803 LoopInfo *LI, DominatorTree &DT) {
804 if (Ops.size() < 2) return; // Noop
805
806 EquivalenceClasses<const SCEV *> EqCacheSCEV;
807 EquivalenceClasses<const Value *> EqCacheValue;
808 if (Ops.size() == 2) {
809 // This is the common case, which also happens to be trivially simple.
810 // Special case it.
811 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
812 if (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0)
813 std::swap(LHS, RHS);
814 return;
815 }
816
817 // Do the rough sort by complexity.
818 llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) {
819 return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT) <
820 0;
821 });
822
823 // Now that we are sorted by complexity, group elements of the same
824 // complexity. Note that this is, at worst, N^2, but the vector is likely to
825 // be extremely short in practice. Note that we take this approach because we
826 // do not want to depend on the addresses of the objects we are grouping.
827 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
828 const SCEV *S = Ops[i];
829 unsigned Complexity = S->getSCEVType();
830
831 // If there are any objects of the same complexity and same value as this
832 // one, group them.
833 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
834 if (Ops[j] == S) { // Found a duplicate.
835 // Move it to immediately after i'th element.
836 std::swap(Ops[i+1], Ops[j]);
837 ++i; // no need to rescan it.
838 if (i == e-2) return; // Done!
839 }
840 }
841 }
842}
843
844// Returns the size of the SCEV S.
845static inline int sizeOfSCEV(const SCEV *S) {
846 struct FindSCEVSize {
847 int Size = 0;
848
849 FindSCEVSize() = default;
850
851 bool follow(const SCEV *S) {
852 ++Size;
853 // Keep looking at all operands of S.
854 return true;
855 }
856
857 bool isDone() const {
858 return false;
859 }
860 };
861
862 FindSCEVSize F;
863 SCEVTraversal<FindSCEVSize> ST(F);
864 ST.visitAll(S);
865 return F.Size;
866}
867
868/// Returns true if the subtree of \p S contains at least HugeExprThreshold
869/// nodes.
870static bool isHugeExpression(const SCEV *S) {
871 return S->getExpressionSize() >= HugeExprThreshold;
872}
873
874/// Returns true of \p Ops contains a huge SCEV (see definition above).
875static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) {
876 return any_of(Ops, isHugeExpression);
877}
878
879namespace {
880
881struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
882public:
883 // Computes the Quotient and Remainder of the division of Numerator by
884 // Denominator.
885 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
886 const SCEV *Denominator, const SCEV **Quotient,
887 const SCEV **Remainder) {
888 assert(Numerator && Denominator && "Uninitialized SCEV")((Numerator && Denominator && "Uninitialized SCEV"
) ? static_cast<void> (0) : __assert_fail ("Numerator && Denominator && \"Uninitialized SCEV\""
, "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 888, __PRETTY_FUNCTION__))
;
889
890 SCEVDivision D(SE, Numerator, Denominator);
891
892 // Check for the trivial case here to avoid having to check for it in the
893 // rest of the code.
894 if (Numerator == Denominator) {
895 *Quotient = D.One;
896 *Remainder = D.Zero;
897 return;
898 }
899
900 if (Numerator->isZero()) {
901 *Quotient = D.Zero;
902 *Remainder = D.Zero;
903 return;
904 }
905
906 // A simple case when N/1. The quotient is N.
907 if (Denominator->isOne()) {
908 *Quotient = Numerator;
909 *Remainder = D.Zero;
910 return;
911 }
912
913 // Split the Denominator when it is a product.
914 if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
915 const SCEV *Q, *R;
916 *Quotient = Numerator;
917 for (const SCEV *Op : T->operands()) {
918 divide(SE, *Quotient, Op, &Q, &R);
919 *Quotient = Q;
920
921 // Bail out when the Numerator is not divisible by one of the terms of
922 // the Denominator.
923 if (!R->isZero()) {
924 *Quotient = D.Zero;
925 *Remainder = Numerator;
926 return;
927 }
928 }
929 *Remainder = D.Zero;
930 return;
931 }
932
933 D.visit(Numerator);
934 *Quotient = D.Quotient;
935 *Remainder = D.Remainder;
936 }
937
938 // Except in the trivial case described above, we do not know how to divide
939 // Expr by Denominator for the following functions with empty implementation.
940 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
941 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
942 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
943 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
944 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
945 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
946 void visitSMinExpr(const SCEVSMinExpr *Numerator) {}
947 void visitUMinExpr(const SCEVUMinExpr *Numerator) {}
948 void visitUnknown(const SCEVUnknown *Numerator) {}
949 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
950
951 void visitConstant(const SCEVConstant *Numerator) {
952 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
953 APInt NumeratorVal = Numerator->getAPInt();
954 APInt DenominatorVal = D->getAPInt();
955 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
956 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
957
958 if (NumeratorBW > DenominatorBW)
959 DenominatorVal = DenominatorVal.sext(NumeratorBW);
960 else if (NumeratorBW < DenominatorBW)
961 NumeratorVal = NumeratorVal.sext(DenominatorBW);
962
963 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
964 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
965 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
966 Quotient = SE.getConstant(QuotientVal);
967 Remainder = SE.getConstant(RemainderVal);
968 return;
969 }
970 }
971
972 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
973 const SCEV *StartQ, *StartR, *StepQ, *StepR;
974 if (!Numerator->isAffine())
975 return cannotDivide(Numerator);
976 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
977 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
978 // Bail out if the types do not match.
979 Type *Ty = Denominator->getType();
980 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
981 Ty != StepQ->getType() || Ty != StepR->getType())
982 return cannotDivide(Numerator);
983 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
984 Numerator->getNoWrapFlags());
985 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
986 Numerator->getNoWrapFlags());
987 }
988
989 void visitAddExpr(const SCEVAddExpr *Numerator) {
990 SmallVector<const SCEV *, 2> Qs, Rs;
991 Type *Ty = Denominator->getType();
992
993 for (const SCEV *Op : Numerator->operands()) {
994 const SCEV *Q, *R;
995 divide(SE, Op, Denominator, &Q, &R);
996
997 // Bail out if types do not match.
998 if (Ty != Q->getType() || Ty != R->getType())
999 return cannotDivide(Numerator);
1000
1001 Qs.push_back(Q);
1002 Rs.push_back(R);
1003 }
1004
1005 if (Qs.size() == 1) {
1006 Quotient = Qs[0];
1007 Remainder = Rs[0];
1008 return;
1009 }
1010
1011 Quotient = SE.getAddExpr(Qs);
1012 Remainder = SE.getAddExpr(Rs);
1013 }
1014
1015 void visitMulExpr(const SCEVMulExpr *Numerator) {
1016 SmallVector<const SCEV *, 2> Qs;
1017 Type *Ty = Denominator->getType();
1018
1019 bool FoundDenominatorTerm = false;
1020 for (const SCEV *Op : Numerator->operands()) {
1021 // Bail out if types do not match.
1022 if (Ty != Op->getType())
1023 return cannotDivide(Numerator);
1024
1025 if (FoundDenominatorTerm) {
1026 Qs.push_back(Op);
1027 continue;
1028 }
1029
1030 // Check whether Denominator divides one of the product operands.
1031 const SCEV *Q, *R;
1032 divide(SE, Op, Denominator, &Q, &R);
1033 if (!R->isZero()) {
1034 Qs.push_back(Op);
1035 continue;
1036 }
1037
1038 // Bail out if types do not match.
1039 if (Ty != Q->getType())
1040 return cannotDivide(Numerator);
1041
1042 FoundDenominatorTerm = true;
1043 Qs.push_back(Q);
1044 }
1045
1046 if (FoundDenominatorTerm) {
1047 Remainder = Zero;
1048 if (Qs.size() == 1)
1049 Quotient = Qs[0];
1050 else
1051 Quotient = SE.getMulExpr(Qs);
1052 return;
1053 }
1054
1055 if (!isa<SCEVUnknown>(Denominator))
1056 return cannotDivide(Numerator);
1057
1058 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
1059 ValueToValueMap RewriteMap;
1060 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1061 cast<SCEVConstant>(Zero)->getValue();
1062 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1063
1064 if (Remainder->isZero()) {
1065 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
1066 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1067 cast<SCEVConstant>(One)->getValue();
1068 Quotient =
1069 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1070 return;
1071 }
1072
1073 // Quotient is (Numerator - Remainder) divided by Denominator.
1074 const SCEV *Q, *R;
1075 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
1076 // This SCEV does not seem to simplify: fail the division here.
1077 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
1078 return cannotDivide(Numerator);
1079 divide(SE, Diff, Denominator, &Q, &R);
1080 if (R != Zero)
1081 return cannotDivide(Numerator);
1082 Quotient = Q;
1083 }
1084
1085private:
1086 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
1087 const SCEV *Denominator)
1088 : SE(S), Denominator(Denominator) {
1089 Zero = SE.getZero(Denominator->getType());
1090 One = SE.getOne(Denominator->getType());
1091
1092 // We generally do not know how to divide Expr by Denominator. We
1093 // initialize the division to a "cannot divide" state to simplify the rest
1094 // of the code.
1095 cannotDivide(Numerator);
1096 }
1097
1098 // Convenience function for giving up on the division. We set the quotient to
1099 // be equal to zero and the remainder to be equal to the numerator.
1100 void cannotDivide(const SCEV *Numerator) {
1101 Quotient = Zero;
1102 Remainder = Numerator;
1103 }
1104
1105 ScalarEvolution &SE;
1106 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
1107};
1108
1109} // end anonymous namespace
1110
1111//===----------------------------------------------------------------------===//
1112// Simple SCEV method implementations
1113//===----------------------------------------------------------------------===//
1114
1115/// Compute BC(It, K). The result has width W. Assume, K > 0.
1116static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
1117 ScalarEvolution &SE,
1118 Type *ResultTy) {
1119 // Handle the simplest case efficiently.
1120 if (K == 1)
1121 return SE.getTruncateOrZeroExtend(It, ResultTy);
1122
1123 // We are using the following formula for BC(It, K):
1124 //
1125 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
1126 //
1127 // Suppose, W is the bitwidth of the return value. We must be prepared for
1128 // overflow. Hence, we must assure that the result of our computation is
1129 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
1130 // safe in modular arithmetic.
1131 //
1132 // However, this code doesn't use exactly that formula; the formula it uses
1133 // is something like the following, where T is the number of factors of 2 in
1134 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
1135 // exponentiation:
1136 //
1137 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
1138 //
1139 // This formula is trivially equivalent to the previous formula. However,
1140 // this formula can be implemented much more efficiently. The trick is that
1141 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
1142 // arithmetic. To do exact division in modular arithmetic, all we have
1143 // to do is multiply by the inverse. Therefore, this step can be done at
1144 // width W.
1145 //
1146 // The next issue is how to safely do the division by 2^T. The way this
1147 // is done is by doing the multiplication step at a width of at least W + T
1148 // bits. This way, the bottom W+T bits of the product are accurate. Then,
1149 // when we perform the division by 2^T (which is equivalent to a right shift
1150 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
1151 // truncated out after the division by 2^T.
1152 //
1153 // In comparison to just directly using the first formula, this technique
1154 // is much more efficient; using the first formula requires W * K bits,
1155 // but this formula less than W + K bits. Also, the first formula requires
1156 // a division step, whereas this formula only requires multiplies and shifts.
1157 //
1158 // It doesn't matter whether the subtraction step is done in the calculation
1159 // width or the input iteration count's width; if the subtraction overflows,
1160 // the result must be zero anyway. We prefer here to do it in the width of
1161 // the induction variable because it helps a lot for certain cases; CodeGen
1162 // isn't smart enough to ignore the overflow, which leads to much less
1163 // efficient code if the width of the subtraction is wider than the native
1164 // register width.
1165 //
1166 // (It's possible to not widen at all by pulling out factors of 2 before
1167 // the multiplication; for example, K=2 can be calculated as
1168 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1169 // extra arithmetic, so it's not an obvious win, and it gets
1170 // much more complicated for K > 3.)
1171
1172 // Protection from insane SCEVs; this bound is conservative,
1173 // but it probably doesn't matter.
1174 if (K > 1000)
1175 return SE.getCouldNotCompute();
1176
1177 unsigned W = SE.getTypeSizeInBits(ResultTy);
1178
1179 // Calculate K! / 2^T and T; we divide out the factors of two before
1180 // multiplying for calculating K! / 2^T to avoid overflow.
1181 // Other overflow doesn't matter because we only care about the bottom
1182 // W bits of the result.
1183 APInt OddFactorial(W, 1);
1184 unsigned T = 1;
1185 for (unsigned i = 3; i <= K; ++i) {
1186 APInt Mult(W, i);
1187 unsigned TwoFactors = Mult.countTrailingZeros();
1188 T += TwoFactors;
1189 Mult.lshrInPlace(TwoFactors);
1190 OddFactorial *= Mult;
1191 }
1192
1193 // We need at least W + T bits for the multiplication step
1194 unsigned CalculationBits = W + T;
1195
1196 // Calculate 2^T, at width T+W.
1197 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1198
1199 // Calculate the multiplicative inverse of K! / 2^T;
1200 // this multiplication factor will perform the exact division by
1201 // K! / 2^T.
1202 APInt Mod = APInt::getSignedMinValue(W+1);
1203 APInt MultiplyFactor = OddFactorial.zext(W+1);
1204 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1205 MultiplyFactor = MultiplyFactor.trunc(W);
1206
1207 // Calculate the product, at width T+W
1208 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1209 CalculationBits);
1210 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1211 for (unsigned i = 1; i != K; ++i) {
1212 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1213 Dividend = SE.getMulExpr(Dividend,
1214 SE.getTruncateOrZeroExtend(S, CalculationTy));
1215 }
1216
1217 // Divide by 2^T
1218 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1219
1220 // Truncate the result, and divide by K! / 2^T.
1221
1222 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1223 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1224}
1225
1226/// Return the value of this chain of recurrences at the specified iteration
1227/// number. We can evaluate this recurrence by multiplying each element in the
1228/// chain by the binomial coefficient corresponding to it. In other words, we
1229/// can evaluate {A,+,B,+,C,+,D} as:
1230///
1231/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1232///
1233/// where BC(It, k) stands for binomial coefficient.
1234const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1235 ScalarEvolution &SE) const {
1236 const SCEV *Result = getStart();
1237 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1238 // The computation is correct in the face of overflow provided that the
1239 // multiplication is performed _after_ the evaluation of the binomial
1240 // coefficient.
1241 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1242 if (isa<SCEVCouldNotCompute>(Coeff))
1243 return Coeff;
1244
1245 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1246 }
1247 return Result;
1248}
1249
1250//===----------------------------------------------------------------------===//
1251// SCEV Expression folder implementations
1252//===----------------------------------------------------------------------===//
1253
1254const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
1255 unsigned Depth) {
1256 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1257, __PRETTY_FUNCTION__))
1257 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1257, __PRETTY_FUNCTION__))
;
1258 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1259, __PRETTY_FUNCTION__))
1259 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1259, __PRETTY_FUNCTION__))
;
1260 Ty = getEffectiveSCEVType(Ty);
1261
1262 FoldingSetNodeID ID;
1263 ID.AddInteger(scTruncate);
1264 ID.AddPointer(Op);
1265 ID.AddPointer(Ty);
1266 void *IP = nullptr;
1267 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1268
1269 // Fold if the operand is constant.
1270 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1271 return getConstant(
1272 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1273
1274 // trunc(trunc(x)) --> trunc(x)
1275 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1276 return getTruncateExpr(ST->getOperand(), Ty, Depth + 1);
1277
1278 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1279 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1280 return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1);
1281
1282 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1283 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1284 return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1);
1285
1286 if (Depth > MaxCastDepth) {
1287 SCEV *S =
1288 new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty);
1289 UniqueSCEVs.InsertNode(S, IP);
1290 addToLoopUseLists(S);
1291 return S;
1292 }
1293
1294 // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
1295 // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
1296 // if after transforming we have at most one truncate, not counting truncates
1297 // that replace other casts.
1298 if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
1299 auto *CommOp = cast<SCEVCommutativeExpr>(Op);
1300 SmallVector<const SCEV *, 4> Operands;
1301 unsigned numTruncs = 0;
1302 for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
1303 ++i) {
1304 const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1);
1305 if (!isa<SCEVCastExpr>(CommOp->getOperand(i)) && isa<SCEVTruncateExpr>(S))
1306 numTruncs++;
1307 Operands.push_back(S);
1308 }
1309 if (numTruncs < 2) {
1310 if (isa<SCEVAddExpr>(Op))
1311 return getAddExpr(Operands);
1312 else if (isa<SCEVMulExpr>(Op))
1313 return getMulExpr(Operands);
1314 else
1315 llvm_unreachable("Unexpected SCEV type for Op.")::llvm::llvm_unreachable_internal("Unexpected SCEV type for Op."
, "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1315)
;
1316 }
1317 // Although we checked in the beginning that ID is not in the cache, it is
1318 // possible that during recursion and different modification ID was inserted
1319 // into the cache. So if we find it, just return it.
1320 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
1321 return S;
1322 }
1323
1324 // If the input value is a chrec scev, truncate the chrec's operands.
1325 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1326 SmallVector<const SCEV *, 4> Operands;
1327 for (const SCEV *Op : AddRec->operands())
1328 Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1));
1329 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1330 }
1331
1332 // The cast wasn't folded; create an explicit cast node. We can reuse
1333 // the existing insert position since if we get here, we won't have
1334 // made any changes which would invalidate it.
1335 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1336 Op, Ty);
1337 UniqueSCEVs.InsertNode(S, IP);
1338 addToLoopUseLists(S);
1339 return S;
1340}
1341
1342// Get the limit of a recurrence such that incrementing by Step cannot cause
1343// signed overflow as long as the value of the recurrence within the
1344// loop does not exceed this limit before incrementing.
1345static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1346 ICmpInst::Predicate *Pred,
1347 ScalarEvolution *SE) {
1348 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1349 if (SE->isKnownPositive(Step)) {
1350 *Pred = ICmpInst::ICMP_SLT;
1351 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1352 SE->getSignedRangeMax(Step));
1353 }
1354 if (SE->isKnownNegative(Step)) {
1355 *Pred = ICmpInst::ICMP_SGT;
1356 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1357 SE->getSignedRangeMin(Step));
1358 }
1359 return nullptr;
1360}
1361
1362// Get the limit of a recurrence such that incrementing by Step cannot cause
1363// unsigned overflow as long as the value of the recurrence within the loop does
1364// not exceed this limit before incrementing.
1365static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1366 ICmpInst::Predicate *Pred,
1367 ScalarEvolution *SE) {
1368 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1369 *Pred = ICmpInst::ICMP_ULT;
1370
1371 return SE->getConstant(APInt::getMinValue(BitWidth) -
1372 SE->getUnsignedRangeMax(Step));
1373}
1374
1375namespace {
1376
1377struct ExtendOpTraitsBase {
1378 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
1379 unsigned);
1380};
1381
1382// Used to make code generic over signed and unsigned overflow.
1383template <typename ExtendOp> struct ExtendOpTraits {
1384 // Members present:
1385 //
1386 // static const SCEV::NoWrapFlags WrapType;
1387 //
1388 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1389 //
1390 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1391 // ICmpInst::Predicate *Pred,
1392 // ScalarEvolution *SE);
1393};
1394
1395template <>
1396struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1397 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1398
1399 static const GetExtendExprTy GetExtendExpr;
1400
1401 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1402 ICmpInst::Predicate *Pred,
1403 ScalarEvolution *SE) {
1404 return getSignedOverflowLimitForStep(Step, Pred, SE);
1405 }
1406};
1407
1408const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1409 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1410
1411template <>
1412struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1413 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1414
1415 static const GetExtendExprTy GetExtendExpr;
1416
1417 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1418 ICmpInst::Predicate *Pred,
1419 ScalarEvolution *SE) {
1420 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1421 }
1422};
1423
1424const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1425 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1426
1427} // end anonymous namespace
1428
1429// The recurrence AR has been shown to have no signed/unsigned wrap or something
1430// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1431// easily prove NSW/NUW for its preincrement or postincrement sibling. This
1432// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1433// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1434// expression "Step + sext/zext(PreIncAR)" is congruent with
1435// "sext/zext(PostIncAR)"
1436template <typename ExtendOpTy>
1437static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1438 ScalarEvolution *SE, unsigned Depth) {
1439 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1440 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1441
1442 const Loop *L = AR->getLoop();
1443 const SCEV *Start = AR->getStart();
1444 const SCEV *Step = AR->getStepRecurrence(*SE);
1445
1446 // Check for a simple looking step prior to loop entry.
