Bug Summary

File:lib/Analysis/ScalarEvolution.cpp
Warning:line 8125, column 21
Value stored to 'MultipleInitValues' is never read

Annotated Source Code

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clang -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name ScalarEvolution.cpp -analyzer-store=region -analyzer-opt-analyze-nested-blocks -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=cplusplus -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -mthread-model posix -fmath-errno -masm-verbose -mconstructor-aliases -munwind-tables -fuse-init-array -target-cpu x86-64 -dwarf-column-info -debugger-tuning=gdb -momit-leaf-frame-pointer -ffunction-sections -fdata-sections -resource-dir /usr/lib/llvm-9/lib/clang/9.0.0 -D _DEBUG -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I /build/llvm-toolchain-snapshot-9~svn362543/build-llvm/lib/Analysis -I /build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis -I /build/llvm-toolchain-snapshot-9~svn362543/build-llvm/include -I /build/llvm-toolchain-snapshot-9~svn362543/include -U NDEBUG -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/x86_64-linux-gnu/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/x86_64-linux-gnu/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/c++/6.3.0/backward -internal-isystem /usr/include/clang/9.0.0/include/ -internal-isystem /usr/local/include -internal-isystem /usr/lib/llvm-9/lib/clang/9.0.0/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -O2 -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-maybe-uninitialized -Wno-comment -std=c++11 -fdeprecated-macro -fdebug-compilation-dir /build/llvm-toolchain-snapshot-9~svn362543/build-llvm/lib/Analysis -fdebug-prefix-map=/build/llvm-toolchain-snapshot-9~svn362543=. -ferror-limit 19 -fmessage-length 0 -fvisibility-inlines-hidden -stack-protector 2 -fobjc-runtime=gcc -fdiagnostics-show-option -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -o /tmp/scan-build-2019-06-05-060531-1271-1 -x c++ /build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp -faddrsig
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"
, {0}, {false}}
141 "Number of trip counts computed with array length")static llvm::Statistic NumArrayLenItCounts = {"scalar-evolution"
, "NumArrayLenItCounts", "Number of trip counts computed with array length"
, {0}, {false}}
;
142STATISTIC(NumTripCountsComputed,static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
, {0}, {false}}
143 "Number of loops with predictable loop counts")static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
, {0}, {false}}
;
144STATISTIC(NumTripCountsNotComputed,static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
, {0}, {false}}
145 "Number of loops without predictable loop counts")static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
, {0}, {false}}
;
146STATISTIC(NumBruteForceTripCountsComputed,static llvm::Statistic NumBruteForceTripCountsComputed = {"scalar-evolution"
, "NumBruteForceTripCountsComputed", "Number of loops with trip counts computed by force"
, {0}, {false}}
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"
, {0}, {false}}
;
148
149static cl::opt<unsigned>
150MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
151 cl::desc("Maximum number of iterations SCEV will "
152 "symbolically execute a constant "
153 "derived loop"),
154 cl::init(100));
155
156// FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
157static cl::opt<bool> VerifySCEV(
158 "verify-scev", cl::Hidden,
159 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
160static cl::opt<bool>
161 VerifySCEVMap("verify-scev-maps", cl::Hidden,
162 cl::desc("Verify no dangling value in ScalarEvolution's "
163 "ExprValueMap (slow)"));
164
165static cl::opt<bool> VerifyIR(
166 "scev-verify-ir", cl::Hidden,
167 cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
168 cl::init(false));
169
170static cl::opt<unsigned> MulOpsInlineThreshold(
171 "scev-mulops-inline-threshold", cl::Hidden,
172 cl::desc("Threshold for inlining multiplication operands into a SCEV"),
173 cl::init(32));
174
175static cl::opt<unsigned> AddOpsInlineThreshold(
176 "scev-addops-inline-threshold", cl::Hidden,
177 cl::desc("Threshold for inlining addition operands into a SCEV"),
178 cl::init(500));
179
180static cl::opt<unsigned> MaxSCEVCompareDepth(
181 "scalar-evolution-max-scev-compare-depth", cl::Hidden,
182 cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
183 cl::init(32));
184
185static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
186 "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
187 cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
188 cl::init(2));
189
190static cl::opt<unsigned> MaxValueCompareDepth(
191 "scalar-evolution-max-value-compare-depth", cl::Hidden,
192 cl::desc("Maximum depth of recursive value complexity comparisons"),
193 cl::init(2));
194
195static cl::opt<unsigned>
196 MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
197 cl::desc("Maximum depth of recursive arithmetics"),
198 cl::init(32));
199
200static cl::opt<unsigned> MaxConstantEvolvingDepth(
201 "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
202 cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
203
204static cl::opt<unsigned>
205 MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
206 cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
207 cl::init(8));
208
209static cl::opt<unsigned>
210 MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
211 cl::desc("Max coefficients in AddRec during evolving"),
212 cl::init(8));
213
214static cl::opt<unsigned>
215 HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
216 cl::desc("Size of the expression which is considered huge"),
217 cl::init(4096));
218
219//===----------------------------------------------------------------------===//
220// SCEV class definitions
221//===----------------------------------------------------------------------===//
222
223//===----------------------------------------------------------------------===//
224// Implementation of the SCEV class.
225//
226
227#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
228LLVM_DUMP_METHOD__attribute__((noinline)) __attribute__((__used__)) void SCEV::dump() const {
229 print(dbgs());
230 dbgs() << '\n';
231}
232#endif
233
234void SCEV::print(raw_ostream &OS) const {
235 switch (static_cast<SCEVTypes>(getSCEVType())) {
236 case scConstant:
237 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
238 return;
239 case scTruncate: {
240 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
241 const SCEV *Op = Trunc->getOperand();
242 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
243 << *Trunc->getType() << ")";
244 return;
245 }
246 case scZeroExtend: {
247 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
248 const SCEV *Op = ZExt->getOperand();
249 OS << "(zext " << *Op->getType() << " " << *Op << " to "
250 << *ZExt->getType() << ")";
251 return;
252 }
253 case scSignExtend: {
254 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
255 const SCEV *Op = SExt->getOperand();
256 OS << "(sext " << *Op->getType() << " " << *Op << " to "
257 << *SExt->getType() << ")";
258 return;
259 }
260 case scAddRecExpr: {
261 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
262 OS << "{" << *AR->getOperand(0);
263 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
264 OS << ",+," << *AR->getOperand(i);
265 OS << "}<";
266 if (AR->hasNoUnsignedWrap())
267 OS << "nuw><";
268 if (AR->hasNoSignedWrap())
269 OS << "nsw><";
270 if (AR->hasNoSelfWrap() &&
271 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
272 OS << "nw><";
273 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
274 OS << ">";
275 return;
276 }
277 case scAddExpr:
278 case scMulExpr:
279 case scUMaxExpr:
280 case scSMaxExpr:
281 case scUMinExpr:
282 case scSMinExpr: {
283 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
284 const char *OpStr = nullptr;
285 switch (NAry->getSCEVType()) {
286 case scAddExpr: OpStr = " + "; break;
287 case scMulExpr: OpStr = " * "; break;
288 case scUMaxExpr: OpStr = " umax "; break;
289 case scSMaxExpr: OpStr = " smax "; break;
290 case scUMinExpr:
291 OpStr = " umin ";
292 break;
293 case scSMinExpr:
294 OpStr = " smin ";
295 break;
296 }
297 OS << "(";
298 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
299 I != E; ++I) {
300 OS << **I;
301 if (std::next(I) != E)
302 OS << OpStr;
303 }
304 OS << ")";
305 switch (NAry->getSCEVType()) {
306 case scAddExpr:
307 case scMulExpr:
308 if (NAry->hasNoUnsignedWrap())
309 OS << "<nuw>";
310 if (NAry->hasNoSignedWrap())
311 OS << "<nsw>";
312 }
313 return;
314 }
315 case scUDivExpr: {
316 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
317 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
318 return;
319 }
320 case scUnknown: {
321 const SCEVUnknown *U = cast<SCEVUnknown>(this);
322 Type *AllocTy;
323 if (U->isSizeOf(AllocTy)) {
324 OS << "sizeof(" << *AllocTy << ")";
325 return;
326 }
327 if (U->isAlignOf(AllocTy)) {
328 OS << "alignof(" << *AllocTy << ")";
329 return;
330 }
331
332 Type *CTy;
333 Constant *FieldNo;
334 if (U->isOffsetOf(CTy, FieldNo)) {
335 OS << "offsetof(" << *CTy << ", ";
336 FieldNo->printAsOperand(OS, false);
337 OS << ")";
338 return;
339 }
340
341 // Otherwise just print it normally.
342 U->getValue()->printAsOperand(OS, false);
343 return;
344 }
345 case scCouldNotCompute:
346 OS << "***COULDNOTCOMPUTE***";
347 return;
348 }
349 llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 349)
;
350}
351
352Type *SCEV::getType() const {
353 switch (static_cast<SCEVTypes>(getSCEVType())) {
354 case scConstant:
355 return cast<SCEVConstant>(this)->getType();
356 case scTruncate:
357 case scZeroExtend:
358 case scSignExtend:
359 return cast<SCEVCastExpr>(this)->getType();
360 case scAddRecExpr:
361 case scMulExpr:
362 case scUMaxExpr:
363 case scSMaxExpr:
364 case scUMinExpr:
365 case scSMinExpr:
366 return cast<SCEVNAryExpr>(this)->getType();
367 case scAddExpr:
368 return cast<SCEVAddExpr>(this)->getType();
369 case scUDivExpr:
370 return cast<SCEVUDivExpr>(this)->getType();
371 case scUnknown:
372 return cast<SCEVUnknown>(this)->getType();
373 case scCouldNotCompute:
374 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 374)
;
375 }
376 llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 376)
;
377}
378
379bool SCEV::isZero() const {
380 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
381 return SC->getValue()->isZero();
382 return false;
383}
384
385bool SCEV::isOne() const {
386 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
387 return SC->getValue()->isOne();
388 return false;
389}
390
391bool SCEV::isAllOnesValue() const {
392 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
393 return SC->getValue()->isMinusOne();
394 return false;
395}
396
397bool SCEV::isNonConstantNegative() const {
398 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
399 if (!Mul) return false;
400
401 // If there is a constant factor, it will be first.
402 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
403 if (!SC) return false;
404
405 // Return true if the value is negative, this matches things like (-42 * V).
406 return SC->getAPInt().isNegative();
407}
408
409SCEVCouldNotCompute::SCEVCouldNotCompute() :
410 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {}
411
412bool SCEVCouldNotCompute::classof(const SCEV *S) {
413 return S->getSCEVType() == scCouldNotCompute;
414}
415
416const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
417 FoldingSetNodeID ID;
418 ID.AddInteger(scConstant);
419 ID.AddPointer(V);
420 void *IP = nullptr;
421 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
422 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
423 UniqueSCEVs.InsertNode(S, IP);
424 return S;
425}
426
427const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
428 return getConstant(ConstantInt::get(getContext(), Val));
429}
430
431const SCEV *
432ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
433 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
434 return getConstant(ConstantInt::get(ITy, V, isSigned));
435}
436
437SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
438 unsigned SCEVTy, const SCEV *op, Type *ty)
439 : SCEV(ID, SCEVTy, computeExpressionSize(op)), Op(op), Ty(ty) {}
440
441SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
442 const SCEV *op, Type *ty)
443 : SCEVCastExpr(ID, scTruncate, op, ty) {
444 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 445, __PRETTY_FUNCTION__))
445 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 445, __PRETTY_FUNCTION__))
;
446}
447
448SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
449 const SCEV *op, Type *ty)
450 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
451 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 452, __PRETTY_FUNCTION__))
452 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 452, __PRETTY_FUNCTION__))
;
453}
454
455SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
456 const SCEV *op, Type *ty)
457 : SCEVCastExpr(ID, scSignExtend, op, ty) {
458 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 459, __PRETTY_FUNCTION__))
459 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 459, __PRETTY_FUNCTION__))
;
460}
461
462void SCEVUnknown::deleted() {
463 // Clear this SCEVUnknown from various maps.
464 SE->forgetMemoizedResults(this);
465
466 // Remove this SCEVUnknown from the uniquing map.
467 SE->UniqueSCEVs.RemoveNode(this);
468
469 // Release the value.
470 setValPtr(nullptr);
471}
472
473void SCEVUnknown::allUsesReplacedWith(Value *New) {
474 // Remove this SCEVUnknown from the uniquing map.
475 SE->UniqueSCEVs.RemoveNode(this);
476
477 // Update this SCEVUnknown to point to the new value. This is needed
478 // because there may still be outstanding SCEVs which still point to
479 // this SCEVUnknown.
480 setValPtr(New);
481}
482
483bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
484 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
485 if (VCE->getOpcode() == Instruction::PtrToInt)
486 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
487 if (CE->getOpcode() == Instruction::GetElementPtr &&
488 CE->getOperand(0)->isNullValue() &&
489 CE->getNumOperands() == 2)
490 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
491 if (CI->isOne()) {
492 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
493 ->getElementType();
494 return true;
495 }
496
497 return false;
498}
499
500bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
501 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
502 if (VCE->getOpcode() == Instruction::PtrToInt)
503 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
504 if (CE->getOpcode() == Instruction::GetElementPtr &&
505 CE->getOperand(0)->isNullValue()) {
506 Type *Ty =
507 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
508 if (StructType *STy = dyn_cast<StructType>(Ty))
509 if (!STy->isPacked() &&
510 CE->getNumOperands() == 3 &&
511 CE->getOperand(1)->isNullValue()) {
512 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
513 if (CI->isOne() &&
514 STy->getNumElements() == 2 &&
515 STy->getElementType(0)->isIntegerTy(1)) {
516 AllocTy = STy->getElementType(1);
517 return true;
518 }
519 }
520 }
521
522 return false;
523}
524
525bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
526 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
527 if (VCE->getOpcode() == Instruction::PtrToInt)
528 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
529 if (CE->getOpcode() == Instruction::GetElementPtr &&
530 CE->getNumOperands() == 3 &&
531 CE->getOperand(0)->isNullValue() &&
532 CE->getOperand(1)->isNullValue()) {
533 Type *Ty =
534 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
535 // Ignore vector types here so that ScalarEvolutionExpander doesn't
536 // emit getelementptrs that index into vectors.
537 if (Ty->isStructTy() || Ty->isArrayTy()) {
538 CTy = Ty;
539 FieldNo = CE->getOperand(2);
540 return true;
541 }
542 }
543
544 return false;
545}
546
547//===----------------------------------------------------------------------===//
548// SCEV Utilities
549//===----------------------------------------------------------------------===//
550
551/// Compare the two values \p LV and \p RV in terms of their "complexity" where
552/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
553/// operands in SCEV expressions. \p EqCache is a set of pairs of values that
554/// have been previously deemed to be "equally complex" by this routine. It is
555/// intended to avoid exponential time complexity in cases like:
556///
557/// %a = f(%x, %y)
558/// %b = f(%a, %a)
559/// %c = f(%b, %b)
560///
561/// %d = f(%x, %y)
562/// %e = f(%d, %d)
563/// %f = f(%e, %e)
564///
565/// CompareValueComplexity(%f, %c)
566///
567/// Since we do not continue running this routine on expression trees once we
568/// have seen unequal values, there is no need to track them in the cache.
569static int
570CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
571 const LoopInfo *const LI, Value *LV, Value *RV,
572 unsigned Depth) {
573 if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
574 return 0;
575
576 // Order pointer values after integer values. This helps SCEVExpander form
577 // GEPs.
578 bool LIsPointer = LV->getType()->isPointerTy(),
579 RIsPointer = RV->getType()->isPointerTy();
580 if (LIsPointer != RIsPointer)
581 return (int)LIsPointer - (int)RIsPointer;
582
583 // Compare getValueID values.
584 unsigned LID = LV->getValueID(), RID = RV->getValueID();
585 if (LID != RID)
586 return (int)LID - (int)RID;
587
588 // Sort arguments by their position.
589 if (const auto *LA = dyn_cast<Argument>(LV)) {
590 const auto *RA = cast<Argument>(RV);
591 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
592 return (int)LArgNo - (int)RArgNo;
593 }
594
595 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
596 const auto *RGV = cast<GlobalValue>(RV);
597
598 const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
599 auto LT = GV->getLinkage();
600 return !(GlobalValue::isPrivateLinkage(LT) ||
601 GlobalValue::isInternalLinkage(LT));
602 };
603
604 // Use the names to distinguish the two values, but only if the
605 // names are semantically important.
606 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
607 return LGV->getName().compare(RGV->getName());
608 }
609
610 // For instructions, compare their loop depth, and their operand count. This
611 // is pretty loose.
612 if (const auto *LInst = dyn_cast<Instruction>(LV)) {
613 const auto *RInst = cast<Instruction>(RV);
614
615 // Compare loop depths.
616 const BasicBlock *LParent = LInst->getParent(),
617 *RParent = RInst->getParent();
618 if (LParent != RParent) {
619 unsigned LDepth = LI->getLoopDepth(LParent),
620 RDepth = LI->getLoopDepth(RParent);
621 if (LDepth != RDepth)
622 return (int)LDepth - (int)RDepth;
623 }
624
625 // Compare the number of operands.
626 unsigned LNumOps = LInst->getNumOperands(),
627 RNumOps = RInst->getNumOperands();
628 if (LNumOps != RNumOps)
629 return (int)LNumOps - (int)RNumOps;
630
631 for (unsigned Idx : seq(0u, LNumOps)) {
632 int Result =
633 CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
634 RInst->getOperand(Idx), Depth + 1);
635 if (Result != 0)
636 return Result;
637 }
638 }
639
640 EqCacheValue.unionSets(LV, RV);
641 return 0;
642}
643
644// Return negative, zero, or positive, if LHS is less than, equal to, or greater
645// than RHS, respectively. A three-way result allows recursive comparisons to be
646// more efficient.
647static int CompareSCEVComplexity(
648 EquivalenceClasses<const SCEV *> &EqCacheSCEV,
649 EquivalenceClasses<const Value *> &EqCacheValue,
650 const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
651 DominatorTree &DT, unsigned Depth = 0) {
652 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
653 if (LHS == RHS)
654 return 0;
655
656 // Primarily, sort the SCEVs by their getSCEVType().
657 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
658 if (LType != RType)
659 return (int)LType - (int)RType;
660
661 if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS))
662 return 0;
663 // Aside from the getSCEVType() ordering, the particular ordering
664 // isn't very important except that it's beneficial to be consistent,
665 // so that (a + b) and (b + a) don't end up as different expressions.
666 switch (static_cast<SCEVTypes>(LType)) {
667 case scUnknown: {
668 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
669 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
670
671 int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
672 RU->getValue(), Depth + 1);
673 if (X == 0)
674 EqCacheSCEV.unionSets(LHS, RHS);
675 return X;
676 }
677
678 case scConstant: {
679 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
680 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
681
682 // Compare constant values.
683 const APInt &LA = LC->getAPInt();
684 const APInt &RA = RC->getAPInt();
685 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
686 if (LBitWidth != RBitWidth)
687 return (int)LBitWidth - (int)RBitWidth;
688 return LA.ult(RA) ? -1 : 1;
689 }
690
691 case scAddRecExpr: {
692 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
693 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
694
695 // There is always a dominance between two recs that are used by one SCEV,
696 // so we can safely sort recs by loop header dominance. We require such
697 // order in getAddExpr.
698 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
699 if (LLoop != RLoop) {
700 const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
701 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 701, __PRETTY_FUNCTION__))
;
702 if (DT.dominates(LHead, RHead))
703 return 1;
704 else
705 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 706, __PRETTY_FUNCTION__))
706 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 706, __PRETTY_FUNCTION__))
;
707 return -1;
708 }
709
710 // Addrec complexity grows with operand count.
711 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
712 if (LNumOps != RNumOps)
713 return (int)LNumOps - (int)RNumOps;
714
715 // Lexicographically compare.
716 for (unsigned i = 0; i != LNumOps; ++i) {
717 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
718 LA->getOperand(i), RA->getOperand(i), DT,
719 Depth + 1);
720 if (X != 0)
721 return X;
722 }
723 EqCacheSCEV.unionSets(LHS, RHS);
724 return 0;
725 }
726
727 case scAddExpr:
728 case scMulExpr:
729 case scSMaxExpr:
730 case scUMaxExpr:
731 case scSMinExpr:
732 case scUMinExpr: {
733 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
734 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
735
736 // Lexicographically compare n-ary expressions.
737 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
738 if (LNumOps != RNumOps)
739 return (int)LNumOps - (int)RNumOps;
740
741 for (unsigned i = 0; i != LNumOps; ++i) {
742 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
743 LC->getOperand(i), RC->getOperand(i), DT,
744 Depth + 1);
745 if (X != 0)
746 return X;
747 }
748 EqCacheSCEV.unionSets(LHS, RHS);
749 return 0;
750 }
751
752 case scUDivExpr: {
753 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
754 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
755
756 // Lexicographically compare udiv expressions.
757 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
758 RC->getLHS(), DT, Depth + 1);
759 if (X != 0)
760 return X;
761 X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
762 RC->getRHS(), DT, Depth + 1);
763 if (X == 0)
764 EqCacheSCEV.unionSets(LHS, RHS);
765 return X;
766 }
767
768 case scTruncate:
769 case scZeroExtend:
770 case scSignExtend: {
771 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
772 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
773
774 // Compare cast expressions by operand.
775 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
776 LC->getOperand(), RC->getOperand(), DT,
777 Depth + 1);
778 if (X == 0)
779 EqCacheSCEV.unionSets(LHS, RHS);
780 return X;
781 }
782
783 case scCouldNotCompute:
784 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 784)
;
785 }
786 llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 786)
;
787}
788
789/// Given a list of SCEV objects, order them by their complexity, and group
790/// objects of the same complexity together by value. When this routine is
791/// finished, we know that any duplicates in the vector are consecutive and that
792/// complexity is monotonically increasing.
793///
794/// Note that we go take special precautions to ensure that we get deterministic
795/// results from this routine. In other words, we don't want the results of
796/// this to depend on where the addresses of various SCEV objects happened to
797/// land in memory.
798static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
799 LoopInfo *LI, DominatorTree &DT) {
800 if (Ops.size() < 2) return; // Noop
801
802 EquivalenceClasses<const SCEV *> EqCacheSCEV;
803 EquivalenceClasses<const Value *> EqCacheValue;
804 if (Ops.size() == 2) {
805 // This is the common case, which also happens to be trivially simple.
806 // Special case it.
807 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
808 if (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0)
809 std::swap(LHS, RHS);
810 return;
811 }
812
813 // Do the rough sort by complexity.
