Bug Summary

File:src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Analysis/ScalarEvolution.cpp
Warning:line 10451, column 35
Called C++ object pointer is null

Annotated Source Code

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clang -cc1 -cc1 -triple amd64-unknown-openbsd7.0 -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 -setup-static-analyzer -mrelocation-model static -mframe-pointer=all -relaxed-aliasing -fno-rounding-math -mconstructor-aliases -munwind-tables -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -fcoverage-compilation-dir=/usr/src/gnu/usr.bin/clang/libLLVM/obj -resource-dir /usr/local/lib/clang/13.0.0 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Analysis -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ASMParser -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/BinaryFormat -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Bitcode -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Bitcode -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Bitstream -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /include/llvm/CodeGen -I /include/llvm/CodeGen/PBQP -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/IR -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/IR -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Coroutines -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ProfileData/Coverage -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/CodeView -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/DWARF -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/MSF -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/PDB -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Demangle -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ExecutionEngine -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ExecutionEngine/JITLink -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ExecutionEngine/Orc -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend/OpenACC -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend/OpenMP -I /include/llvm/CodeGen/GlobalISel -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/IRReader -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/InstCombine -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/Transforms/InstCombine -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/LTO -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Linker -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/MC -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/MC/MCParser -I /include/llvm/CodeGen/MIRParser -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Object -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Option -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Passes -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ProfileData -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Scalar -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ADT -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Support -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/Symbolize -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Target -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Utils -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Vectorize -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/IPO -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include -I /usr/src/gnu/usr.bin/clang/libLLVM/../include -I /usr/src/gnu/usr.bin/clang/libLLVM/obj -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include -D NDEBUG -D __STDC_LIMIT_MACROS -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D LLVM_PREFIX="/usr" -internal-isystem /usr/include/c++/v1 -internal-isystem /usr/local/lib/clang/13.0.0/include -internal-externc-isystem /usr/include -O2 -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-comment -std=c++14 -fdeprecated-macro -fdebug-compilation-dir=/usr/src/gnu/usr.bin/clang/libLLVM/obj -ferror-limit 19 -fvisibility-inlines-hidden -fwrapv -stack-protector 2 -fno-rtti -fgnuc-version=4.2.1 -vectorize-loops -vectorize-slp -fno-builtin-malloc -fno-builtin-calloc -fno-builtin-realloc -fno-builtin-valloc -fno-builtin-free -fno-builtin-strdup -fno-builtin-strndup -analyzer-output=html -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /home/ben/Projects/vmm/scan-build/2022-01-12-194120-40624-1 -x c++ /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Analysis/ScalarEvolution.cpp

/usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Analysis/ScalarEvolution.cpp