1447 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1448 if (!SA)
1449 return nullptr;
1450
1451 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1452 // subtraction is expensive. For this purpose, perform a quick and dirty
1453 // difference, by checking for Step in the operand list.
1454 SmallVector<const SCEV *, 4> DiffOps;
1455 for (const SCEV *Op : SA->operands())
1456 if (Op != Step)
1457 DiffOps.push_back(Op);
1458
1459 if (DiffOps.size() == SA->getNumOperands())
1460 return nullptr;
1461
1462 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1463 // `Step`:
1464
1465 // 1. NSW/NUW flags on the step increment.
1466 auto PreStartFlags =
1467 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1468 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1469 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1470 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1471
1472 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1473 // "S+X does not sign/unsign-overflow".
1474 //
1475
1476 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1477 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1478 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1479 return PreStart;
1480
1481 // 2. Direct overflow check on the step operation's expression.
1482 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1483 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1484 const SCEV *OperandExtendedStart =
1485 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
1486 (SE->*GetExtendExpr)(Step, WideTy, Depth));
1487 if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
1488 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1489 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1490 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1491 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1492 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1493 }
1494 return PreStart;
1495 }
1496
1497 // 3. Loop precondition.
1498 ICmpInst::Predicate Pred;
1499 const SCEV *OverflowLimit =
1500 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1501
1502 if (OverflowLimit &&
1503 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1504 return PreStart;
1505
1506 return nullptr;
1507}
1508
1509// Get the normalized zero or sign extended expression for this AddRec's Start.
1510template <typename ExtendOpTy>
1511static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1512 ScalarEvolution *SE,
1513 unsigned Depth) {
1514 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1515
1516 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
1517 if (!PreStart)
1518 return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
1519
1520 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
1521 Depth),
1522 (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1523}
1524
1525// Try to prove away overflow by looking at "nearby" add recurrences. A
1526// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1527// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1528//
1529// Formally:
1530//
1531// {S,+,X} == {S-T,+,X} + T
1532// => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1533//
1534// If ({S-T,+,X} + T) does not overflow ... (1)
1535//
1536// RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1537//
1538// If {S-T,+,X} does not overflow ... (2)
1539//
1540// RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1541// == {Ext(S-T)+Ext(T),+,Ext(X)}
1542//
1543// If (S-T)+T does not overflow ... (3)
1544//
1545// RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1546// == {Ext(S),+,Ext(X)} == LHS
1547//
1548// Thus, if (1), (2) and (3) are true for some T, then
1549// Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1550//
1551// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1552// does not overflow" restricted to the 0th iteration. Therefore we only need
1553// to check for (1) and (2).
1554//
1555// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1556// is `Delta` (defined below).
1557template <typename ExtendOpTy>
1558bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1559 const SCEV *Step,
1560 const Loop *L) {
1561 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1562
1563 // We restrict `Start` to a constant to prevent SCEV from spending too much
1564 // time here. It is correct (but more expensive) to continue with a
1565 // non-constant `Start` and do a general SCEV subtraction to compute
1566 // `PreStart` below.
1567 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1568 if (!StartC)
1569 return false;
1570
1571 APInt StartAI = StartC->getAPInt();
1572
1573 for (unsigned Delta : {-2, -1, 1, 2}) {
1574 const SCEV *PreStart = getConstant(StartAI - Delta);
1575
1576 FoldingSetNodeID ID;
1577 ID.AddInteger(scAddRecExpr);
1578 ID.AddPointer(PreStart);
1579 ID.AddPointer(Step);
1580 ID.AddPointer(L);
1581 void *IP = nullptr;
1582 const auto *PreAR =
1583 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1584
1585 // Give up if we don't already have the add recurrence we need because
1586 // actually constructing an add recurrence is relatively expensive.
1587 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1588 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1589 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1590 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1591 DeltaS, &Pred, this);
1592 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1593 return true;
1594 }
1595 }
1596
1597 return false;
1598}
1599
1600// Finds an integer D for an expression (C + x + y + ...) such that the top
1601// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
1602// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
1603// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
1604// the (C + x + y + ...) expression is \p WholeAddExpr.
1605static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1606 const SCEVConstant *ConstantTerm,
1607 const SCEVAddExpr *WholeAddExpr) {
1608 const APInt C = ConstantTerm->getAPInt();
1609 const unsigned BitWidth = C.getBitWidth();
1610 // Find number of trailing zeros of (x + y + ...) w/o the C first:
1611 uint32_t TZ = BitWidth;
1612 for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
1613 TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I)));
1614 if (TZ) {
1615 // Set D to be as many least significant bits of C as possible while still
1616 // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
1617 return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
1618 }
1619 return APInt(BitWidth, 0);
1620}
1621
1622// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
1623// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
1624// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
1625// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
1626static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1627 const APInt &ConstantStart,
1628 const SCEV *Step) {
1629 const unsigned BitWidth = ConstantStart.getBitWidth();
1630 const uint32_t TZ = SE.GetMinTrailingZeros(Step);
1631 if (TZ)
1632 return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
1633 : ConstantStart;
1634 return APInt(BitWidth, 0);
1635}
1636
1637const SCEV *
1638ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1639 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1640, __PRETTY_FUNCTION__))
1640 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1640, __PRETTY_FUNCTION__))
;
1641 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1642, __PRETTY_FUNCTION__))
1642 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1642, __PRETTY_FUNCTION__))
;
1643 Ty = getEffectiveSCEVType(Ty);
1644
1645 // Fold if the operand is constant.
1646 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1647 return getConstant(
1648 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1649
1650 // zext(zext(x)) --> zext(x)
1651 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1652 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1653
1654 // Before doing any expensive analysis, check to see if we've already
1655 // computed a SCEV for this Op and Ty.
1656 FoldingSetNodeID ID;
1657 ID.AddInteger(scZeroExtend);
1658 ID.AddPointer(Op);
1659 ID.AddPointer(Ty);
1660 void *IP = nullptr;
1661 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1662 if (Depth > MaxCastDepth) {
1663 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1664 Op, Ty);
1665 UniqueSCEVs.InsertNode(S, IP);
1666 addToLoopUseLists(S);
1667 return S;
1668 }
1669
1670 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1671 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1672 // It's possible the bits taken off by the truncate were all zero bits. If
1673 // so, we should be able to simplify this further.
1674 const SCEV *X = ST->getOperand();
1675 ConstantRange CR = getUnsignedRange(X);
1676 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1677 unsigned NewBits = getTypeSizeInBits(Ty);
1678 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1679 CR.zextOrTrunc(NewBits)))
1680 return getTruncateOrZeroExtend(X, Ty, Depth);
1681 }
1682
1683 // If the input value is a chrec scev, and we can prove that the value
1684 // did not overflow the old, smaller, value, we can zero extend all of the
1685 // operands (often constants). This allows analysis of something like
1686 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1687 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1688 if (AR->isAffine()) {
1689 const SCEV *Start = AR->getStart();
1690 const SCEV *Step = AR->getStepRecurrence(*this);
1691 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1692 const Loop *L = AR->getLoop();
1693
1694 if (!AR->hasNoUnsignedWrap()) {
1695 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1696 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1697 }
1698
1699 // If we have special knowledge that this addrec won't overflow,
1700 // we don't need to do any further analysis.
1701 if (AR->hasNoUnsignedWrap())
1702 return getAddRecExpr(
1703 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1704 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1705
1706 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1707 // Note that this serves two purposes: It filters out loops that are
1708 // simply not analyzable, and it covers the case where this code is
1709 // being called from within backedge-taken count analysis, such that
1710 // attempting to ask for the backedge-taken count would likely result
1711 // in infinite recursion. In the later case, the analysis code will
1712 // cope with a conservative value, and it will take care to purge
1713 // that value once it has finished.
1714 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
1715 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1716 // Manually compute the final value for AR, checking for
1717 // overflow.
1718
1719 // Check whether the backedge-taken count can be losslessly casted to
1720 // the addrec's type. The count is always unsigned.
1721 const SCEV *CastedMaxBECount =
1722 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
1723 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
1724 CastedMaxBECount, MaxBECount->getType(), Depth);
1725 if (MaxBECount == RecastedMaxBECount) {
1726 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1727 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1728 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
1729 SCEV::FlagAnyWrap, Depth + 1);
1730 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
1731 SCEV::FlagAnyWrap,
1732 Depth + 1),
1733 WideTy, Depth + 1);
1734 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
1735 const SCEV *WideMaxBECount =
1736 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1737 const SCEV *OperandExtendedAdd =
1738 getAddExpr(WideStart,
1739 getMulExpr(WideMaxBECount,
1740 getZeroExtendExpr(Step, WideTy, Depth + 1),
1741 SCEV::FlagAnyWrap, Depth + 1),
1742 SCEV::FlagAnyWrap, Depth + 1);
1743 if (ZAdd == OperandExtendedAdd) {
1744 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1745 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1746 // Return the expression with the addrec on the outside.
1747 return getAddRecExpr(
1748 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1749 Depth + 1),
1750 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1751 AR->getNoWrapFlags());
1752 }
1753 // Similar to above, only this time treat the step value as signed.
1754 // This covers loops that count down.
1755 OperandExtendedAdd =
1756 getAddExpr(WideStart,
1757 getMulExpr(WideMaxBECount,
1758 getSignExtendExpr(Step, WideTy, Depth + 1),
1759 SCEV::FlagAnyWrap, Depth + 1),
1760 SCEV::FlagAnyWrap, Depth + 1);
1761 if (ZAdd == OperandExtendedAdd) {
1762 // Cache knowledge of AR NW, which is propagated to this AddRec.
1763 // Negative step causes unsigned wrap, but it still can't self-wrap.
1764 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1765 // Return the expression with the addrec on the outside.
1766 return getAddRecExpr(
1767 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1768 Depth + 1),
1769 getSignExtendExpr(Step, Ty, Depth + 1), L,
1770 AR->getNoWrapFlags());
1771 }
1772 }
1773 }
1774
1775 // Normally, in the cases we can prove no-overflow via a
1776 // backedge guarding condition, we can also compute a backedge
1777 // taken count for the loop. The exceptions are assumptions and
1778 // guards present in the loop -- SCEV is not great at exploiting
1779 // these to compute max backedge taken counts, but can still use
1780 // these to prove lack of overflow. Use this fact to avoid
1781 // doing extra work that may not pay off.
1782 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1783 !AC.assumptions().empty()) {
1784 // If the backedge is guarded by a comparison with the pre-inc
1785 // value the addrec is safe. Also, if the entry is guarded by
1786 // a comparison with the start value and the backedge is
1787 // guarded by a comparison with the post-inc value, the addrec
1788 // is safe.
1789 if (isKnownPositive(Step)) {
1790 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1791 getUnsignedRangeMax(Step));
1792 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1793 isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
1794 // Cache knowledge of AR NUW, which is propagated to this
1795 // AddRec.
1796 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1797 // Return the expression with the addrec on the outside.
1798 return getAddRecExpr(
1799 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1800 Depth + 1),
1801 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1802 AR->getNoWrapFlags());
1803 }
1804 } else if (isKnownNegative(Step)) {
1805 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1806 getSignedRangeMin(Step));
1807 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1808 isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
1809 // Cache knowledge of AR NW, which is propagated to this
1810 // AddRec. Negative step causes unsigned wrap, but it
1811 // still can't self-wrap.
1812 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1813 // Return the expression with the addrec on the outside.
1814 return getAddRecExpr(
1815 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1816 Depth + 1),
1817 getSignExtendExpr(Step, Ty, Depth + 1), L,
1818 AR->getNoWrapFlags());
1819 }
1820 }
1821 }
1822
1823 // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
1824 // if D + (C - D + Step * n) could be proven to not unsigned wrap
1825 // where D maximizes the number of trailing zeros of (C - D + Step * n)
1826 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
1827 const APInt &C = SC->getAPInt();
1828 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
1829 if (D != 0) {
1830 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1831 const SCEV *SResidual =
1832 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
1833 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1834 return getAddExpr(SZExtD, SZExtR,
1835 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1836 Depth + 1);
1837 }
1838 }
1839
1840 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1841 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1842 return getAddRecExpr(
1843 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1844 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1845 }
1846 }
1847
1848 // zext(A % B) --> zext(A) % zext(B)
1849 {
1850 const SCEV *LHS;
1851 const SCEV *RHS;
1852 if (matchURem(Op, LHS, RHS))
1853 return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
1854 getZeroExtendExpr(RHS, Ty, Depth + 1));
1855 }
1856
1857 // zext(A / B) --> zext(A) / zext(B).
1858 if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
1859 return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
1860 getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
1861
1862 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1863 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1864 if (SA->hasNoUnsignedWrap()) {
1865 // If the addition does not unsign overflow then we can, by definition,
1866 // commute the zero extension with the addition operation.
1867 SmallVector<const SCEV *, 4> Ops;
1868 for (const auto *Op : SA->operands())
1869 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1870 return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
1871 }
1872
1873 // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
1874 // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
1875 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1876 //
1877 // Often address arithmetics contain expressions like
1878 // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
1879 // This transformation is useful while proving that such expressions are
1880 // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
1881 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
1882 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
1883 if (D != 0) {
1884 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1885 const SCEV *SResidual =
1886 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
1887 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1888 return getAddExpr(SZExtD, SZExtR,
1889 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1890 Depth + 1);
1891 }
1892 }
1893 }
1894
1895 if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
1896 // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
1897 if (SM->hasNoUnsignedWrap()) {
1898 // If the multiply does not unsign overflow then we can, by definition,
1899 // commute the zero extension with the multiply operation.
1900 SmallVector<const SCEV *, 4> Ops;
1901 for (const auto *Op : SM->operands())
1902 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1903 return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
1904 }
1905
1906 // zext(2^K * (trunc X to iN)) to iM ->
1907 // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
1908 //
1909 // Proof:
1910 //
1911 // zext(2^K * (trunc X to iN)) to iM
1912 // = zext((trunc X to iN) << K) to iM
1913 // = zext((trunc X to i{N-K}) << K)<nuw> to iM
1914 // (because shl removes the top K bits)
1915 // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
1916 // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
1917 //
1918 if (SM->getNumOperands() == 2)
1919 if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0)))
1920 if (MulLHS->getAPInt().isPowerOf2())
1921 if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) {
1922 int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) -
1923 MulLHS->getAPInt().logBase2();
1924 Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
1925 return getMulExpr(
1926 getZeroExtendExpr(MulLHS, Ty),
1927 getZeroExtendExpr(
1928 getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty),
1929 SCEV::FlagNUW, Depth + 1);
1930 }
1931 }
1932
1933 // The cast wasn't folded; create an explicit cast node.
1934 // Recompute the insert position, as it may have been invalidated.
1935 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1936 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1937 Op, Ty);
1938 UniqueSCEVs.InsertNode(S, IP);
1939 addToLoopUseLists(S);
1940 return S;
1941}
1942
1943const SCEV *
1944ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1945 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1946, __PRETTY_FUNCTION__))
1946 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1946, __PRETTY_FUNCTION__))
;
1947 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1948, __PRETTY_FUNCTION__))
1948 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 1948, __PRETTY_FUNCTION__))
;
1949 Ty = getEffectiveSCEVType(Ty);
1950
1951 // Fold if the operand is constant.
1952 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1953 return getConstant(
1954 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1955
1956 // sext(sext(x)) --> sext(x)
1957 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1958 return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
1959
1960 // sext(zext(x)) --> zext(x)
1961 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1962 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1963
1964 // Before doing any expensive analysis, check to see if we've already
1965 // computed a SCEV for this Op and Ty.
1966 FoldingSetNodeID ID;
1967 ID.AddInteger(scSignExtend);
1968 ID.AddPointer(Op);
1969 ID.AddPointer(Ty);
1970 void *IP = nullptr;
1971 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1972 // Limit recursion depth.
1973 if (Depth > MaxCastDepth) {
1974 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1975 Op, Ty);
1976 UniqueSCEVs.InsertNode(S, IP);
1977 addToLoopUseLists(S);
1978 return S;
1979 }
1980
1981 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1982 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1983 // It's possible the bits taken off by the truncate were all sign bits. If
1984 // so, we should be able to simplify this further.
1985 const SCEV *X = ST->getOperand();
1986 ConstantRange CR = getSignedRange(X);
1987 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1988 unsigned NewBits = getTypeSizeInBits(Ty);
1989 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1990 CR.sextOrTrunc(NewBits)))
1991 return getTruncateOrSignExtend(X, Ty, Depth);
1992 }
1993
1994 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1995 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1996 if (SA->hasNoSignedWrap()) {
1997 // If the addition does not sign overflow then we can, by definition,
1998 // commute the sign extension with the addition operation.
1999 SmallVector<const SCEV *, 4> Ops;
2000 for (const auto *Op : SA->operands())
2001 Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
2002 return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
2003 }
2004
2005 // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
2006 // if D + (C - D + x + y + ...) could be proven to not signed wrap
2007 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
2008 //
2009 // For instance, this will bring two seemingly different expressions:
2010 // 1 + sext(5 + 20 * %x + 24 * %y) and
2011 // sext(6 + 20 * %x + 24 * %y)
2012 // to the same form:
2013 // 2 + sext(4 + 20 * %x + 24 * %y)
2014 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
2015 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
2016 if (D != 0) {
2017 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
2018 const SCEV *SResidual =
2019 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
2020 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
2021 return getAddExpr(SSExtD, SSExtR,
2022 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
2023 Depth + 1);
2024 }
2025 }
2026 }
2027 // If the input value is a chrec scev, and we can prove that the value
2028 // did not overflow the old, smaller, value, we can sign extend all of the
2029 // operands (often constants). This allows analysis of something like
2030 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
2031 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
2032 if (AR->isAffine()) {
2033 const SCEV *Start = AR->getStart();
2034 const SCEV *Step = AR->getStepRecurrence(*this);
2035 unsigned BitWidth = getTypeSizeInBits(AR->getType());
2036 const Loop *L = AR->getLoop();
2037
2038 if (!AR->hasNoSignedWrap()) {
2039 auto NewFlags = proveNoWrapViaConstantRanges(AR);
2040 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
2041 }
2042
2043 // If we have special knowledge that this addrec won't overflow,
2044 // we don't need to do any further analysis.
2045 if (AR->hasNoSignedWrap())
2046 return getAddRecExpr(
2047 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2048 getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
2049
2050 // Check whether the backedge-taken count is SCEVCouldNotCompute.
2051 // Note that this serves two purposes: It filters out loops that are
2052 // simply not analyzable, and it covers the case where this code is
2053 // being called from within backedge-taken count analysis, such that
2054 // attempting to ask for the backedge-taken count would likely result
2055 // in infinite recursion. In the later case, the analysis code will
2056 // cope with a conservative value, and it will take care to purge
2057 // that value once it has finished.
2058 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
2059 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
2060 // Manually compute the final value for AR, checking for
2061 // overflow.
2062
2063 // Check whether the backedge-taken count can be losslessly casted to
2064 // the addrec's type. The count is always unsigned.
2065 const SCEV *CastedMaxBECount =
2066 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
2067 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
2068 CastedMaxBECount, MaxBECount->getType(), Depth);
2069 if (MaxBECount == RecastedMaxBECount) {
2070 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
2071 // Check whether Start+Step*MaxBECount has no signed overflow.