814 llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) {
815 return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT) <
816 0;
817 });
818
819 // Now that we are sorted by complexity, group elements of the same
820 // complexity. Note that this is, at worst, N^2, but the vector is likely to
821 // be extremely short in practice. Note that we take this approach because we
822 // do not want to depend on the addresses of the objects we are grouping.
823 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
824 const SCEV *S = Ops[i];
825 unsigned Complexity = S->getSCEVType();
826
827 // If there are any objects of the same complexity and same value as this
828 // one, group them.
829 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
830 if (Ops[j] == S) { // Found a duplicate.
831 // Move it to immediately after i'th element.
832 std::swap(Ops[i+1], Ops[j]);
833 ++i; // no need to rescan it.
834 if (i == e-2) return; // Done!
835 }
836 }
837 }
838}
839
840// Returns the size of the SCEV S.
841static inline int sizeOfSCEV(const SCEV *S) {
842 struct FindSCEVSize {
843 int Size = 0;
844
845 FindSCEVSize() = default;
846
847 bool follow(const SCEV *S) {
848 ++Size;
849 // Keep looking at all operands of S.
850 return true;
851 }
852
853 bool isDone() const {
854 return false;
855 }
856 };
857
858 FindSCEVSize F;
859 SCEVTraversal<FindSCEVSize> ST(F);
860 ST.visitAll(S);
861 return F.Size;
862}
863
864/// Returns true if the subtree of \p S contains at least HugeExprThreshold
865/// nodes.
866static bool isHugeExpression(const SCEV *S) {
867 return S->getExpressionSize() >= HugeExprThreshold;
868}
869
870/// Returns true of \p Ops contains a huge SCEV (see definition above).
871static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) {
872 return any_of(Ops, isHugeExpression);
873}
874
875namespace {
876
877struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
878public:
879 // Computes the Quotient and Remainder of the division of Numerator by
880 // Denominator.
881 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
882 const SCEV *Denominator, const SCEV **Quotient,
883 const SCEV **Remainder) {
884 assert(Numerator && Denominator && "Uninitialized SCEV")((Numerator && Denominator && "Uninitialized SCEV"
) ? static_cast<void> (0) : __assert_fail ("Numerator && Denominator && \"Uninitialized SCEV\""
, "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 884, __PRETTY_FUNCTION__))
;
885
886 SCEVDivision D(SE, Numerator, Denominator);
887
888 // Check for the trivial case here to avoid having to check for it in the
889 // rest of the code.
890 if (Numerator == Denominator) {
891 *Quotient = D.One;
892 *Remainder = D.Zero;
893 return;
894 }
895
896 if (Numerator->isZero()) {
897 *Quotient = D.Zero;
898 *Remainder = D.Zero;
899 return;
900 }
901
902 // A simple case when N/1. The quotient is N.
903 if (Denominator->isOne()) {
904 *Quotient = Numerator;
905 *Remainder = D.Zero;
906 return;
907 }
908
909 // Split the Denominator when it is a product.
910 if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
911 const SCEV *Q, *R;
912 *Quotient = Numerator;
913 for (const SCEV *Op : T->operands()) {
914 divide(SE, *Quotient, Op, &Q, &R);
915 *Quotient = Q;
916
917 // Bail out when the Numerator is not divisible by one of the terms of
918 // the Denominator.
919 if (!R->isZero()) {
920 *Quotient = D.Zero;
921 *Remainder = Numerator;
922 return;
923 }
924 }
925 *Remainder = D.Zero;
926 return;
927 }
928
929 D.visit(Numerator);
930 *Quotient = D.Quotient;
931 *Remainder = D.Remainder;
932 }
933
934 // Except in the trivial case described above, we do not know how to divide
935 // Expr by Denominator for the following functions with empty implementation.
936 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
937 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
938 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
939 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
940 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
941 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
942 void visitSMinExpr(const SCEVSMinExpr *Numerator) {}
943 void visitUMinExpr(const SCEVUMinExpr *Numerator) {}
944 void visitUnknown(const SCEVUnknown *Numerator) {}
945 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
946
947 void visitConstant(const SCEVConstant *Numerator) {
948 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
949 APInt NumeratorVal = Numerator->getAPInt();
950 APInt DenominatorVal = D->getAPInt();
951 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
952 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
953
954 if (NumeratorBW > DenominatorBW)
955 DenominatorVal = DenominatorVal.sext(NumeratorBW);
956 else if (NumeratorBW < DenominatorBW)
957 NumeratorVal = NumeratorVal.sext(DenominatorBW);
958
959 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
960 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
961 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
962 Quotient = SE.getConstant(QuotientVal);
963 Remainder = SE.getConstant(RemainderVal);
964 return;
965 }
966 }
967
968 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
969 const SCEV *StartQ, *StartR, *StepQ, *StepR;
970 if (!Numerator->isAffine())
971 return cannotDivide(Numerator);
972 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
973 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
974 // Bail out if the types do not match.
975 Type *Ty = Denominator->getType();
976 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
977 Ty != StepQ->getType() || Ty != StepR->getType())
978 return cannotDivide(Numerator);
979 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
980 Numerator->getNoWrapFlags());
981 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
982 Numerator->getNoWrapFlags());
983 }
984
985 void visitAddExpr(const SCEVAddExpr *Numerator) {
986 SmallVector<const SCEV *, 2> Qs, Rs;
987 Type *Ty = Denominator->getType();
988
989 for (const SCEV *Op : Numerator->operands()) {
990 const SCEV *Q, *R;
991 divide(SE, Op, Denominator, &Q, &R);
992
993 // Bail out if types do not match.
994 if (Ty != Q->getType() || Ty != R->getType())
995 return cannotDivide(Numerator);
996
997 Qs.push_back(Q);
998 Rs.push_back(R);
999 }
1000
1001 if (Qs.size() == 1) {
1002 Quotient = Qs[0];
1003 Remainder = Rs[0];
1004 return;
1005 }
1006
1007 Quotient = SE.getAddExpr(Qs);
1008 Remainder = SE.getAddExpr(Rs);
1009 }
1010
1011 void visitMulExpr(const SCEVMulExpr *Numerator) {
1012 SmallVector<const SCEV *, 2> Qs;
1013 Type *Ty = Denominator->getType();
1014
1015 bool FoundDenominatorTerm = false;
1016 for (const SCEV *Op : Numerator->operands()) {
1017 // Bail out if types do not match.
1018 if (Ty != Op->getType())
1019 return cannotDivide(Numerator);
1020
1021 if (FoundDenominatorTerm) {
1022 Qs.push_back(Op);
1023 continue;
1024 }
1025
1026 // Check whether Denominator divides one of the product operands.
1027 const SCEV *Q, *R;
1028 divide(SE, Op, Denominator, &Q, &R);
1029 if (!R->isZero()) {
1030 Qs.push_back(Op);
1031 continue;
1032 }
1033
1034 // Bail out if types do not match.
1035 if (Ty != Q->getType())
1036 return cannotDivide(Numerator);
1037
1038 FoundDenominatorTerm = true;
1039 Qs.push_back(Q);
1040 }
1041
1042 if (FoundDenominatorTerm) {
1043 Remainder = Zero;
1044 if (Qs.size() == 1)
1045 Quotient = Qs[0];
1046 else
1047 Quotient = SE.getMulExpr(Qs);
1048 return;
1049 }
1050
1051 if (!isa<SCEVUnknown>(Denominator))
1052 return cannotDivide(Numerator);
1053
1054 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
1055 ValueToValueMap RewriteMap;
1056 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1057 cast<SCEVConstant>(Zero)->getValue();
1058 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1059
1060 if (Remainder->isZero()) {
1061 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
1062 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1063 cast<SCEVConstant>(One)->getValue();
1064 Quotient =
1065 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1066 return;
1067 }
1068
1069 // Quotient is (Numerator - Remainder) divided by Denominator.
1070 const SCEV *Q, *R;
1071 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
1072 // This SCEV does not seem to simplify: fail the division here.
1073 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
1074 return cannotDivide(Numerator);
1075 divide(SE, Diff, Denominator, &Q, &R);
1076 if (R != Zero)
1077 return cannotDivide(Numerator);
1078 Quotient = Q;
1079 }
1080
1081private:
1082 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
1083 const SCEV *Denominator)
1084 : SE(S), Denominator(Denominator) {
1085 Zero = SE.getZero(Denominator->getType());
1086 One = SE.getOne(Denominator->getType());
1087
1088 // We generally do not know how to divide Expr by Denominator. We
1089 // initialize the division to a "cannot divide" state to simplify the rest
1090 // of the code.
1091 cannotDivide(Numerator);
1092 }
1093
1094 // Convenience function for giving up on the division. We set the quotient to
1095 // be equal to zero and the remainder to be equal to the numerator.
1096 void cannotDivide(const SCEV *Numerator) {
1097 Quotient = Zero;
1098 Remainder = Numerator;
1099 }
1100
1101 ScalarEvolution &SE;
1102 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
1103};
1104
1105} // end anonymous namespace
1106
1107//===----------------------------------------------------------------------===//
1108// Simple SCEV method implementations
1109//===----------------------------------------------------------------------===//
1110
1111/// Compute BC(It, K). The result has width W. Assume, K > 0.
1112static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
1113 ScalarEvolution &SE,
1114 Type *ResultTy) {
1115 // Handle the simplest case efficiently.
1116 if (K == 1)
1117 return SE.getTruncateOrZeroExtend(It, ResultTy);
1118
1119 // We are using the following formula for BC(It, K):
1120 //
1121 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
1122 //
1123 // Suppose, W is the bitwidth of the return value. We must be prepared for
1124 // overflow. Hence, we must assure that the result of our computation is
1125 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
1126 // safe in modular arithmetic.
1127 //
1128 // However, this code doesn't use exactly that formula; the formula it uses
1129 // is something like the following, where T is the number of factors of 2 in
1130 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
1131 // exponentiation:
1132 //
1133 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
1134 //
1135 // This formula is trivially equivalent to the previous formula. However,
1136 // this formula can be implemented much more efficiently. The trick is that
1137 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
1138 // arithmetic. To do exact division in modular arithmetic, all we have
1139 // to do is multiply by the inverse. Therefore, this step can be done at
1140 // width W.
1141 //
1142 // The next issue is how to safely do the division by 2^T. The way this
1143 // is done is by doing the multiplication step at a width of at least W + T
1144 // bits. This way, the bottom W+T bits of the product are accurate. Then,
1145 // when we perform the division by 2^T (which is equivalent to a right shift
1146 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
1147 // truncated out after the division by 2^T.
1148 //
1149 // In comparison to just directly using the first formula, this technique
1150 // is much more efficient; using the first formula requires W * K bits,
1151 // but this formula less than W + K bits. Also, the first formula requires
1152 // a division step, whereas this formula only requires multiplies and shifts.
1153 //
1154 // It doesn't matter whether the subtraction step is done in the calculation
1155 // width or the input iteration count's width; if the subtraction overflows,
1156 // the result must be zero anyway. We prefer here to do it in the width of
1157 // the induction variable because it helps a lot for certain cases; CodeGen
1158 // isn't smart enough to ignore the overflow, which leads to much less
1159 // efficient code if the width of the subtraction is wider than the native
1160 // register width.
1161 //
1162 // (It's possible to not widen at all by pulling out factors of 2 before
1163 // the multiplication; for example, K=2 can be calculated as
1164 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1165 // extra arithmetic, so it's not an obvious win, and it gets
1166 // much more complicated for K > 3.)
1167
1168 // Protection from insane SCEVs; this bound is conservative,
1169 // but it probably doesn't matter.
1170 if (K > 1000)
1171 return SE.getCouldNotCompute();
1172
1173 unsigned W = SE.getTypeSizeInBits(ResultTy);
1174
1175 // Calculate K! / 2^T and T; we divide out the factors of two before
1176 // multiplying for calculating K! / 2^T to avoid overflow.
1177 // Other overflow doesn't matter because we only care about the bottom
1178 // W bits of the result.
1179 APInt OddFactorial(W, 1);
1180 unsigned T = 1;
1181 for (unsigned i = 3; i <= K; ++i) {
1182 APInt Mult(W, i);
1183 unsigned TwoFactors = Mult.countTrailingZeros();
1184 T += TwoFactors;
1185 Mult.lshrInPlace(TwoFactors);
1186 OddFactorial *= Mult;
1187 }
1188
1189 // We need at least W + T bits for the multiplication step
1190 unsigned CalculationBits = W + T;
1191
1192 // Calculate 2^T, at width T+W.
1193 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1194
1195 // Calculate the multiplicative inverse of K! / 2^T;
1196 // this multiplication factor will perform the exact division by
1197 // K! / 2^T.
1198 APInt Mod = APInt::getSignedMinValue(W+1);
1199 APInt MultiplyFactor = OddFactorial.zext(W+1);
1200 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1201 MultiplyFactor = MultiplyFactor.trunc(W);
1202
1203 // Calculate the product, at width T+W
1204 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1205 CalculationBits);
1206 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1207 for (unsigned i = 1; i != K; ++i) {
1208 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1209 Dividend = SE.getMulExpr(Dividend,
1210 SE.getTruncateOrZeroExtend(S, CalculationTy));
1211 }
1212
1213 // Divide by 2^T
1214 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1215
1216 // Truncate the result, and divide by K! / 2^T.
1217
1218 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1219 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1220}
1221
1222/// Return the value of this chain of recurrences at the specified iteration
1223/// number. We can evaluate this recurrence by multiplying each element in the
1224/// chain by the binomial coefficient corresponding to it. In other words, we
1225/// can evaluate {A,+,B,+,C,+,D} as:
1226///
1227/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1228///
1229/// where BC(It, k) stands for binomial coefficient.
1230const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1231 ScalarEvolution &SE) const {
1232 const SCEV *Result = getStart();
1233 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1234 // The computation is correct in the face of overflow provided that the
1235 // multiplication is performed _after_ the evaluation of the binomial
1236 // coefficient.
1237 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1238 if (isa<SCEVCouldNotCompute>(Coeff))
1239 return Coeff;
1240
1241 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1242 }
1243 return Result;
1244}
1245
1246//===----------------------------------------------------------------------===//
1247// SCEV Expression folder implementations
1248//===----------------------------------------------------------------------===//
1249
1250const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
1251 unsigned Depth) {
1252 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1253, __PRETTY_FUNCTION__))
1253 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1253, __PRETTY_FUNCTION__))
;
1254 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1255, __PRETTY_FUNCTION__))
1255 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1255, __PRETTY_FUNCTION__))
;
1256 Ty = getEffectiveSCEVType(Ty);
1257
1258 FoldingSetNodeID ID;
1259 ID.AddInteger(scTruncate);
1260 ID.AddPointer(Op);
1261 ID.AddPointer(Ty);
1262 void *IP = nullptr;
1263 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1264
1265 // Fold if the operand is constant.
1266 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1267 return getConstant(
1268 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1269
1270 // trunc(trunc(x)) --> trunc(x)
1271 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1272 return getTruncateExpr(ST->getOperand(), Ty, Depth + 1);
1273
1274 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1275 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1276 return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1);
1277
1278 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1279 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1280 return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1);
1281
1282 if (Depth > MaxCastDepth) {
1283 SCEV *S =
1284 new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty);
1285 UniqueSCEVs.InsertNode(S, IP);
1286 addToLoopUseLists(S);
1287 return S;
1288 }
1289
1290 // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
1291 // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
1292 // if after transforming we have at most one truncate, not counting truncates
1293 // that replace other casts.
1294 if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
1295 auto *CommOp = cast<SCEVCommutativeExpr>(Op);
1296 SmallVector<const SCEV *, 4> Operands;
1297 unsigned numTruncs = 0;
1298 for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
1299 ++i) {
1300 const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1);
1301 if (!isa<SCEVCastExpr>(CommOp->getOperand(i)) && isa<SCEVTruncateExpr>(S))
1302 numTruncs++;
1303 Operands.push_back(S);
1304 }
1305 if (numTruncs < 2) {
1306 if (isa<SCEVAddExpr>(Op))
1307 return getAddExpr(Operands);
1308 else if (isa<SCEVMulExpr>(Op))
1309 return getMulExpr(Operands);
1310 else
1311 llvm_unreachable("Unexpected SCEV type for Op.")::llvm::llvm_unreachable_internal("Unexpected SCEV type for Op."
, "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1311)
;
1312 }
1313 // Although we checked in the beginning that ID is not in the cache, it is
1314 // possible that during recursion and different modification ID was inserted
1315 // into the cache. So if we find it, just return it.
1316 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
1317 return S;
1318 }
1319
1320 // If the input value is a chrec scev, truncate the chrec's operands.
1321 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1322 SmallVector<const SCEV *, 4> Operands;
1323 for (const SCEV *Op : AddRec->operands())
1324 Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1));
1325 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1326 }
1327
1328 // The cast wasn't folded; create an explicit cast node. We can reuse
1329 // the existing insert position since if we get here, we won't have
1330 // made any changes which would invalidate it.
1331 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1332 Op, Ty);
1333 UniqueSCEVs.InsertNode(S, IP);
1334 addToLoopUseLists(S);
1335 return S;
1336}
1337
1338// Get the limit of a recurrence such that incrementing by Step cannot cause
1339// signed overflow as long as the value of the recurrence within the
1340// loop does not exceed this limit before incrementing.
1341static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1342 ICmpInst::Predicate *Pred,
1343 ScalarEvolution *SE) {
1344 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1345 if (SE->isKnownPositive(Step)) {
1346 *Pred = ICmpInst::ICMP_SLT;
1347 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1348 SE->getSignedRangeMax(Step));
1349 }
1350 if (SE->isKnownNegative(Step)) {
1351 *Pred = ICmpInst::ICMP_SGT;
1352 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1353 SE->getSignedRangeMin(Step));
1354 }
1355 return nullptr;
1356}
1357
1358// Get the limit of a recurrence such that incrementing by Step cannot cause
1359// unsigned overflow as long as the value of the recurrence within the loop does
1360// not exceed this limit before incrementing.
1361static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1362 ICmpInst::Predicate *Pred,
1363 ScalarEvolution *SE) {
1364 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1365 *Pred = ICmpInst::ICMP_ULT;
1366
1367 return SE->getConstant(APInt::getMinValue(BitWidth) -
1368 SE->getUnsignedRangeMax(Step));
1369}
1370
1371namespace {
1372
1373struct ExtendOpTraitsBase {
1374 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
1375 unsigned);
1376};
1377
1378// Used to make code generic over signed and unsigned overflow.
1379template <typename ExtendOp> struct ExtendOpTraits {
1380 // Members present:
1381 //
1382 // static const SCEV::NoWrapFlags WrapType;
1383 //
1384 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1385 //
1386 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1387 // ICmpInst::Predicate *Pred,
1388 // ScalarEvolution *SE);
1389};
1390
1391template <>
1392struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1393 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1394
1395 static const GetExtendExprTy GetExtendExpr;
1396
1397 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1398 ICmpInst::Predicate *Pred,
1399 ScalarEvolution *SE) {
1400 return getSignedOverflowLimitForStep(Step, Pred, SE);
1401 }
1402};
1403
1404const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1405 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1406
1407template <>
1408struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1409 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1410
1411 static const GetExtendExprTy GetExtendExpr;
1412
1413 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1414 ICmpInst::Predicate *Pred,
1415 ScalarEvolution *SE) {
1416 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1417 }
1418};
1419
1420const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1421 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1422
1423} // end anonymous namespace
1424
1425// The recurrence AR has been shown to have no signed/unsigned wrap or something
1426// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1427// easily prove NSW/NUW for its preincrement or postincrement sibling. This
1428// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1429// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1430// expression "Step + sext/zext(PreIncAR)" is congruent with
1431// "sext/zext(PostIncAR)"
1432template <typename ExtendOpTy>
1433static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1434 ScalarEvolution *SE, unsigned Depth) {
1435 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1436 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1437
1438 const Loop *L = AR->getLoop();
1439 const SCEV *Start = AR->getStart();
1440 const SCEV *Step = AR->getStepRecurrence(*SE);
1441
1442 // Check for a simple looking step prior to loop entry.
1443 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1444 if (!SA)
1445 return nullptr;
1446
1447 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1448 // subtraction is expensive. For this purpose, perform a quick and dirty
1449 // difference, by checking for Step in the operand list.
1450 SmallVector<const SCEV *, 4> DiffOps;
1451 for (const SCEV *Op : SA->operands())
1452 if (Op != Step)
1453 DiffOps.push_back(Op);
1454
1455 if (DiffOps.size() == SA->getNumOperands())
1456 return nullptr;
1457
1458 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1459 // `Step`:
1460
1461 // 1. NSW/NUW flags on the step increment.
1462 auto PreStartFlags =
1463 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1464 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1465 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1466 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1467
1468 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1469 // "S+X does not sign/unsign-overflow".
1470 //
1471
1472 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1473 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1474 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1475 return PreStart;
1476
1477 // 2. Direct overflow check on the step operation's expression.
1478 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1479 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1480 const SCEV *OperandExtendedStart =
1481 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
1482 (SE->*GetExtendExpr)(Step, WideTy, Depth));
1483 if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
1484 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1485 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1486 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1487 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1488 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1489 }
1490 return PreStart;
1491 }
1492
1493 // 3. Loop precondition.
1494 ICmpInst::Predicate Pred;
1495 const SCEV *OverflowLimit =
1496 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1497
1498 if (OverflowLimit &&
1499 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1500 return PreStart;
1501
1502 return nullptr;
1503}
1504
1505// Get the normalized zero or sign extended expression for this AddRec's Start.
1506template <typename ExtendOpTy>
1507static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1508 ScalarEvolution *SE,
1509 unsigned Depth) {
1510 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1511
1512 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
1513 if (!PreStart)
1514 return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
1515
1516 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
1517 Depth),
1518 (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1519}
1520
1521// Try to prove away overflow by looking at "nearby" add recurrences. A
1522// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1523// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1524//
1525// Formally:
1526//
1527// {S,+,X} == {S-T,+,X} + T
1528// => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1529//
1530// If ({S-T,+,X} + T) does not overflow ... (1)
1531//
1532// RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1533//
1534// If {S-T,+,X} does not overflow ... (2)
1535//
1536// RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1537// == {Ext(S-T)+Ext(T),+,Ext(X)}
1538//
1539// If (S-T)+T does not overflow ... (3)
1540//
1541// RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1542// == {Ext(S),+,Ext(X)} == LHS
1543//
1544// Thus, if (1), (2) and (3) are true for some T, then
1545// Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1546//
1547// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1548// does not overflow" restricted to the 0th iteration. Therefore we only need
1549// to check for (1) and (2).
1550//
1551// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1552// is `Delta` (defined below).
1553template <typename ExtendOpTy>
1554bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1555 const SCEV *Step,
1556 const Loop *L) {
1557 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1558
1559 // We restrict `Start` to a constant to prevent SCEV from spending too much
1560 // time here. It is correct (but more expensive) to continue with a
1561 // non-constant `Start` and do a general SCEV subtraction to compute
1562 // `PreStart` below.