2072 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
2073 SCEV::FlagAnyWrap, Depth + 1);
2074 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
2075 SCEV::FlagAnyWrap,
2076 Depth + 1),
2077 WideTy, Depth + 1);
2078 const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
2079 const SCEV *WideMaxBECount =
2080 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
2081 const SCEV *OperandExtendedAdd =
2082 getAddExpr(WideStart,
2083 getMulExpr(WideMaxBECount,
2084 getSignExtendExpr(Step, WideTy, Depth + 1),
2085 SCEV::FlagAnyWrap, Depth + 1),
2086 SCEV::FlagAnyWrap, Depth + 1);
2087 if (SAdd == OperandExtendedAdd) {
2088 // Cache knowledge of AR NSW, which is propagated to this AddRec.
2089 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2090 // Return the expression with the addrec on the outside.
2091 return getAddRecExpr(
2092 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
2093 Depth + 1),
2094 getSignExtendExpr(Step, Ty, Depth + 1), L,
2095 AR->getNoWrapFlags());
2096 }
2097 // Similar to above, only this time treat the step value as unsigned.
2098 // This covers loops that count up with an unsigned step.
2099 OperandExtendedAdd =
2100 getAddExpr(WideStart,
2101 getMulExpr(WideMaxBECount,
2102 getZeroExtendExpr(Step, WideTy, Depth + 1),
2103 SCEV::FlagAnyWrap, Depth + 1),
2104 SCEV::FlagAnyWrap, Depth + 1);
2105 if (SAdd == OperandExtendedAdd) {
2106 // If AR wraps around then
2107 //
2108 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
2109 // => SAdd != OperandExtendedAdd
2110 //
2111 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
2112 // (SAdd == OperandExtendedAdd => AR is NW)
2113
2114 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
2115
2116 // Return the expression with the addrec on the outside.
2117 return getAddRecExpr(
2118 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
2119 Depth + 1),
2120 getZeroExtendExpr(Step, Ty, Depth + 1), L,
2121 AR->getNoWrapFlags());
2122 }
2123 }
2124 }
2125
2126 // Normally, in the cases we can prove no-overflow via a
2127 // backedge guarding condition, we can also compute a backedge
2128 // taken count for the loop. The exceptions are assumptions and
2129 // guards present in the loop -- SCEV is not great at exploiting
2130 // these to compute max backedge taken counts, but can still use
2131 // these to prove lack of overflow. Use this fact to avoid
2132 // doing extra work that may not pay off.
2133
2134 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
2135 !AC.assumptions().empty()) {
2136 // If the backedge is guarded by a comparison with the pre-inc
2137 // value the addrec is safe. Also, if the entry is guarded by
2138 // a comparison with the start value and the backedge is
2139 // guarded by a comparison with the post-inc value, the addrec
2140 // is safe.
2141 ICmpInst::Predicate Pred;
2142 const SCEV *OverflowLimit =
2143 getSignedOverflowLimitForStep(Step, &Pred, this);
2144 if (OverflowLimit &&
2145 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
2146 isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
2147 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
2148 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2149 return getAddRecExpr(
2150 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2151 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2152 }
2153 }
2154
2155 // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
2156 // if D + (C - D + Step * n) could be proven to not signed wrap
2157 // where D maximizes the number of trailing zeros of (C - D + Step * n)
2158 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
2159 const APInt &C = SC->getAPInt();
2160 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
2161 if (D != 0) {
2162 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
2163 const SCEV *SResidual =
2164 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
2165 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
2166 return getAddExpr(SSExtD, SSExtR,
2167 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
2168 Depth + 1);
2169 }
2170 }
2171
2172 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
2173 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2174 return getAddRecExpr(
2175 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2176 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2177 }
2178 }
2179
2180 // If the input value is provably positive and we could not simplify
2181 // away the sext build a zext instead.
2182 if (isKnownNonNegative(Op))
2183 return getZeroExtendExpr(Op, Ty, Depth + 1);
2184
2185 // The cast wasn't folded; create an explicit cast node.
2186 // Recompute the insert position, as it may have been invalidated.
2187 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2188 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
2189 Op, Ty);
2190 UniqueSCEVs.InsertNode(S, IP);
2191 addToLoopUseLists(S);
2192 return S;
2193}
2194
2195/// getAnyExtendExpr - Return a SCEV for the given operand extended with
2196/// unspecified bits out to the given type.
2197const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
2198 Type *Ty) {
2199 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2200, __PRETTY_FUNCTION__))
2200 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2200, __PRETTY_FUNCTION__))
;
2201 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2202, __PRETTY_FUNCTION__))
2202 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2202, __PRETTY_FUNCTION__))
;
2203 Ty = getEffectiveSCEVType(Ty);
2204
2205 // Sign-extend negative constants.
2206 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
2207 if (SC->getAPInt().isNegative())
2208 return getSignExtendExpr(Op, Ty);
2209
2210 // Peel off a truncate cast.
2211 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
2212 const SCEV *NewOp = T->getOperand();
2213 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
2214 return getAnyExtendExpr(NewOp, Ty);
2215 return getTruncateOrNoop(NewOp, Ty);
2216 }
2217
2218 // Next try a zext cast. If the cast is folded, use it.
2219 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
2220 if (!isa<SCEVZeroExtendExpr>(ZExt))
2221 return ZExt;
2222
2223 // Next try a sext cast. If the cast is folded, use it.
2224 const SCEV *SExt = getSignExtendExpr(Op, Ty);
2225 if (!isa<SCEVSignExtendExpr>(SExt))
2226 return SExt;
2227
2228 // Force the cast to be folded into the operands of an addrec.
2229 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
2230 SmallVector<const SCEV *, 4> Ops;
2231 for (const SCEV *Op : AR->operands())
2232 Ops.push_back(getAnyExtendExpr(Op, Ty));
2233 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
2234 }
2235
2236 // If the expression is obviously signed, use the sext cast value.
2237 if (isa<SCEVSMaxExpr>(Op))
2238 return SExt;
2239
2240 // Absent any other information, use the zext cast value.
2241 return ZExt;
2242}
2243
2244/// Process the given Ops list, which is a list of operands to be added under
2245/// the given scale, update the given map. This is a helper function for
2246/// getAddRecExpr. As an example of what it does, given a sequence of operands
2247/// that would form an add expression like this:
2248///
2249/// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2250///
2251/// where A and B are constants, update the map with these values:
2252///
2253/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2254///
2255/// and add 13 + A*B*29 to AccumulatedConstant.
2256/// This will allow getAddRecExpr to produce this:
2257///
2258/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2259///
2260/// This form often exposes folding opportunities that are hidden in
2261/// the original operand list.
2262///
2263/// Return true iff it appears that any interesting folding opportunities
2264/// may be exposed. This helps getAddRecExpr short-circuit extra work in
2265/// the common case where no interesting opportunities are present, and
2266/// is also used as a check to avoid infinite recursion.
2267static bool
2268CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
2269 SmallVectorImpl<const SCEV *> &NewOps,
2270 APInt &AccumulatedConstant,
2271 const SCEV *const *Ops, size_t NumOperands,
2272 const APInt &Scale,
2273 ScalarEvolution &SE) {
2274 bool Interesting = false;
2275
2276 // Iterate over the add operands. They are sorted, with constants first.
2277 unsigned i = 0;
2278 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2279 ++i;
2280 // Pull a buried constant out to the outside.
2281 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
2282 Interesting = true;
2283 AccumulatedConstant += Scale * C->getAPInt();
2284 }
2285
2286 // Next comes everything else. We're especially interested in multiplies
2287 // here, but they're in the middle, so just visit the rest with one loop.
2288 for (; i != NumOperands; ++i) {
2289 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
2290 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
2291 APInt NewScale =
2292 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
2293 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
2294 // A multiplication of a constant with another add; recurse.
2295 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2296 Interesting |=
2297 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2298 Add->op_begin(), Add->getNumOperands(),
2299 NewScale, SE);
2300 } else {
2301 // A multiplication of a constant with some other value. Update
2302 // the map.
2303 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
2304 const SCEV *Key = SE.getMulExpr(MulOps);
2305 auto Pair = M.insert({Key, NewScale});
2306 if (Pair.second) {
2307 NewOps.push_back(Pair.first->first);
2308 } else {
2309 Pair.first->second += NewScale;
2310 // The map already had an entry for this value, which may indicate
2311 // a folding opportunity.
2312 Interesting = true;
2313 }
2314 }
2315 } else {
2316 // An ordinary operand. Update the map.
2317 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2318 M.insert({Ops[i], Scale});
2319 if (Pair.second) {
2320 NewOps.push_back(Pair.first->first);
2321 } else {
2322 Pair.first->second += Scale;
2323 // The map already had an entry for this value, which may indicate
2324 // a folding opportunity.
2325 Interesting = true;
2326 }
2327 }
2328 }
2329
2330 return Interesting;
2331}
2332
2333// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2334// `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2335// can't-overflow flags for the operation if possible.
2336static SCEV::NoWrapFlags
2337StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
2338 const ArrayRef<const SCEV *> Ops,
2339 SCEV::NoWrapFlags Flags) {
2340 using namespace std::placeholders;
2341
2342 using OBO = OverflowingBinaryOperator;
2343
2344 bool CanAnalyze =
2345 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2346 (void)CanAnalyze;
2347 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2347, __PRETTY_FUNCTION__))
;
2348
2349 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2350 SCEV::NoWrapFlags SignOrUnsignWrap =
2351 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2352
2353 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2354 auto IsKnownNonNegative = [&](const SCEV *S) {
2355 return SE->isKnownNonNegative(S);
2356 };
2357
2358 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2359 Flags =
2360 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2361
2362 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2363
2364 if (SignOrUnsignWrap != SignOrUnsignMask &&
2365 (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
2366 isa<SCEVConstant>(Ops[0])) {
2367
2368 auto Opcode = [&] {
2369 switch (Type) {
2370 case scAddExpr:
2371 return Instruction::Add;
2372 case scMulExpr:
2373 return Instruction::Mul;
2374 default:
2375 llvm_unreachable("Unexpected SCEV op.")::llvm::llvm_unreachable_internal("Unexpected SCEV op.", "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2375)
;
2376 }
2377 }();
2378
2379 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2380
2381 // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
2382 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2383 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2384 Opcode, C, OBO::NoSignedWrap);
2385 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2386 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2387 }
2388
2389 // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
2390 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2391 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2392 Opcode, C, OBO::NoUnsignedWrap);
2393 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2394 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2395 }
2396 }
2397
2398 return Flags;
2399}
2400
2401bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
2402 return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
2403}
2404
2405/// Get a canonical add expression, or something simpler if possible.
2406const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2407 SCEV::NoWrapFlags Flags,
2408 unsigned Depth) {
2409 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2410, __PRETTY_FUNCTION__))
2410 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2410, __PRETTY_FUNCTION__))
;
2411 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2411, __PRETTY_FUNCTION__))
;
2412 if (Ops.size() == 1) return Ops[0];
2413#ifndef NDEBUG
2414 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2415 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2416 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2417, __PRETTY_FUNCTION__))
2417 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2417, __PRETTY_FUNCTION__))
;
2418#endif
2419
2420 // Sort by complexity, this groups all similar expression types together.
2421 GroupByComplexity(Ops, &LI, DT);
2422
2423 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2424
2425 // If there are any constants, fold them together.
2426 unsigned Idx = 0;
2427 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2428 ++Idx;
2429 assert(Idx < Ops.size())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2429, __PRETTY_FUNCTION__))
;
2430 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2431 // We found two constants, fold them together!
2432 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2433 if (Ops.size() == 2) return Ops[0];
2434 Ops.erase(Ops.begin()+1); // Erase the folded element
2435 LHSC = cast<SCEVConstant>(Ops[0]);
2436 }
2437
2438 // If we are left with a constant zero being added, strip it off.
2439 if (LHSC->getValue()->isZero()) {
2440 Ops.erase(Ops.begin());
2441 --Idx;
2442 }
2443
2444 if (Ops.size() == 1) return Ops[0];
2445 }
2446
2447 // Limit recursion calls depth.
2448 if (Depth > MaxArithDepth || hasHugeExpression(Ops))
2449 return getOrCreateAddExpr(Ops, Flags);
2450
2451 // Okay, check to see if the same value occurs in the operand list more than
2452 // once. If so, merge them together into an multiply expression. Since we
2453 // sorted the list, these values are required to be adjacent.
2454 Type *Ty = Ops[0]->getType();
2455 bool FoundMatch = false;
2456 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2457 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2458 // Scan ahead to count how many equal operands there are.
2459 unsigned Count = 2;
2460 while (i+Count != e && Ops[i+Count] == Ops[i])
2461 ++Count;
2462 // Merge the values into a multiply.
2463 const SCEV *Scale = getConstant(Ty, Count);
2464 const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
2465 if (Ops.size() == Count)
2466 return Mul;
2467 Ops[i] = Mul;
2468 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2469 --i; e -= Count - 1;
2470 FoundMatch = true;
2471 }
2472 if (FoundMatch)
2473 return getAddExpr(Ops, Flags, Depth + 1);
2474
2475 // Check for truncates. If all the operands are truncated from the same
2476 // type, see if factoring out the truncate would permit the result to be
2477 // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
2478 // if the contents of the resulting outer trunc fold to something simple.
2479 auto FindTruncSrcType = [&]() -> Type * {
2480 // We're ultimately looking to fold an addrec of truncs and muls of only
2481 // constants and truncs, so if we find any other types of SCEV
2482 // as operands of the addrec then we bail and return nullptr here.
2483 // Otherwise, we return the type of the operand of a trunc that we find.
2484 if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
2485 return T->getOperand()->getType();
2486 if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2487 const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
2488 if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
2489 return T->getOperand()->getType();
2490 }
2491 return nullptr;
2492 };
2493 if (auto *SrcType = FindTruncSrcType()) {
2494 SmallVector<const SCEV *, 8> LargeOps;
2495 bool Ok = true;
2496 // Check all the operands to see if they can be represented in the
2497 // source type of the truncate.
2498 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2499 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2500 if (T->getOperand()->getType() != SrcType) {
2501 Ok = false;
2502 break;
2503 }
2504 LargeOps.push_back(T->getOperand());
2505 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2506 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2507 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2508 SmallVector<const SCEV *, 8> LargeMulOps;
2509 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2510 if (const SCEVTruncateExpr *T =
2511 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2512 if (T->getOperand()->getType() != SrcType) {
2513 Ok = false;
2514 break;
2515 }
2516 LargeMulOps.push_back(T->getOperand());
2517 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2518 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2519 } else {
2520 Ok = false;
2521 break;
2522 }
2523 }
2524 if (Ok)
2525 LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
2526 } else {
2527 Ok = false;
2528 break;
2529 }
2530 }
2531 if (Ok) {
2532 // Evaluate the expression in the larger type.
2533 const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
2534 // If it folds to something simple, use it. Otherwise, don't.
2535 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2536 return getTruncateExpr(Fold, Ty);
2537 }
2538 }
2539
2540 // Skip past any other cast SCEVs.
2541 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2542 ++Idx;
2543
2544 // If there are add operands they would be next.
2545 if (Idx < Ops.size()) {
2546 bool DeletedAdd = false;
2547 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2548 if (Ops.size() > AddOpsInlineThreshold ||
2549 Add->getNumOperands() > AddOpsInlineThreshold)
2550 break;
2551 // If we have an add, expand the add operands onto the end of the operands
2552 // list.
2553 Ops.erase(Ops.begin()+Idx);
2554 Ops.append(Add->op_begin(), Add->op_end());
2555 DeletedAdd = true;
2556 }
2557
2558 // If we deleted at least one add, we added operands to the end of the list,
2559 // and they are not necessarily sorted. Recurse to resort and resimplify
2560 // any operands we just acquired.
2561 if (DeletedAdd)
2562 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2563 }
2564
2565 // Skip over the add expression until we get to a multiply.
2566 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2567 ++Idx;
2568
2569 // Check to see if there are any folding opportunities present with
2570 // operands multiplied by constant values.
2571 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2572 uint64_t BitWidth = getTypeSizeInBits(Ty);
2573 DenseMap<const SCEV *, APInt> M;
2574 SmallVector<const SCEV *, 8> NewOps;
2575 APInt AccumulatedConstant(BitWidth, 0);
2576 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2577 Ops.data(), Ops.size(),
2578 APInt(BitWidth, 1), *this)) {
2579 struct APIntCompare {
2580 bool operator()(const APInt &LHS, const APInt &RHS) const {
2581 return LHS.ult(RHS);
2582 }
2583 };
2584
2585 // Some interesting folding opportunity is present, so its worthwhile to
2586 // re-generate the operands list. Group the operands by constant scale,
2587 // to avoid multiplying by the same constant scale multiple times.
2588 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2589 for (const SCEV *NewOp : NewOps)
2590 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2591 // Re-generate the operands list.
2592 Ops.clear();
2593 if (AccumulatedConstant != 0)
2594 Ops.push_back(getConstant(AccumulatedConstant));
2595 for (auto &MulOp : MulOpLists)
2596 if (MulOp.first != 0)
2597 Ops.push_back(getMulExpr(
2598 getConstant(MulOp.first),
2599 getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
2600 SCEV::FlagAnyWrap, Depth + 1));
2601 if (Ops.empty())
2602 return getZero(Ty);
2603 if (Ops.size() == 1)
2604 return Ops[0];
2605 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2606 }
2607 }
2608
2609 // If we are adding something to a multiply expression, make sure the
2610 // something is not already an operand of the multiply. If so, merge it into
2611 // the multiply.
2612 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2613 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2614 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2615 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2616 if (isa<SCEVConstant>(MulOpSCEV))
2617 continue;
2618 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2619 if (MulOpSCEV == Ops[AddOp]) {
2620 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2621 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2622 if (Mul->getNumOperands() != 2) {
2623 // If the multiply has more than two operands, we must get the
2624 // Y*Z term.
2625 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2626 Mul->op_begin()+MulOp);
2627 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2628 InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2629 }
2630 SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
2631 const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2632 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
2633 SCEV::FlagAnyWrap, Depth + 1);
2634 if (Ops.size() == 2) return OuterMul;
2635 if (AddOp < Idx) {
2636 Ops.erase(Ops.begin()+AddOp);
2637 Ops.erase(Ops.begin()+Idx-1);
2638 } else {
2639 Ops.erase(Ops.begin()+Idx);
2640 Ops.erase(Ops.begin()+AddOp-1);
2641 }
2642 Ops.push_back(OuterMul);
2643 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2644 }
2645
2646 // Check this multiply against other multiplies being added together.
2647 for (unsigned OtherMulIdx = Idx+1;
2648 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2649 ++OtherMulIdx) {
2650 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2651 // If MulOp occurs in OtherMul, we can fold the two multiplies
2652 // together.
2653 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2654 OMulOp != e; ++OMulOp)
2655 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2656 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2657 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2658 if (Mul->getNumOperands() != 2) {
2659 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2660 Mul->op_begin()+MulOp);
2661 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2662 InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2663 }
2664 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2665 if (OtherMul->getNumOperands() != 2) {
2666 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2667 OtherMul->op_begin()+OMulOp);
2668 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2669 InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2670 }
2671 SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
2672 const SCEV *InnerMulSum =
2673 getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2674 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
2675 SCEV::FlagAnyWrap, Depth + 1);
2676 if (Ops.size() == 2) return OuterMul;
2677 Ops.erase(Ops.begin()+Idx);
2678 Ops.erase(Ops.begin()+OtherMulIdx-1);
2679 Ops.push_back(OuterMul);
2680 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2681 }
2682 }
2683 }
2684 }
2685
2686 // If there are any add recurrences in the operands list, see if any other
2687 // added values are loop invariant. If so, we can fold them into the
2688 // recurrence.
2689 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2690 ++Idx;
2691
2692 // Scan over all recurrences, trying to fold loop invariants into them.
2693 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2694 // Scan all of the other operands to this add and add them to the vector if
2695 // they are loop invariant w.r.t. the recurrence.
2696 SmallVector<const SCEV *, 8> LIOps;
2697 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2698 const Loop *AddRecLoop = AddRec->getLoop();
2699 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2700 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2701 LIOps.push_back(Ops[i]);
2702 Ops.erase(Ops.begin()+i);
2703 --i; --e;
2704 }
2705
2706 // If we found some loop invariants, fold them into the recurrence.
2707 if (!LIOps.empty()) {
2708 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2709 LIOps.push_back(AddRec->getStart());
2710
2711 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2712 AddRec->op_end());
2713 // This follows from the fact that the no-wrap flags on the outer add
2714 // expression are applicable on the 0th iteration, when the add recurrence
2715 // will be equal to its start value.
2716 AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
2717
2718 // Build the new addrec. Propagate the NUW and NSW flags if both the
2719 // outer add and the inner addrec are guaranteed to have no overflow.
2720 // Always propagate NW.
2721 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2722 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2723
2724 // If all of the other operands were loop invariant, we are done.
2725 if (Ops.size() == 1) return NewRec;
2726
2727 // Otherwise, add the folded AddRec by the non-invariant parts.
2728 for (unsigned i = 0;; ++i)
2729 if (Ops[i] == AddRec) {
2730 Ops[i] = NewRec;
2731 break;
2732 }
2733 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2734 }
2735
2736 // Okay, if there weren't any loop invariants to be folded, check to see if
2737 // there are multiple AddRec's with the same loop induction variable being
2738 // added together. If so, we can fold them.
2739 for (unsigned OtherIdx = Idx+1;
2740 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2741 ++OtherIdx) {
2742 // We expect the AddRecExpr's to be sorted in reverse dominance order,
2743 // so that the 1st found AddRecExpr is dominated by all others.
2744 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2747, __PRETTY_FUNCTION__))
2745 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2747, __PRETTY_FUNCTION__))
2746 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2747, __PRETTY_FUNCTION__))
2747 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2747, __PRETTY_FUNCTION__))
;
2748 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2749 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2750 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2751 AddRec->op_end());
2752 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2753 ++OtherIdx) {
2754 const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2755 if (OtherAddRec->getLoop() == AddRecLoop) {
2756 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2757 i != e; ++i) {
2758 if (i >= AddRecOps.size()) {
2759 AddRecOps.append(OtherAddRec->op_begin()+i,
2760 OtherAddRec->op_end());
2761 break;
2762 }
2763 SmallVector<const SCEV *, 2> TwoOps = {
2764 AddRecOps[i], OtherAddRec->getOperand(i)};
2765 AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2766 }
2767 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2768 }
2769 }
2770 // Step size has changed, so we cannot guarantee no self-wraparound.
2771 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2772 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2773 }
2774 }
2775
2776 // Otherwise couldn't fold anything into this recurrence. Move onto the
2777 // next one.
2778 }
2779
2780 // Okay, it looks like we really DO need an add expr. Check to see if we
2781 // already have one, otherwise create a new one.
2782 return getOrCreateAddExpr(Ops, Flags);
2783}
2784
2785const SCEV *
2786ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
2787 SCEV::NoWrapFlags Flags) {
2788 FoldingSetNodeID ID;
2789 ID.AddInteger(scAddExpr);
2790 for (const SCEV *Op : Ops)
2791 ID.AddPointer(Op);
2792 void *IP = nullptr;
2793 SCEVAddExpr *S =
2794 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2795 if (!S) {
2796 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2797 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2798 S = new (SCEVAllocator)
2799 SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
2800 UniqueSCEVs.InsertNode(S, IP);
2801 addToLoopUseLists(S);
2802 }
2803 S->setNoWrapFlags(Flags);
2804 return S;
2805}
2806
2807const SCEV *
2808ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
2809 const Loop *L, SCEV::NoWrapFlags Flags) {
2810 FoldingSetNodeID ID;
2811 ID.AddInteger(scAddRecExpr);
2812 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2813 ID.AddPointer(Ops[i]);
2814 ID.AddPointer(L);
2815 void *IP = nullptr;
2816 SCEVAddRecExpr *S =
2817 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2818 if (!S) {
2819 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2820 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2821 S = new (SCEVAllocator)
2822 SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
2823 UniqueSCEVs.InsertNode(S, IP);
2824 addToLoopUseLists(S);
2825 }
2826 S->setNoWrapFlags(Flags);
2827 return S;
2828}
2829
2830const SCEV *
2831ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
2832 SCEV::NoWrapFlags Flags) {
2833 FoldingSetNodeID ID;
2834 ID.AddInteger(scMulExpr);
2835 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2836 ID.AddPointer(Ops[i]);
2837 void *IP = nullptr;
2838 SCEVMulExpr *S =
2839 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2840 if (!S) {
2841 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2842 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2843 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2844 O, Ops.size());
2845 UniqueSCEVs.InsertNode(S, IP);
2846 addToLoopUseLists(S);
2847 }
2848 S->setNoWrapFlags(Flags);
2849 return S;
2850}
2851
2852static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2853 uint64_t k = i*j;
2854 if (j > 1 && k / j != i) Overflow = true;
2855 return k;
2856}
2857
2858/// Compute the result of "n choose k", the binomial coefficient. If an
2859/// intermediate computation overflows, Overflow will be set and the return will
2860/// be garbage. Overflow is not cleared on absence of overflow.
2861static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2862 // We use the multiplicative formula:
2863 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2864 // At each iteration, we take the n-th term of the numeral and divide by the
2865 // (k-n)th term of the denominator. This division will always produce an
2866 // integral result, and helps reduce the chance of overflow in the
2867 // intermediate computations. However, we can still overflow even when the
2868 // final result would fit.
2869
2870 if (n == 0 || n == k) return 1;
2871 if (k > n) return 0;
2872
2873 if (k > n/2)
2874 k = n-k;
2875
2876 uint64_t r = 1;
2877 for (uint64_t i = 1; i <= k; ++i) {
2878 r = umul_ov(r, n-(i-1), Overflow);
2879 r /= i;
2880 }
2881 return r;
2882}
2883
2884/// Determine if any of the operands in this SCEV are a constant or if
2885/// any of the add or multiply expressions in this SCEV contain a constant.
2886static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
2887 struct FindConstantInAddMulChain {
2888 bool FoundConstant = false;
2889
2890 bool follow(const SCEV *S) {
2891 FoundConstant |= isa<SCEVConstant>(S);
2892 return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
2893 }
2894
2895 bool isDone() const {
2896 return FoundConstant;
2897 }
2898 };
2899
2900 FindConstantInAddMulChain F;
2901 SCEVTraversal<FindConstantInAddMulChain> ST(F);
2902 ST.visitAll(StartExpr);
2903 return F.FoundConstant;
2904}
2905
2906/// Get a canonical multiply expression, or something simpler if possible.
2907const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2908 SCEV::NoWrapFlags Flags,
2909 unsigned Depth) {
2910 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2911, __PRETTY_FUNCTION__))
2911 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2911, __PRETTY_FUNCTION__))
;
2912 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2912, __PRETTY_FUNCTION__))
;
2913 if (Ops.size() == 1) return Ops[0];
2914#ifndef NDEBUG
2915 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2916 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2917 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2918, __PRETTY_FUNCTION__))
2918 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 2918, __PRETTY_FUNCTION__))
;
2919#endif
2920
2921 // Sort by complexity, this groups all similar expression types together.
2922 GroupByComplexity(Ops, &LI, DT);
2923
2924 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2925
2926 // Limit recursion calls depth.
2927 if (Depth > MaxArithDepth || hasHugeExpression(Ops))
2928 return getOrCreateMulExpr(Ops, Flags);
2929
2930 // If there are any constants, fold them together.
2931 unsigned Idx = 0;
2932 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2933
2934 if (Ops.size() == 2)
2935 // C1*(C2+V) -> C1*C2 + C1*V
2936 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2937 // If any of Add's ops are Adds or Muls with a constant, apply this
2938 // transformation as well.
2939 //
2940 // TODO: There are some cases where this transformation is not
2941 // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
2942 // this transformation should be narrowed down.
2943 if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add))
2944 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
2945 SCEV::FlagAnyWrap, Depth + 1),
2946 getMulExpr(LHSC, Add->getOperand(1),
2947 SCEV::FlagAnyWrap, Depth + 1),
2948 SCEV::FlagAnyWrap, Depth + 1);
2949
2950 ++Idx;
2951 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2952 // We found two constants, fold them together!
2953 ConstantInt *Fold =
2954 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2955 Ops[0] = getConstant(Fold);
2956 Ops.erase(Ops.begin()+1); // Erase the folded element
2957 if (Ops.size() == 1) return Ops[0];
2958 LHSC = cast<SCEVConstant>(Ops[0]);
2959 }
2960
2961 // If we are left with a constant one being multiplied, strip it off.
2962 if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
2963 Ops.erase(Ops.begin());
2964 --Idx;
2965 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2966 // If we have a multiply of zero, it will always be zero.
2967 return Ops[0];
2968 } else if (Ops[0]->isAllOnesValue()) {
2969 // If we have a mul by -1 of an add, try distributing the -1 among the
2970 // add operands.
2971 if (Ops.size() == 2) {
2972 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2973 SmallVector<const SCEV *, 4> NewOps;
2974 bool AnyFolded = false;
2975 for (const SCEV *AddOp : Add->operands()) {
2976 const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
2977 Depth + 1);
2978 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2979 NewOps.push_back(Mul);
2980 }
2981 if (AnyFolded)
2982 return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
2983 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2984 // Negation preserves a recurrence's no self-wrap property.
2985 SmallVector<const SCEV *, 4> Operands;
2986 for (const SCEV *AddRecOp : AddRec->operands())
2987 Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
2988 Depth + 1));
2989
2990 return getAddRecExpr(Operands, AddRec->getLoop(),
2991 AddRec->getNoWrapFlags(SCEV::FlagNW));
2992 }
2993 }
2994 }
2995
2996 if (Ops.size() == 1)
2997 return Ops[0];
2998 }
2999
3000 // Skip over the add expression until we get to a multiply.
3001 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
3002 ++Idx;
3003
3004 // If there are mul operands inline them all into this expression.
3005 if (Idx < Ops.size()) {
3006 bool DeletedMul = false;
3007 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
3008 if (Ops.size() > MulOpsInlineThreshold)
3009 break;
3010 // If we have an mul, expand the mul operands onto the end of the
3011 // operands list.
3012 Ops.erase(Ops.begin()+Idx);
3013 Ops.append(Mul->op_begin(), Mul->op_end());
3014 DeletedMul = true;
3015 }
3016
3017 // If we deleted at least one mul, we added operands to the end of the
3018 // list, and they are not necessarily sorted. Recurse to resort and
3019 // resimplify any operands we just acquired.
3020 if (DeletedMul)
3021 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3022 }
3023
3024 // If there are any add recurrences in the operands list, see if any other
3025 // added values are loop invariant. If so, we can fold them into the
3026 // recurrence.
3027 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
3028 ++Idx;
3029
3030 // Scan over all recurrences, trying to fold loop invariants into them.
3031 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
3032 // Scan all of the other operands to this mul and add them to the vector
3033 // if they are loop invariant w.r.t. the recurrence.
3034 SmallVector<const SCEV *, 8> LIOps;
3035 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
3036 const Loop *AddRecLoop = AddRec->getLoop();
3037 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3038 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
3039 LIOps.push_back(Ops[i]);
3040 Ops.erase(Ops.begin()+i);
3041 --i; --e;
3042 }
3043
3044 // If we found some loop invariants, fold them into the recurrence.
3045 if (!LIOps.empty()) {
3046 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
3047 SmallVector<const SCEV *, 4> NewOps;
3048 NewOps.reserve(AddRec->getNumOperands());
3049 const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
3050 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
3051 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
3052 SCEV::FlagAnyWrap, Depth + 1));
3053
3054 // Build the new addrec. Propagate the NUW and NSW flags if both the
3055 // outer mul and the inner addrec are guaranteed to have no overflow.
3056 //
3057 // No self-wrap cannot be guaranteed after changing the step size, but
3058 // will be inferred if either NUW or NSW is true.
3059 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
3060 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
3061
3062 // If all of the other operands were loop invariant, we are done.
3063 if (Ops.size() == 1) return NewRec;
3064
3065 // Otherwise, multiply the folded AddRec by the non-invariant parts.
3066 for (unsigned i = 0;; ++i)
3067 if (Ops[i] == AddRec) {
3068 Ops[i] = NewRec;
3069 break;
3070 }
3071 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3072 }
3073
3074 // Okay, if there weren't any loop invariants to be folded, check to see
3075 // if there are multiple AddRec's with the same loop induction variable
3076 // being multiplied together. If so, we can fold them.
3077
3078 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
3079 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
3080 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
3081 // ]]],+,...up to x=2n}.
3082 // Note that the arguments to choose() are always integers with values
3083 // known at compile time, never SCEV objects.
3084 //
3085 // The implementation avoids pointless extra computations when the two
3086 // addrec's are of different length (mathematically, it's equivalent to
3087 // an infinite stream of zeros on the right).
3088 bool OpsModified = false;
3089 for (unsigned OtherIdx = Idx+1;
3090 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
3091 ++OtherIdx) {
3092 const SCEVAddRecExpr *OtherAddRec =
3093 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
3094 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
3095 continue;
3096
3097 // Limit max number of arguments to avoid creation of unreasonably big
3098 // SCEVAddRecs with very complex operands.
3099 if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
3100 MaxAddRecSize || isHugeExpression(AddRec) ||
3101 isHugeExpression(OtherAddRec))
3102 continue;
3103
3104 bool Overflow = false;
3105 Type *Ty = AddRec->getType();
3106 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
3107 SmallVector<const SCEV*, 7> AddRecOps;
3108 for (int x = 0, xe = AddRec->getNumOperands() +
3109 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
3110 SmallVector <const SCEV *, 7> SumOps;
3111 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
3112 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
3113 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
3114 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
3115 z < ze && !Overflow; ++z) {
3116 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
3117 uint64_t Coeff;
3118 if (LargerThan64Bits)
3119 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
3120 else
3121 Coeff = Coeff1*Coeff2;
3122 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
3123 const SCEV *Term1 = AddRec->getOperand(y-z);
3124 const SCEV *Term2 = OtherAddRec->getOperand(z);
3125 SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
3126 SCEV::FlagAnyWrap, Depth + 1));
3127 }
3128 }
3129 if (SumOps.empty())
3130 SumOps.push_back(getZero(Ty));
3131 AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
3132 }
3133 if (!Overflow) {
3134 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRecLoop,
3135 SCEV::FlagAnyWrap);
3136 if (Ops.size() == 2) return NewAddRec;
3137 Ops[Idx] = NewAddRec;
3138 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
3139 OpsModified = true;
3140 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
3141 if (!AddRec)
3142 break;
3143 }
3144 }
3145 if (OpsModified)
3146 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3147
3148 // Otherwise couldn't fold anything into this recurrence. Move onto the
3149 // next one.
3150 }
3151
3152 // Okay, it looks like we really DO need an mul expr. Check to see if we
3153 // already have one, otherwise create a new one.
3154 return getOrCreateMulExpr(Ops, Flags);
3155}
3156
3157/// Represents an unsigned remainder expression based on unsigned division.
3158const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
3159 const SCEV *RHS) {
3160 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3162, __PRETTY_FUNCTION__))
3161 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3162, __PRETTY_FUNCTION__))
3162 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3162, __PRETTY_FUNCTION__))
;
3163
3164 // Short-circuit easy cases
3165 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3166 // If constant is one, the result is trivial
3167 if (RHSC->getValue()->isOne())
3168 return getZero(LHS->getType()); // X urem 1 --> 0
3169
3170 // If constant is a power of two, fold into a zext(trunc(LHS)).
3171 if (RHSC->getAPInt().isPowerOf2()) {
3172 Type *FullTy = LHS->getType();
3173 Type *TruncTy =
3174 IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
3175 return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
3176 }
3177 }
3178
3179 // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
3180 const SCEV *UDiv = getUDivExpr(LHS, RHS);
3181 const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
3182 return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
3183}
3184
3185/// Get a canonical unsigned division expression, or something simpler if
3186/// possible.
3187const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
3188 const SCEV *RHS) {
3189 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3191, __PRETTY_FUNCTION__))
3190 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3191, __PRETTY_FUNCTION__))
3191 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3191, __PRETTY_FUNCTION__))
;
3192
3193 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3194 if (RHSC->getValue()->isOne())
3195 return LHS; // X udiv 1 --> x
3196 // If the denominator is zero, the result of the udiv is undefined. Don't
3197 // try to analyze it, because the resolution chosen here may differ from
3198 // the resolution chosen in other parts of the compiler.
3199 if (!RHSC->getValue()->isZero()) {
3200 // Determine if the division can be folded into the operands of
3201 // its operands.
3202 // TODO: Generalize this to non-constants by using known-bits information.
3203 Type *Ty = LHS->getType();
3204 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
3205 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
3206 // For non-power-of-two values, effectively round the value up to the
3207 // nearest power of two.
3208 if (!RHSC->getAPInt().isPowerOf2())
3209 ++MaxShiftAmt;
3210 IntegerType *ExtTy =
3211 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
3212 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
3213 if (const SCEVConstant *Step =
3214 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
3215 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
3216 const APInt &StepInt = Step->getAPInt();
3217 const APInt &DivInt = RHSC->getAPInt();
3218 if (!StepInt.urem(DivInt) &&
3219 getZeroExtendExpr(AR, ExtTy) ==
3220 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3221 getZeroExtendExpr(Step, ExtTy),
3222 AR->getLoop(), SCEV::FlagAnyWrap)) {
3223 SmallVector<const SCEV *, 4> Operands;
3224 for (const SCEV *Op : AR->operands())
3225 Operands.push_back(getUDivExpr(Op, RHS));
3226 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
3227 }
3228 /// Get a canonical UDivExpr for a recurrence.
3229 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
3230 // We can currently only fold X%N if X is constant.
3231 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
3232 if (StartC && !DivInt.urem(StepInt) &&
3233 getZeroExtendExpr(AR, ExtTy) ==
3234 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3235 getZeroExtendExpr(Step, ExtTy),
3236 AR->getLoop(), SCEV::FlagAnyWrap)) {
3237 const APInt &StartInt = StartC->getAPInt();
3238 const APInt &StartRem = StartInt.urem(StepInt);
3239 if (StartRem != 0)
3240 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
3241 AR->getLoop(), SCEV::FlagNW);
3242 }
3243 }
3244 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
3245 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
3246 SmallVector<const SCEV *, 4> Operands;
3247 for (const SCEV *Op : M->operands())
3248 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3249 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
3250 // Find an operand that's safely divisible.
3251 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
3252 const SCEV *Op = M->getOperand(i);
3253 const SCEV *Div = getUDivExpr(Op, RHSC);
3254 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
3255 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
3256 M->op_end());
3257 Operands[i] = Div;
3258 return getMulExpr(Operands);
3259 }
3260 }
3261 }
3262
3263 // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
3264 if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
3265 if (auto *DivisorConstant =
3266 dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
3267 bool Overflow = false;
3268 APInt NewRHS =
3269 DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
3270 if (Overflow) {
3271 return getConstant(RHSC->getType(), 0, false);
3272 }
3273 return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
3274 }
3275 }
3276
3277 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
3278 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
3279 SmallVector<const SCEV *, 4> Operands;
3280 for (const SCEV *Op : A->operands())
3281 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3282 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
3283 Operands.clear();
3284 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
3285 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
3286 if (isa<SCEVUDivExpr>(Op) ||
3287 getMulExpr(Op, RHS) != A->getOperand(i))
3288 break;
3289 Operands.push_back(Op);
3290 }
3291 if (Operands.size() == A->getNumOperands())
3292 return getAddExpr(Operands);
3293 }
3294 }
3295
3296 // Fold if both operands are constant.