1563 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1564 if (!StartC)
1565 return false;
1566
1567 APInt StartAI = StartC->getAPInt();
1568
1569 for (unsigned Delta : {-2, -1, 1, 2}) {
1570 const SCEV *PreStart = getConstant(StartAI - Delta);
1571
1572 FoldingSetNodeID ID;
1573 ID.AddInteger(scAddRecExpr);
1574 ID.AddPointer(PreStart);
1575 ID.AddPointer(Step);
1576 ID.AddPointer(L);
1577 void *IP = nullptr;
1578 const auto *PreAR =
1579 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1580
1581 // Give up if we don't already have the add recurrence we need because
1582 // actually constructing an add recurrence is relatively expensive.
1583 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1584 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1585 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1586 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1587 DeltaS, &Pred, this);
1588 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1589 return true;
1590 }
1591 }
1592
1593 return false;
1594}
1595
1596// Finds an integer D for an expression (C + x + y + ...) such that the top
1597// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
1598// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
1599// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
1600// the (C + x + y + ...) expression is \p WholeAddExpr.
1601static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1602 const SCEVConstant *ConstantTerm,
1603 const SCEVAddExpr *WholeAddExpr) {
1604 const APInt C = ConstantTerm->getAPInt();
1605 const unsigned BitWidth = C.getBitWidth();
1606 // Find number of trailing zeros of (x + y + ...) w/o the C first:
1607 uint32_t TZ = BitWidth;
1608 for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
1609 TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I)));
1610 if (TZ) {
1611 // Set D to be as many least significant bits of C as possible while still
1612 // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
1613 return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
1614 }
1615 return APInt(BitWidth, 0);
1616}
1617
1618// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
1619// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
1620// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
1621// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
1622static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1623 const APInt &ConstantStart,
1624 const SCEV *Step) {
1625 const unsigned BitWidth = ConstantStart.getBitWidth();
1626 const uint32_t TZ = SE.GetMinTrailingZeros(Step);
1627 if (TZ)
1628 return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
1629 : ConstantStart;
1630 return APInt(BitWidth, 0);
1631}
1632
1633const SCEV *
1634ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1635 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1636, __PRETTY_FUNCTION__))
1636 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1636, __PRETTY_FUNCTION__))
;
1637 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1638, __PRETTY_FUNCTION__))
1638 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1638, __PRETTY_FUNCTION__))
;
1639 Ty = getEffectiveSCEVType(Ty);
1640
1641 // Fold if the operand is constant.
1642 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1643 return getConstant(
1644 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1645
1646 // zext(zext(x)) --> zext(x)
1647 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1648 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1649
1650 // Before doing any expensive analysis, check to see if we've already
1651 // computed a SCEV for this Op and Ty.
1652 FoldingSetNodeID ID;
1653 ID.AddInteger(scZeroExtend);
1654 ID.AddPointer(Op);
1655 ID.AddPointer(Ty);
1656 void *IP = nullptr;
1657 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1658 if (Depth > MaxCastDepth) {
1659 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1660 Op, Ty);
1661 UniqueSCEVs.InsertNode(S, IP);
1662 addToLoopUseLists(S);
1663 return S;
1664 }
1665
1666 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1667 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1668 // It's possible the bits taken off by the truncate were all zero bits. If
1669 // so, we should be able to simplify this further.
1670 const SCEV *X = ST->getOperand();
1671 ConstantRange CR = getUnsignedRange(X);
1672 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1673 unsigned NewBits = getTypeSizeInBits(Ty);
1674 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1675 CR.zextOrTrunc(NewBits)))
1676 return getTruncateOrZeroExtend(X, Ty, Depth);
1677 }
1678
1679 // If the input value is a chrec scev, and we can prove that the value
1680 // did not overflow the old, smaller, value, we can zero extend all of the
1681 // operands (often constants). This allows analysis of something like
1682 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1683 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1684 if (AR->isAffine()) {
1685 const SCEV *Start = AR->getStart();
1686 const SCEV *Step = AR->getStepRecurrence(*this);
1687 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1688 const Loop *L = AR->getLoop();
1689
1690 if (!AR->hasNoUnsignedWrap()) {
1691 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1692 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1693 }
1694
1695 // If we have special knowledge that this addrec won't overflow,
1696 // we don't need to do any further analysis.
1697 if (AR->hasNoUnsignedWrap())
1698 return getAddRecExpr(
1699 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1700 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1701
1702 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1703 // Note that this serves two purposes: It filters out loops that are
1704 // simply not analyzable, and it covers the case where this code is
1705 // being called from within backedge-taken count analysis, such that
1706 // attempting to ask for the backedge-taken count would likely result
1707 // in infinite recursion. In the later case, the analysis code will
1708 // cope with a conservative value, and it will take care to purge
1709 // that value once it has finished.
1710 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1711 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1712 // Manually compute the final value for AR, checking for
1713 // overflow.
1714
1715 // Check whether the backedge-taken count can be losslessly casted to
1716 // the addrec's type. The count is always unsigned.
1717 const SCEV *CastedMaxBECount =
1718 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
1719 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
1720 CastedMaxBECount, MaxBECount->getType(), Depth);
1721 if (MaxBECount == RecastedMaxBECount) {
1722 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1723 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1724 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
1725 SCEV::FlagAnyWrap, Depth + 1);
1726 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
1727 SCEV::FlagAnyWrap,
1728 Depth + 1),
1729 WideTy, Depth + 1);
1730 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
1731 const SCEV *WideMaxBECount =
1732 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1733 const SCEV *OperandExtendedAdd =
1734 getAddExpr(WideStart,
1735 getMulExpr(WideMaxBECount,
1736 getZeroExtendExpr(Step, WideTy, Depth + 1),
1737 SCEV::FlagAnyWrap, Depth + 1),
1738 SCEV::FlagAnyWrap, Depth + 1);
1739 if (ZAdd == OperandExtendedAdd) {
1740 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1741 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1742 // Return the expression with the addrec on the outside.
1743 return getAddRecExpr(
1744 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1745 Depth + 1),
1746 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1747 AR->getNoWrapFlags());
1748 }
1749 // Similar to above, only this time treat the step value as signed.
1750 // This covers loops that count down.
1751 OperandExtendedAdd =
1752 getAddExpr(WideStart,
1753 getMulExpr(WideMaxBECount,
1754 getSignExtendExpr(Step, WideTy, Depth + 1),
1755 SCEV::FlagAnyWrap, Depth + 1),
1756 SCEV::FlagAnyWrap, Depth + 1);
1757 if (ZAdd == OperandExtendedAdd) {
1758 // Cache knowledge of AR NW, which is propagated to this AddRec.
1759 // Negative step causes unsigned wrap, but it still can't self-wrap.
1760 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1761 // Return the expression with the addrec on the outside.
1762 return getAddRecExpr(
1763 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1764 Depth + 1),
1765 getSignExtendExpr(Step, Ty, Depth + 1), L,
1766 AR->getNoWrapFlags());
1767 }
1768 }
1769 }
1770
1771 // Normally, in the cases we can prove no-overflow via a
1772 // backedge guarding condition, we can also compute a backedge
1773 // taken count for the loop. The exceptions are assumptions and
1774 // guards present in the loop -- SCEV is not great at exploiting
1775 // these to compute max backedge taken counts, but can still use
1776 // these to prove lack of overflow. Use this fact to avoid
1777 // doing extra work that may not pay off.
1778 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1779 !AC.assumptions().empty()) {
1780 // If the backedge is guarded by a comparison with the pre-inc
1781 // value the addrec is safe. Also, if the entry is guarded by
1782 // a comparison with the start value and the backedge is
1783 // guarded by a comparison with the post-inc value, the addrec
1784 // is safe.
1785 if (isKnownPositive(Step)) {
1786 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1787 getUnsignedRangeMax(Step));
1788 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1789 isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
1790 // Cache knowledge of AR NUW, which is propagated to this
1791 // AddRec.
1792 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1793 // Return the expression with the addrec on the outside.
1794 return getAddRecExpr(
1795 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1796 Depth + 1),
1797 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1798 AR->getNoWrapFlags());
1799 }
1800 } else if (isKnownNegative(Step)) {
1801 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1802 getSignedRangeMin(Step));
1803 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1804 isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
1805 // Cache knowledge of AR NW, which is propagated to this
1806 // AddRec. Negative step causes unsigned wrap, but it
1807 // still can't self-wrap.
1808 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1809 // Return the expression with the addrec on the outside.
1810 return getAddRecExpr(
1811 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1812 Depth + 1),
1813 getSignExtendExpr(Step, Ty, Depth + 1), L,
1814 AR->getNoWrapFlags());
1815 }
1816 }
1817 }
1818
1819 // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
1820 // if D + (C - D + Step * n) could be proven to not unsigned wrap
1821 // where D maximizes the number of trailing zeros of (C - D + Step * n)
1822 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
1823 const APInt &C = SC->getAPInt();
1824 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
1825 if (D != 0) {
1826 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1827 const SCEV *SResidual =
1828 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
1829 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1830 return getAddExpr(SZExtD, SZExtR,
1831 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1832 Depth + 1);
1833 }
1834 }
1835
1836 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1837 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1838 return getAddRecExpr(
1839 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1840 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1841 }
1842 }
1843
1844 // zext(A % B) --> zext(A) % zext(B)
1845 {
1846 const SCEV *LHS;
1847 const SCEV *RHS;
1848 if (matchURem(Op, LHS, RHS))
1849 return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
1850 getZeroExtendExpr(RHS, Ty, Depth + 1));
1851 }
1852
1853 // zext(A / B) --> zext(A) / zext(B).
1854 if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
1855 return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
1856 getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
1857
1858 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1859 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1860 if (SA->hasNoUnsignedWrap()) {
1861 // If the addition does not unsign overflow then we can, by definition,
1862 // commute the zero extension with the addition operation.
1863 SmallVector<const SCEV *, 4> Ops;
1864 for (const auto *Op : SA->operands())
1865 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1866 return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
1867 }
1868
1869 // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
1870 // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
1871 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1872 //
1873 // Often address arithmetics contain expressions like
1874 // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
1875 // This transformation is useful while proving that such expressions are
1876 // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
1877 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
1878 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
1879 if (D != 0) {
1880 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1881 const SCEV *SResidual =
1882 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
1883 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1884 return getAddExpr(SZExtD, SZExtR,
1885 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1886 Depth + 1);
1887 }
1888 }
1889 }
1890
1891 if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
1892 // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
1893 if (SM->hasNoUnsignedWrap()) {
1894 // If the multiply does not unsign overflow then we can, by definition,
1895 // commute the zero extension with the multiply operation.
1896 SmallVector<const SCEV *, 4> Ops;
1897 for (const auto *Op : SM->operands())
1898 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1899 return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
1900 }
1901
1902 // zext(2^K * (trunc X to iN)) to iM ->
1903 // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
1904 //
1905 // Proof:
1906 //
1907 // zext(2^K * (trunc X to iN)) to iM
1908 // = zext((trunc X to iN) << K) to iM
1909 // = zext((trunc X to i{N-K}) << K)<nuw> to iM
1910 // (because shl removes the top K bits)
1911 // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
1912 // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
1913 //
1914 if (SM->getNumOperands() == 2)
1915 if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0)))
1916 if (MulLHS->getAPInt().isPowerOf2())
1917 if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) {
1918 int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) -
1919 MulLHS->getAPInt().logBase2();
1920 Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
1921 return getMulExpr(
1922 getZeroExtendExpr(MulLHS, Ty),
1923 getZeroExtendExpr(
1924 getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty),
1925 SCEV::FlagNUW, Depth + 1);
1926 }
1927 }
1928
1929 // The cast wasn't folded; create an explicit cast node.
1930 // Recompute the insert position, as it may have been invalidated.
1931 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1932 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1933 Op, Ty);
1934 UniqueSCEVs.InsertNode(S, IP);
1935 addToLoopUseLists(S);
1936 return S;
1937}
1938
1939const SCEV *
1940ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1941 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1942, __PRETTY_FUNCTION__))
1942 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1942, __PRETTY_FUNCTION__))
;
1943 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1944, __PRETTY_FUNCTION__))
1944 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 1944, __PRETTY_FUNCTION__))
;
1945 Ty = getEffectiveSCEVType(Ty);
1946
1947 // Fold if the operand is constant.
1948 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1949 return getConstant(
1950 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1951
1952 // sext(sext(x)) --> sext(x)
1953 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1954 return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
1955
1956 // sext(zext(x)) --> zext(x)
1957 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1958 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1959
1960 // Before doing any expensive analysis, check to see if we've already
1961 // computed a SCEV for this Op and Ty.
1962 FoldingSetNodeID ID;
1963 ID.AddInteger(scSignExtend);
1964 ID.AddPointer(Op);
1965 ID.AddPointer(Ty);
1966 void *IP = nullptr;
1967 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1968 // Limit recursion depth.
1969 if (Depth > MaxCastDepth) {
1970 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1971 Op, Ty);
1972 UniqueSCEVs.InsertNode(S, IP);
1973 addToLoopUseLists(S);
1974 return S;
1975 }
1976
1977 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1978 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1979 // It's possible the bits taken off by the truncate were all sign bits. If
1980 // so, we should be able to simplify this further.
1981 const SCEV *X = ST->getOperand();
1982 ConstantRange CR = getSignedRange(X);
1983 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1984 unsigned NewBits = getTypeSizeInBits(Ty);
1985 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1986 CR.sextOrTrunc(NewBits)))
1987 return getTruncateOrSignExtend(X, Ty, Depth);
1988 }
1989
1990 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1991 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1992 if (SA->hasNoSignedWrap()) {
1993 // If the addition does not sign overflow then we can, by definition,
1994 // commute the sign extension with the addition operation.
1995 SmallVector<const SCEV *, 4> Ops;
1996 for (const auto *Op : SA->operands())
1997 Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
1998 return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
1999 }
2000
2001 // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
2002 // if D + (C - D + x + y + ...) could be proven to not signed wrap
2003 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
2004 //
2005 // For instance, this will bring two seemingly different expressions:
2006 // 1 + sext(5 + 20 * %x + 24 * %y) and
2007 // sext(6 + 20 * %x + 24 * %y)
2008 // to the same form:
2009 // 2 + sext(4 + 20 * %x + 24 * %y)
2010 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
2011 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
2012 if (D != 0) {
2013 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
2014 const SCEV *SResidual =
2015 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
2016 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
2017 return getAddExpr(SSExtD, SSExtR,
2018 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
2019 Depth + 1);
2020 }
2021 }
2022 }
2023 // If the input value is a chrec scev, and we can prove that the value
2024 // did not overflow the old, smaller, value, we can sign extend all of the
2025 // operands (often constants). This allows analysis of something like
2026 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
2027 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
2028 if (AR->isAffine()) {
2029 const SCEV *Start = AR->getStart();
2030 const SCEV *Step = AR->getStepRecurrence(*this);
2031 unsigned BitWidth = getTypeSizeInBits(AR->getType());
2032 const Loop *L = AR->getLoop();
2033
2034 if (!AR->hasNoSignedWrap()) {
2035 auto NewFlags = proveNoWrapViaConstantRanges(AR);
2036 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
2037 }
2038
2039 // If we have special knowledge that this addrec won't overflow,
2040 // we don't need to do any further analysis.
2041 if (AR->hasNoSignedWrap())
2042 return getAddRecExpr(
2043 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2044 getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
2045
2046 // Check whether the backedge-taken count is SCEVCouldNotCompute.
2047 // Note that this serves two purposes: It filters out loops that are
2048 // simply not analyzable, and it covers the case where this code is
2049 // being called from within backedge-taken count analysis, such that
2050 // attempting to ask for the backedge-taken count would likely result
2051 // in infinite recursion. In the later case, the analysis code will
2052 // cope with a conservative value, and it will take care to purge
2053 // that value once it has finished.
2054 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
2055 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
2056 // Manually compute the final value for AR, checking for
2057 // overflow.
2058
2059 // Check whether the backedge-taken count can be losslessly casted to
2060 // the addrec's type. The count is always unsigned.
2061 const SCEV *CastedMaxBECount =
2062 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
2063 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
2064 CastedMaxBECount, MaxBECount->getType(), Depth);
2065 if (MaxBECount == RecastedMaxBECount) {
2066 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
2067 // Check whether Start+Step*MaxBECount has no signed overflow.
2068 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
2069 SCEV::FlagAnyWrap, Depth + 1);
2070 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
2071 SCEV::FlagAnyWrap,
2072 Depth + 1),
2073 WideTy, Depth + 1);
2074 const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
2075 const SCEV *WideMaxBECount =
2076 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
2077 const SCEV *OperandExtendedAdd =
2078 getAddExpr(WideStart,
2079 getMulExpr(WideMaxBECount,
2080 getSignExtendExpr(Step, WideTy, Depth + 1),
2081 SCEV::FlagAnyWrap, Depth + 1),
2082 SCEV::FlagAnyWrap, Depth + 1);
2083 if (SAdd == OperandExtendedAdd) {
2084 // Cache knowledge of AR NSW, which is propagated to this AddRec.
2085 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2086 // Return the expression with the addrec on the outside.
2087 return getAddRecExpr(
2088 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
2089 Depth + 1),
2090 getSignExtendExpr(Step, Ty, Depth + 1), L,
2091 AR->getNoWrapFlags());
2092 }
2093 // Similar to above, only this time treat the step value as unsigned.
2094 // This covers loops that count up with an unsigned step.
2095 OperandExtendedAdd =
2096 getAddExpr(WideStart,
2097 getMulExpr(WideMaxBECount,
2098 getZeroExtendExpr(Step, WideTy, Depth + 1),
2099 SCEV::FlagAnyWrap, Depth + 1),
2100 SCEV::FlagAnyWrap, Depth + 1);
2101 if (SAdd == OperandExtendedAdd) {
2102 // If AR wraps around then
2103 //
2104 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
2105 // => SAdd != OperandExtendedAdd
2106 //
2107 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
2108 // (SAdd == OperandExtendedAdd => AR is NW)
2109
2110 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
2111
2112 // Return the expression with the addrec on the outside.
2113 return getAddRecExpr(
2114 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
2115 Depth + 1),
2116 getZeroExtendExpr(Step, Ty, Depth + 1), L,
2117 AR->getNoWrapFlags());
2118 }
2119 }
2120 }
2121
2122 // Normally, in the cases we can prove no-overflow via a
2123 // backedge guarding condition, we can also compute a backedge
2124 // taken count for the loop. The exceptions are assumptions and
2125 // guards present in the loop -- SCEV is not great at exploiting
2126 // these to compute max backedge taken counts, but can still use
2127 // these to prove lack of overflow. Use this fact to avoid
2128 // doing extra work that may not pay off.
2129
2130 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
2131 !AC.assumptions().empty()) {
2132 // If the backedge is guarded by a comparison with the pre-inc
2133 // value the addrec is safe. Also, if the entry is guarded by
2134 // a comparison with the start value and the backedge is
2135 // guarded by a comparison with the post-inc value, the addrec
2136 // is safe.
2137 ICmpInst::Predicate Pred;
2138 const SCEV *OverflowLimit =
2139 getSignedOverflowLimitForStep(Step, &Pred, this);
2140 if (OverflowLimit &&
2141 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
2142 isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
2143 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
2144 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2145 return getAddRecExpr(
2146 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2147 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2148 }
2149 }
2150
2151 // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
2152 // if D + (C - D + Step * n) could be proven to not signed wrap
2153 // where D maximizes the number of trailing zeros of (C - D + Step * n)
2154 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
2155 const APInt &C = SC->getAPInt();
2156 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
2157 if (D != 0) {
2158 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
2159 const SCEV *SResidual =
2160 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
2161 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
2162 return getAddExpr(SSExtD, SSExtR,
2163 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
2164 Depth + 1);
2165 }
2166 }
2167
2168 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
2169 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2170 return getAddRecExpr(
2171 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2172 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2173 }
2174 }
2175
2176 // If the input value is provably positive and we could not simplify
2177 // away the sext build a zext instead.
2178 if (isKnownNonNegative(Op))
2179 return getZeroExtendExpr(Op, Ty, Depth + 1);
2180
2181 // The cast wasn't folded; create an explicit cast node.
2182 // Recompute the insert position, as it may have been invalidated.
2183 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2184 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
2185 Op, Ty);
2186 UniqueSCEVs.InsertNode(S, IP);
2187 addToLoopUseLists(S);
2188 return S;
2189}
2190
2191/// getAnyExtendExpr - Return a SCEV for the given operand extended with
2192/// unspecified bits out to the given type.
2193const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
2194 Type *Ty) {
2195 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2196, __PRETTY_FUNCTION__))
2196 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2196, __PRETTY_FUNCTION__))
;
2197 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2198, __PRETTY_FUNCTION__))
2198 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2198, __PRETTY_FUNCTION__))
;
2199 Ty = getEffectiveSCEVType(Ty);
2200
2201 // Sign-extend negative constants.
2202 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
2203 if (SC->getAPInt().isNegative())
2204 return getSignExtendExpr(Op, Ty);
2205
2206 // Peel off a truncate cast.
2207 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
2208 const SCEV *NewOp = T->getOperand();
2209 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
2210 return getAnyExtendExpr(NewOp, Ty);
2211 return getTruncateOrNoop(NewOp, Ty);
2212 }
2213
2214 // Next try a zext cast. If the cast is folded, use it.
2215 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
2216 if (!isa<SCEVZeroExtendExpr>(ZExt))
2217 return ZExt;
2218
2219 // Next try a sext cast. If the cast is folded, use it.
2220 const SCEV *SExt = getSignExtendExpr(Op, Ty);
2221 if (!isa<SCEVSignExtendExpr>(SExt))
2222 return SExt;
2223
2224 // Force the cast to be folded into the operands of an addrec.
2225 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
2226 SmallVector<const SCEV *, 4> Ops;
2227 for (const SCEV *Op : AR->operands())
2228 Ops.push_back(getAnyExtendExpr(Op, Ty));
2229 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
2230 }
2231
2232 // If the expression is obviously signed, use the sext cast value.
2233 if (isa<SCEVSMaxExpr>(Op))
2234 return SExt;
2235
2236 // Absent any other information, use the zext cast value.
2237 return ZExt;
2238}
2239
2240/// Process the given Ops list, which is a list of operands to be added under
2241/// the given scale, update the given map. This is a helper function for
2242/// getAddRecExpr. As an example of what it does, given a sequence of operands
2243/// that would form an add expression like this:
2244///
2245/// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2246///
2247/// where A and B are constants, update the map with these values:
2248///
2249/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2250///
2251/// and add 13 + A*B*29 to AccumulatedConstant.