3297 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
3298 Constant *LHSCV = LHSC->getValue();
3299 Constant *RHSCV = RHSC->getValue();
3300 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
3301 RHSCV)));
3302 }
3303 }
3304 }
3305
3306 FoldingSetNodeID ID;
3307 ID.AddInteger(scUDivExpr);
3308 ID.AddPointer(LHS);
3309 ID.AddPointer(RHS);
3310 void *IP = nullptr;
3311 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3312 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
3313 LHS, RHS);
3314 UniqueSCEVs.InsertNode(S, IP);
3315 addToLoopUseLists(S);
3316 return S;
3317}
3318
3319static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
3320 APInt A = C1->getAPInt().abs();
3321 APInt B = C2->getAPInt().abs();
3322 uint32_t ABW = A.getBitWidth();
3323 uint32_t BBW = B.getBitWidth();
3324
3325 if (ABW > BBW)
3326 B = B.zext(ABW);
3327 else if (ABW < BBW)
3328 A = A.zext(BBW);
3329
3330 return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
3331}
3332
3333/// Get a canonical unsigned division expression, or something simpler if
3334/// possible. There is no representation for an exact udiv in SCEV IR, but we
3335/// can attempt to remove factors from the LHS and RHS. We can't do this when
3336/// it's not exact because the udiv may be clearing bits.
3337const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
3338 const SCEV *RHS) {
3339 // TODO: we could try to find factors in all sorts of things, but for now we
3340 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
3341 // end of this file for inspiration.
3342
3343 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
3344 if (!Mul || !Mul->hasNoUnsignedWrap())
3345 return getUDivExpr(LHS, RHS);
3346
3347 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
3348 // If the mulexpr multiplies by a constant, then that constant must be the
3349 // first element of the mulexpr.
3350 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
3351 if (LHSCst == RHSCst) {
3352 SmallVector<const SCEV *, 2> Operands;
3353 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3354 return getMulExpr(Operands);
3355 }
3356
3357 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
3358 // that there's a factor provided by one of the other terms. We need to
3359 // check.
3360 APInt Factor = gcd(LHSCst, RHSCst);
3361 if (!Factor.isIntN(1)) {
3362 LHSCst =
3363 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
3364 RHSCst =
3365 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
3366 SmallVector<const SCEV *, 2> Operands;
3367 Operands.push_back(LHSCst);
3368 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3369 LHS = getMulExpr(Operands);
3370 RHS = RHSCst;
3371 Mul = dyn_cast<SCEVMulExpr>(LHS);
3372 if (!Mul)
3373 return getUDivExactExpr(LHS, RHS);
3374 }
3375 }
3376 }
3377
3378 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
3379 if (Mul->getOperand(i) == RHS) {
3380 SmallVector<const SCEV *, 2> Operands;
3381 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
3382 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
3383 return getMulExpr(Operands);
3384 }
3385 }
3386
3387 return getUDivExpr(LHS, RHS);
3388}
3389
3390/// Get an add recurrence expression for the specified loop. Simplify the
3391/// expression as much as possible.
3392const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
3393 const Loop *L,
3394 SCEV::NoWrapFlags Flags) {
3395 SmallVector<const SCEV *, 4> Operands;
3396 Operands.push_back(Start);
3397 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
3398 if (StepChrec->getLoop() == L) {
3399 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
3400 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
3401 }
3402
3403 Operands.push_back(Step);
3404 return getAddRecExpr(Operands, L, Flags);
3405}
3406
3407/// Get an add recurrence expression for the specified loop. Simplify the
3408/// expression as much as possible.
3409const SCEV *
3410ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
3411 const Loop *L, SCEV::NoWrapFlags Flags) {
3412 if (Operands.size() == 1) return Operands[0];
3413#ifndef NDEBUG
3414 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
3415 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
3416 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3417, __PRETTY_FUNCTION__))
3417 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3417, __PRETTY_FUNCTION__))
;
3418 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3419 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3420, __PRETTY_FUNCTION__))
3420 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3420, __PRETTY_FUNCTION__))
;
3421#endif
3422
3423 if (Operands.back()->isZero()) {
3424 Operands.pop_back();
3425 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
3426 }
3427
3428 // It's tempting to want to call getConstantMaxBackedgeTakenCount count here and
3429 // use that information to infer NUW and NSW flags. However, computing a
3430 // BE count requires calling getAddRecExpr, so we may not yet have a
3431 // meaningful BE count at this point (and if we don't, we'd be stuck
3432 // with a SCEVCouldNotCompute as the cached BE count).
3433
3434 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
3435
3436 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
3437 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
3438 const Loop *NestedLoop = NestedAR->getLoop();
3439 if (L->contains(NestedLoop)
3440 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
3441 : (!NestedLoop->contains(L) &&
3442 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
3443 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
3444 NestedAR->op_end());
3445 Operands[0] = NestedAR->getStart();
3446 // AddRecs require their operands be loop-invariant with respect to their
3447 // loops. Don't perform this transformation if it would break this
3448 // requirement.
3449 bool AllInvariant = all_of(
3450 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
3451
3452 if (AllInvariant) {
3453 // Create a recurrence for the outer loop with the same step size.
3454 //
3455 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3456 // inner recurrence has the same property.
3457 SCEV::NoWrapFlags OuterFlags =
3458 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3459
3460 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3461 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3462 return isLoopInvariant(Op, NestedLoop);
3463 });
3464
3465 if (AllInvariant) {
3466 // Ok, both add recurrences are valid after the transformation.
3467 //
3468 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3469 // the outer recurrence has the same property.
3470 SCEV::NoWrapFlags InnerFlags =
3471 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3472 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3473 }
3474 }
3475 // Reset Operands to its original state.
3476 Operands[0] = NestedAR;
3477 }
3478 }
3479
3480 // Okay, it looks like we really DO need an addrec expr. Check to see if we
3481 // already have one, otherwise create a new one.
3482 return getOrCreateAddRecExpr(Operands, L, Flags);
3483}
3484
3485const SCEV *
3486ScalarEvolution::getGEPExpr(GEPOperator *GEP,
3487 const SmallVectorImpl<const SCEV *> &IndexExprs) {
3488 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3489 // getSCEV(Base)->getType() has the same address space as Base->getType()
3490 // because SCEV::getType() preserves the address space.
3491 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
3492 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3493 // instruction to its SCEV, because the Instruction may be guarded by control
3494 // flow and the no-overflow bits may not be valid for the expression in any
3495 // context. This can be fixed similarly to how these flags are handled for
3496 // adds.
3497 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
3498 : SCEV::FlagAnyWrap;
3499
3500 const SCEV *TotalOffset = getZero(IntPtrTy);
3501 // The array size is unimportant. The first thing we do on CurTy is getting
3502 // its element type.
3503 Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
3504 for (const SCEV *IndexExpr : IndexExprs) {
3505 // Compute the (potentially symbolic) offset in bytes for this index.
3506 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3507 // For a struct, add the member offset.
3508 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3509 unsigned FieldNo = Index->getZExtValue();
3510 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3511
3512 // Add the field offset to the running total offset.
3513 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3514
3515 // Update CurTy to the type of the field at Index.
3516 CurTy = STy->getTypeAtIndex(Index);
3517 } else {
3518 // Update CurTy to its element type.
3519 CurTy = cast<SequentialType>(CurTy)->getElementType();
3520 // For an array, add the element offset, explicitly scaled.
3521 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3522 // Getelementptr indices are signed.
3523 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3524
3525 // Multiply the index by the element size to compute the element offset.
3526 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3527
3528 // Add the element offset to the running total offset.
3529 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3530 }
3531 }
3532
3533 // Add the total offset from all the GEP indices to the base.
3534 return getAddExpr(BaseExpr, TotalOffset, Wrap);
3535}
3536
3537std::tuple<const SCEV *, FoldingSetNodeID, void *>
3538ScalarEvolution::findExistingSCEVInCache(int SCEVType,
3539 ArrayRef<const SCEV *> Ops) {
3540 FoldingSetNodeID ID;
3541 void *IP = nullptr;
3542 ID.AddInteger(SCEVType);
3543 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3544 ID.AddPointer(Ops[i]);
3545 return std::tuple<const SCEV *, FoldingSetNodeID, void *>(
3546 UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP);
3547}
3548
3549const SCEV *ScalarEvolution::getMinMaxExpr(unsigned Kind,
3550 SmallVectorImpl<const SCEV *> &Ops) {
3551 assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!")((!Ops.empty() && "Cannot get empty (u|s)(min|max)!")
? static_cast<void> (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty (u|s)(min|max)!\""
, "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3551, __PRETTY_FUNCTION__))
;
3552 if (Ops.size() == 1) return Ops[0];
3553#ifndef NDEBUG
3554 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3555 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3556 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"Operand types don't match!") ? static_cast<void> (0) :
__assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"Operand types don't match!\""
, "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3557, __PRETTY_FUNCTION__))
3557 "Operand types don't match!")((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"Operand types don't match!") ? static_cast<void> (0) :
__assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"Operand types don't match!\""
, "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3557, __PRETTY_FUNCTION__))
;
3558#endif
3559
3560 bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
3561 bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;
3562
3563 // Sort by complexity, this groups all similar expression types together.
3564 GroupByComplexity(Ops, &LI, DT);
3565
3566 // Check if we have created the same expression before.
3567 if (const SCEV *S = std::get<0>(findExistingSCEVInCache(Kind, Ops))) {
3568 return S;
3569 }
3570
3571 // If there are any constants, fold them together.
3572 unsigned Idx = 0;
3573 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3574 ++Idx;
3575 assert(Idx < Ops.size())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3575, __PRETTY_FUNCTION__))
;
3576 auto FoldOp = [&](const APInt &LHS, const APInt &RHS) {
3577 if (Kind == scSMaxExpr)
3578 return APIntOps::smax(LHS, RHS);
3579 else if (Kind == scSMinExpr)
3580 return APIntOps::smin(LHS, RHS);
3581 else if (Kind == scUMaxExpr)
3582 return APIntOps::umax(LHS, RHS);
3583 else if (Kind == scUMinExpr)
3584 return APIntOps::umin(LHS, RHS);
3585 llvm_unreachable("Unknown SCEV min/max opcode")::llvm::llvm_unreachable_internal("Unknown SCEV min/max opcode"
, "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3585)
;
3586 };
3587
3588 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3589 // We found two constants, fold them together!
3590 ConstantInt *Fold = ConstantInt::get(
3591 getContext(), FoldOp(LHSC->getAPInt(), RHSC->getAPInt()));
3592 Ops[0] = getConstant(Fold);
3593 Ops.erase(Ops.begin()+1); // Erase the folded element
3594 if (Ops.size() == 1) return Ops[0];
3595 LHSC = cast<SCEVConstant>(Ops[0]);
3596 }
3597
3598 bool IsMinV = LHSC->getValue()->isMinValue(IsSigned);
3599 bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned);
3600
3601 if (IsMax ? IsMinV : IsMaxV) {
3602 // If we are left with a constant minimum(/maximum)-int, strip it off.
3603 Ops.erase(Ops.begin());
3604 --Idx;
3605 } else if (IsMax ? IsMaxV : IsMinV) {
3606 // If we have a max(/min) with a constant maximum(/minimum)-int,
3607 // it will always be the extremum.
3608 return LHSC;
3609 }
3610
3611 if (Ops.size() == 1) return Ops[0];
3612 }
3613
3614 // Find the first operation of the same kind
3615 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
3616 ++Idx;
3617
3618 // Check to see if one of the operands is of the same kind. If so, expand its
3619 // operands onto our operand list, and recurse to simplify.
3620 if (Idx < Ops.size()) {
3621 bool DeletedAny = false;
3622 while (Ops[Idx]->getSCEVType() == Kind) {
3623 const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]);
3624 Ops.erase(Ops.begin()+Idx);
3625 Ops.append(SMME->op_begin(), SMME->op_end());
3626 DeletedAny = true;
3627 }
3628
3629 if (DeletedAny)
3630 return getMinMaxExpr(Kind, Ops);
3631 }
3632
3633 // Okay, check to see if the same value occurs in the operand list twice. If
3634 // so, delete one. Since we sorted the list, these values are required to
3635 // be adjacent.
3636 llvm::CmpInst::Predicate GEPred =
3637 IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
3638 llvm::CmpInst::Predicate LEPred =
3639 IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
3640 llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
3641 llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
3642 for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
3643 if (Ops[i] == Ops[i + 1] ||
3644 isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) {
3645 // X op Y op Y --> X op Y
3646 // X op Y --> X, if we know X, Y are ordered appropriately
3647 Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
3648 --i;
3649 --e;
3650 } else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i],
3651 Ops[i + 1])) {
3652 // X op Y --> Y, if we know X, Y are ordered appropriately
3653 Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
3654 --i;
3655 --e;
3656 }
3657 }
3658
3659 if (Ops.size() == 1) return Ops[0];
3660
3661 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3661, __PRETTY_FUNCTION__))
;
3662
3663 // Okay, it looks like we really DO need an expr. Check to see if we
3664 // already have one, otherwise create a new one.
3665 const SCEV *ExistingSCEV;
3666 FoldingSetNodeID ID;
3667 void *IP;
3668 std::tie(ExistingSCEV, ID, IP) = findExistingSCEVInCache(Kind, Ops);
3669 if (ExistingSCEV)
3670 return ExistingSCEV;
3671 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3672 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3673 SCEV *S = new (SCEVAllocator) SCEVMinMaxExpr(
3674 ID.Intern(SCEVAllocator), static_cast<SCEVTypes>(Kind), O, Ops.size());
3675
3676 UniqueSCEVs.InsertNode(S, IP);
3677 addToLoopUseLists(S);
3678 return S;
3679}
3680
3681const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) {
3682 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3683 return getSMaxExpr(Ops);
3684}
3685
3686const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3687 return getMinMaxExpr(scSMaxExpr, Ops);
3688}
3689
3690const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) {
3691 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3692 return getUMaxExpr(Ops);
3693}
3694
3695const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3696 return getMinMaxExpr(scUMaxExpr, Ops);
3697}
3698
3699const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3700 const SCEV *RHS) {
3701 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3702 return getSMinExpr(Ops);
3703}
3704
3705const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3706 return getMinMaxExpr(scSMinExpr, Ops);
3707}
3708
3709const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3710 const SCEV *RHS) {
3711 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3712 return getUMinExpr(Ops);
3713}
3714
3715const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3716 return getMinMaxExpr(scUMinExpr, Ops);
3717}
3718
3719const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3720 // We can bypass creating a target-independent
3721 // constant expression and then folding it back into a ConstantInt.
3722 // This is just a compile-time optimization.
3723 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3724}
3725
3726const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3727 StructType *STy,
3728 unsigned FieldNo) {
3729 // We can bypass creating a target-independent
3730 // constant expression and then folding it back into a ConstantInt.
3731 // This is just a compile-time optimization.
3732 return getConstant(
3733 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3734}
3735
3736const SCEV *ScalarEvolution::getUnknown(Value *V) {
3737 // Don't attempt to do anything other than create a SCEVUnknown object
3738 // here. createSCEV only calls getUnknown after checking for all other
3739 // interesting possibilities, and any other code that calls getUnknown
3740 // is doing so in order to hide a value from SCEV canonicalization.
3741
3742 FoldingSetNodeID ID;
3743 ID.AddInteger(scUnknown);
3744 ID.AddPointer(V);
3745 void *IP = nullptr;
3746 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3747 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3748, __PRETTY_FUNCTION__))
3748 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3748, __PRETTY_FUNCTION__))
;
3749 return S;
3750 }
3751 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3752 FirstUnknown);
3753 FirstUnknown = cast<SCEVUnknown>(S);
3754 UniqueSCEVs.InsertNode(S, IP);
3755 return S;
3756}
3757
3758//===----------------------------------------------------------------------===//
3759// Basic SCEV Analysis and PHI Idiom Recognition Code
3760//
3761
3762/// Test if values of the given type are analyzable within the SCEV
3763/// framework. This primarily includes integer types, and it can optionally
3764/// include pointer types if the ScalarEvolution class has access to
3765/// target-specific information.
3766bool ScalarEvolution::isSCEVable(Type *Ty) const {
3767 // Integers and pointers are always SCEVable.
3768 return Ty->isIntOrPtrTy();
2
Calling 'Type::isIntOrPtrTy'
4
Returning from 'Type::isIntOrPtrTy'
5
Returning the value 1, which participates in a condition later
3769}
3770
3771/// Return the size in bits of the specified type, for which isSCEVable must
3772/// return true.
3773uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3774 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3774, __PRETTY_FUNCTION__))
;
3775 if (Ty->isPointerTy())
3776 return getDataLayout().getIndexTypeSizeInBits(Ty);
3777 return getDataLayout().getTypeSizeInBits(Ty);
3778}
3779
3780/// Return a type with the same bitwidth as the given type and which represents
3781/// how SCEV will treat the given type, for which isSCEVable must return
3782/// true. For pointer types, this is the pointer-sized integer type.
3783Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3784 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3784, __PRETTY_FUNCTION__))
;
3785
3786 if (Ty->isIntegerTy())
3787 return Ty;
3788
3789 // The only other support type is pointer.
3790 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3790, __PRETTY_FUNCTION__))
;
3791 return getDataLayout().getIntPtrType(Ty);
3792}
3793
3794Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
3795 return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
3796}
3797
3798const SCEV *ScalarEvolution::getCouldNotCompute() {
3799 return CouldNotCompute.get();
3800}
3801
3802bool ScalarEvolution::checkValidity(const SCEV *S) const {
3803 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3804 auto *SU = dyn_cast<SCEVUnknown>(S);
3805 return SU && SU->getValue() == nullptr;
3806 });
3807
3808 return !ContainsNulls;
3809}
3810
3811bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3812 HasRecMapType::iterator I = HasRecMap.find(S);
3813 if (I != HasRecMap.end())
3814 return I->second;
3815
3816 bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
3817 HasRecMap.insert({S, FoundAddRec});
3818 return FoundAddRec;
3819}
3820
3821/// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3822/// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3823/// offset I, then return {S', I}, else return {\p S, nullptr}.
3824static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3825 const auto *Add = dyn_cast<SCEVAddExpr>(S);
3826 if (!Add)
3827 return {S, nullptr};
3828
3829 if (Add->getNumOperands() != 2)
3830 return {S, nullptr};
3831
3832 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3833 if (!ConstOp)
3834 return {S, nullptr};
3835
3836 return {Add->getOperand(1), ConstOp->getValue()};
3837}
3838
3839/// Return the ValueOffsetPair set for \p S. \p S can be represented
3840/// by the value and offset from any ValueOffsetPair in the set.
3841SetVector<ScalarEvolution::ValueOffsetPair> *
3842ScalarEvolution::getSCEVValues(const SCEV *S) {
3843 ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3844 if (SI == ExprValueMap.end())
3845 return nullptr;
3846#ifndef NDEBUG
3847 if (VerifySCEVMap) {
3848 // Check there is no dangling Value in the set returned.
3849 for (const auto &VE : SI->second)
3850 assert(ValueExprMap.count(VE.first))((ValueExprMap.count(VE.first)) ? static_cast<void> (0)
: __assert_fail ("ValueExprMap.count(VE.first)", "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3850, __PRETTY_FUNCTION__))
;
3851 }
3852#endif
3853 return &SI->second;
3854}
3855
3856/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3857/// cannot be used separately. eraseValueFromMap should be used to remove
3858/// V from ValueExprMap and ExprValueMap at the same time.
3859void ScalarEvolution::eraseValueFromMap(Value *V) {
3860 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3861 if (I != ValueExprMap.end()) {
3862 const SCEV *S = I->second;
3863 // Remove {V, 0} from the set of ExprValueMap[S]
3864 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
3865 SV->remove({V, nullptr});
3866
3867 // Remove {V, Offset} from the set of ExprValueMap[Stripped]
3868 const SCEV *Stripped;
3869 ConstantInt *Offset;
3870 std::tie(Stripped, Offset) = splitAddExpr(S);
3871 if (Offset != nullptr) {
3872 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
3873 SV->remove({V, Offset});
3874 }
3875 ValueExprMap.erase(V);
3876 }
3877}
3878
3879/// Check whether value has nuw/nsw/exact set but SCEV does not.
3880/// TODO: In reality it is better to check the poison recursively
3881/// but this is better than nothing.
3882static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) {
3883 if (auto *I = dyn_cast<Instruction>(V)) {
3884 if (isa<OverflowingBinaryOperator>(I)) {
3885 if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) {
3886 if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap())
3887 return true;
3888 if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap())
3889 return true;
3890 }
3891 } else if (isa<PossiblyExactOperator>(I) && I->isExact())
3892 return true;
3893 }
3894 return false;
3895}
3896
3897/// Return an existing SCEV if it exists, otherwise analyze the expression and
3898/// create a new one.
3899const SCEV *ScalarEvolution::getSCEV(Value *V) {
3900 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3900, __PRETTY_FUNCTION__))
;
3901
3902 const SCEV *S = getExistingSCEV(V);
3903 if (S == nullptr) {
3904 S = createSCEV(V);
3905 // During PHI resolution, it is possible to create two SCEVs for the same
3906 // V, so it is needed to double check whether V->S is inserted into
3907 // ValueExprMap before insert S->{V, 0} into ExprValueMap.
3908 std::pair<ValueExprMapType::iterator, bool> Pair =
3909 ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3910 if (Pair.second && !SCEVLostPoisonFlags(S, V)) {
3911 ExprValueMap[S].insert({V, nullptr});
3912
3913 // If S == Stripped + Offset, add Stripped -> {V, Offset} into
3914 // ExprValueMap.
3915 const SCEV *Stripped = S;
3916 ConstantInt *Offset = nullptr;
3917 std::tie(Stripped, Offset) = splitAddExpr(S);
3918 // If stripped is SCEVUnknown, don't bother to save
3919 // Stripped -> {V, offset}. It doesn't simplify and sometimes even
3920 // increase the complexity of the expansion code.
3921 // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
3922 // because it may generate add/sub instead of GEP in SCEV expansion.
3923 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
3924 !isa<GetElementPtrInst>(V))
3925 ExprValueMap[Stripped].insert({V, Offset});
3926 }
3927 }
3928 return S;
3929}
3930
3931const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3932 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 3932, __PRETTY_FUNCTION__))
;
3933
3934 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3935 if (I != ValueExprMap.end()) {
3936 const SCEV *S = I->second;
3937 if (checkValidity(S))
3938 return S;
3939 eraseValueFromMap(V);
3940 forgetMemoizedResults(S);
3941 }
3942 return nullptr;
3943}
3944
3945/// Return a SCEV corresponding to -V = -1*V
3946const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3947 SCEV::NoWrapFlags Flags) {
3948 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3949 return getConstant(
3950 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3951
3952 Type *Ty = V->getType();
3953 Ty = getEffectiveSCEVType(Ty);
3954 return getMulExpr(
3955 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3956}
3957
3958/// If Expr computes ~A, return A else return nullptr
3959static const SCEV *MatchNotExpr(const SCEV *Expr) {
3960 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
3961 if (!Add || Add->getNumOperands() != 2 ||
3962 !Add->getOperand(0)->isAllOnesValue())
3963 return nullptr;
3964
3965 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
3966 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
3967 !AddRHS->getOperand(0)->isAllOnesValue())
3968 return nullptr;
3969
3970 return AddRHS->getOperand(1);
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 // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
3980 if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) {
3981 auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
3982 SmallVector<const SCEV *, 2> MatchedOperands;
3983 for (const SCEV *Operand : MME->operands()) {
3984 const SCEV *Matched = MatchNotExpr(Operand);
3985 if (!Matched)
3986 return (const SCEV *)nullptr;
3987 MatchedOperands.push_back(Matched);
3988 }
3989 return getMinMaxExpr(
3990 SCEVMinMaxExpr::negate(static_cast<SCEVTypes>(MME->getSCEVType())),
3991 MatchedOperands);
3992 };
3993 if (const SCEV *Replaced = MatchMinMaxNegation(MME))
3994 return Replaced;
3995 }
3996
3997 Type *Ty = V->getType();
3998 Ty = getEffectiveSCEVType(Ty);
3999 const SCEV *AllOnes =
4000 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
4001 return getMinusSCEV(AllOnes, V);
4002}
4003
4004const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
4005 SCEV::NoWrapFlags Flags,
4006 unsigned Depth) {
4007 // Fast path: X - X --> 0.
4008 if (LHS == RHS)
4009 return getZero(LHS->getType());
4010
4011 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
4012 // makes it so that we cannot make much use of NUW.
4013 auto AddFlags = SCEV::FlagAnyWrap;
4014 const bool RHSIsNotMinSigned =
4015 !getSignedRangeMin(RHS).isMinSignedValue();
4016 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
4017 // Let M be the minimum representable signed value. Then (-1)*RHS
4018 // signed-wraps if and only if RHS is M. That can happen even for
4019 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
4020 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
4021 // (-1)*RHS, we need to prove that RHS != M.
4022 //
4023 // If LHS is non-negative and we know that LHS - RHS does not
4024 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
4025 // either by proving that RHS > M or that LHS >= 0.
4026 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
4027 AddFlags = SCEV::FlagNSW;
4028 }
4029 }
4030
4031 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
4032 // RHS is NSW and LHS >= 0.
4033 //
4034 // The difficulty here is that the NSW flag may have been proven
4035 // relative to a loop that is to be found in a recurrence in LHS and
4036 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
4037 // larger scope than intended.
4038 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
4039
4040 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
4041}
4042
4043const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
4044 unsigned Depth) {
4045 Type *SrcTy = V->getType();
4046 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4047, __PRETTY_FUNCTION__))
4047 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4047, __PRETTY_FUNCTION__))
;
4048 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4049 return V; // No conversion
4050 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
4051 return getTruncateExpr(V, Ty, Depth);
4052 return getZeroExtendExpr(V, Ty, Depth);
4053}
4054
4055const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
4056 unsigned Depth) {
4057 Type *SrcTy = V->getType();
4058 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4059, __PRETTY_FUNCTION__))
4059 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4059, __PRETTY_FUNCTION__))
;
4060 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4061 return V; // No conversion
4062 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
4063 return getTruncateExpr(V, Ty, Depth);
4064 return getSignExtendExpr(V, Ty, Depth);
4065}
4066
4067const SCEV *
4068ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
4069 Type *SrcTy = V->getType();
4070 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4071, __PRETTY_FUNCTION__))
4071 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4071, __PRETTY_FUNCTION__))
;
4072 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4073, __PRETTY_FUNCTION__))
4073 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4073, __PRETTY_FUNCTION__))
;
4074 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4075 return V; // No conversion
4076 return getZeroExtendExpr(V, Ty);
4077}
4078
4079const SCEV *
4080ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
4081 Type *SrcTy = V->getType();
4082 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4083, __PRETTY_FUNCTION__))
4083 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4083, __PRETTY_FUNCTION__))
;
4084 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4085, __PRETTY_FUNCTION__))
4085 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4085, __PRETTY_FUNCTION__))
;
4086 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4087 return V; // No conversion
4088 return getSignExtendExpr(V, Ty);
4089}
4090
4091const SCEV *
4092ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
4093 Type *SrcTy = V->getType();
4094 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4095, __PRETTY_FUNCTION__))
4095 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4095, __PRETTY_FUNCTION__))
;
4096 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4097, __PRETTY_FUNCTION__))
4097 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4097, __PRETTY_FUNCTION__))
;
4098 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4099 return V; // No conversion
4100 return getAnyExtendExpr(V, Ty);
4101}
4102
4103const SCEV *
4104ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
4105 Type *SrcTy = V->getType();
4106 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4107, __PRETTY_FUNCTION__))
4107 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4107, __PRETTY_FUNCTION__))
;
4108 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4109, __PRETTY_FUNCTION__))
4109 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4109, __PRETTY_FUNCTION__))
;
4110 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4111 return V; // No conversion
4112 return getTruncateExpr(V, Ty);
4113}
4114
4115const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
4116 const SCEV *RHS) {
4117 const SCEV *PromotedLHS = LHS;
4118 const SCEV *PromotedRHS = RHS;
4119
4120 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
4121 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
4122 else
4123 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
4124
4125 return getUMaxExpr(PromotedLHS, PromotedRHS);
4126}
4127
4128const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
4129 const SCEV *RHS) {
4130 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
4131 return getUMinFromMismatchedTypes(Ops);
4132}
4133
4134const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(
4135 SmallVectorImpl<const SCEV *> &Ops) {
4136 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4136, __PRETTY_FUNCTION__))
;
4137 // Trivial case.
4138 if (Ops.size() == 1)
4139 return Ops[0];
4140
4141 // Find the max type first.
4142 Type *MaxType = nullptr;
4143 for (auto *S : Ops)
4144 if (MaxType)
4145 MaxType = getWiderType(MaxType, S->getType());
4146 else
4147 MaxType = S->getType();
4148
4149 // Extend all ops to max type.
4150 SmallVector<const SCEV *, 2> PromotedOps;
4151 for (auto *S : Ops)
4152 PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
4153
4154 // Generate umin.
4155 return getUMinExpr(PromotedOps);
4156}
4157
4158const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
4159 // A pointer operand may evaluate to a nonpointer expression, such as null.
4160 if (!V->getType()->isPointerTy())
4161 return V;
4162
4163 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
4164 return getPointerBase(Cast->getOperand());
4165 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
4166 const SCEV *PtrOp = nullptr;
4167 for (const SCEV *NAryOp : NAry->operands()) {
4168 if (NAryOp->getType()->isPointerTy()) {
4169 // Cannot find the base of an expression with multiple pointer operands.
4170 if (PtrOp)
4171 return V;
4172 PtrOp = NAryOp;
4173 }
4174 }
4175 if (!PtrOp)
4176 return V;
4177 return getPointerBase(PtrOp);
4178 }
4179 return V;
4180}
4181
4182/// Push users of the given Instruction onto the given Worklist.
4183static void
4184PushDefUseChildren(Instruction *I,
4185 SmallVectorImpl<Instruction *> &Worklist) {
4186 // Push the def-use children onto the Worklist stack.
4187 for (User *U : I->users())
4188 Worklist.push_back(cast<Instruction>(U));
4189}
4190
4191void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
4192 SmallVector<Instruction *, 16> Worklist;
4193 PushDefUseChildren(PN, Worklist);
4194
4195 SmallPtrSet<Instruction *, 8> Visited;
4196 Visited.insert(PN);
4197 while (!Worklist.empty()) {
4198 Instruction *I = Worklist.pop_back_val();
4199 if (!Visited.insert(I).second)
4200 continue;
4201
4202 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
4203 if (It != ValueExprMap.end()) {
4204 const SCEV *Old = It->second;
4205
4206 // Short-circuit the def-use traversal if the symbolic name
4207 // ceases to appear in expressions.
4208 if (Old != SymName && !hasOperand(Old, SymName))
4209 continue;
4210
4211 // SCEVUnknown for a PHI either means that it has an unrecognized
4212 // structure, it's a PHI that's in the progress of being computed
4213 // by createNodeForPHI, or it's a single-value PHI. In the first case,
4214 // additional loop trip count information isn't going to change anything.
4215 // In the second case, createNodeForPHI will perform the necessary
4216 // updates on its own when it gets to that point. In the third, we do
4217 // want to forget the SCEVUnknown.
4218 if (!isa<PHINode>(I) ||
4219 !isa<SCEVUnknown>(Old) ||
4220 (I != PN && Old == SymName)) {
4221 eraseValueFromMap(It->first);
4222 forgetMemoizedResults(Old);
4223 }
4224 }
4225
4226 PushDefUseChildren(I, Worklist);
4227 }
4228}
4229
4230namespace {
4231
4232/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
4233/// expression in case its Loop is L. If it is not L then
4234/// if IgnoreOtherLoops is true then use AddRec itself
4235/// otherwise rewrite cannot be done.
4236/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4237class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4238public:
4239 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
4240 bool IgnoreOtherLoops = true) {
4241 SCEVInitRewriter Rewriter(L, SE);
4242 const SCEV *Result = Rewriter.visit(S);
4243 if (Rewriter.hasSeenLoopVariantSCEVUnknown())
4244 return SE.getCouldNotCompute();
4245 return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
4246 ? SE.getCouldNotCompute()
4247 : Result;
4248 }
4249
4250 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4251 if (!SE.isLoopInvariant(Expr, L))
4252 SeenLoopVariantSCEVUnknown = true;
4253 return Expr;
4254 }
4255
4256 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4257 // Only re-write AddRecExprs for this loop.
4258 if (Expr->getLoop() == L)
4259 return Expr->getStart();
4260 SeenOtherLoops = true;
4261 return Expr;
4262 }
4263
4264 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4265
4266 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4267
4268private:
4269 explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
4270 : SCEVRewriteVisitor(SE), L(L) {}
4271
4272 const Loop *L;
4273 bool SeenLoopVariantSCEVUnknown = false;
4274 bool SeenOtherLoops = false;
4275};
4276
4277/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
4278/// increment expression in case its Loop is L. If it is not L then
4279/// use AddRec itself.
4280/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4281class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
4282public:
4283 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
4284 SCEVPostIncRewriter Rewriter(L, SE);
4285 const SCEV *Result = Rewriter.visit(S);
4286 return Rewriter.hasSeenLoopVariantSCEVUnknown()
4287 ? SE.getCouldNotCompute()
4288 : Result;
4289 }
4290
4291 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4292 if (!SE.isLoopInvariant(Expr, L))
4293 SeenLoopVariantSCEVUnknown = true;
4294 return Expr;
4295 }
4296
4297 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4298 // Only re-write AddRecExprs for this loop.
4299 if (Expr->getLoop() == L)
4300 return Expr->getPostIncExpr(SE);
4301 SeenOtherLoops = true;
4302 return Expr;
4303 }
4304
4305 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4306
4307 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4308
4309private:
4310 explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
4311 : SCEVRewriteVisitor(SE), L(L) {}
4312
4313 const Loop *L;
4314 bool SeenLoopVariantSCEVUnknown = false;
4315 bool SeenOtherLoops = false;
4316};
4317
4318/// This class evaluates the compare condition by matching it against the
4319/// condition of loop latch. If there is a match we assume a true value
4320/// for the condition while building SCEV nodes.
4321class SCEVBackedgeConditionFolder
4322 : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4323public:
4324 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4325 ScalarEvolution &SE) {
4326 bool IsPosBECond = false;
4327 Value *BECond = nullptr;
4328 if (BasicBlock *Latch = L->getLoopLatch()) {
4329 BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
4330 if (BI && BI->isConditional()) {
4331 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4332, __PRETTY_FUNCTION__))
4332 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4332, __PRETTY_FUNCTION__))
;
4333 BECond = BI->getCondition();
4334 IsPosBECond = BI->getSuccessor(0) == L->getHeader();
4335 } else {
4336 return S;
4337 }
4338 }
4339 SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
4340 return Rewriter.visit(S);
4341 }
4342
4343 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4344 const SCEV *Result = Expr;
4345 bool InvariantF = SE.isLoopInvariant(Expr, L);
4346
4347 if (!InvariantF) {
4348 Instruction *I = cast<Instruction>(Expr->getValue());
4349 switch (I->getOpcode()) {
4350 case Instruction::Select: {
4351 SelectInst *SI = cast<SelectInst>(I);
4352 Optional<const SCEV *> Res =
4353 compareWithBackedgeCondition(SI->getCondition());
4354 if (Res.hasValue()) {
4355 bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
4356 Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
4357 }
4358 break;
4359 }
4360 default: {
4361 Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
4362 if (Res.hasValue())
4363 Result = Res.getValue();
4364 break;
4365 }
4366 }
4367 }
4368 return Result;
4369 }
4370
4371private:
4372 explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
4373 bool IsPosBECond, ScalarEvolution &SE)
4374 : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
4375 IsPositiveBECond(IsPosBECond) {}
4376
4377 Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
4378
4379 const Loop *L;
4380 /// Loop back condition.
4381 Value *BackedgeCond = nullptr;
4382 /// Set to true if loop back is on positive branch condition.
4383 bool IsPositiveBECond;
4384};
4385
4386Optional<const SCEV *>
4387SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
4388
4389 // If value matches the backedge condition for loop latch,
4390 // then return a constant evolution node based on loopback
4391 // branch taken.
4392 if (BackedgeCond == IC)
4393 return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
4394 : SE.getZero(Type::getInt1Ty(SE.getContext()));
4395 return None;
4396}
4397
4398class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4399public:
4400 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4401 ScalarEvolution &SE) {
4402 SCEVShiftRewriter Rewriter(L, SE);
4403 const SCEV *Result = Rewriter.visit(S);
4404 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4405 }
4406
4407 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4408 // Only allow AddRecExprs for this loop.
4409 if (!SE.isLoopInvariant(Expr, L))
4410 Valid = false;
4411 return Expr;
4412 }
4413
4414 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4415 if (Expr->getLoop() == L && Expr->isAffine())
4416 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
4417 Valid = false;
4418 return Expr;
4419 }
4420
4421 bool isValid() { return Valid; }
4422
4423private:
4424 explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
4425 : SCEVRewriteVisitor(SE), L(L) {}
4426
4427 const Loop *L;
4428 bool Valid = true;
4429};
4430
4431} // end anonymous namespace
4432
4433SCEV::NoWrapFlags
4434ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
4435 if (!AR->isAffine())
4436 return SCEV::FlagAnyWrap;
4437
4438 using OBO = OverflowingBinaryOperator;
4439
4440 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
4441
4442 if (!AR->hasNoSignedWrap()) {
4443 ConstantRange AddRecRange = getSignedRange(AR);
4444 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
4445
4446 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4447 Instruction::Add, IncRange, OBO::NoSignedWrap);
4448 if (NSWRegion.contains(AddRecRange))
4449 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
4450 }
4451
4452 if (!AR->hasNoUnsignedWrap()) {
4453 ConstantRange AddRecRange = getUnsignedRange(AR);
4454 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
4455
4456 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4457 Instruction::Add, IncRange, OBO::NoUnsignedWrap);
4458 if (NUWRegion.contains(AddRecRange))
4459 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
4460 }
4461
4462 return Result;
4463}
4464
4465namespace {
4466
4467/// Represents an abstract binary operation. This may exist as a
4468/// normal instruction or constant expression, or may have been
4469/// derived from an expression tree.
4470struct BinaryOp {
4471 unsigned Opcode;
4472 Value *LHS;
4473 Value *RHS;
4474 bool IsNSW = false;
4475 bool IsNUW = false;
4476
4477 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
4478 /// constant expression.
4479 Operator *Op = nullptr;
4480
4481 explicit BinaryOp(Operator *Op)
4482 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
4483 Op(Op) {
4484 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
4485 IsNSW = OBO->hasNoSignedWrap();
4486 IsNUW = OBO->hasNoUnsignedWrap();
4487 }
4488 }
4489
4490 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
4491 bool IsNUW = false)
4492 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
4493};
4494
4495} // end anonymous namespace
4496
4497/// Try to map \p V into a BinaryOp, and return \c None on failure.
4498static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
4499 auto *Op = dyn_cast<Operator>(V);
20
Assuming 'V' is a 'Operator'
4500 if (!Op
20.1
'Op' is non-null
20.1
'Op' is non-null
20.1
'Op' is non-null
20.1
'Op' is non-null
20.1
'Op' is non-null
)
21
Taking false branch
4501 return None;
4502
4503 // Implementation detail: all the cleverness here should happen without
4504 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
4505 // SCEV expressions when possible, and we should not break that.