2252/// This will allow getAddRecExpr to produce this:
2253///
2254/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2255///
2256/// This form often exposes folding opportunities that are hidden in
2257/// the original operand list.
2258///
2259/// Return true iff it appears that any interesting folding opportunities
2260/// may be exposed. This helps getAddRecExpr short-circuit extra work in
2261/// the common case where no interesting opportunities are present, and
2262/// is also used as a check to avoid infinite recursion.
2263static bool
2264CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
2265 SmallVectorImpl<const SCEV *> &NewOps,
2266 APInt &AccumulatedConstant,
2267 const SCEV *const *Ops, size_t NumOperands,
2268 const APInt &Scale,
2269 ScalarEvolution &SE) {
2270 bool Interesting = false;
2271
2272 // Iterate over the add operands. They are sorted, with constants first.
2273 unsigned i = 0;
2274 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2275 ++i;
2276 // Pull a buried constant out to the outside.
2277 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
2278 Interesting = true;
2279 AccumulatedConstant += Scale * C->getAPInt();
2280 }
2281
2282 // Next comes everything else. We're especially interested in multiplies
2283 // here, but they're in the middle, so just visit the rest with one loop.
2284 for (; i != NumOperands; ++i) {
2285 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
2286 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
2287 APInt NewScale =
2288 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
2289 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
2290 // A multiplication of a constant with another add; recurse.
2291 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2292 Interesting |=
2293 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2294 Add->op_begin(), Add->getNumOperands(),
2295 NewScale, SE);
2296 } else {
2297 // A multiplication of a constant with some other value. Update
2298 // the map.
2299 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
2300 const SCEV *Key = SE.getMulExpr(MulOps);
2301 auto Pair = M.insert({Key, NewScale});
2302 if (Pair.second) {
2303 NewOps.push_back(Pair.first->first);
2304 } else {
2305 Pair.first->second += NewScale;
2306 // The map already had an entry for this value, which may indicate
2307 // a folding opportunity.
2308 Interesting = true;
2309 }
2310 }
2311 } else {
2312 // An ordinary operand. Update the map.
2313 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2314 M.insert({Ops[i], Scale});
2315 if (Pair.second) {
2316 NewOps.push_back(Pair.first->first);
2317 } else {
2318 Pair.first->second += Scale;
2319 // The map already had an entry for this value, which may indicate
2320 // a folding opportunity.
2321 Interesting = true;
2322 }
2323 }
2324 }
2325
2326 return Interesting;
2327}
2328
2329// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2330// `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2331// can't-overflow flags for the operation if possible.
2332static SCEV::NoWrapFlags
2333StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
2334 const ArrayRef<const SCEV *> Ops,
2335 SCEV::NoWrapFlags Flags) {
2336 using namespace std::placeholders;
2337
2338 using OBO = OverflowingBinaryOperator;
2339
2340 bool CanAnalyze =
2341 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2342 (void)CanAnalyze;
2343 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2343, __PRETTY_FUNCTION__))
;
2344
2345 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2346 SCEV::NoWrapFlags SignOrUnsignWrap =
2347 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2348
2349 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2350 auto IsKnownNonNegative = [&](const SCEV *S) {
2351 return SE->isKnownNonNegative(S);
2352 };
2353
2354 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2355 Flags =
2356 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2357
2358 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2359
2360 if (SignOrUnsignWrap != SignOrUnsignMask &&
2361 (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
2362 isa<SCEVConstant>(Ops[0])) {
2363
2364 auto Opcode = [&] {
2365 switch (Type) {
2366 case scAddExpr:
2367 return Instruction::Add;
2368 case scMulExpr:
2369 return Instruction::Mul;
2370 default:
2371 llvm_unreachable("Unexpected SCEV op.")::llvm::llvm_unreachable_internal("Unexpected SCEV op.", "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2371)
;
2372 }
2373 }();
2374
2375 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2376
2377 // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
2378 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2379 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2380 Opcode, C, OBO::NoSignedWrap);
2381 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2382 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2383 }
2384
2385 // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
2386 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2387 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2388 Opcode, C, OBO::NoUnsignedWrap);
2389 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2390 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2391 }
2392 }
2393
2394 return Flags;
2395}
2396
2397bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
2398 return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
2399}
2400
2401/// Get a canonical add expression, or something simpler if possible.
2402const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2403 SCEV::NoWrapFlags Flags,
2404 unsigned Depth) {
2405 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2406, __PRETTY_FUNCTION__))
2406 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2406, __PRETTY_FUNCTION__))
;
2407 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2407, __PRETTY_FUNCTION__))
;
2408 if (Ops.size() == 1) return Ops[0];
2409#ifndef NDEBUG
2410 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2411 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2412 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2413, __PRETTY_FUNCTION__))
2413 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2413, __PRETTY_FUNCTION__))
;
2414#endif
2415
2416 // Sort by complexity, this groups all similar expression types together.
2417 GroupByComplexity(Ops, &LI, DT);
2418
2419 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2420
2421 // If there are any constants, fold them together.
2422 unsigned Idx = 0;
2423 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2424 ++Idx;
2425 assert(Idx < Ops.size())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2425, __PRETTY_FUNCTION__))
;
2426 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2427 // We found two constants, fold them together!
2428 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2429 if (Ops.size() == 2) return Ops[0];
2430 Ops.erase(Ops.begin()+1); // Erase the folded element
2431 LHSC = cast<SCEVConstant>(Ops[0]);
2432 }
2433
2434 // If we are left with a constant zero being added, strip it off.
2435 if (LHSC->getValue()->isZero()) {
2436 Ops.erase(Ops.begin());
2437 --Idx;
2438 }
2439
2440 if (Ops.size() == 1) return Ops[0];
2441 }
2442
2443 // Limit recursion calls depth.
2444 if (Depth > MaxArithDepth || hasHugeExpression(Ops))
2445 return getOrCreateAddExpr(Ops, Flags);
2446
2447 // Okay, check to see if the same value occurs in the operand list more than
2448 // once. If so, merge them together into an multiply expression. Since we
2449 // sorted the list, these values are required to be adjacent.
2450 Type *Ty = Ops[0]->getType();
2451 bool FoundMatch = false;
2452 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2453 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2454 // Scan ahead to count how many equal operands there are.
2455 unsigned Count = 2;
2456 while (i+Count != e && Ops[i+Count] == Ops[i])
2457 ++Count;
2458 // Merge the values into a multiply.
2459 const SCEV *Scale = getConstant(Ty, Count);
2460 const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
2461 if (Ops.size() == Count)
2462 return Mul;
2463 Ops[i] = Mul;
2464 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2465 --i; e -= Count - 1;
2466 FoundMatch = true;
2467 }
2468 if (FoundMatch)
2469 return getAddExpr(Ops, Flags, Depth + 1);
2470
2471 // Check for truncates. If all the operands are truncated from the same
2472 // type, see if factoring out the truncate would permit the result to be
2473 // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
2474 // if the contents of the resulting outer trunc fold to something simple.
2475 auto FindTruncSrcType = [&]() -> Type * {
2476 // We're ultimately looking to fold an addrec of truncs and muls of only
2477 // constants and truncs, so if we find any other types of SCEV
2478 // as operands of the addrec then we bail and return nullptr here.
2479 // Otherwise, we return the type of the operand of a trunc that we find.
2480 if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
2481 return T->getOperand()->getType();
2482 if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2483 const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
2484 if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
2485 return T->getOperand()->getType();
2486 }
2487 return nullptr;
2488 };
2489 if (auto *SrcType = FindTruncSrcType()) {
2490 SmallVector<const SCEV *, 8> LargeOps;
2491 bool Ok = true;
2492 // Check all the operands to see if they can be represented in the
2493 // source type of the truncate.
2494 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2495 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2496 if (T->getOperand()->getType() != SrcType) {
2497 Ok = false;
2498 break;
2499 }
2500 LargeOps.push_back(T->getOperand());
2501 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2502 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2503 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2504 SmallVector<const SCEV *, 8> LargeMulOps;
2505 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2506 if (const SCEVTruncateExpr *T =
2507 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2508 if (T->getOperand()->getType() != SrcType) {
2509 Ok = false;
2510 break;
2511 }
2512 LargeMulOps.push_back(T->getOperand());
2513 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2514 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2515 } else {
2516 Ok = false;
2517 break;
2518 }
2519 }
2520 if (Ok)
2521 LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
2522 } else {
2523 Ok = false;
2524 break;
2525 }
2526 }
2527 if (Ok) {
2528 // Evaluate the expression in the larger type.
2529 const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
2530 // If it folds to something simple, use it. Otherwise, don't.
2531 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2532 return getTruncateExpr(Fold, Ty);
2533 }
2534 }
2535
2536 // Skip past any other cast SCEVs.
2537 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2538 ++Idx;
2539
2540 // If there are add operands they would be next.
2541 if (Idx < Ops.size()) {
2542 bool DeletedAdd = false;
2543 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2544 if (Ops.size() > AddOpsInlineThreshold ||
2545 Add->getNumOperands() > AddOpsInlineThreshold)
2546 break;
2547 // If we have an add, expand the add operands onto the end of the operands
2548 // list.
2549 Ops.erase(Ops.begin()+Idx);
2550 Ops.append(Add->op_begin(), Add->op_end());
2551 DeletedAdd = true;
2552 }
2553
2554 // If we deleted at least one add, we added operands to the end of the list,
2555 // and they are not necessarily sorted. Recurse to resort and resimplify
2556 // any operands we just acquired.
2557 if (DeletedAdd)
2558 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2559 }
2560
2561 // Skip over the add expression until we get to a multiply.
2562 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2563 ++Idx;
2564
2565 // Check to see if there are any folding opportunities present with
2566 // operands multiplied by constant values.
2567 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2568 uint64_t BitWidth = getTypeSizeInBits(Ty);
2569 DenseMap<const SCEV *, APInt> M;
2570 SmallVector<const SCEV *, 8> NewOps;
2571 APInt AccumulatedConstant(BitWidth, 0);
2572 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2573 Ops.data(), Ops.size(),
2574 APInt(BitWidth, 1), *this)) {
2575 struct APIntCompare {
2576 bool operator()(const APInt &LHS, const APInt &RHS) const {
2577 return LHS.ult(RHS);
2578 }
2579 };
2580
2581 // Some interesting folding opportunity is present, so its worthwhile to
2582 // re-generate the operands list. Group the operands by constant scale,
2583 // to avoid multiplying by the same constant scale multiple times.
2584 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2585 for (const SCEV *NewOp : NewOps)
2586 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2587 // Re-generate the operands list.
2588 Ops.clear();
2589 if (AccumulatedConstant != 0)
2590 Ops.push_back(getConstant(AccumulatedConstant));
2591 for (auto &MulOp : MulOpLists)
2592 if (MulOp.first != 0)
2593 Ops.push_back(getMulExpr(
2594 getConstant(MulOp.first),
2595 getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
2596 SCEV::FlagAnyWrap, Depth + 1));
2597 if (Ops.empty())
2598 return getZero(Ty);
2599 if (Ops.size() == 1)
2600 return Ops[0];
2601 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2602 }
2603 }
2604
2605 // If we are adding something to a multiply expression, make sure the
2606 // something is not already an operand of the multiply. If so, merge it into
2607 // the multiply.
2608 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2609 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2610 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2611 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2612 if (isa<SCEVConstant>(MulOpSCEV))
2613 continue;
2614 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2615 if (MulOpSCEV == Ops[AddOp]) {
2616 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2617 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2618 if (Mul->getNumOperands() != 2) {
2619 // If the multiply has more than two operands, we must get the
2620 // Y*Z term.
2621 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2622 Mul->op_begin()+MulOp);
2623 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2624 InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2625 }
2626 SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
2627 const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2628 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
2629 SCEV::FlagAnyWrap, Depth + 1);
2630 if (Ops.size() == 2) return OuterMul;
2631 if (AddOp < Idx) {
2632 Ops.erase(Ops.begin()+AddOp);
2633 Ops.erase(Ops.begin()+Idx-1);
2634 } else {
2635 Ops.erase(Ops.begin()+Idx);
2636 Ops.erase(Ops.begin()+AddOp-1);
2637 }
2638 Ops.push_back(OuterMul);
2639 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2640 }
2641
2642 // Check this multiply against other multiplies being added together.
2643 for (unsigned OtherMulIdx = Idx+1;
2644 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2645 ++OtherMulIdx) {
2646 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2647 // If MulOp occurs in OtherMul, we can fold the two multiplies
2648 // together.
2649 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2650 OMulOp != e; ++OMulOp)
2651 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2652 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2653 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2654 if (Mul->getNumOperands() != 2) {
2655 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2656 Mul->op_begin()+MulOp);
2657 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2658 InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2659 }
2660 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2661 if (OtherMul->getNumOperands() != 2) {
2662 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2663 OtherMul->op_begin()+OMulOp);
2664 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2665 InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2666 }
2667 SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
2668 const SCEV *InnerMulSum =
2669 getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2670 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
2671 SCEV::FlagAnyWrap, Depth + 1);
2672 if (Ops.size() == 2) return OuterMul;
2673 Ops.erase(Ops.begin()+Idx);
2674 Ops.erase(Ops.begin()+OtherMulIdx-1);
2675 Ops.push_back(OuterMul);
2676 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2677 }
2678 }
2679 }
2680 }
2681
2682 // If there are any add recurrences in the operands list, see if any other
2683 // added values are loop invariant. If so, we can fold them into the
2684 // recurrence.
2685 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2686 ++Idx;
2687
2688 // Scan over all recurrences, trying to fold loop invariants into them.
2689 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2690 // Scan all of the other operands to this add and add them to the vector if
2691 // they are loop invariant w.r.t. the recurrence.
2692 SmallVector<const SCEV *, 8> LIOps;
2693 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2694 const Loop *AddRecLoop = AddRec->getLoop();
2695 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2696 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2697 LIOps.push_back(Ops[i]);
2698 Ops.erase(Ops.begin()+i);
2699 --i; --e;
2700 }
2701
2702 // If we found some loop invariants, fold them into the recurrence.
2703 if (!LIOps.empty()) {
2704 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2705 LIOps.push_back(AddRec->getStart());
2706
2707 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2708 AddRec->op_end());
2709 // This follows from the fact that the no-wrap flags on the outer add
2710 // expression are applicable on the 0th iteration, when the add recurrence
2711 // will be equal to its start value.
2712 AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
2713
2714 // Build the new addrec. Propagate the NUW and NSW flags if both the
2715 // outer add and the inner addrec are guaranteed to have no overflow.
2716 // Always propagate NW.
2717 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2718 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2719
2720 // If all of the other operands were loop invariant, we are done.
2721 if (Ops.size() == 1) return NewRec;
2722
2723 // Otherwise, add the folded AddRec by the non-invariant parts.
2724 for (unsigned i = 0;; ++i)
2725 if (Ops[i] == AddRec) {
2726 Ops[i] = NewRec;
2727 break;
2728 }
2729 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2730 }
2731
2732 // Okay, if there weren't any loop invariants to be folded, check to see if
2733 // there are multiple AddRec's with the same loop induction variable being
2734 // added together. If so, we can fold them.
2735 for (unsigned OtherIdx = Idx+1;
2736 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2737 ++OtherIdx) {
2738 // We expect the AddRecExpr's to be sorted in reverse dominance order,
2739 // so that the 1st found AddRecExpr is dominated by all others.
2740 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2743, __PRETTY_FUNCTION__))
2741 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2743, __PRETTY_FUNCTION__))
2742 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2743, __PRETTY_FUNCTION__))
2743 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2743, __PRETTY_FUNCTION__))
;
2744 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2745 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2746 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2747 AddRec->op_end());
2748 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2749 ++OtherIdx) {
2750 const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2751 if (OtherAddRec->getLoop() == AddRecLoop) {
2752 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2753 i != e; ++i) {
2754 if (i >= AddRecOps.size()) {
2755 AddRecOps.append(OtherAddRec->op_begin()+i,
2756 OtherAddRec->op_end());
2757 break;
2758 }
2759 SmallVector<const SCEV *, 2> TwoOps = {
2760 AddRecOps[i], OtherAddRec->getOperand(i)};
2761 AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2762 }
2763 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2764 }
2765 }
2766 // Step size has changed, so we cannot guarantee no self-wraparound.
2767 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2768 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2769 }
2770 }
2771
2772 // Otherwise couldn't fold anything into this recurrence. Move onto the
2773 // next one.
2774 }
2775
2776 // Okay, it looks like we really DO need an add expr. Check to see if we
2777 // already have one, otherwise create a new one.
2778 return getOrCreateAddExpr(Ops, Flags);
2779}
2780
2781const SCEV *
2782ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
2783 SCEV::NoWrapFlags Flags) {
2784 FoldingSetNodeID ID;
2785 ID.AddInteger(scAddExpr);
2786 for (const SCEV *Op : Ops)
2787 ID.AddPointer(Op);
2788 void *IP = nullptr;
2789 SCEVAddExpr *S =
2790 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2791 if (!S) {
2792 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2793 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2794 S = new (SCEVAllocator)
2795 SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
2796 UniqueSCEVs.InsertNode(S, IP);
2797 addToLoopUseLists(S);
2798 }
2799 S->setNoWrapFlags(Flags);
2800 return S;
2801}
2802
2803const SCEV *
2804ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
2805 const Loop *L, SCEV::NoWrapFlags Flags) {
2806 FoldingSetNodeID ID;
2807 ID.AddInteger(scAddRecExpr);
2808 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2809 ID.AddPointer(Ops[i]);
2810 ID.AddPointer(L);
2811 void *IP = nullptr;
2812 SCEVAddRecExpr *S =
2813 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2814 if (!S) {
2815 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2816 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2817 S = new (SCEVAllocator)
2818 SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
2819 UniqueSCEVs.InsertNode(S, IP);
2820 addToLoopUseLists(S);
2821 }
2822 S->setNoWrapFlags(Flags);
2823 return S;
2824}
2825
2826const SCEV *
2827ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
2828 SCEV::NoWrapFlags Flags) {
2829 FoldingSetNodeID ID;
2830 ID.AddInteger(scMulExpr);
2831 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2832 ID.AddPointer(Ops[i]);
2833 void *IP = nullptr;
2834 SCEVMulExpr *S =
2835 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2836 if (!S) {
2837 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2838 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2839 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2840 O, Ops.size());
2841 UniqueSCEVs.InsertNode(S, IP);
2842 addToLoopUseLists(S);
2843 }
2844 S->setNoWrapFlags(Flags);
2845 return S;
2846}
2847
2848static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2849 uint64_t k = i*j;
2850 if (j > 1 && k / j != i) Overflow = true;
2851 return k;
2852}
2853
2854/// Compute the result of "n choose k", the binomial coefficient. If an
2855/// intermediate computation overflows, Overflow will be set and the return will
2856/// be garbage. Overflow is not cleared on absence of overflow.
2857static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2858 // We use the multiplicative formula:
2859 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2860 // At each iteration, we take the n-th term of the numeral and divide by the
2861 // (k-n)th term of the denominator. This division will always produce an
2862 // integral result, and helps reduce the chance of overflow in the
2863 // intermediate computations. However, we can still overflow even when the
2864 // final result would fit.
2865
2866 if (n == 0 || n == k) return 1;
2867 if (k > n) return 0;
2868
2869 if (k > n/2)
2870 k = n-k;
2871
2872 uint64_t r = 1;
2873 for (uint64_t i = 1; i <= k; ++i) {
2874 r = umul_ov(r, n-(i-1), Overflow);
2875 r /= i;
2876 }
2877 return r;
2878}
2879
2880/// Determine if any of the operands in this SCEV are a constant or if
2881/// any of the add or multiply expressions in this SCEV contain a constant.
2882static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
2883 struct FindConstantInAddMulChain {
2884 bool FoundConstant = false;
2885
2886 bool follow(const SCEV *S) {
2887 FoundConstant |= isa<SCEVConstant>(S);
2888 return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
2889 }
2890
2891 bool isDone() const {
2892 return FoundConstant;
2893 }
2894 };
2895
2896 FindConstantInAddMulChain F;
2897 SCEVTraversal<FindConstantInAddMulChain> ST(F);
2898 ST.visitAll(StartExpr);
2899 return F.FoundConstant;
2900}
2901
2902/// Get a canonical multiply expression, or something simpler if possible.
2903const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2904 SCEV::NoWrapFlags Flags,
2905 unsigned Depth) {
2906 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2907, __PRETTY_FUNCTION__))
2907 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2907, __PRETTY_FUNCTION__))
;
2908 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2908, __PRETTY_FUNCTION__))
;
2909 if (Ops.size() == 1) return Ops[0];
2910#ifndef NDEBUG
2911 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2912 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2913 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2914, __PRETTY_FUNCTION__))
2914 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 2914, __PRETTY_FUNCTION__))
;
2915#endif
2916
2917 // Sort by complexity, this groups all similar expression types together.
2918 GroupByComplexity(Ops, &LI, DT);
2919
2920 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2921
2922 // Limit recursion calls depth.
2923 if (Depth > MaxArithDepth || hasHugeExpression(Ops))
2924 return getOrCreateMulExpr(Ops, Flags);
2925
2926 // If there are any constants, fold them together.
2927 unsigned Idx = 0;
2928 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2929
2930 if (Ops.size() == 2)
2931 // C1*(C2+V) -> C1*C2 + C1*V
2932 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2933 // If any of Add's ops are Adds or Muls with a constant, apply this
2934 // transformation as well.
2935 //
2936 // TODO: There are some cases where this transformation is not
2937 // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
2938 // this transformation should be narrowed down.
2939 if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add))
2940 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
2941 SCEV::FlagAnyWrap, Depth + 1),
2942 getMulExpr(LHSC, Add->getOperand(1),
2943 SCEV::FlagAnyWrap, Depth + 1),
2944 SCEV::FlagAnyWrap, Depth + 1);
2945
2946 ++Idx;
2947 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2948 // We found two constants, fold them together!
2949 ConstantInt *Fold =
2950 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2951 Ops[0] = getConstant(Fold);
2952 Ops.erase(Ops.begin()+1); // Erase the folded element
2953 if (Ops.size() == 1) return Ops[0];
2954 LHSC = cast<SCEVConstant>(Ops[0]);
2955 }
2956
2957 // If we are left with a constant one being multiplied, strip it off.
2958 if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
2959 Ops.erase(Ops.begin());
2960 --Idx;
2961 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2962 // If we have a multiply of zero, it will always be zero.
2963 return Ops[0];
2964 } else if (Ops[0]->isAllOnesValue()) {
2965 // If we have a mul by -1 of an add, try distributing the -1 among the
2966 // add operands.
2967 if (Ops.size() == 2) {
2968 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2969 SmallVector<const SCEV *, 4> NewOps;
2970 bool AnyFolded = false;
2971 for (const SCEV *AddOp : Add->operands()) {
2972 const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
2973 Depth + 1);
2974 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2975 NewOps.push_back(Mul);
2976 }
2977 if (AnyFolded)
2978 return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
2979 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2980 // Negation preserves a recurrence's no self-wrap property.
2981 SmallVector<const SCEV *, 4> Operands;
2982 for (const SCEV *AddRecOp : AddRec->operands())
2983 Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
2984 Depth + 1));
2985
2986 return getAddRecExpr(Operands, AddRec->getLoop(),
2987 AddRec->getNoWrapFlags(SCEV::FlagNW));
2988 }
2989 }
2990 }
2991
2992 if (Ops.size() == 1)
2993 return Ops[0];
2994 }
2995
2996 // Skip over the add expression until we get to a multiply.
2997 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2998 ++Idx;
2999
3000 // If there are mul operands inline them all into this expression.
3001 if (Idx < Ops.size()) {
3002 bool DeletedMul = false;
3003 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
3004 if (Ops.size() > MulOpsInlineThreshold)
3005 break;
3006 // If we have an mul, expand the mul operands onto the end of the
3007 // operands list.
3008 Ops.erase(Ops.begin()+Idx);
3009 Ops.append(Mul->op_begin(), Mul->op_end());
3010 DeletedMul = true;
3011 }
3012
3013 // If we deleted at least one mul, we added operands to the end of the
3014 // list, and they are not necessarily sorted. Recurse to resort and
3015 // resimplify any operands we just acquired.
3016 if (DeletedMul)
3017 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3018 }
3019
3020 // If there are any add recurrences in the operands list, see if any other
3021 // added values are loop invariant. If so, we can fold them into the
3022 // recurrence.
3023 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
3024 ++Idx;
3025
3026 // Scan over all recurrences, trying to fold loop invariants into them.
3027 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
3028 // Scan all of the other operands to this mul and add them to the vector
3029 // if they are loop invariant w.r.t. the recurrence.
3030 SmallVector<const SCEV *, 8> LIOps;
3031 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
3032 const Loop *AddRecLoop = AddRec->getLoop();
3033 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3034 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
3035 LIOps.push_back(Ops[i]);
3036 Ops.erase(Ops.begin()+i);
3037 --i; --e;
3038 }
3039
3040 // If we found some loop invariants, fold them into the recurrence.
3041 if (!LIOps.empty()) {
3042 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
3043 SmallVector<const SCEV *, 4> NewOps;
3044 NewOps.reserve(AddRec->getNumOperands());
3045 const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
3046 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
3047 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
3048 SCEV::FlagAnyWrap, Depth + 1));
3049
3050 // Build the new addrec. Propagate the NUW and NSW flags if both the
3051 // outer mul and the inner addrec are guaranteed to have no overflow.
3052 //
3053 // No self-wrap cannot be guaranteed after changing the step size, but
3054 // will be inferred if either NUW or NSW is true.
3055 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
3056 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
3057
3058 // If all of the other operands were loop invariant, we are done.
3059 if (Ops.size() == 1) return NewRec;
3060
3061 // Otherwise, multiply the folded AddRec by the non-invariant parts.
3062 for (unsigned i = 0;; ++i)
3063 if (Ops[i] == AddRec) {
3064 Ops[i] = NewRec;
3065 break;
3066 }
3067 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3068 }
3069
3070 // Okay, if there weren't any loop invariants to be folded, check to see
3071 // if there are multiple AddRec's with the same loop induction variable
3072 // being multiplied together. If so, we can fold them.
3073
3074 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
3075 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
3076 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
3077 // ]]],+,...up to x=2n}.
3078 // Note that the arguments to choose() are always integers with values
3079 // known at compile time, never SCEV objects.
3080 //
3081 // The implementation avoids pointless extra computations when the two
3082 // addrec's are of different length (mathematically, it's equivalent to
3083 // an infinite stream of zeros on the right).
3084 bool OpsModified = false;
3085 for (unsigned OtherIdx = Idx+1;
3086 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
3087 ++OtherIdx) {
3088 const SCEVAddRecExpr *OtherAddRec =
3089 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
3090 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
3091 continue;
3092
3093 // Limit max number of arguments to avoid creation of unreasonably big
3094 // SCEVAddRecs with very complex operands.
3095 if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
3096 MaxAddRecSize || isHugeExpression(AddRec) ||
3097 isHugeExpression(OtherAddRec))
3098 continue;
3099
3100 bool Overflow = false;
3101 Type *Ty = AddRec->getType();
3102 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
3103 SmallVector<const SCEV*, 7> AddRecOps;
3104 for (int x = 0, xe = AddRec->getNumOperands() +
3105 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
3106 SmallVector <const SCEV *, 7> SumOps;
3107 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
3108 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
3109 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
3110 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
3111 z < ze && !Overflow; ++z) {
3112 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
3113 uint64_t Coeff;
3114 if (LargerThan64Bits)
3115 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
3116 else
3117 Coeff = Coeff1*Coeff2;
3118 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
3119 const SCEV *Term1 = AddRec->getOperand(y-z);
3120 const SCEV *Term2 = OtherAddRec->getOperand(z);
3121 SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
3122 SCEV::FlagAnyWrap, Depth + 1));
3123 }
3124 }
3125 if (SumOps.empty())
3126 SumOps.push_back(getZero(Ty));
3127 AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
3128 }
3129 if (!Overflow) {
3130 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRecLoop,
3131 SCEV::FlagAnyWrap);
3132 if (Ops.size() == 2) return NewAddRec;
3133 Ops[Idx] = NewAddRec;
3134 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
3135 OpsModified = true;
3136 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
3137 if (!AddRec)
3138 break;
3139 }
3140 }
3141 if (OpsModified)
3142 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3143
3144 // Otherwise couldn't fold anything into this recurrence. Move onto the
3145 // next one.
3146 }
3147
3148 // Okay, it looks like we really DO need an mul expr. Check to see if we
3149 // already have one, otherwise create a new one.
3150 return getOrCreateMulExpr(Ops, Flags);
3151}
3152
3153/// Represents an unsigned remainder expression based on unsigned division.
3154const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
3155 const SCEV *RHS) {
3156 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3158, __PRETTY_FUNCTION__))
3157 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3158, __PRETTY_FUNCTION__))
3158 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3158, __PRETTY_FUNCTION__))
;
3159
3160 // Short-circuit easy cases
3161 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3162 // If constant is one, the result is trivial
3163 if (RHSC->getValue()->isOne())
3164 return getZero(LHS->getType()); // X urem 1 --> 0
3165
3166 // If constant is a power of two, fold into a zext(trunc(LHS)).
3167 if (RHSC->getAPInt().isPowerOf2()) {
3168 Type *FullTy = LHS->getType();
3169 Type *TruncTy =
3170 IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
3171 return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
3172 }
3173 }
3174
3175 // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
3176 const SCEV *UDiv = getUDivExpr(LHS, RHS);
3177 const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
3178 return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
3179}
3180
3181/// Get a canonical unsigned division expression, or something simpler if
3182/// possible.
3183const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
3184 const SCEV *RHS) {
3185 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3187, __PRETTY_FUNCTION__))
3186 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3187, __PRETTY_FUNCTION__))
3187 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3187, __PRETTY_FUNCTION__))
;
3188
3189 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3190 if (RHSC->getValue()->isOne())
3191 return LHS; // X udiv 1 --> x
3192 // If the denominator is zero, the result of the udiv is undefined. Don't
3193 // try to analyze it, because the resolution chosen here may differ from
3194 // the resolution chosen in other parts of the compiler.
3195 if (!RHSC->getValue()->isZero()) {
3196 // Determine if the division can be folded into the operands of
3197 // its operands.
3198 // TODO: Generalize this to non-constants by using known-bits information.
3199 Type *Ty = LHS->getType();
3200 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
3201 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
3202 // For non-power-of-two values, effectively round the value up to the
3203 // nearest power of two.
3204 if (!RHSC->getAPInt().isPowerOf2())
3205 ++MaxShiftAmt;
3206 IntegerType *ExtTy =
3207 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
3208 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
3209 if (const SCEVConstant *Step =
3210 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
3211 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
3212 const APInt &StepInt = Step->getAPInt();
3213 const APInt &DivInt = RHSC->getAPInt();
3214 if (!StepInt.urem(DivInt) &&
3215 getZeroExtendExpr(AR, ExtTy) ==
3216 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3217 getZeroExtendExpr(Step, ExtTy),
3218 AR->getLoop(), SCEV::FlagAnyWrap)) {
3219 SmallVector<const SCEV *, 4> Operands;
3220 for (const SCEV *Op : AR->operands())
3221 Operands.push_back(getUDivExpr(Op, RHS));
3222 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
3223 }
3224 /// Get a canonical UDivExpr for a recurrence.
3225 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
3226 // We can currently only fold X%N if X is constant.
3227 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
3228 if (StartC && !DivInt.urem(StepInt) &&
3229 getZeroExtendExpr(AR, ExtTy) ==
3230 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3231 getZeroExtendExpr(Step, ExtTy),
3232 AR->getLoop(), SCEV::FlagAnyWrap)) {
3233 const APInt &StartInt = StartC->getAPInt();
3234 const APInt &StartRem = StartInt.urem(StepInt);
3235 if (StartRem != 0)
3236 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
3237 AR->getLoop(), SCEV::FlagNW);
3238 }
3239 }
3240 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
3241 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
3242 SmallVector<const SCEV *, 4> Operands;
3243 for (const SCEV *Op : M->operands())
3244 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3245 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
3246 // Find an operand that's safely divisible.
3247 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
3248 const SCEV *Op = M->getOperand(i);
3249 const SCEV *Div = getUDivExpr(Op, RHSC);
3250 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
3251 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
3252 M->op_end());
3253 Operands[i] = Div;
3254 return getMulExpr(Operands);
3255 }
3256 }
3257 }
3258
3259 // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
3260 if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
3261 if (auto *DivisorConstant =
3262 dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
3263 bool Overflow = false;
3264 APInt NewRHS =
3265 DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
3266 if (Overflow) {
3267 return getConstant(RHSC->getType(), 0, false);
3268 }
3269 return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
3270 }
3271 }
3272
3273 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
3274 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
3275 SmallVector<const SCEV *, 4> Operands;
3276 for (const SCEV *Op : A->operands())
3277 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3278 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
3279 Operands.clear();
3280 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
3281 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
3282 if (isa<SCEVUDivExpr>(Op) ||
3283 getMulExpr(Op, RHS) != A->getOperand(i))
3284 break;
3285 Operands.push_back(Op);
3286 }
3287 if (Operands.size() == A->getNumOperands())
3288 return getAddExpr(Operands);
3289 }
3290 }
3291
3292 // Fold if both operands are constant.
3293 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
3294 Constant *LHSCV = LHSC->getValue();
3295 Constant *RHSCV = RHSC->getValue();
3296 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
3297 RHSCV)));
3298 }
3299 }
3300 }
3301
3302 FoldingSetNodeID ID;
3303 ID.AddInteger(scUDivExpr);
3304 ID.AddPointer(LHS);
3305 ID.AddPointer(RHS);
3306 void *IP = nullptr;
3307 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3308 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
3309 LHS, RHS);
3310 UniqueSCEVs.InsertNode(S, IP);
3311 addToLoopUseLists(S);
3312 return S;
3313}
3314
3315static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
3316 APInt A = C1->getAPInt().abs();
3317 APInt B = C2->getAPInt().abs();
3318 uint32_t ABW = A.getBitWidth();
3319 uint32_t BBW = B.getBitWidth();
3320
3321 if (ABW > BBW)
3322 B = B.zext(ABW);
3323 else if (ABW < BBW)
3324 A = A.zext(BBW);
3325
3326 return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
3327}
3328
3329/// Get a canonical unsigned division expression, or something simpler if
3330/// possible. There is no representation for an exact udiv in SCEV IR, but we
3331/// can attempt to remove factors from the LHS and RHS. We can't do this when
3332/// it's not exact because the udiv may be clearing bits.
3333const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
3334 const SCEV *RHS) {
3335 // TODO: we could try to find factors in all sorts of things, but for now we
3336 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
3337 // end of this file for inspiration.
3338
3339 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
3340 if (!Mul || !Mul->hasNoUnsignedWrap())
3341 return getUDivExpr(LHS, RHS);
3342
3343 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
3344 // If the mulexpr multiplies by a constant, then that constant must be the
3345 // first element of the mulexpr.
3346 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
3347 if (LHSCst == RHSCst) {
3348 SmallVector<const SCEV *, 2> Operands;
3349 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3350 return getMulExpr(Operands);
3351 }
3352
3353 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
3354 // that there's a factor provided by one of the other terms. We need to
3355 // check.
3356 APInt Factor = gcd(LHSCst, RHSCst);
3357 if (!Factor.isIntN(1)) {
3358 LHSCst =
3359 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
3360 RHSCst =
3361 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
3362 SmallVector<const SCEV *, 2> Operands;
3363 Operands.push_back(LHSCst);
3364 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3365 LHS = getMulExpr(Operands);
3366 RHS = RHSCst;
3367 Mul = dyn_cast<SCEVMulExpr>(LHS);
3368 if (!Mul)
3369 return getUDivExactExpr(LHS, RHS);
3370 }
3371 }
3372 }
3373
3374 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
3375 if (Mul->getOperand(i) == RHS) {
3376 SmallVector<const SCEV *, 2> Operands;
3377 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
3378 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
3379 return getMulExpr(Operands);
3380 }
3381 }
3382
3383 return getUDivExpr(LHS, RHS);
3384}
3385
3386/// Get an add recurrence expression for the specified loop. Simplify the
3387/// expression as much as possible.
3388const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
3389 const Loop *L,
3390 SCEV::NoWrapFlags Flags) {
3391 SmallVector<const SCEV *, 4> Operands;
3392 Operands.push_back(Start);
3393 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
3394 if (StepChrec->getLoop() == L) {
3395 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
3396 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
3397 }
3398
3399 Operands.push_back(Step);
3400 return getAddRecExpr(Operands, L, Flags);
3401}
3402
3403/// Get an add recurrence expression for the specified loop. Simplify the
3404/// expression as much as possible.
3405const SCEV *
3406ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
3407 const Loop *L, SCEV::NoWrapFlags Flags) {
3408 if (Operands.size() == 1) return Operands[0];
3409#ifndef NDEBUG
3410 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
3411 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
3412 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3413, __PRETTY_FUNCTION__))
3413 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3413, __PRETTY_FUNCTION__))
;
3414 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3415 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3416, __PRETTY_FUNCTION__))
3416 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3416, __PRETTY_FUNCTION__))
;
3417#endif
3418
3419 if (Operands.back()->isZero()) {
3420 Operands.pop_back();
3421 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
3422 }
3423
3424 // It's tempting to want to call getMaxBackedgeTakenCount count here and
3425 // use that information to infer NUW and NSW flags. However, computing a
3426 // BE count requires calling getAddRecExpr, so we may not yet have a
3427 // meaningful BE count at this point (and if we don't, we'd be stuck
3428 // with a SCEVCouldNotCompute as the cached BE count).
3429
3430 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
3431
3432 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
3433 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
3434 const Loop *NestedLoop = NestedAR->getLoop();
3435 if (L->contains(NestedLoop)
3436 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
3437 : (!NestedLoop->contains(L) &&
3438 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
3439 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
3440 NestedAR->op_end());
3441 Operands[0] = NestedAR->getStart();
3442 // AddRecs require their operands be loop-invariant with respect to their
3443 // loops. Don't perform this transformation if it would break this
3444 // requirement.
3445 bool AllInvariant = all_of(
3446 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
3447
3448 if (AllInvariant) {
3449 // Create a recurrence for the outer loop with the same step size.
3450 //
3451 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3452 // inner recurrence has the same property.
3453 SCEV::NoWrapFlags OuterFlags =
3454 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3455
3456 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3457 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3458 return isLoopInvariant(Op, NestedLoop);
3459 });
3460
3461 if (AllInvariant) {
3462 // Ok, both add recurrences are valid after the transformation.
3463 //
3464 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3465 // the outer recurrence has the same property.
3466 SCEV::NoWrapFlags InnerFlags =
3467 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3468 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3469 }
3470 }
3471 // Reset Operands to its original state.
3472 Operands[0] = NestedAR;
3473 }
3474 }
3475
3476 // Okay, it looks like we really DO need an addrec expr. Check to see if we
3477 // already have one, otherwise create a new one.
3478 return getOrCreateAddRecExpr(Operands, L, Flags);
3479}
3480
3481const SCEV *
3482ScalarEvolution::getGEPExpr(GEPOperator *GEP,
3483 const SmallVectorImpl<const SCEV *> &IndexExprs) {
3484 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3485 // getSCEV(Base)->getType() has the same address space as Base->getType()
3486 // because SCEV::getType() preserves the address space.
3487 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
3488 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3489 // instruction to its SCEV, because the Instruction may be guarded by control
3490 // flow and the no-overflow bits may not be valid for the expression in any
3491 // context. This can be fixed similarly to how these flags are handled for
3492 // adds.
3493 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
3494 : SCEV::FlagAnyWrap;
3495
3496 const SCEV *TotalOffset = getZero(IntPtrTy);
3497 // The array size is unimportant. The first thing we do on CurTy is getting
3498 // its element type.
3499 Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
3500 for (const SCEV *IndexExpr : IndexExprs) {
3501 // Compute the (potentially symbolic) offset in bytes for this index.
3502 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3503 // For a struct, add the member offset.
3504 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3505 unsigned FieldNo = Index->getZExtValue();
3506 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3507
3508 // Add the field offset to the running total offset.
3509 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3510
3511 // Update CurTy to the type of the field at Index.
3512 CurTy = STy->getTypeAtIndex(Index);
3513 } else {
3514 // Update CurTy to its element type.
3515 CurTy = cast<SequentialType>(CurTy)->getElementType();
3516 // For an array, add the element offset, explicitly scaled.
3517 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3518 // Getelementptr indices are signed.
3519 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3520
3521 // Multiply the index by the element size to compute the element offset.
3522 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3523
3524 // Add the element offset to the running total offset.
3525 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3526 }
3527 }
3528
3529 // Add the total offset from all the GEP indices to the base.
3530 return getAddExpr(BaseExpr, TotalOffset, Wrap);
3531}
3532
3533std::tuple<const SCEV *, FoldingSetNodeID, void *>
3534ScalarEvolution::findExistingSCEVInCache(int SCEVType,
3535 ArrayRef<const SCEV *> Ops) {
3536 FoldingSetNodeID ID;
3537 void *IP = nullptr;
3538 ID.AddInteger(SCEVType);
3539 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3540 ID.AddPointer(Ops[i]);
3541 return std::tuple<const SCEV *, FoldingSetNodeID, void *>(
3542 UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP);
3543}
3544
3545const SCEV *ScalarEvolution::getMinMaxExpr(unsigned Kind,
3546 SmallVectorImpl<const SCEV *> &Ops) {
3547 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3547, __PRETTY_FUNCTION__))
;
3548 if (Ops.size() == 1) return Ops[0];
3549#ifndef NDEBUG
3550 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3551 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3552 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3553, __PRETTY_FUNCTION__))
3553 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3553, __PRETTY_FUNCTION__))
;
3554#endif
3555
3556 bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
3557 bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;
3558
3559 // Sort by complexity, this groups all similar expression types together.
3560 GroupByComplexity(Ops, &LI, DT);
3561
3562 // Check if we have created the same expression before.
3563 if (const SCEV *S = std::get<0>(findExistingSCEVInCache(Kind, Ops))) {
3564 return S;
3565 }
3566
3567 // If there are any constants, fold them together.
3568 unsigned Idx = 0;
3569 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3570 ++Idx;
3571 assert(Idx < Ops.size())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3571, __PRETTY_FUNCTION__))
;
3572 auto FoldOp = [&](const APInt &LHS, const APInt &RHS) {
3573 if (Kind == scSMaxExpr)
3574 return APIntOps::smax(LHS, RHS);
3575 else if (Kind == scSMinExpr)
3576 return APIntOps::smin(LHS, RHS);
3577 else if (Kind == scUMaxExpr)
3578 return APIntOps::umax(LHS, RHS);
3579 else if (Kind == scUMinExpr)
3580 return APIntOps::umin(LHS, RHS);
3581 llvm_unreachable("Unknown SCEV min/max opcode")::llvm::llvm_unreachable_internal("Unknown SCEV min/max opcode"
, "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3581)
;
3582 };
3583
3584 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3585 // We found two constants, fold them together!
3586 ConstantInt *Fold = ConstantInt::get(
3587 getContext(), FoldOp(LHSC->getAPInt(), RHSC->getAPInt()));
3588 Ops[0] = getConstant(Fold);
3589 Ops.erase(Ops.begin()+1); // Erase the folded element
3590 if (Ops.size() == 1) return Ops[0];
3591 LHSC = cast<SCEVConstant>(Ops[0]);
3592 }
3593
3594 bool IsMinV = LHSC->getValue()->isMinValue(IsSigned);
3595 bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned);
3596
3597 if (IsMax ? IsMinV : IsMaxV) {
3598 // If we are left with a constant minimum(/maximum)-int, strip it off.
3599 Ops.erase(Ops.begin());
3600 --Idx;
3601 } else if (IsMax ? IsMaxV : IsMinV) {
3602 // If we have a max(/min) with a constant maximum(/minimum)-int,
3603 // it will always be the extremum.
3604 return LHSC;
3605 }
3606
3607 if (Ops.size() == 1) return Ops[0];
3608 }
3609
3610 // Find the first operation of the same kind
3611 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
3612 ++Idx;
3613
3614 // Check to see if one of the operands is of the same kind. If so, expand its
3615 // operands onto our operand list, and recurse to simplify.
3616 if (Idx < Ops.size()) {
3617 bool DeletedAny = false;
3618 while (Ops[Idx]->getSCEVType() == Kind) {
3619 const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]);
3620 Ops.erase(Ops.begin()+Idx);
3621 Ops.append(SMME->op_begin(), SMME->op_end());
3622 DeletedAny = true;
3623 }
3624
3625 if (DeletedAny)
3626 return getMinMaxExpr(Kind, Ops);
3627 }
3628
3629 // Okay, check to see if the same value occurs in the operand list twice. If
3630 // so, delete one. Since we sorted the list, these values are required to
3631 // be adjacent.