4506
4507 switch (Op->getOpcode()) {
22
Control jumps to 'case ExtractValue:' at line 4545
4508 case Instruction::Add:
4509 case Instruction::Sub:
4510 case Instruction::Mul:
4511 case Instruction::UDiv:
4512 case Instruction::URem:
4513 case Instruction::And:
4514 case Instruction::Or:
4515 case Instruction::AShr:
4516 case Instruction::Shl:
4517 return BinaryOp(Op);
4518
4519 case Instruction::Xor:
4520 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
4521 // If the RHS of the xor is a signmask, then this is just an add.
4522 // Instcombine turns add of signmask into xor as a strength reduction step.
4523 if (RHSC->getValue().isSignMask())
4524 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
4525 return BinaryOp(Op);
4526
4527 case Instruction::LShr:
4528 // Turn logical shift right of a constant into a unsigned divide.
4529 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
4530 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
4531
4532 // If the shift count is not less than the bitwidth, the result of
4533 // the shift is undefined. Don't try to analyze it, because the
4534 // resolution chosen here may differ from the resolution chosen in
4535 // other parts of the compiler.
4536 if (SA->getValue().ult(BitWidth)) {
4537 Constant *X =
4538 ConstantInt::get(SA->getContext(),
4539 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4540 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
4541 }
4542 }
4543 return BinaryOp(Op);
4544
4545 case Instruction::ExtractValue: {
4546 auto *EVI = cast<ExtractValueInst>(Op);
23
'Op' is a 'ExtractValueInst'
4547 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
24
Assuming the condition is false
25
Assuming the condition is false
26
Taking false branch
4548 break;
4549
4550 auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand());
4551 if (!WO)
27
Assuming 'WO' is non-null
28
Taking false branch
4552 break;
4553
4554 Instruction::BinaryOps BinOp = WO->getBinaryOp();
4555 bool Signed = WO->isSigned();
4556 // TODO: Should add nuw/nsw flags for mul as well.
4557 if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
29
Assuming 'BinOp' is not equal to Mul, which participates in a condition later
30
Assuming the condition is false
31
Taking false branch
4558 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());
4559
4560 // Now that we know that all uses of the arithmetic-result component of
4561 // CI are guarded by the overflow check, we can go ahead and pretend
4562 // that the arithmetic is non-overflowing.
4563 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
33
Calling constructor for 'Optional<(anonymous namespace)::BinaryOp>'
38
Returning from constructor for 'Optional<(anonymous namespace)::BinaryOp>'
4564 /* IsNSW = */ Signed, /* IsNUW = */ !Signed);
32
Assuming 'Signed' is true
4565 }
4566
4567 default:
4568 break;
4569 }
4570
4571 return None;
4572}
4573
4574/// Helper function to createAddRecFromPHIWithCasts. We have a phi
4575/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
4576/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
4577/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
4578/// follows one of the following patterns:
4579/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4580/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4581/// If the SCEV expression of \p Op conforms with one of the expected patterns
4582/// we return the type of the truncation operation, and indicate whether the
4583/// truncated type should be treated as signed/unsigned by setting
4584/// \p Signed to true/false, respectively.
4585static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
4586 bool &Signed, ScalarEvolution &SE) {
4587 // The case where Op == SymbolicPHI (that is, with no type conversions on
4588 // the way) is handled by the regular add recurrence creating logic and
4589 // would have already been triggered in createAddRecForPHI. Reaching it here
4590 // means that createAddRecFromPHI had failed for this PHI before (e.g.,
4591 // because one of the other operands of the SCEVAddExpr updating this PHI is
4592 // not invariant).
4593 //
4594 // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
4595 // this case predicates that allow us to prove that Op == SymbolicPHI will
4596 // be added.
4597 if (Op == SymbolicPHI)
4598 return nullptr;
4599
4600 unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
4601 unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
4602 if (SourceBits != NewBits)
4603 return nullptr;
4604
4605 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
4606 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
4607 if (!SExt && !ZExt)
4608 return nullptr;
4609 const SCEVTruncateExpr *Trunc =
4610 SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
4611 : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
4612 if (!Trunc)
4613 return nullptr;
4614 const SCEV *X = Trunc->getOperand();
4615 if (X != SymbolicPHI)
4616 return nullptr;
4617 Signed = SExt != nullptr;
4618 return Trunc->getType();
4619}
4620
4621static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
4622 if (!PN->getType()->isIntegerTy())
4623 return nullptr;
4624 const Loop *L = LI.getLoopFor(PN->getParent());
4625 if (!L || L->getHeader() != PN->getParent())
4626 return nullptr;
4627 return L;
4628}
4629
4630// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
4631// computation that updates the phi follows the following pattern:
4632// (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
4633// which correspond to a phi->trunc->sext/zext->add->phi update chain.
4634// If so, try to see if it can be rewritten as an AddRecExpr under some
4635// Predicates. If successful, return them as a pair. Also cache the results
4636// of the analysis.
4637//
4638// Example usage scenario:
4639// Say the Rewriter is called for the following SCEV:
4640// 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4641// where:
4642// %X = phi i64 (%Start, %BEValue)
4643// It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
4644// and call this function with %SymbolicPHI = %X.
4645//
4646// The analysis will find that the value coming around the backedge has
4647// the following SCEV:
4648// BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4649// Upon concluding that this matches the desired pattern, the function
4650// will return the pair {NewAddRec, SmallPredsVec} where:
4651// NewAddRec = {%Start,+,%Step}
4652// SmallPredsVec = {P1, P2, P3} as follows:
4653// P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
4654// P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
4655// P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
4656// The returned pair means that SymbolicPHI can be rewritten into NewAddRec
4657// under the predicates {P1,P2,P3}.
4658// This predicated rewrite will be cached in PredicatedSCEVRewrites:
4659// PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
4660//
4661// TODO's:
4662//
4663// 1) Extend the Induction descriptor to also support inductions that involve
4664// casts: When needed (namely, when we are called in the context of the
4665// vectorizer induction analysis), a Set of cast instructions will be
4666// populated by this method, and provided back to isInductionPHI. This is
4667// needed to allow the vectorizer to properly record them to be ignored by
4668// the cost model and to avoid vectorizing them (otherwise these casts,
4669// which are redundant under the runtime overflow checks, will be
4670// vectorized, which can be costly).
4671//
4672// 2) Support additional induction/PHISCEV patterns: We also want to support
4673// inductions where the sext-trunc / zext-trunc operations (partly) occur
4674// after the induction update operation (the induction increment):
4675//
4676// (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
4677// which correspond to a phi->add->trunc->sext/zext->phi update chain.
4678//
4679// (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
4680// which correspond to a phi->trunc->add->sext/zext->phi update chain.
4681//
4682// 3) Outline common code with createAddRecFromPHI to avoid duplication.
4683Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4684ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
4685 SmallVector<const SCEVPredicate *, 3> Predicates;
4686
4687 // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
4688 // return an AddRec expression under some predicate.
4689
4690 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4691 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4692 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4692, __PRETTY_FUNCTION__))
;
4693
4694 // The loop may have multiple entrances or multiple exits; we can analyze
4695 // this phi as an addrec if it has a unique entry value and a unique
4696 // backedge value.
4697 Value *BEValueV = nullptr, *StartValueV = nullptr;
4698 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4699 Value *V = PN->getIncomingValue(i);
4700 if (L->contains(PN->getIncomingBlock(i))) {
4701 if (!BEValueV) {
4702 BEValueV = V;
4703 } else if (BEValueV != V) {
4704 BEValueV = nullptr;
4705 break;
4706 }
4707 } else if (!StartValueV) {
4708 StartValueV = V;
4709 } else if (StartValueV != V) {
4710 StartValueV = nullptr;
4711 break;
4712 }
4713 }
4714 if (!BEValueV || !StartValueV)
4715 return None;
4716
4717 const SCEV *BEValue = getSCEV(BEValueV);
4718
4719 // If the value coming around the backedge is an add with the symbolic
4720 // value we just inserted, possibly with casts that we can ignore under
4721 // an appropriate runtime guard, then we found a simple induction variable!
4722 const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
4723 if (!Add)
4724 return None;
4725
4726 // If there is a single occurrence of the symbolic value, possibly
4727 // casted, replace it with a recurrence.
4728 unsigned FoundIndex = Add->getNumOperands();
4729 Type *TruncTy = nullptr;
4730 bool Signed;
4731 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4732 if ((TruncTy =
4733 isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
4734 if (FoundIndex == e) {
4735 FoundIndex = i;
4736 break;
4737 }
4738
4739 if (FoundIndex == Add->getNumOperands())
4740 return None;
4741
4742 // Create an add with everything but the specified operand.
4743 SmallVector<const SCEV *, 8> Ops;
4744 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4745 if (i != FoundIndex)
4746 Ops.push_back(Add->getOperand(i));
4747 const SCEV *Accum = getAddExpr(Ops);
4748
4749 // The runtime checks will not be valid if the step amount is
4750 // varying inside the loop.
4751 if (!isLoopInvariant(Accum, L))
4752 return None;
4753
4754 // *** Part2: Create the predicates
4755
4756 // Analysis was successful: we have a phi-with-cast pattern for which we
4757 // can return an AddRec expression under the following predicates:
4758 //
4759 // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
4760 // fits within the truncated type (does not overflow) for i = 0 to n-1.
4761 // P2: An Equal predicate that guarantees that
4762 // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
4763 // P3: An Equal predicate that guarantees that
4764 // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
4765 //
4766 // As we next prove, the above predicates guarantee that:
4767 // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
4768 //
4769 //
4770 // More formally, we want to prove that:
4771 // Expr(i+1) = Start + (i+1) * Accum
4772 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4773 //
4774 // Given that:
4775 // 1) Expr(0) = Start
4776 // 2) Expr(1) = Start + Accum
4777 // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
4778 // 3) Induction hypothesis (step i):
4779 // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
4780 //
4781 // Proof:
4782 // Expr(i+1) =
4783 // = Start + (i+1)*Accum
4784 // = (Start + i*Accum) + Accum
4785 // = Expr(i) + Accum
4786 // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
4787 // :: from step i
4788 //
4789 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
4790 //
4791 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
4792 // + (Ext ix (Trunc iy (Accum) to ix) to iy)
4793 // + Accum :: from P3
4794 //
4795 // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
4796 // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
4797 //
4798 // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
4799 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4800 //
4801 // By induction, the same applies to all iterations 1<=i<n:
4802 //
4803
4804 // Create a truncated addrec for which we will add a no overflow check (P1).
4805 const SCEV *StartVal = getSCEV(StartValueV);
4806 const SCEV *PHISCEV =
4807 getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
4808 getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
4809
4810 // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
4811 // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
4812 // will be constant.
4813 //
4814 // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
4815 // add P1.
4816 if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
4817 SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
4818 Signed ? SCEVWrapPredicate::IncrementNSSW
4819 : SCEVWrapPredicate::IncrementNUSW;
4820 const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
4821 Predicates.push_back(AddRecPred);
4822 }
4823
4824 // Create the Equal Predicates P2,P3:
4825
4826 // It is possible that the predicates P2 and/or P3 are computable at
4827 // compile time due to StartVal and/or Accum being constants.
4828 // If either one is, then we can check that now and escape if either P2
4829 // or P3 is false.
4830
4831 // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
4832 // for each of StartVal and Accum
4833 auto getExtendedExpr = [&](const SCEV *Expr,
4834 bool CreateSignExtend) -> const SCEV * {
4835 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4835, __PRETTY_FUNCTION__))
;
4836 const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
4837 const SCEV *ExtendedExpr =
4838 CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
4839 : getZeroExtendExpr(TruncatedExpr, Expr->getType());
4840 return ExtendedExpr;
4841 };
4842
4843 // Given:
4844 // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
4845 // = getExtendedExpr(Expr)
4846 // Determine whether the predicate P: Expr == ExtendedExpr
4847 // is known to be false at compile time
4848 auto PredIsKnownFalse = [&](const SCEV *Expr,
4849 const SCEV *ExtendedExpr) -> bool {
4850 return Expr != ExtendedExpr &&
4851 isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
4852 };
4853
4854 const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
4855 if (PredIsKnownFalse(StartVal, StartExtended)) {
4856 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)
;
4857 return None;
4858 }
4859
4860 // The Step is always Signed (because the overflow checks are either
4861 // NSSW or NUSW)
4862 const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
4863 if (PredIsKnownFalse(Accum, AccumExtended)) {
4864 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)
;
4865 return None;
4866 }
4867
4868 auto AppendPredicate = [&](const SCEV *Expr,
4869 const SCEV *ExtendedExpr) -> void {
4870 if (Expr != ExtendedExpr &&
4871 !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
4872 const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
4873 LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred)do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "Added Predicate: " <<
*Pred; } } while (false)
;
4874 Predicates.push_back(Pred);
4875 }
4876 };
4877
4878 AppendPredicate(StartVal, StartExtended);
4879 AppendPredicate(Accum, AccumExtended);
4880
4881 // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
4882 // which the casts had been folded away. The caller can rewrite SymbolicPHI
4883 // into NewAR if it will also add the runtime overflow checks specified in
4884 // Predicates.
4885 auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
4886
4887 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
4888 std::make_pair(NewAR, Predicates);
4889 // Remember the result of the analysis for this SCEV at this locayyytion.
4890 PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
4891 return PredRewrite;
4892}
4893
4894Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4895ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
4896 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4897 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4898 if (!L)
4899 return None;
4900
4901 // Check to see if we already analyzed this PHI.
4902 auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
4903 if (I != PredicatedSCEVRewrites.end()) {
4904 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
4905 I->second;
4906 // Analysis was done before and failed to create an AddRec:
4907 if (Rewrite.first == SymbolicPHI)
4908 return None;
4909 // Analysis was done before and succeeded to create an AddRec under
4910 // a predicate:
4911 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4911, __PRETTY_FUNCTION__))
;
4912 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4912, __PRETTY_FUNCTION__))
;
4913 return Rewrite;
4914 }
4915
4916 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4917 Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
4918
4919 // Record in the cache that the analysis failed
4920 if (!Rewrite) {
4921 SmallVector<const SCEVPredicate *, 3> Predicates;
4922 PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
4923 return None;
4924 }
4925
4926 return Rewrite;
4927}
4928
4929// FIXME: This utility is currently required because the Rewriter currently
4930// does not rewrite this expression:
4931// {0, +, (sext ix (trunc iy to ix) to iy)}
4932// into {0, +, %step},
4933// even when the following Equal predicate exists:
4934// "%step == (sext ix (trunc iy to ix) to iy)".
4935bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
4936 const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
4937 if (AR1 == AR2)
4938 return true;
4939
4940 auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
4941 if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
4942 !Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
4943 return false;
4944 return true;
4945 };
4946
4947 if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
4948 !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
4949 return false;
4950 return true;
4951}
4952
4953/// A helper function for createAddRecFromPHI to handle simple cases.
4954///
4955/// This function tries to find an AddRec expression for the simplest (yet most
4956/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
4957/// If it fails, createAddRecFromPHI will use a more general, but slow,
4958/// technique for finding the AddRec expression.
4959const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
4960 Value *BEValueV,
4961 Value *StartValueV) {
4962 const Loop *L = LI.getLoopFor(PN->getParent());
4963 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4963, __PRETTY_FUNCTION__))
;
4964 assert(BEValueV && StartValueV)((BEValueV && StartValueV) ? static_cast<void> (
0) : __assert_fail ("BEValueV && StartValueV", "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 4964, __PRETTY_FUNCTION__))
;
4965
4966 auto BO = MatchBinaryOp(BEValueV, DT);
4967 if (!BO)
4968 return nullptr;
4969
4970 if (BO->Opcode != Instruction::Add)
4971 return nullptr;
4972
4973 const SCEV *Accum = nullptr;
4974 if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
4975 Accum = getSCEV(BO->RHS);
4976 else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
4977 Accum = getSCEV(BO->LHS);
4978
4979 if (!Accum)
4980 return nullptr;
4981
4982 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4983 if (BO->IsNUW)
4984 Flags = setFlags(Flags, SCEV::FlagNUW);
4985 if (BO->IsNSW)
4986 Flags = setFlags(Flags, SCEV::FlagNSW);
4987
4988 const SCEV *StartVal = getSCEV(StartValueV);
4989 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4990
4991 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4992
4993 // We can add Flags to the post-inc expression only if we
4994 // know that it is *undefined behavior* for BEValueV to
4995 // overflow.
4996 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4997 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4998 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4999
5000 return PHISCEV;
5001}
5002
5003const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
5004 const Loop *L = LI.getLoopFor(PN->getParent());
5005 if (!L || L->getHeader() != PN->getParent())
5006 return nullptr;
5007
5008 // The loop may have multiple entrances or multiple exits; we can analyze
5009 // this phi as an addrec if it has a unique entry value and a unique
5010 // backedge value.
5011 Value *BEValueV = nullptr, *StartValueV = nullptr;
5012 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5013 Value *V = PN->getIncomingValue(i);
5014 if (L->contains(PN->getIncomingBlock(i))) {
5015 if (!BEValueV) {
5016 BEValueV = V;
5017 } else if (BEValueV != V) {
5018 BEValueV = nullptr;
5019 break;
5020 }
5021 } else if (!StartValueV) {
5022 StartValueV = V;
5023 } else if (StartValueV != V) {
5024 StartValueV = nullptr;
5025 break;
5026 }
5027 }
5028 if (!BEValueV || !StartValueV)
5029 return nullptr;
5030
5031 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 5032, __PRETTY_FUNCTION__))
5032 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 5032, __PRETTY_FUNCTION__))
;
5033
5034 // First, try to find AddRec expression without creating a fictituos symbolic
5035 // value for PN.
5036 if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
5037 return S;
5038
5039 // Handle PHI node value symbolically.
5040 const SCEV *SymbolicName = getUnknown(PN);
5041 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
5042
5043 // Using this symbolic name for the PHI, analyze the value coming around
5044 // the back-edge.
5045 const SCEV *BEValue = getSCEV(BEValueV);
5046
5047 // NOTE: If BEValue is loop invariant, we know that the PHI node just
5048 // has a special value for the first iteration of the loop.
5049
5050 // If the value coming around the backedge is an add with the symbolic
5051 // value we just inserted, then we found a simple induction variable!
5052 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
5053 // If there is a single occurrence of the symbolic value, replace it
5054 // with a recurrence.
5055 unsigned FoundIndex = Add->getNumOperands();
5056 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5057 if (Add->getOperand(i) == SymbolicName)
5058 if (FoundIndex == e) {
5059 FoundIndex = i;
5060 break;
5061 }
5062
5063 if (FoundIndex != Add->getNumOperands()) {
5064 // Create an add with everything but the specified operand.
5065 SmallVector<const SCEV *, 8> Ops;
5066 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5067 if (i != FoundIndex)
5068 Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
5069 L, *this));
5070 const SCEV *Accum = getAddExpr(Ops);
5071
5072 // This is not a valid addrec if the step amount is varying each
5073 // loop iteration, but is not itself an addrec in this loop.
5074 if (isLoopInvariant(Accum, L) ||
5075 (isa<SCEVAddRecExpr>(Accum) &&
5076 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
5077 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5078
5079 if (auto BO = MatchBinaryOp(BEValueV, DT)) {
5080 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
5081 if (BO->IsNUW)
5082 Flags = setFlags(Flags, SCEV::FlagNUW);
5083 if (BO->IsNSW)
5084 Flags = setFlags(Flags, SCEV::FlagNSW);
5085 }
5086 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
5087 // If the increment is an inbounds GEP, then we know the address
5088 // space cannot be wrapped around. We cannot make any guarantee
5089 // about signed or unsigned overflow because pointers are
5090 // unsigned but we may have a negative index from the base
5091 // pointer. We can guarantee that no unsigned wrap occurs if the
5092 // indices form a positive value.