3632 llvm::CmpInst::Predicate GEPred =
3633 IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
3634 llvm::CmpInst::Predicate LEPred =
3635 IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
3636 llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
3637 llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
3638 for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
3639 if (Ops[i] == Ops[i + 1] ||
3640 isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) {
3641 // X op Y op Y --> X op Y
3642 // X op Y --> X, if we know X, Y are ordered appropriately
3643 Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
3644 --i;
3645 --e;
3646 } else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i],
3647 Ops[i + 1])) {
3648 // X op Y --> Y, if we know X, Y are ordered appropriately
3649 Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
3650 --i;
3651 --e;
3652 }
3653 }
3654
3655 if (Ops.size() == 1) return Ops[0];
3656
3657 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3657, __PRETTY_FUNCTION__))
;
3658
3659 // Okay, it looks like we really DO need an expr. Check to see if we
3660 // already have one, otherwise create a new one.
3661 const SCEV *ExistingSCEV;
3662 FoldingSetNodeID ID;
3663 void *IP;
3664 std::tie(ExistingSCEV, ID, IP) = findExistingSCEVInCache(Kind, Ops);
3665 if (ExistingSCEV)
3666 return ExistingSCEV;
3667 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3668 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3669 SCEV *S = new (SCEVAllocator) SCEVMinMaxExpr(
3670 ID.Intern(SCEVAllocator), static_cast<SCEVTypes>(Kind), O, Ops.size());
3671
3672 UniqueSCEVs.InsertNode(S, IP);
3673 addToLoopUseLists(S);
3674 return S;
3675}
3676
3677const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) {
3678 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3679 return getSMaxExpr(Ops);
3680}
3681
3682const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3683 return getMinMaxExpr(scSMaxExpr, Ops);
3684}
3685
3686const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) {
3687 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3688 return getUMaxExpr(Ops);
3689}
3690
3691const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3692 return getMinMaxExpr(scUMaxExpr, Ops);
3693}
3694
3695const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3696 const SCEV *RHS) {
3697 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3698 return getSMinExpr(Ops);
3699}
3700
3701const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3702 return getMinMaxExpr(scSMinExpr, Ops);
3703}
3704
3705const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3706 const SCEV *RHS) {
3707 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3708 return getUMinExpr(Ops);
3709}
3710
3711const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3712 return getMinMaxExpr(scUMinExpr, Ops);
3713}
3714
3715const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3716 // We can bypass creating a target-independent
3717 // constant expression and then folding it back into a ConstantInt.
3718 // This is just a compile-time optimization.
3719 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3720}
3721
3722const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3723 StructType *STy,
3724 unsigned FieldNo) {
3725 // We can bypass creating a target-independent
3726 // constant expression and then folding it back into a ConstantInt.
3727 // This is just a compile-time optimization.
3728 return getConstant(
3729 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3730}
3731
3732const SCEV *ScalarEvolution::getUnknown(Value *V) {
3733 // Don't attempt to do anything other than create a SCEVUnknown object
3734 // here. createSCEV only calls getUnknown after checking for all other
3735 // interesting possibilities, and any other code that calls getUnknown
3736 // is doing so in order to hide a value from SCEV canonicalization.
3737
3738 FoldingSetNodeID ID;
3739 ID.AddInteger(scUnknown);
3740 ID.AddPointer(V);
3741 void *IP = nullptr;
3742 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3743 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3744, __PRETTY_FUNCTION__))
3744 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3744, __PRETTY_FUNCTION__))
;
3745 return S;
3746 }
3747 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3748 FirstUnknown);
3749 FirstUnknown = cast<SCEVUnknown>(S);
3750 UniqueSCEVs.InsertNode(S, IP);
3751 return S;
3752}
3753
3754//===----------------------------------------------------------------------===//
3755// Basic SCEV Analysis and PHI Idiom Recognition Code
3756//
3757
3758/// Test if values of the given type are analyzable within the SCEV
3759/// framework. This primarily includes integer types, and it can optionally
3760/// include pointer types if the ScalarEvolution class has access to
3761/// target-specific information.
3762bool ScalarEvolution::isSCEVable(Type *Ty) const {
3763 // Integers and pointers are always SCEVable.
3764 return Ty->isIntOrPtrTy();
3765}
3766
3767/// Return the size in bits of the specified type, for which isSCEVable must
3768/// return true.
3769uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3770 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3770, __PRETTY_FUNCTION__))
;
3771 if (Ty->isPointerTy())
3772 return getDataLayout().getIndexTypeSizeInBits(Ty);
3773 return getDataLayout().getTypeSizeInBits(Ty);
3774}
3775
3776/// Return a type with the same bitwidth as the given type and which represents
3777/// how SCEV will treat the given type, for which isSCEVable must return
3778/// true. For pointer types, this is the pointer-sized integer type.
3779Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3780 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3780, __PRETTY_FUNCTION__))
;
3781
3782 if (Ty->isIntegerTy())
3783 return Ty;
3784
3785 // The only other support type is pointer.
3786 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3786, __PRETTY_FUNCTION__))
;
3787 return getDataLayout().getIntPtrType(Ty);
3788}
3789
3790Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
3791 return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
3792}
3793
3794const SCEV *ScalarEvolution::getCouldNotCompute() {
3795 return CouldNotCompute.get();
3796}
3797
3798bool ScalarEvolution::checkValidity(const SCEV *S) const {
3799 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3800 auto *SU = dyn_cast<SCEVUnknown>(S);
3801 return SU && SU->getValue() == nullptr;
3802 });
3803
3804 return !ContainsNulls;
3805}
3806
3807bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3808 HasRecMapType::iterator I = HasRecMap.find(S);
3809 if (I != HasRecMap.end())
3810 return I->second;
3811
3812 bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
3813 HasRecMap.insert({S, FoundAddRec});
3814 return FoundAddRec;
3815}
3816
3817/// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3818/// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3819/// offset I, then return {S', I}, else return {\p S, nullptr}.
3820static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3821 const auto *Add = dyn_cast<SCEVAddExpr>(S);
3822 if (!Add)
3823 return {S, nullptr};
3824
3825 if (Add->getNumOperands() != 2)
3826 return {S, nullptr};
3827
3828 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3829 if (!ConstOp)
3830 return {S, nullptr};
3831
3832 return {Add->getOperand(1), ConstOp->getValue()};
3833}
3834
3835/// Return the ValueOffsetPair set for \p S. \p S can be represented
3836/// by the value and offset from any ValueOffsetPair in the set.
3837SetVector<ScalarEvolution::ValueOffsetPair> *
3838ScalarEvolution::getSCEVValues(const SCEV *S) {
3839 ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3840 if (SI == ExprValueMap.end())
3841 return nullptr;
3842#ifndef NDEBUG
3843 if (VerifySCEVMap) {
3844 // Check there is no dangling Value in the set returned.
3845 for (const auto &VE : SI->second)
3846 assert(ValueExprMap.count(VE.first))((ValueExprMap.count(VE.first)) ? static_cast<void> (0)
: __assert_fail ("ValueExprMap.count(VE.first)", "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3846, __PRETTY_FUNCTION__))
;
3847 }
3848#endif
3849 return &SI->second;
3850}
3851
3852/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3853/// cannot be used separately. eraseValueFromMap should be used to remove
3854/// V from ValueExprMap and ExprValueMap at the same time.
3855void ScalarEvolution::eraseValueFromMap(Value *V) {
3856 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3857 if (I != ValueExprMap.end()) {
3858 const SCEV *S = I->second;
3859 // Remove {V, 0} from the set of ExprValueMap[S]
3860 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
3861 SV->remove({V, nullptr});
3862
3863 // Remove {V, Offset} from the set of ExprValueMap[Stripped]
3864 const SCEV *Stripped;
3865 ConstantInt *Offset;
3866 std::tie(Stripped, Offset) = splitAddExpr(S);
3867 if (Offset != nullptr) {
3868 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
3869 SV->remove({V, Offset});
3870 }
3871 ValueExprMap.erase(V);
3872 }
3873}
3874
3875/// Check whether value has nuw/nsw/exact set but SCEV does not.
3876/// TODO: In reality it is better to check the poison recursively
3877/// but this is better than nothing.
3878static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) {
3879 if (auto *I = dyn_cast<Instruction>(V)) {
3880 if (isa<OverflowingBinaryOperator>(I)) {
3881 if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) {
3882 if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap())
3883 return true;
3884 if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap())
3885 return true;
3886 }
3887 } else if (isa<PossiblyExactOperator>(I) && I->isExact())
3888 return true;
3889 }
3890 return false;
3891}
3892
3893/// Return an existing SCEV if it exists, otherwise analyze the expression and
3894/// create a new one.
3895const SCEV *ScalarEvolution::getSCEV(Value *V) {
3896 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3896, __PRETTY_FUNCTION__))
;
3897
3898 const SCEV *S = getExistingSCEV(V);
3899 if (S == nullptr) {
3900 S = createSCEV(V);
3901 // During PHI resolution, it is possible to create two SCEVs for the same
3902 // V, so it is needed to double check whether V->S is inserted into
3903 // ValueExprMap before insert S->{V, 0} into ExprValueMap.
3904 std::pair<ValueExprMapType::iterator, bool> Pair =
3905 ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3906 if (Pair.second && !SCEVLostPoisonFlags(S, V)) {
3907 ExprValueMap[S].insert({V, nullptr});
3908
3909 // If S == Stripped + Offset, add Stripped -> {V, Offset} into
3910 // ExprValueMap.
3911 const SCEV *Stripped = S;
3912 ConstantInt *Offset = nullptr;
3913 std::tie(Stripped, Offset) = splitAddExpr(S);
3914 // If stripped is SCEVUnknown, don't bother to save
3915 // Stripped -> {V, offset}. It doesn't simplify and sometimes even
3916 // increase the complexity of the expansion code.
3917 // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
3918 // because it may generate add/sub instead of GEP in SCEV expansion.
3919 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
3920 !isa<GetElementPtrInst>(V))
3921 ExprValueMap[Stripped].insert({V, Offset});
3922 }
3923 }
3924 return S;
3925}
3926
3927const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3928 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 3928, __PRETTY_FUNCTION__))
;
3929
3930 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3931 if (I != ValueExprMap.end()) {
3932 const SCEV *S = I->second;
3933 if (checkValidity(S))
3934 return S;
3935 eraseValueFromMap(V);
3936 forgetMemoizedResults(S);
3937 }
3938 return nullptr;
3939}
3940
3941/// Return a SCEV corresponding to -V = -1*V
3942const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3943 SCEV::NoWrapFlags Flags) {
3944 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3945 return getConstant(
3946 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3947
3948 Type *Ty = V->getType();
3949 Ty = getEffectiveSCEVType(Ty);
3950 return getMulExpr(
3951 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3952}
3953
3954/// If Expr computes ~A, return A else return nullptr
3955static const SCEV *MatchNotExpr(const SCEV *Expr) {
3956 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
3957 if (!Add || Add->getNumOperands() != 2 ||
3958 !Add->getOperand(0)->isAllOnesValue())
3959 return nullptr;
3960
3961 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
3962 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
3963 !AddRHS->getOperand(0)->isAllOnesValue())
3964 return nullptr;
3965
3966 return AddRHS->getOperand(1);
3967}
3968
3969/// Return a SCEV corresponding to ~V = -1-V
3970const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3971 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3972 return getConstant(
3973 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3974
3975 // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
3976 if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) {
3977 auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
3978 SmallVector<const SCEV *, 2> MatchedOperands;
3979 for (const SCEV *Operand : MME->operands()) {
3980 const SCEV *Matched = MatchNotExpr(Operand);
3981 if (!Matched)
3982 return (const SCEV *)nullptr;
3983 MatchedOperands.push_back(Matched);
3984 }
3985 return getMinMaxExpr(
3986 SCEVMinMaxExpr::negate(static_cast<SCEVTypes>(MME->getSCEVType())),
3987 MatchedOperands);
3988 };
3989 if (const SCEV *Replaced = MatchMinMaxNegation(MME))
3990 return Replaced;
3991 }
3992
3993 Type *Ty = V->getType();
3994 Ty = getEffectiveSCEVType(Ty);
3995 const SCEV *AllOnes =
3996 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3997 return getMinusSCEV(AllOnes, V);
3998}
3999
4000const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
4001 SCEV::NoWrapFlags Flags,
4002 unsigned Depth) {
4003 // Fast path: X - X --> 0.
4004 if (LHS == RHS)
4005 return getZero(LHS->getType());
4006
4007 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
4008 // makes it so that we cannot make much use of NUW.
4009 auto AddFlags = SCEV::FlagAnyWrap;
4010 const bool RHSIsNotMinSigned =
4011 !getSignedRangeMin(RHS).isMinSignedValue();
4012 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
4013 // Let M be the minimum representable signed value. Then (-1)*RHS
4014 // signed-wraps if and only if RHS is M. That can happen even for
4015 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
4016 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
4017 // (-1)*RHS, we need to prove that RHS != M.
4018 //
4019 // If LHS is non-negative and we know that LHS - RHS does not
4020 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
4021 // either by proving that RHS > M or that LHS >= 0.
4022 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
4023 AddFlags = SCEV::FlagNSW;
4024 }
4025 }
4026
4027 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
4028 // RHS is NSW and LHS >= 0.
4029 //
4030 // The difficulty here is that the NSW flag may have been proven
4031 // relative to a loop that is to be found in a recurrence in LHS and
4032 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
4033 // larger scope than intended.
4034 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
4035
4036 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
4037}
4038
4039const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
4040 unsigned Depth) {
4041 Type *SrcTy = V->getType();
4042 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4043, __PRETTY_FUNCTION__))
4043 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4043, __PRETTY_FUNCTION__))
;
4044 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4045 return V; // No conversion
4046 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
4047 return getTruncateExpr(V, Ty, Depth);
4048 return getZeroExtendExpr(V, Ty, Depth);
4049}
4050
4051const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
4052 unsigned Depth) {
4053 Type *SrcTy = V->getType();
4054 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4055, __PRETTY_FUNCTION__))
4055 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4055, __PRETTY_FUNCTION__))
;
4056 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4057 return V; // No conversion
4058 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
4059 return getTruncateExpr(V, Ty, Depth);
4060 return getSignExtendExpr(V, Ty, Depth);
4061}
4062
4063const SCEV *
4064ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
4065 Type *SrcTy = V->getType();
4066 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4067, __PRETTY_FUNCTION__))
4067 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4067, __PRETTY_FUNCTION__))
;
4068 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4069, __PRETTY_FUNCTION__))
4069 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4069, __PRETTY_FUNCTION__))
;
4070 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4071 return V; // No conversion
4072 return getZeroExtendExpr(V, Ty);
4073}
4074
4075const SCEV *
4076ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
4077 Type *SrcTy = V->getType();
4078 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4079, __PRETTY_FUNCTION__))
4079 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4079, __PRETTY_FUNCTION__))
;
4080 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4081, __PRETTY_FUNCTION__))
4081 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4081, __PRETTY_FUNCTION__))
;
4082 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4083 return V; // No conversion
4084 return getSignExtendExpr(V, Ty);
4085}
4086
4087const SCEV *
4088ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
4089 Type *SrcTy = V->getType();
4090 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4091, __PRETTY_FUNCTION__))
4091 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4091, __PRETTY_FUNCTION__))
;
4092 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4093, __PRETTY_FUNCTION__))
4093 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4093, __PRETTY_FUNCTION__))
;
4094 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4095 return V; // No conversion
4096 return getAnyExtendExpr(V, Ty);
4097}
4098
4099const SCEV *
4100ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
4101 Type *SrcTy = V->getType();
4102 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4103, __PRETTY_FUNCTION__))
4103 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4103, __PRETTY_FUNCTION__))
;
4104 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4105, __PRETTY_FUNCTION__))
4105 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4105, __PRETTY_FUNCTION__))
;
4106 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4107 return V; // No conversion
4108 return getTruncateExpr(V, Ty);
4109}
4110
4111const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
4112 const SCEV *RHS) {
4113 const SCEV *PromotedLHS = LHS;
4114 const SCEV *PromotedRHS = RHS;
4115
4116 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
4117 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
4118 else
4119 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
4120
4121 return getUMaxExpr(PromotedLHS, PromotedRHS);
4122}
4123
4124const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
4125 const SCEV *RHS) {
4126 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
4127 return getUMinFromMismatchedTypes(Ops);
4128}
4129
4130const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(
4131 SmallVectorImpl<const SCEV *> &Ops) {
4132 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4132, __PRETTY_FUNCTION__))
;
4133 // Trivial case.
4134 if (Ops.size() == 1)
4135 return Ops[0];
4136
4137 // Find the max type first.
4138 Type *MaxType = nullptr;
4139 for (auto *S : Ops)
4140 if (MaxType)
4141 MaxType = getWiderType(MaxType, S->getType());
4142 else
4143 MaxType = S->getType();
4144
4145 // Extend all ops to max type.
4146 SmallVector<const SCEV *, 2> PromotedOps;
4147 for (auto *S : Ops)
4148 PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
4149
4150 // Generate umin.
4151 return getUMinExpr(PromotedOps);
4152}
4153
4154const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
4155 // A pointer operand may evaluate to a nonpointer expression, such as null.
4156 if (!V->getType()->isPointerTy())
4157 return V;
4158
4159 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
4160 return getPointerBase(Cast->getOperand());
4161 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
4162 const SCEV *PtrOp = nullptr;
4163 for (const SCEV *NAryOp : NAry->operands()) {
4164 if (NAryOp->getType()->isPointerTy()) {
4165 // Cannot find the base of an expression with multiple pointer operands.
4166 if (PtrOp)
4167 return V;
4168 PtrOp = NAryOp;
4169 }
4170 }
4171 if (!PtrOp)
4172 return V;
4173 return getPointerBase(PtrOp);
4174 }
4175 return V;
4176}
4177
4178/// Push users of the given Instruction onto the given Worklist.
4179static void
4180PushDefUseChildren(Instruction *I,
4181 SmallVectorImpl<Instruction *> &Worklist) {
4182 // Push the def-use children onto the Worklist stack.
4183 for (User *U : I->users())
4184 Worklist.push_back(cast<Instruction>(U));
4185}
4186
4187void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
4188 SmallVector<Instruction *, 16> Worklist;
4189 PushDefUseChildren(PN, Worklist);
4190
4191 SmallPtrSet<Instruction *, 8> Visited;
4192 Visited.insert(PN);
4193 while (!Worklist.empty()) {
4194 Instruction *I = Worklist.pop_back_val();
4195 if (!Visited.insert(I).second)
4196 continue;
4197
4198 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
4199 if (It != ValueExprMap.end()) {
4200 const SCEV *Old = It->second;
4201
4202 // Short-circuit the def-use traversal if the symbolic name
4203 // ceases to appear in expressions.
4204 if (Old != SymName && !hasOperand(Old, SymName))
4205 continue;
4206
4207 // SCEVUnknown for a PHI either means that it has an unrecognized
4208 // structure, it's a PHI that's in the progress of being computed
4209 // by createNodeForPHI, or it's a single-value PHI. In the first case,
4210 // additional loop trip count information isn't going to change anything.
4211 // In the second case, createNodeForPHI will perform the necessary
4212 // updates on its own when it gets to that point. In the third, we do
4213 // want to forget the SCEVUnknown.
4214 if (!isa<PHINode>(I) ||
4215 !isa<SCEVUnknown>(Old) ||
4216 (I != PN && Old == SymName)) {
4217 eraseValueFromMap(It->first);
4218 forgetMemoizedResults(Old);
4219 }
4220 }
4221
4222 PushDefUseChildren(I, Worklist);
4223 }
4224}
4225
4226namespace {
4227
4228/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
4229/// expression in case its Loop is L. If it is not L then
4230/// if IgnoreOtherLoops is true then use AddRec itself
4231/// otherwise rewrite cannot be done.
4232/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4233class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4234public:
4235 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
4236 bool IgnoreOtherLoops = true) {
4237 SCEVInitRewriter Rewriter(L, SE);
4238 const SCEV *Result = Rewriter.visit(S);
4239 if (Rewriter.hasSeenLoopVariantSCEVUnknown())
4240 return SE.getCouldNotCompute();
4241 return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
4242 ? SE.getCouldNotCompute()
4243 : Result;
4244 }
4245
4246 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4247 if (!SE.isLoopInvariant(Expr, L))
4248 SeenLoopVariantSCEVUnknown = true;
4249 return Expr;
4250 }
4251
4252 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4253 // Only re-write AddRecExprs for this loop.
4254 if (Expr->getLoop() == L)
4255 return Expr->getStart();
4256 SeenOtherLoops = true;
4257 return Expr;
4258 }
4259
4260 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4261
4262 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4263
4264private:
4265 explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
4266 : SCEVRewriteVisitor(SE), L(L) {}
4267
4268 const Loop *L;
4269 bool SeenLoopVariantSCEVUnknown = false;
4270 bool SeenOtherLoops = false;
4271};
4272
4273/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
4274/// increment expression in case its Loop is L. If it is not L then
4275/// use AddRec itself.
4276/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4277class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
4278public:
4279 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
4280 SCEVPostIncRewriter Rewriter(L, SE);
4281 const SCEV *Result = Rewriter.visit(S);
4282 return Rewriter.hasSeenLoopVariantSCEVUnknown()
4283 ? SE.getCouldNotCompute()
4284 : Result;
4285 }
4286
4287 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4288 if (!SE.isLoopInvariant(Expr, L))
4289 SeenLoopVariantSCEVUnknown = true;
4290 return Expr;
4291 }
4292
4293 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4294 // Only re-write AddRecExprs for this loop.
4295 if (Expr->getLoop() == L)
4296 return Expr->getPostIncExpr(SE);
4297 SeenOtherLoops = true;
4298 return Expr;
4299 }
4300
4301 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4302
4303 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4304
4305private:
4306 explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
4307 : SCEVRewriteVisitor(SE), L(L) {}
4308
4309 const Loop *L;
4310 bool SeenLoopVariantSCEVUnknown = false;
4311 bool SeenOtherLoops = false;
4312};
4313
4314/// This class evaluates the compare condition by matching it against the
4315/// condition of loop latch. If there is a match we assume a true value
4316/// for the condition while building SCEV nodes.
4317class SCEVBackedgeConditionFolder
4318 : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4319public:
4320 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4321 ScalarEvolution &SE) {
4322 bool IsPosBECond = false;
4323 Value *BECond = nullptr;
4324 if (BasicBlock *Latch = L->getLoopLatch()) {
4325 BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
4326 if (BI && BI->isConditional()) {
4327 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4328, __PRETTY_FUNCTION__))
4328 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4328, __PRETTY_FUNCTION__))
;
4329 BECond = BI->getCondition();
4330 IsPosBECond = BI->getSuccessor(0) == L->getHeader();
4331 } else {
4332 return S;
4333 }
4334 }
4335 SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
4336 return Rewriter.visit(S);
4337 }
4338
4339 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4340 const SCEV *Result = Expr;
4341 bool InvariantF = SE.isLoopInvariant(Expr, L);
4342
4343 if (!InvariantF) {
4344 Instruction *I = cast<Instruction>(Expr->getValue());
4345 switch (I->getOpcode()) {
4346 case Instruction::Select: {
4347 SelectInst *SI = cast<SelectInst>(I);
4348 Optional<const SCEV *> Res =
4349 compareWithBackedgeCondition(SI->getCondition());
4350 if (Res.hasValue()) {
4351 bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
4352 Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
4353 }
4354 break;
4355 }
4356 default: {
4357 Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
4358 if (Res.hasValue())
4359 Result = Res.getValue();
4360 break;
4361 }
4362 }
4363 }
4364 return Result;
4365 }
4366
4367private:
4368 explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
4369 bool IsPosBECond, ScalarEvolution &SE)
4370 : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
4371 IsPositiveBECond(IsPosBECond) {}
4372
4373 Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
4374
4375 const Loop *L;
4376 /// Loop back condition.