5093 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
5094 Flags = setFlags(Flags, SCEV::FlagNW);
5095
5096 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
5097 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
5098 Flags = setFlags(Flags, SCEV::FlagNUW);
5099 }
5100
5101 // We cannot transfer nuw and nsw flags from subtraction
5102 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
5103 // for instance.
5104 }
5105
5106 const SCEV *StartVal = getSCEV(StartValueV);
5107 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
5108
5109 // Okay, for the entire analysis of this edge we assumed the PHI
5110 // to be symbolic. We now need to go back and purge all of the
5111 // entries for the scalars that use the symbolic expression.
5112 forgetSymbolicName(PN, SymbolicName);
5113 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
5114
5115 // We can add Flags to the post-inc expression only if we
5116 // know that it is *undefined behavior* for BEValueV to
5117 // overflow.
5118 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
5119 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
5120 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
5121
5122 return PHISCEV;
5123 }
5124 }
5125 } else {
5126 // Otherwise, this could be a loop like this:
5127 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
5128 // In this case, j = {1,+,1} and BEValue is j.
5129 // Because the other in-value of i (0) fits the evolution of BEValue
5130 // i really is an addrec evolution.
5131 //
5132 // We can generalize this saying that i is the shifted value of BEValue
5133 // by one iteration:
5134 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
5135 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
5136 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
5137 if (Shifted != getCouldNotCompute() &&
5138 Start != getCouldNotCompute()) {
5139 const SCEV *StartVal = getSCEV(StartValueV);
5140 if (Start == StartVal) {
5141 // Okay, for the entire analysis of this edge we assumed the PHI
5142 // to be symbolic. We now need to go back and purge all of the
5143 // entries for the scalars that use the symbolic expression.
5144 forgetSymbolicName(PN, SymbolicName);
5145 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
5146 return Shifted;
5147 }
5148 }
5149 }
5150
5151 // Remove the temporary PHI node SCEV that has been inserted while intending
5152 // to create an AddRecExpr for this PHI node. We can not keep this temporary
5153 // as it will prevent later (possibly simpler) SCEV expressions to be added
5154 // to the ValueExprMap.
5155 eraseValueFromMap(PN);
5156
5157 return nullptr;
5158}
5159
5160// Checks if the SCEV S is available at BB. S is considered available at BB
5161// if S can be materialized at BB without introducing a fault.
5162static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
5163 BasicBlock *BB) {
5164 struct CheckAvailable {
5165 bool TraversalDone = false;
5166 bool Available = true;
5167
5168 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
5169 BasicBlock *BB = nullptr;
5170 DominatorTree &DT;
5171
5172 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
5173 : L(L), BB(BB), DT(DT) {}
5174
5175 bool setUnavailable() {
5176 TraversalDone = true;
5177 Available = false;
5178 return false;
5179 }
5180
5181 bool follow(const SCEV *S) {
5182 switch (S->getSCEVType()) {
5183 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
5184 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
5185 case scUMinExpr:
5186 case scSMinExpr:
5187 // These expressions are available if their operand(s) is/are.
5188 return true;
5189
5190 case scAddRecExpr: {
5191 // We allow add recurrences that are on the loop BB is in, or some
5192 // outer loop. This guarantees availability because the value of the
5193 // add recurrence at BB is simply the "current" value of the induction
5194 // variable. We can relax this in the future; for instance an add
5195 // recurrence on a sibling dominating loop is also available at BB.
5196 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
5197 if (L && (ARLoop == L || ARLoop->contains(L)))
5198 return true;
5199
5200 return setUnavailable();
5201 }
5202
5203 case scUnknown: {
5204 // For SCEVUnknown, we check for simple dominance.
5205 const auto *SU = cast<SCEVUnknown>(S);
5206 Value *V = SU->getValue();
5207
5208 if (isa<Argument>(V))
5209 return false;
5210
5211 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
5212 return false;
5213
5214 return setUnavailable();
5215 }
5216
5217 case scUDivExpr:
5218 case scCouldNotCompute:
5219 // We do not try to smart about these at all.
5220 return setUnavailable();
5221 }
5222 llvm_unreachable("switch should be fully covered!")::llvm::llvm_unreachable_internal("switch should be fully covered!"
, "/build/llvm-toolchain-snapshot-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 5222)
;
5223 }
5224
5225 bool isDone() { return TraversalDone; }
5226 };
5227
5228 CheckAvailable CA(L, BB, DT);
5229 SCEVTraversal<CheckAvailable> ST(CA);
5230
5231 ST.visitAll(S);
5232 return CA.Available;
5233}
5234
5235// Try to match a control flow sequence that branches out at BI and merges back
5236// at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
5237// match.
5238static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
5239 Value *&C, Value *&LHS, Value *&RHS) {
5240 C = BI->getCondition();
5241
5242 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
5243 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
5244
5245 if (!LeftEdge.isSingleEdge())
5246 return false;
5247
5248 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 5248, __PRETTY_FUNCTION__))
;
5249
5250 Use &LeftUse = Merge->getOperandUse(0);
5251 Use &RightUse = Merge->getOperandUse(1);
5252
5253 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
5254 LHS = LeftUse;
5255 RHS = RightUse;
5256 return true;
5257 }
5258
5259 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
5260 LHS = RightUse;
5261 RHS = LeftUse;
5262 return true;
5263 }
5264
5265 return false;
5266}
5267
5268const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
5269 auto IsReachable =
5270 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
5271 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
5272 const Loop *L = LI.getLoopFor(PN->getParent());
5273
5274 // We don't want to break LCSSA, even in a SCEV expression tree.
5275 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
5276 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
5277 return nullptr;
5278
5279 // Try to match
5280 //
5281 // br %cond, label %left, label %right
5282 // left:
5283 // br label %merge
5284 // right:
5285 // br label %merge
5286 // merge:
5287 // V = phi [ %x, %left ], [ %y, %right ]
5288 //
5289 // as "select %cond, %x, %y"
5290
5291 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
5292 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 5292, __PRETTY_FUNCTION__))
;
5293
5294 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
5295 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
5296
5297 if (BI && BI->isConditional() &&
5298 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
5299 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
5300 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
5301 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
5302 }
5303
5304 return nullptr;
5305}
5306
5307const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
5308 if (const SCEV *S = createAddRecFromPHI(PN))
5309 return S;
5310
5311 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
5312 return S;
5313
5314 // If the PHI has a single incoming value, follow that value, unless the
5315 // PHI's incoming blocks are in a different loop, in which case doing so
5316 // risks breaking LCSSA form. Instcombine would normally zap these, but
5317 // it doesn't have DominatorTree information, so it may miss cases.
5318 if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
5319 if (LI.replacementPreservesLCSSAForm(PN, V))
5320 return getSCEV(V);
5321
5322 // If it's not a loop phi, we can't handle it yet.
5323 return getUnknown(PN);
5324}
5325
5326const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
5327 Value *Cond,
5328 Value *TrueVal,
5329 Value *FalseVal) {
5330 // Handle "constant" branch or select. This can occur for instance when a
5331 // loop pass transforms an inner loop and moves on to process the outer loop.
5332 if (auto *CI = dyn_cast<ConstantInt>(Cond))
5333 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
5334
5335 // Try to match some simple smax or umax patterns.
5336 auto *ICI = dyn_cast<ICmpInst>(Cond);
5337 if (!ICI)
5338 return getUnknown(I);
5339
5340 Value *LHS = ICI->getOperand(0);
5341 Value *RHS = ICI->getOperand(1);
5342
5343 switch (ICI->getPredicate()) {
5344 case ICmpInst::ICMP_SLT:
5345 case ICmpInst::ICMP_SLE:
5346 std::swap(LHS, RHS);
5347 LLVM_FALLTHROUGH[[gnu::fallthrough]];
5348 case ICmpInst::ICMP_SGT:
5349 case ICmpInst::ICMP_SGE:
5350 // a >s b ? a+x : b+x -> smax(a, b)+x
5351 // a >s b ? b+x : a+x -> smin(a, b)+x
5352 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5353 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
5354 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
5355 const SCEV *LA = getSCEV(TrueVal);
5356 const SCEV *RA = getSCEV(FalseVal);
5357 const SCEV *LDiff = getMinusSCEV(LA, LS);
5358 const SCEV *RDiff = getMinusSCEV(RA, RS);
5359 if (LDiff == RDiff)
5360 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
5361 LDiff = getMinusSCEV(LA, RS);
5362 RDiff = getMinusSCEV(RA, LS);
5363 if (LDiff == RDiff)
5364 return getAddExpr(getSMinExpr(LS, RS), LDiff);
5365 }
5366 break;
5367 case ICmpInst::ICMP_ULT:
5368 case ICmpInst::ICMP_ULE:
5369 std::swap(LHS, RHS);
5370 LLVM_FALLTHROUGH[[gnu::fallthrough]];
5371 case ICmpInst::ICMP_UGT:
5372 case ICmpInst::ICMP_UGE:
5373 // a >u b ? a+x : b+x -> umax(a, b)+x
5374 // a >u b ? b+x : a+x -> umin(a, b)+x
5375 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5376 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5377 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
5378 const SCEV *LA = getSCEV(TrueVal);
5379 const SCEV *RA = getSCEV(FalseVal);
5380 const SCEV *LDiff = getMinusSCEV(LA, LS);
5381 const SCEV *RDiff = getMinusSCEV(RA, RS);
5382 if (LDiff == RDiff)
5383 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
5384 LDiff = getMinusSCEV(LA, RS);
5385 RDiff = getMinusSCEV(RA, LS);
5386 if (LDiff == RDiff)
5387 return getAddExpr(getUMinExpr(LS, RS), LDiff);
5388 }
5389 break;
5390 case ICmpInst::ICMP_NE:
5391 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
5392 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5393 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5394 const SCEV *One = getOne(I->getType());
5395 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5396 const SCEV *LA = getSCEV(TrueVal);
5397 const SCEV *RA = getSCEV(FalseVal);
5398 const SCEV *LDiff = getMinusSCEV(LA, LS);
5399 const SCEV *RDiff = getMinusSCEV(RA, One);
5400 if (LDiff == RDiff)
5401 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5402 }
5403 break;
5404 case ICmpInst::ICMP_EQ:
5405 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
5406 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5407 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5408 const SCEV *One = getOne(I->getType());
5409 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5410 const SCEV *LA = getSCEV(TrueVal);
5411 const SCEV *RA = getSCEV(FalseVal);
5412 const SCEV *LDiff = getMinusSCEV(LA, One);
5413 const SCEV *RDiff = getMinusSCEV(RA, LS);
5414 if (LDiff == RDiff)
5415 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5416 }
5417 break;
5418 default:
5419 break;
5420 }
5421
5422 return getUnknown(I);
5423}
5424
5425/// Expand GEP instructions into add and multiply operations. This allows them
5426/// to be analyzed by regular SCEV code.
5427const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
5428 // Don't attempt to analyze GEPs over unsized objects.
5429 if (!GEP->getSourceElementType()->isSized())
5430 return getUnknown(GEP);
5431
5432 SmallVector<const SCEV *, 4> IndexExprs;
5433 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
5434 IndexExprs.push_back(getSCEV(*Index));
5435 return getGEPExpr(GEP, IndexExprs);
5436}
5437
5438uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
5439 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5440 return C->getAPInt().countTrailingZeros();
5441
5442 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
5443 return std::min(GetMinTrailingZeros(T->getOperand()),
5444 (uint32_t)getTypeSizeInBits(T->getType()));
5445
5446 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
5447 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5448 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5449 ? getTypeSizeInBits(E->getType())
5450 : OpRes;
5451 }
5452
5453 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
5454 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5455 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5456 ? getTypeSizeInBits(E->getType())
5457 : OpRes;
5458 }
5459
5460 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
5461 // The result is the min of all operands results.
5462 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5463 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5464 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5465 return MinOpRes;
5466 }
5467
5468 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
5469 // The result is the sum of all operands results.
5470 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
5471 uint32_t BitWidth = getTypeSizeInBits(M->getType());
5472 for (unsigned i = 1, e = M->getNumOperands();
5473 SumOpRes != BitWidth && i != e; ++i)
5474 SumOpRes =
5475 std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
5476 return SumOpRes;
5477 }
5478
5479 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
5480 // The result is the min of all operands results.
5481 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5482 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5483 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5484 return MinOpRes;
5485 }
5486
5487 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
5488 // The result is the min of all operands results.
5489 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5490 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5491 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5492 return MinOpRes;
5493 }
5494
5495 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
5496 // The result is the min of all operands results.
5497 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5498 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5499 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5500 return MinOpRes;
5501 }
5502
5503 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5504 // For a SCEVUnknown, ask ValueTracking.
5505 KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
5506 return Known.countMinTrailingZeros();
5507 }
5508
5509 // SCEVUDivExpr
5510 return 0;
5511}
5512
5513uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
5514 auto I = MinTrailingZerosCache.find(S);
5515 if (I != MinTrailingZerosCache.end())
5516 return I->second;
5517
5518 uint32_t Result = GetMinTrailingZerosImpl(S);
5519 auto InsertPair = MinTrailingZerosCache.insert({S, Result});
5520 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 5520, __PRETTY_FUNCTION__))
;
5521 return InsertPair.first->second;
5522}
5523
5524/// Helper method to assign a range to V from metadata present in the IR.
5525static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
5526 if (Instruction *I = dyn_cast<Instruction>(V))
5527 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
5528 return getConstantRangeFromMetadata(*MD);
5529
5530 return None;
5531}
5532
5533/// Determine the range for a particular SCEV. If SignHint is
5534/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
5535/// with a "cleaner" unsigned (resp. signed) representation.
5536const ConstantRange &
5537ScalarEvolution::getRangeRef(const SCEV *S,
5538 ScalarEvolution::RangeSignHint SignHint) {
5539 DenseMap<const SCEV *, ConstantRange> &Cache =
5540 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
5541 : SignedRanges;
5542 ConstantRange::PreferredRangeType RangeType =
5543 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED
5544 ? ConstantRange::Unsigned : ConstantRange::Signed;
5545
5546 // See if we've computed this range already.
5547 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
5548 if (I != Cache.end())
5549 return I->second;
5550
5551 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5552 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
5553
5554 unsigned BitWidth = getTypeSizeInBits(S->getType());
5555 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
5556
5557 // If the value has known zeros, the maximum value will have those known zeros
5558 // as well.
5559 uint32_t TZ = GetMinTrailingZeros(S);
5560 if (TZ != 0) {
5561 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
5562 ConservativeResult =
5563 ConstantRange(APInt::getMinValue(BitWidth),
5564 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
5565 else
5566 ConservativeResult = ConstantRange(
5567 APInt::getSignedMinValue(BitWidth),
5568 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
5569 }
5570
5571 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
5572 ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
5573 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
5574 X = X.add(getRangeRef(Add->getOperand(i), SignHint));
5575 return setRange(Add, SignHint,
5576 ConservativeResult.intersectWith(X, RangeType));
5577 }
5578
5579 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
5580 ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
5581 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
5582 X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
5583 return setRange(Mul, SignHint,
5584 ConservativeResult.intersectWith(X, RangeType));
5585 }
5586
5587 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
5588 ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
5589 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
5590 X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
5591 return setRange(SMax, SignHint,
5592 ConservativeResult.intersectWith(X, RangeType));
5593 }
5594
5595 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
5596 ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
5597 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
5598 X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
5599 return setRange(UMax, SignHint,
5600 ConservativeResult.intersectWith(X, RangeType));
5601 }
5602
5603 if (const SCEVSMinExpr *SMin = dyn_cast<SCEVSMinExpr>(S)) {
5604 ConstantRange X = getRangeRef(SMin->getOperand(0), SignHint);
5605 for (unsigned i = 1, e = SMin->getNumOperands(); i != e; ++i)
5606 X = X.smin(getRangeRef(SMin->getOperand(i), SignHint));
5607 return setRange(SMin, SignHint,
5608 ConservativeResult.intersectWith(X, RangeType));
5609 }
5610
5611 if (const SCEVUMinExpr *UMin = dyn_cast<SCEVUMinExpr>(S)) {
5612 ConstantRange X = getRangeRef(UMin->getOperand(0), SignHint);
5613 for (unsigned i = 1, e = UMin->getNumOperands(); i != e; ++i)
5614 X = X.umin(getRangeRef(UMin->getOperand(i), SignHint));
5615 return setRange(UMin, SignHint,
5616 ConservativeResult.intersectWith(X, RangeType));
5617 }
5618
5619 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
5620 ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
5621 ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
5622 return setRange(UDiv, SignHint,
5623 ConservativeResult.intersectWith(X.udiv(Y), RangeType));
5624 }
5625
5626 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
5627 ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
5628 return setRange(ZExt, SignHint,
5629 ConservativeResult.intersectWith(X.zeroExtend(BitWidth),
5630 RangeType));
5631 }
5632
5633 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
5634 ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
5635 return setRange(SExt, SignHint,
5636 ConservativeResult.intersectWith(X.signExtend(BitWidth),
5637 RangeType));
5638 }
5639
5640 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
5641 ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
5642 return setRange(Trunc, SignHint,
5643 ConservativeResult.intersectWith(X.truncate(BitWidth),
5644 RangeType));
5645 }
5646
5647 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
5648 // If there's no unsigned wrap, the value will never be less than its
5649 // initial value.
5650 if (AddRec->hasNoUnsignedWrap())
5651 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
5652 if (!C->getValue()->isZero())
5653 ConservativeResult = ConservativeResult.intersectWith(
5654 ConstantRange(C->getAPInt(), APInt(BitWidth, 0)), RangeType);
5655
5656 // If there's no signed wrap, and all the operands have the same sign or
5657 // zero, the value won't ever change sign.
5658 if (AddRec->hasNoSignedWrap()) {
5659 bool AllNonNeg = true;
5660 bool AllNonPos = true;
5661 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5662 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
5663 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
5664 }
5665 if (AllNonNeg)
5666 ConservativeResult = ConservativeResult.intersectWith(
5667 ConstantRange(APInt(BitWidth, 0),
5668 APInt::getSignedMinValue(BitWidth)), RangeType);
5669 else if (AllNonPos)
5670 ConservativeResult = ConservativeResult.intersectWith(
5671 ConstantRange(APInt::getSignedMinValue(BitWidth),
5672 APInt(BitWidth, 1)), RangeType);
5673 }
5674
5675 // TODO: non-affine addrec
5676 if (AddRec->isAffine()) {
5677 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(AddRec->getLoop());
5678 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
5679 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
5680 auto RangeFromAffine = getRangeForAffineAR(
5681 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5682 BitWidth);
5683 if (!RangeFromAffine.isFullSet())
5684 ConservativeResult =
5685 ConservativeResult.intersectWith(RangeFromAffine, RangeType);
5686
5687 auto RangeFromFactoring = getRangeViaFactoring(
5688 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5689 BitWidth);
5690 if (!RangeFromFactoring.isFullSet())
5691 ConservativeResult =
5692 ConservativeResult.intersectWith(RangeFromFactoring, RangeType);
5693 }
5694 }
5695
5696 return setRange(AddRec, SignHint, std::move(ConservativeResult));
5697 }
5698
5699 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5700 // Check if the IR explicitly contains !range metadata.
5701 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
5702 if (MDRange.hasValue())
5703 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue(),
5704 RangeType);
5705
5706 // Split here to avoid paying the compile-time cost of calling both
5707 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
5708 // if needed.
5709 const DataLayout &DL = getDataLayout();
5710 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
5711 // For a SCEVUnknown, ask ValueTracking.
5712 KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5713 if (Known.One != ~Known.Zero + 1)
5714 ConservativeResult =
5715 ConservativeResult.intersectWith(
5716 ConstantRange(Known.One, ~Known.Zero + 1), RangeType);
5717 } else {
5718 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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 5719, __PRETTY_FUNCTION__))
5719 "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-10~svn374877/lib/Analysis/ScalarEvolution.cpp"
, 5719, __PRETTY_FUNCTION__))
;
5720 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);