4377 Value *BackedgeCond = nullptr;
4378 /// Set to true if loop back is on positive branch condition.
4379 bool IsPositiveBECond;
4380};
4381
4382Optional<const SCEV *>
4383SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
4384
4385 // If value matches the backedge condition for loop latch,
4386 // then return a constant evolution node based on loopback
4387 // branch taken.
4388 if (BackedgeCond == IC)
4389 return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
4390 : SE.getZero(Type::getInt1Ty(SE.getContext()));
4391 return None;
4392}
4393
4394class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4395public:
4396 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4397 ScalarEvolution &SE) {
4398 SCEVShiftRewriter Rewriter(L, SE);
4399 const SCEV *Result = Rewriter.visit(S);
4400 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4401 }
4402
4403 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4404 // Only allow AddRecExprs for this loop.
4405 if (!SE.isLoopInvariant(Expr, L))
4406 Valid = false;
4407 return Expr;
4408 }
4409
4410 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4411 if (Expr->getLoop() == L && Expr->isAffine())
4412 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
4413 Valid = false;
4414 return Expr;
4415 }
4416
4417 bool isValid() { return Valid; }
4418
4419private:
4420 explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
4421 : SCEVRewriteVisitor(SE), L(L) {}
4422
4423 const Loop *L;
4424 bool Valid = true;
4425};
4426
4427} // end anonymous namespace
4428
4429SCEV::NoWrapFlags
4430ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
4431 if (!AR->isAffine())
4432 return SCEV::FlagAnyWrap;
4433
4434 using OBO = OverflowingBinaryOperator;
4435
4436 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
4437
4438 if (!AR->hasNoSignedWrap()) {
4439 ConstantRange AddRecRange = getSignedRange(AR);
4440 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
4441
4442 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4443 Instruction::Add, IncRange, OBO::NoSignedWrap);
4444 if (NSWRegion.contains(AddRecRange))
4445 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
4446 }
4447
4448 if (!AR->hasNoUnsignedWrap()) {
4449 ConstantRange AddRecRange = getUnsignedRange(AR);
4450 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
4451
4452 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4453 Instruction::Add, IncRange, OBO::NoUnsignedWrap);
4454 if (NUWRegion.contains(AddRecRange))
4455 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
4456 }
4457
4458 return Result;
4459}
4460
4461namespace {
4462
4463/// Represents an abstract binary operation. This may exist as a
4464/// normal instruction or constant expression, or may have been
4465/// derived from an expression tree.
4466struct BinaryOp {
4467 unsigned Opcode;
4468 Value *LHS;
4469 Value *RHS;
4470 bool IsNSW = false;
4471 bool IsNUW = false;
4472
4473 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
4474 /// constant expression.
4475 Operator *Op = nullptr;
4476
4477 explicit BinaryOp(Operator *Op)
4478 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
4479 Op(Op) {
4480 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
4481 IsNSW = OBO->hasNoSignedWrap();
4482 IsNUW = OBO->hasNoUnsignedWrap();
4483 }
4484 }
4485
4486 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
4487 bool IsNUW = false)
4488 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
4489};
4490
4491} // end anonymous namespace
4492
4493/// Try to map \p V into a BinaryOp, and return \c None on failure.
4494static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
4495 auto *Op = dyn_cast<Operator>(V);
4496 if (!Op)
4497 return None;
4498
4499 // Implementation detail: all the cleverness here should happen without
4500 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
4501 // SCEV expressions when possible, and we should not break that.
4502
4503 switch (Op->getOpcode()) {
4504 case Instruction::Add:
4505 case Instruction::Sub:
4506 case Instruction::Mul:
4507 case Instruction::UDiv:
4508 case Instruction::URem:
4509 case Instruction::And:
4510 case Instruction::Or:
4511 case Instruction::AShr:
4512 case Instruction::Shl:
4513 return BinaryOp(Op);
4514
4515 case Instruction::Xor:
4516 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
4517 // If the RHS of the xor is a signmask, then this is just an add.
4518 // Instcombine turns add of signmask into xor as a strength reduction step.
4519 if (RHSC->getValue().isSignMask())
4520 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
4521 return BinaryOp(Op);
4522
4523 case Instruction::LShr:
4524 // Turn logical shift right of a constant into a unsigned divide.
4525 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
4526 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
4527
4528 // If the shift count is not less than the bitwidth, the result of
4529 // the shift is undefined. Don't try to analyze it, because the
4530 // resolution chosen here may differ from the resolution chosen in
4531 // other parts of the compiler.
4532 if (SA->getValue().ult(BitWidth)) {
4533 Constant *X =
4534 ConstantInt::get(SA->getContext(),
4535 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4536 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
4537 }
4538 }
4539 return BinaryOp(Op);
4540
4541 case Instruction::ExtractValue: {
4542 auto *EVI = cast<ExtractValueInst>(Op);
4543 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
4544 break;
4545
4546 auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand());
4547 if (!WO)
4548 break;
4549
4550 Instruction::BinaryOps BinOp = WO->getBinaryOp();
4551 bool Signed = WO->isSigned();
4552 // TODO: Should add nuw/nsw flags for mul as well.
4553 if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
4554 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());
4555
4556 // Now that we know that all uses of the arithmetic-result component of
4557 // CI are guarded by the overflow check, we can go ahead and pretend
4558 // that the arithmetic is non-overflowing.
4559 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
4560 /* IsNSW = */ Signed, /* IsNUW = */ !Signed);
4561 }
4562
4563 default:
4564 break;
4565 }
4566
4567 return None;
4568}
4569
4570/// Helper function to createAddRecFromPHIWithCasts. We have a phi
4571/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
4572/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
4573/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
4574/// follows one of the following patterns:
4575/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4576/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4577/// If the SCEV expression of \p Op conforms with one of the expected patterns
4578/// we return the type of the truncation operation, and indicate whether the
4579/// truncated type should be treated as signed/unsigned by setting
4580/// \p Signed to true/false, respectively.
4581static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
4582 bool &Signed, ScalarEvolution &SE) {
4583 // The case where Op == SymbolicPHI (that is, with no type conversions on
4584 // the way) is handled by the regular add recurrence creating logic and
4585 // would have already been triggered in createAddRecForPHI. Reaching it here
4586 // means that createAddRecFromPHI had failed for this PHI before (e.g.,
4587 // because one of the other operands of the SCEVAddExpr updating this PHI is
4588 // not invariant).
4589 //
4590 // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
4591 // this case predicates that allow us to prove that Op == SymbolicPHI will
4592 // be added.
4593 if (Op == SymbolicPHI)
4594 return nullptr;
4595
4596 unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
4597 unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
4598 if (SourceBits != NewBits)
4599 return nullptr;
4600
4601 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
4602 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
4603 if (!SExt && !ZExt)
4604 return nullptr;
4605 const SCEVTruncateExpr *Trunc =
4606 SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
4607 : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
4608 if (!Trunc)
4609 return nullptr;
4610 const SCEV *X = Trunc->getOperand();
4611 if (X != SymbolicPHI)
4612 return nullptr;
4613 Signed = SExt != nullptr;
4614 return Trunc->getType();
4615}
4616
4617static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
4618 if (!PN->getType()->isIntegerTy())
4619 return nullptr;
4620 const Loop *L = LI.getLoopFor(PN->getParent());
4621 if (!L || L->getHeader() != PN->getParent())
4622 return nullptr;
4623 return L;
4624}
4625
4626// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
4627// computation that updates the phi follows the following pattern:
4628// (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
4629// which correspond to a phi->trunc->sext/zext->add->phi update chain.
4630// If so, try to see if it can be rewritten as an AddRecExpr under some
4631// Predicates. If successful, return them as a pair. Also cache the results
4632// of the analysis.
4633//
4634// Example usage scenario:
4635// Say the Rewriter is called for the following SCEV:
4636// 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4637// where:
4638// %X = phi i64 (%Start, %BEValue)
4639// It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
4640// and call this function with %SymbolicPHI = %X.
4641//
4642// The analysis will find that the value coming around the backedge has
4643// the following SCEV:
4644// BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4645// Upon concluding that this matches the desired pattern, the function
4646// will return the pair {NewAddRec, SmallPredsVec} where:
4647// NewAddRec = {%Start,+,%Step}
4648// SmallPredsVec = {P1, P2, P3} as follows:
4649// P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
4650// P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
4651// P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
4652// The returned pair means that SymbolicPHI can be rewritten into NewAddRec
4653// under the predicates {P1,P2,P3}.
4654// This predicated rewrite will be cached in PredicatedSCEVRewrites:
4655// PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
4656//
4657// TODO's:
4658//
4659// 1) Extend the Induction descriptor to also support inductions that involve
4660// casts: When needed (namely, when we are called in the context of the
4661// vectorizer induction analysis), a Set of cast instructions will be
4662// populated by this method, and provided back to isInductionPHI. This is
4663// needed to allow the vectorizer to properly record them to be ignored by
4664// the cost model and to avoid vectorizing them (otherwise these casts,
4665// which are redundant under the runtime overflow checks, will be
4666// vectorized, which can be costly).
4667//
4668// 2) Support additional induction/PHISCEV patterns: We also want to support
4669// inductions where the sext-trunc / zext-trunc operations (partly) occur
4670// after the induction update operation (the induction increment):
4671//
4672// (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
4673// which correspond to a phi->add->trunc->sext/zext->phi update chain.
4674//
4675// (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
4676// which correspond to a phi->trunc->add->sext/zext->phi update chain.
4677//
4678// 3) Outline common code with createAddRecFromPHI to avoid duplication.
4679Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4680ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
4681 SmallVector<const SCEVPredicate *, 3> Predicates;
4682
4683 // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
4684 // return an AddRec expression under some predicate.
4685
4686 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4687 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4688 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4688, __PRETTY_FUNCTION__))
;
4689
4690 // The loop may have multiple entrances or multiple exits; we can analyze
4691 // this phi as an addrec if it has a unique entry value and a unique
4692 // backedge value.
4693 Value *BEValueV = nullptr, *StartValueV = nullptr;
4694 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4695 Value *V = PN->getIncomingValue(i);
4696 if (L->contains(PN->getIncomingBlock(i))) {
4697 if (!BEValueV) {
4698 BEValueV = V;
4699 } else if (BEValueV != V) {
4700 BEValueV = nullptr;
4701 break;
4702 }
4703 } else if (!StartValueV) {
4704 StartValueV = V;
4705 } else if (StartValueV != V) {
4706 StartValueV = nullptr;
4707 break;
4708 }
4709 }
4710 if (!BEValueV || !StartValueV)
4711 return None;
4712
4713 const SCEV *BEValue = getSCEV(BEValueV);
4714
4715 // If the value coming around the backedge is an add with the symbolic
4716 // value we just inserted, possibly with casts that we can ignore under
4717 // an appropriate runtime guard, then we found a simple induction variable!
4718 const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
4719 if (!Add)
4720 return None;
4721
4722 // If there is a single occurrence of the symbolic value, possibly
4723 // casted, replace it with a recurrence.
4724 unsigned FoundIndex = Add->getNumOperands();
4725 Type *TruncTy = nullptr;
4726 bool Signed;
4727 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4728 if ((TruncTy =
4729 isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
4730 if (FoundIndex == e) {
4731 FoundIndex = i;
4732 break;
4733 }
4734
4735 if (FoundIndex == Add->getNumOperands())
4736 return None;
4737
4738 // Create an add with everything but the specified operand.
4739 SmallVector<const SCEV *, 8> Ops;
4740 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4741 if (i != FoundIndex)
4742 Ops.push_back(Add->getOperand(i));
4743 const SCEV *Accum = getAddExpr(Ops);
4744
4745 // The runtime checks will not be valid if the step amount is
4746 // varying inside the loop.
4747 if (!isLoopInvariant(Accum, L))
4748 return None;
4749
4750 // *** Part2: Create the predicates
4751
4752 // Analysis was successful: we have a phi-with-cast pattern for which we
4753 // can return an AddRec expression under the following predicates:
4754 //
4755 // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
4756 // fits within the truncated type (does not overflow) for i = 0 to n-1.
4757 // P2: An Equal predicate that guarantees that
4758 // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
4759 // P3: An Equal predicate that guarantees that
4760 // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
4761 //
4762 // As we next prove, the above predicates guarantee that:
4763 // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
4764 //
4765 //
4766 // More formally, we want to prove that:
4767 // Expr(i+1) = Start + (i+1) * Accum
4768 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4769 //
4770 // Given that:
4771 // 1) Expr(0) = Start
4772 // 2) Expr(1) = Start + Accum
4773 // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
4774 // 3) Induction hypothesis (step i):
4775 // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
4776 //
4777 // Proof:
4778 // Expr(i+1) =
4779 // = Start + (i+1)*Accum
4780 // = (Start + i*Accum) + Accum
4781 // = Expr(i) + Accum
4782 // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
4783 // :: from step i
4784 //
4785 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
4786 //
4787 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
4788 // + (Ext ix (Trunc iy (Accum) to ix) to iy)
4789 // + Accum :: from P3
4790 //
4791 // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
4792 // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
4793 //
4794 // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
4795 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4796 //
4797 // By induction, the same applies to all iterations 1<=i<n:
4798 //
4799
4800 // Create a truncated addrec for which we will add a no overflow check (P1).
4801 const SCEV *StartVal = getSCEV(StartValueV);
4802 const SCEV *PHISCEV =
4803 getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
4804 getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
4805
4806 // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
4807 // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
4808 // will be constant.
4809 //
4810 // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
4811 // add P1.
4812 if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
4813 SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
4814 Signed ? SCEVWrapPredicate::IncrementNSSW
4815 : SCEVWrapPredicate::IncrementNUSW;
4816 const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
4817 Predicates.push_back(AddRecPred);
4818 }
4819
4820 // Create the Equal Predicates P2,P3:
4821
4822 // It is possible that the predicates P2 and/or P3 are computable at
4823 // compile time due to StartVal and/or Accum being constants.
4824 // If either one is, then we can check that now and escape if either P2
4825 // or P3 is false.
4826
4827 // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
4828 // for each of StartVal and Accum
4829 auto getExtendedExpr = [&](const SCEV *Expr,
4830 bool CreateSignExtend) -> const SCEV * {
4831 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4831, __PRETTY_FUNCTION__))
;
4832 const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
4833 const SCEV *ExtendedExpr =
4834 CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
4835 : getZeroExtendExpr(TruncatedExpr, Expr->getType());
4836 return ExtendedExpr;
4837 };
4838
4839 // Given:
4840 // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
4841 // = getExtendedExpr(Expr)
4842 // Determine whether the predicate P: Expr == ExtendedExpr
4843 // is known to be false at compile time
4844 auto PredIsKnownFalse = [&](const SCEV *Expr,
4845 const SCEV *ExtendedExpr) -> bool {
4846 return Expr != ExtendedExpr &&
4847 isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
4848 };
4849
4850 const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
4851 if (PredIsKnownFalse(StartVal, StartExtended)) {
4852 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)
;
4853 return None;
4854 }
4855
4856 // The Step is always Signed (because the overflow checks are either
4857 // NSSW or NUSW)
4858 const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
4859 if (PredIsKnownFalse(Accum, AccumExtended)) {
4860 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)
;
4861 return None;
4862 }
4863
4864 auto AppendPredicate = [&](const SCEV *Expr,
4865 const SCEV *ExtendedExpr) -> void {
4866 if (Expr != ExtendedExpr &&
4867 !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
4868 const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
4869 LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred)do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "Added Predicate: " <<
*Pred; } } while (false)
;
4870 Predicates.push_back(Pred);
4871 }
4872 };
4873
4874 AppendPredicate(StartVal, StartExtended);
4875 AppendPredicate(Accum, AccumExtended);
4876
4877 // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
4878 // which the casts had been folded away. The caller can rewrite SymbolicPHI
4879 // into NewAR if it will also add the runtime overflow checks specified in
4880 // Predicates.
4881 auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
4882
4883 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
4884 std::make_pair(NewAR, Predicates);
4885 // Remember the result of the analysis for this SCEV at this locayyytion.
4886 PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
4887 return PredRewrite;
4888}
4889
4890Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4891ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
4892 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4893 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4894 if (!L)
4895 return None;
4896
4897 // Check to see if we already analyzed this PHI.
4898 auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
4899 if (I != PredicatedSCEVRewrites.end()) {
4900 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
4901 I->second;
4902 // Analysis was done before and failed to create an AddRec:
4903 if (Rewrite.first == SymbolicPHI)
4904 return None;
4905 // Analysis was done before and succeeded to create an AddRec under
4906 // a predicate:
4907 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4907, __PRETTY_FUNCTION__))
;
4908 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4908, __PRETTY_FUNCTION__))
;
4909 return Rewrite;
4910 }
4911
4912 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4913 Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
4914
4915 // Record in the cache that the analysis failed
4916 if (!Rewrite) {
4917 SmallVector<const SCEVPredicate *, 3> Predicates;
4918 PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
4919 return None;
4920 }
4921
4922 return Rewrite;
4923}
4924
4925// FIXME: This utility is currently required because the Rewriter currently
4926// does not rewrite this expression:
4927// {0, +, (sext ix (trunc iy to ix) to iy)}
4928// into {0, +, %step},
4929// even when the following Equal predicate exists:
4930// "%step == (sext ix (trunc iy to ix) to iy)".
4931bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
4932 const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
4933 if (AR1 == AR2)
4934 return true;
4935
4936 auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
4937 if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
4938 !Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
4939 return false;
4940 return true;
4941 };
4942
4943 if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
4944 !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
4945 return false;
4946 return true;
4947}
4948
4949/// A helper function for createAddRecFromPHI to handle simple cases.
4950///
4951/// This function tries to find an AddRec expression for the simplest (yet most
4952/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
4953/// If it fails, createAddRecFromPHI will use a more general, but slow,
4954/// technique for finding the AddRec expression.
4955const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
4956 Value *BEValueV,
4957 Value *StartValueV) {
4958 const Loop *L = LI.getLoopFor(PN->getParent());
4959 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4959, __PRETTY_FUNCTION__))
;
4960 assert(BEValueV && StartValueV)((BEValueV && StartValueV) ? static_cast<void> (
0) : __assert_fail ("BEValueV && StartValueV", "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 4960, __PRETTY_FUNCTION__))
;
4961
4962 auto BO = MatchBinaryOp(BEValueV, DT);
4963 if (!BO)
4964 return nullptr;
4965
4966 if (BO->Opcode != Instruction::Add)
4967 return nullptr;
4968
4969 const SCEV *Accum = nullptr;
4970 if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
4971 Accum = getSCEV(BO->RHS);
4972 else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
4973 Accum = getSCEV(BO->LHS);
4974
4975 if (!Accum)
4976 return nullptr;
4977
4978 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4979 if (BO->IsNUW)
4980 Flags = setFlags(Flags, SCEV::FlagNUW);
4981 if (BO->IsNSW)
4982 Flags = setFlags(Flags, SCEV::FlagNSW);
4983
4984 const SCEV *StartVal = getSCEV(StartValueV);
4985 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4986
4987 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4988
4989 // We can add Flags to the post-inc expression only if we
4990 // know that it is *undefined behavior* for BEValueV to
4991 // overflow.
4992 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4993 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4994 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4995
4996 return PHISCEV;
4997}
4998
4999const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
5000 const Loop *L = LI.getLoopFor(PN->getParent());
5001 if (!L || L->getHeader() != PN->getParent())
5002 return nullptr;
5003
5004 // The loop may have multiple entrances or multiple exits; we can analyze
5005 // this phi as an addrec if it has a unique entry value and a unique
5006 // backedge value.
5007 Value *BEValueV = nullptr, *StartValueV = nullptr;
5008 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5009 Value *V = PN->getIncomingValue(i);
5010 if (L->contains(PN->getIncomingBlock(i))) {
5011 if (!BEValueV) {
5012 BEValueV = V;
5013 } else if (BEValueV != V) {
5014 BEValueV = nullptr;
5015 break;
5016 }
5017 } else if (!StartValueV) {
5018 StartValueV = V;
5019 } else if (StartValueV != V) {
5020 StartValueV = nullptr;
5021 break;
5022 }
5023 }
5024 if (!BEValueV || !StartValueV)
5025 return nullptr;
5026
5027 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 5028, __PRETTY_FUNCTION__))
5028 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 5028, __PRETTY_FUNCTION__))
;
5029
5030 // First, try to find AddRec expression without creating a fictituos symbolic
5031 // value for PN.
5032 if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
5033 return S;
5034
5035 // Handle PHI node value symbolically.
5036 const SCEV *SymbolicName = getUnknown(PN);
5037 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
5038
5039 // Using this symbolic name for the PHI, analyze the value coming around
5040 // the back-edge.
5041 const SCEV *BEValue = getSCEV(BEValueV);
5042
5043 // NOTE: If BEValue is loop invariant, we know that the PHI node just
5044 // has a special value for the first iteration of the loop.
5045
5046 // If the value coming around the backedge is an add with the symbolic
5047 // value we just inserted, then we found a simple induction variable!
5048 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
5049 // If there is a single occurrence of the symbolic value, replace it
5050 // with a recurrence.
5051 unsigned FoundIndex = Add->getNumOperands();
5052 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5053 if (Add->getOperand(i) == SymbolicName)
5054 if (FoundIndex == e) {
5055 FoundIndex = i;
5056 break;
5057 }
5058
5059 if (FoundIndex != Add->getNumOperands()) {
5060 // Create an add with everything but the specified operand.
5061 SmallVector<const SCEV *, 8> Ops;
5062 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5063 if (i != FoundIndex)
5064 Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
5065 L, *this));
5066 const SCEV *Accum = getAddExpr(Ops);
5067
5068 // This is not a valid addrec if the step amount is varying each
5069 // loop iteration, but is not itself an addrec in this loop.
5070 if (isLoopInvariant(Accum, L) ||
5071 (isa<SCEVAddRecExpr>(Accum) &&
5072 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
5073 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5074
5075 if (auto BO = MatchBinaryOp(BEValueV, DT)) {
5076 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
5077 if (BO->IsNUW)
5078 Flags = setFlags(Flags, SCEV::FlagNUW);
5079 if (BO->IsNSW)
5080 Flags = setFlags(Flags, SCEV::FlagNSW);
5081 }
5082 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
5083 // If the increment is an inbounds GEP, then we know the address
5084 // space cannot be wrapped around. We cannot make any guarantee
5085 // about signed or unsigned overflow because pointers are
5086 // unsigned but we may have a negative index from the base
5087 // pointer. We can guarantee that no unsigned wrap occurs if the
5088 // indices form a positive value.
5089 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
5090 Flags = setFlags(Flags, SCEV::FlagNW);
5091
5092 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
5093 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
5094 Flags = setFlags(Flags, SCEV::FlagNUW);
5095 }
5096
5097 // We cannot transfer nuw and nsw flags from subtraction
5098 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
5099 // for instance.
5100 }
5101
5102 const SCEV *StartVal = getSCEV(StartValueV);
5103 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
5104
5105 // Okay, for the entire analysis of this edge we assumed the PHI
5106 // to be symbolic. We now need to go back and purge all of the
5107 // entries for the scalars that use the symbolic expression.
5108 forgetSymbolicName(PN, SymbolicName);
5109 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
5110
5111 // We can add Flags to the post-inc expression only if we
5112 // know that it is *undefined behavior* for BEValueV to
5113 // overflow.
5114 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
5115 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
5116 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
5117
5118 return PHISCEV;
5119 }
5120 }
5121 } else {
5122 // Otherwise, this could be a loop like this:
5123 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
5124 // In this case, j = {1,+,1} and BEValue is j.
5125 // Because the other in-value of i (0) fits the evolution of BEValue
5126 // i really is an addrec evolution.
5127 //
5128 // We can generalize this saying that i is the shifted value of BEValue
5129 // by one iteration:
5130 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
5131 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
5132 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
5133 if (Shifted != getCouldNotCompute() &&
5134 Start != getCouldNotCompute()) {
5135 const SCEV *StartVal = getSCEV(StartValueV);
5136 if (Start == StartVal) {
5137 // Okay, for the entire analysis of this edge we assumed the PHI
5138 // to be symbolic. We now need to go back and purge all of the
5139 // entries for the scalars that use the symbolic expression.
5140 forgetSymbolicName(PN, SymbolicName);
5141 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
5142 return Shifted;
5143 }
5144 }
5145 }
5146
5147 // Remove the temporary PHI node SCEV that has been inserted while intending
5148 // to create an AddRecExpr for this PHI node. We can not keep this temporary
5149 // as it will prevent later (possibly simpler) SCEV expressions to be added
5150 // to the ValueExprMap.
5151 eraseValueFromMap(PN);
5152
5153 return nullptr;
5154}
5155
5156// Checks if the SCEV S is available at BB. S is considered available at BB
5157// if S can be materialized at BB without introducing a fault.
5158static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
5159 BasicBlock *BB) {
5160 struct CheckAvailable {
5161 bool TraversalDone = false;
5162 bool Available = true;
5163
5164 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
5165 BasicBlock *BB = nullptr;
5166 DominatorTree &DT;
5167
5168 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
5169 : L(L), BB(BB), DT(DT) {}
5170
5171 bool setUnavailable() {
5172 TraversalDone = true;
5173 Available = false;
5174 return false;
5175 }
5176
5177 bool follow(const SCEV *S) {
5178 switch (S->getSCEVType()) {
5179 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
5180 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
5181 case scUMinExpr:
5182 case scSMinExpr:
5183 // These expressions are available if their operand(s) is/are.
5184 return true;
5185
5186 case scAddRecExpr: {
5187 // We allow add recurrences that are on the loop BB is in, or some
5188 // outer loop. This guarantees availability because the value of the
5189 // add recurrence at BB is simply the "current" value of the induction
5190 // variable. We can relax this in the future; for instance an add
5191 // recurrence on a sibling dominating loop is also available at BB.
5192 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
5193 if (L && (ARLoop == L || ARLoop->contains(L)))
5194 return true;
5195
5196 return setUnavailable();
5197 }
5198
5199 case scUnknown: {
5200 // For SCEVUnknown, we check for simple dominance.
5201 const auto *SU = cast<SCEVUnknown>(S);
5202 Value *V = SU->getValue();
5203
5204 if (isa<Argument>(V))
5205 return false;
5206
5207 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
5208 return false;
5209
5210 return setUnavailable();
5211 }
5212
5213 case scUDivExpr:
5214 case scCouldNotCompute:
5215 // We do not try to smart about these at all.
5216 return setUnavailable();
5217 }
5218 llvm_unreachable("switch should be fully covered!")::llvm::llvm_unreachable_internal("switch should be fully covered!"
, "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 5218)
;
5219 }
5220
5221 bool isDone() { return TraversalDone; }
5222 };
5223
5224 CheckAvailable CA(L, BB, DT);
5225 SCEVTraversal<CheckAvailable> ST(CA);
5226
5227 ST.visitAll(S);
5228 return CA.Available;
5229}
5230
5231// Try to match a control flow sequence that branches out at BI and merges back
5232// at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
5233// match.
5234static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
5235 Value *&C, Value *&LHS, Value *&RHS) {
5236 C = BI->getCondition();
5237
5238 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
5239 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
5240
5241 if (!LeftEdge.isSingleEdge())
5242 return false;
5243
5244 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 5244, __PRETTY_FUNCTION__))
;
5245
5246 Use &LeftUse = Merge->getOperandUse(0);
5247 Use &RightUse = Merge->getOperandUse(1);
5248
5249 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
5250 LHS = LeftUse;
5251 RHS = RightUse;
5252 return true;
5253 }
5254
5255 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
5256 LHS = RightUse;
5257 RHS = LeftUse;
5258 return true;
5259 }
5260
5261 return false;
5262}
5263
5264const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
5265 auto IsReachable =
5266 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
5267 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
5268 const Loop *L = LI.getLoopFor(PN->getParent());
5269
5270 // We don't want to break LCSSA, even in a SCEV expression tree.
5271 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
5272 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
5273 return nullptr;
5274
5275 // Try to match
5276 //
5277 // br %cond, label %left, label %right
5278 // left:
5279 // br label %merge
5280 // right:
5281 // br label %merge
5282 // merge:
5283 // V = phi [ %x, %left ], [ %y, %right ]
5284 //
5285 // as "select %cond, %x, %y"
5286
5287 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
5288 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 5288, __PRETTY_FUNCTION__))
;
5289
5290 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
5291 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
5292
5293 if (BI && BI->isConditional() &&
5294 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
5295 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
5296 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
5297 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
5298 }
5299
5300 return nullptr;
5301}
5302
5303const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
5304 if (const SCEV *S = createAddRecFromPHI(PN))
5305 return S;
5306
5307 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
5308 return S;
5309
5310 // If the PHI has a single incoming value, follow that value, unless the
5311 // PHI's incoming blocks are in a different loop, in which case doing so
5312 // risks breaking LCSSA form. Instcombine would normally zap these, but
5313 // it doesn't have DominatorTree information, so it may miss cases.
5314 if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
5315 if (LI.replacementPreservesLCSSAForm(PN, V))
5316 return getSCEV(V);
5317
5318 // If it's not a loop phi, we can't handle it yet.
5319 return getUnknown(PN);
5320}
5321
5322const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
5323 Value *Cond,
5324 Value *TrueVal,
5325 Value *FalseVal) {
5326 // Handle "constant" branch or select. This can occur for instance when a
5327 // loop pass transforms an inner loop and moves on to process the outer loop.
5328 if (auto *CI = dyn_cast<ConstantInt>(Cond))
5329 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
5330
5331 // Try to match some simple smax or umax patterns.
5332 auto *ICI = dyn_cast<ICmpInst>(Cond);
5333 if (!ICI)
5334 return getUnknown(I);
5335
5336 Value *LHS = ICI->getOperand(0);
5337 Value *RHS = ICI->getOperand(1);
5338
5339 switch (ICI->getPredicate()) {
5340 case ICmpInst::ICMP_SLT:
5341 case ICmpInst::ICMP_SLE:
5342 std::swap(LHS, RHS);
5343 LLVM_FALLTHROUGH[[clang::fallthrough]];
5344 case ICmpInst::ICMP_SGT:
5345 case ICmpInst::ICMP_SGE:
5346 // a >s b ? a+x : b+x -> smax(a, b)+x
5347 // a >s b ? b+x : a+x -> smin(a, b)+x
5348 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5349 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
5350 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
5351 const SCEV *LA = getSCEV(TrueVal);
5352 const SCEV *RA = getSCEV(FalseVal);
5353 const SCEV *LDiff = getMinusSCEV(LA, LS);
5354 const SCEV *RDiff = getMinusSCEV(RA, RS);
5355 if (LDiff == RDiff)
5356 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
5357 LDiff = getMinusSCEV(LA, RS);
5358 RDiff = getMinusSCEV(RA, LS);
5359 if (LDiff == RDiff)
5360 return getAddExpr(getSMinExpr(LS, RS), LDiff);
5361 }
5362 break;
5363 case ICmpInst::ICMP_ULT:
5364 case ICmpInst::ICMP_ULE:
5365 std::swap(LHS, RHS);
5366 LLVM_FALLTHROUGH[[clang::fallthrough]];
5367 case ICmpInst::ICMP_UGT:
5368 case ICmpInst::ICMP_UGE:
5369 // a >u b ? a+x : b+x -> umax(a, b)+x
5370 // a >u b ? b+x : a+x -> umin(a, b)+x
5371 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5372 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5373 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
5374 const SCEV *LA = getSCEV(TrueVal);
5375 const SCEV *RA = getSCEV(FalseVal);
5376 const SCEV *LDiff = getMinusSCEV(LA, LS);
5377 const SCEV *RDiff = getMinusSCEV(RA, RS);
5378 if (LDiff == RDiff)
5379 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
5380 LDiff = getMinusSCEV(LA, RS);
5381 RDiff = getMinusSCEV(RA, LS);
5382 if (LDiff == RDiff)
5383 return getAddExpr(getUMinExpr(LS, RS), LDiff);
5384 }
5385 break;
5386 case ICmpInst::ICMP_NE:
5387 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
5388 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5389 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5390 const SCEV *One = getOne(I->getType());
5391 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5392 const SCEV *LA = getSCEV(TrueVal);
5393 const SCEV *RA = getSCEV(FalseVal);
5394 const SCEV *LDiff = getMinusSCEV(LA, LS);
5395 const SCEV *RDiff = getMinusSCEV(RA, One);
5396 if (LDiff == RDiff)
5397 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5398 }
5399 break;
5400 case ICmpInst::ICMP_EQ:
5401 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
5402 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5403 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5404 const SCEV *One = getOne(I->getType());
5405 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5406 const SCEV *LA = getSCEV(TrueVal);
5407 const SCEV *RA = getSCEV(FalseVal);
5408 const SCEV *LDiff = getMinusSCEV(LA, One);
5409 const SCEV *RDiff = getMinusSCEV(RA, LS);
5410 if (LDiff == RDiff)
5411 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5412 }
5413 break;
5414 default:
5415 break;
5416 }
5417
5418 return getUnknown(I);
5419}
5420
5421/// Expand GEP instructions into add and multiply operations. This allows them
5422/// to be analyzed by regular SCEV code.
5423const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
5424 // Don't attempt to analyze GEPs over unsized objects.
5425 if (!GEP->getSourceElementType()->isSized())
5426 return getUnknown(GEP);
5427
5428 SmallVector<const SCEV *, 4> IndexExprs;
5429 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
5430 IndexExprs.push_back(getSCEV(*Index));
5431 return getGEPExpr(GEP, IndexExprs);
5432}
5433
5434uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
5435 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5436 return C->getAPInt().countTrailingZeros();
5437
5438 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
5439 return std::min(GetMinTrailingZeros(T->getOperand()),
5440 (uint32_t)getTypeSizeInBits(T->getType()));
5441
5442 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
5443 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5444 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5445 ? getTypeSizeInBits(E->getType())
5446 : OpRes;
5447 }
5448
5449 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
5450 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5451 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5452 ? getTypeSizeInBits(E->getType())
5453 : OpRes;
5454 }
5455
5456 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
5457 // The result is the min of all operands results.
5458 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5459 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5460 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5461 return MinOpRes;
5462 }
5463
5464 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
5465 // The result is the sum of all operands results.
5466 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
5467 uint32_t BitWidth = getTypeSizeInBits(M->getType());
5468 for (unsigned i = 1, e = M->getNumOperands();
5469 SumOpRes != BitWidth && i != e; ++i)
5470 SumOpRes =
5471 std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
5472 return SumOpRes;
5473 }
5474
5475 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
5476 // The result is the min of all operands results.
5477 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5478 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5479 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5480 return MinOpRes;
5481 }
5482
5483 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
5484 // The result is the min of all operands results.
5485 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5486 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5487 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5488 return MinOpRes;
5489 }
5490
5491 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
5492 // The result is the min of all operands results.
5493 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5494 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5495 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5496 return MinOpRes;
5497 }
5498
5499 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5500 // For a SCEVUnknown, ask ValueTracking.
5501 KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
5502 return Known.countMinTrailingZeros();
5503 }
5504
5505 // SCEVUDivExpr
5506 return 0;
5507}
5508
5509uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
5510 auto I = MinTrailingZerosCache.find(S);
5511 if (I != MinTrailingZerosCache.end())
5512 return I->second;
5513
5514 uint32_t Result = GetMinTrailingZerosImpl(S);
5515 auto InsertPair = MinTrailingZerosCache.insert({S, Result});
5516 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 5516, __PRETTY_FUNCTION__))
;
5517 return InsertPair.first->second;
5518}
5519
5520/// Helper method to assign a range to V from metadata present in the IR.
5521static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
5522 if (Instruction *I = dyn_cast<Instruction>(V))
5523 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
5524 return getConstantRangeFromMetadata(*MD);
5525
5526 return None;
5527}
5528
5529/// Determine the range for a particular SCEV. If SignHint is
5530/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
5531/// with a "cleaner" unsigned (resp. signed) representation.
5532const ConstantRange &
5533ScalarEvolution::getRangeRef(const SCEV *S,
5534 ScalarEvolution::RangeSignHint SignHint) {
5535 DenseMap<const SCEV *, ConstantRange> &Cache =
5536 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
5537 : SignedRanges;
5538
5539 // See if we've computed this range already.
5540 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
5541 if (I != Cache.end())
5542 return I->second;
5543
5544 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5545 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
5546
5547 unsigned BitWidth = getTypeSizeInBits(S->getType());
5548 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
5549
5550 // If the value has known zeros, the maximum value will have those known zeros
5551 // as well.
5552 uint32_t TZ = GetMinTrailingZeros(S);
5553 if (TZ != 0) {
5554 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
5555 ConservativeResult =
5556 ConstantRange(APInt::getMinValue(BitWidth),
5557 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
5558 else
5559 ConservativeResult = ConstantRange(
5560 APInt::getSignedMinValue(BitWidth),
5561 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
5562 }
5563
5564 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
5565 ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
5566 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
5567 X = X.add(getRangeRef(Add->getOperand(i), SignHint));
5568 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
5569 }
5570
5571 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
5572 ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
5573 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
5574 X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
5575 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
5576 }
5577
5578 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
5579 ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
5580 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
5581 X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
5582 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
5583 }
5584
5585 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
5586 ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
5587 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
5588 X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
5589 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
5590 }
5591
5592 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
5593 ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
5594 ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
5595 return setRange(UDiv, SignHint,
5596 ConservativeResult.intersectWith(X.udiv(Y)));
5597 }
5598
5599 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
5600 ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
5601 return setRange(ZExt, SignHint,
5602 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
5603 }
5604
5605 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
5606 ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
5607 return setRange(SExt, SignHint,
5608 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
5609 }
5610
5611 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
5612 ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
5613 return setRange(Trunc, SignHint,
5614 ConservativeResult.intersectWith(X.truncate(BitWidth)));
5615 }
5616
5617 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
5618 // If there's no unsigned wrap, the value will never be less than its
5619 // initial value.
5620 if (AddRec->hasNoUnsignedWrap())
5621 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
5622 if (!C->getValue()->isZero())
5623 ConservativeResult = ConservativeResult.intersectWith(
5624 ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
5625
5626 // If there's no signed wrap, and all the operands have the same sign or
5627 // zero, the value won't ever change sign.
5628 if (AddRec->hasNoSignedWrap()) {
5629 bool AllNonNeg = true;
5630 bool AllNonPos = true;
5631 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5632 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
5633 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
5634 }
5635 if (AllNonNeg)
5636 ConservativeResult = ConservativeResult.intersectWith(
5637 ConstantRange(APInt(BitWidth, 0),
5638 APInt::getSignedMinValue(BitWidth)));
5639 else if (AllNonPos)
5640 ConservativeResult = ConservativeResult.intersectWith(
5641 ConstantRange(APInt::getSignedMinValue(BitWidth),
5642 APInt(BitWidth, 1)));
5643 }
5644
5645 // TODO: non-affine addrec
5646 if (AddRec->isAffine()) {
5647 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
5648 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
5649 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
5650 auto RangeFromAffine = getRangeForAffineAR(
5651 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5652 BitWidth);
5653 if (!RangeFromAffine.isFullSet())
5654 ConservativeResult =
5655 ConservativeResult.intersectWith(RangeFromAffine);
5656
5657 auto RangeFromFactoring = getRangeViaFactoring(
5658 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5659 BitWidth);
5660 if (!RangeFromFactoring.isFullSet())
5661 ConservativeResult =
5662 ConservativeResult.intersectWith(RangeFromFactoring);
5663 }
5664 }
5665
5666 return setRange(AddRec, SignHint, std::move(ConservativeResult));
5667 }
5668
5669 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5670 // Check if the IR explicitly contains !range metadata.
5671 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
5672 if (MDRange.hasValue())
5673 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
5674
5675 // Split here to avoid paying the compile-time cost of calling both
5676 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
5677 // if needed.
5678 const DataLayout &DL = getDataLayout();
5679 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
5680 // For a SCEVUnknown, ask ValueTracking.
5681 KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5682 if (Known.One != ~Known.Zero + 1)
5683 ConservativeResult =
5684 ConservativeResult.intersectWith(ConstantRange(Known.One,
5685 ~Known.Zero + 1));
5686 } else {
5687 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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 5688, __PRETTY_FUNCTION__))
5688 "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-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 5688, __PRETTY_FUNCTION__))
;
5689 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5690 if (NS > 1)
5691 ConservativeResult = ConservativeResult.intersectWith(
5692 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
5693 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
5694 }
5695
5696 // A range of Phi is a subset of union of all ranges of its input.
5697 if (const PHINode *Phi = dyn_cast<PHINode>(U->getValue())) {
5698 // Make sure that we do not run over cycled Phis.
5699 if (PendingPhiRanges.insert(Phi).second) {
5700 ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
5701 for (auto &Op : Phi->operands()) {
5702 auto OpRange = getRangeRef(getSCEV(Op), SignHint);
5703 RangeFromOps = RangeFromOps.unionWith(OpRange);
5704 // No point to continue if we already have a full set.
5705 if (RangeFromOps.isFullSet())
5706 break;
5707 }
5708 ConservativeResult = ConservativeResult.intersectWith(RangeFromOps);
5709 bool Erased = PendingPhiRanges.erase(Phi);
5710 assert(Erased && "Failed to erase Phi properly?")((Erased && "Failed to erase Phi properly?") ? static_cast
<void> (0) : __assert_fail ("Erased && \"Failed to erase Phi properly?\""
, "/build/llvm-toolchain-snapshot-9~svn362543/lib/Analysis/ScalarEvolution.cpp"
, 5710, __PRETTY_FUNCTION__))
;
5711 (void) Erased;
5712 }
5713 }
5714
5715 return setRange(U, SignHint, std::move(ConservativeResult));
5716 }
5717
5718 return setRange(S, SignHint, std::move(ConservativeResult));
5719}
5720
5721// Given a StartRange, Step and MaxBECount for an expression compute a range of
5722// values that the expression can take. Initially, the expression has a value
5723// from StartRange and then is changed by Step up to MaxBECount times. Signed
5724// argument defines if we treat Step as signed or unsigned.
5725static ConstantRange getRangeForAffineARHelper(APInt Step,
5726 const ConstantRange &StartRange,
5727 const APInt &MaxBECount,
5728 unsigned BitWidth, bool Signed) {
5729 // If either Step or MaxBECount is 0, then the expression won't change, and we
5730 // just need to return the initial range.
5731 if (Step == 0 || MaxBECount == 0)
5732 return StartRange;
5733
5734 // If we don't know anything about the initial value (i.e. StartRange is
5735 // FullRange), then we don't know anything about the final range either.
5736 // Return FullRange.
5737 if (StartRange.isFullSet())
5738 return ConstantRange::getFull(BitWidth);
5739
5740 // If Step is signed and negative, then we use its absolute value, but we also
5741 // note that we're moving in the opposite direction.
5742 bool Descending = Signed && Step.isNegative();
5743
5744 if (Signed)
5745 // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
5746 // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
5747 // This equations hold true due to the well-defined wrap-around behavior of
5748 // APInt.
5749 Step = Step.abs();
5750
5751 // Check if Offset is more than full span of BitWidth. If it is, the
5752 // expression is guaranteed to overflow.
5753 if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
5754 return ConstantRange::getFull(BitWidth);
5755
5756 // Offset is by how much the expression can change. Checks above guarantee no
5757 // overflow here.
5758 APInt Offset = Step * MaxBECount;
5759
5760 // Minimum value of the final range will match the minimal value of StartRange
5761 // if the expression is increasing and will be decreased by Offset otherwise.
5762 // Maximum value of the final range will match the maximal value of StartRange
5763 // if the expression is decreasing and will be increased by Offset otherwise.
5764 APInt StartLower = StartRange.getLower();
5765 APInt StartUpper = StartRange.getUpper() - 1;
5766 APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
5767 : (StartUpper + std::move(Offset));
5768
5769 // It's possible that the new minimum/maximum value will fall into the initial
5770 // range (due to wrap around). This means that the expression can take any
5771 // value in this bitwidth, and we have to return full range.
5772 if (StartRange.contains(MovedBoundary))
5773 return ConstantRange::getFull(BitWidth);
5774
5775 APInt NewLower =
5776 Descending ? std::move(MovedBoundary) : std::move(StartLower);
5777 APInt NewUpper =
5778 Descending ? std::move(StartUpper) : std::move(MovedBoundary);
5779 NewUpper += 1;
5780
5781 // No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
5782 return ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper));
5783}
5784
5785ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
5786 const SCEV *Step,
5787 const SCEV *MaxBECount,
5788 unsigned BitWidth) {
5789 a