1//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// This file contains the implementation of the scalar evolution analysis
10// engine, which is used primarily to analyze expressions involving induction
11// variables in loops.
12//
13// There are several aspects to this library. First is the representation of
14// scalar expressions, which are represented as subclasses of the SCEV class.
15// These classes are used to represent certain types of subexpressions that we
16// can handle. We only create one SCEV of a particular shape, so
17// pointer-comparisons for equality are legal.
18//
19// One important aspect of the SCEV objects is that they are never cyclic, even
20// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
21// the PHI node is one of the idioms that we can represent (e.g., a polynomial
22// recurrence) then we represent it directly as a recurrence node, otherwise we
23// represent it as a SCEVUnknown node.
24//
25// In addition to being able to represent expressions of various types, we also
26// have folders that are used to build the *canonical* representation for a
27// particular expression. These folders are capable of using a variety of
28// rewrite rules to simplify the expressions.
29//
30// Once the folders are defined, we can implement the more interesting
31// higher-level code, such as the code that recognizes PHI nodes of various
32// types, computes the execution count of a loop, etc.
33//
34// TODO: We should use these routines and value representations to implement
35// dependence analysis!
36//
37//===----------------------------------------------------------------------===//
38//
39// There are several good references for the techniques used in this analysis.
40//
41// Chains of recurrences -- a method to expedite the evaluation
42// of closed-form functions
43// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
44//
45// On computational properties of chains of recurrences
46// Eugene V. Zima
47//
48// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
49// Robert A. van Engelen
50//
51// Efficient Symbolic Analysis for Optimizing Compilers
52// Robert A. van Engelen
53//
54// Using the chains of recurrences algebra for data dependence testing and
55// induction variable substitution
56// MS Thesis, Johnie Birch
57//
58//===----------------------------------------------------------------------===//
59
60#include "llvm/Analysis/ScalarEvolution.h"
61#include "llvm/ADT/APInt.h"
62#include "llvm/ADT/ArrayRef.h"
63#include "llvm/ADT/DenseMap.h"
64#include "llvm/ADT/DepthFirstIterator.h"
65#include "llvm/ADT/EquivalenceClasses.h"
66#include "llvm/ADT/FoldingSet.h"
67#include "llvm/ADT/None.h"
68#include "llvm/ADT/Optional.h"
69#include "llvm/ADT/STLExtras.h"
70#include "llvm/ADT/ScopeExit.h"
71#include "llvm/ADT/Sequence.h"
72#include "llvm/ADT/SetVector.h"
73#include "llvm/ADT/SmallPtrSet.h"
74#include "llvm/ADT/SmallSet.h"
75#include "llvm/ADT/SmallVector.h"
76#include "llvm/ADT/Statistic.h"
77#include "llvm/ADT/StringRef.h"
78#include "llvm/Analysis/AssumptionCache.h"
79#include "llvm/Analysis/ConstantFolding.h"
80#include "llvm/Analysis/InstructionSimplify.h"
81#include "llvm/Analysis/LoopInfo.h"
82#include "llvm/Analysis/ScalarEvolutionDivision.h"
83#include "llvm/Analysis/ScalarEvolutionExpressions.h"
84#include "llvm/Analysis/TargetLibraryInfo.h"
85#include "llvm/Analysis/ValueTracking.h"
86#include "llvm/Config/llvm-config.h"
87#include "llvm/IR/Argument.h"
88#include "llvm/IR/BasicBlock.h"
89#include "llvm/IR/CFG.h"
90#include "llvm/IR/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/InitializePasses.h"
116#include "llvm/Pass.h"
117#include "llvm/Support/Casting.h"
118#include "llvm/Support/CommandLine.h"
119#include "llvm/Support/Compiler.h"
120#include "llvm/Support/Debug.h"
121#include "llvm/Support/ErrorHandling.h"
122#include "llvm/Support/KnownBits.h"
123#include "llvm/Support/SaveAndRestore.h"
124#include "llvm/Support/raw_ostream.h"
125#include <algorithm>
126#include <cassert>
127#include <climits>
128#include <cstddef>
129#include <cstdint>
130#include <cstdlib>
131#include <map>
132#include <memory>
133#include <tuple>
134#include <utility>
135#include <vector>
136
137using namespace llvm;
138using namespace PatternMatch;
139
140#define DEBUG_TYPE"scalar-evolution" "scalar-evolution"
141
142STATISTIC(NumArrayLenItCounts,static llvm::Statistic NumArrayLenItCounts = {"scalar-evolution"
, "NumArrayLenItCounts", "Number of trip counts computed with array length"
}
143 "Number of trip counts computed with array length")static llvm::Statistic NumArrayLenItCounts = {"scalar-evolution"
, "NumArrayLenItCounts", "Number of trip counts computed with array length"
}
;
144STATISTIC(NumTripCountsComputed,static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
}
145 "Number of loops with predictable loop counts")static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
}
;
146STATISTIC(NumTripCountsNotComputed,static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
}
147 "Number of loops without predictable loop counts")static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
}
;
148STATISTIC(NumBruteForceTripCountsComputed,static llvm::Statistic NumBruteForceTripCountsComputed = {"scalar-evolution"
, "NumBruteForceTripCountsComputed", "Number of loops with trip counts computed by force"
}
149 "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"
}
;
150
151static cl::opt<unsigned>
152MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
153 cl::ZeroOrMore,
154 cl::desc("Maximum number of iterations SCEV will "
155 "symbolically execute a constant "
156 "derived loop"),
157 cl::init(100));
158
159// FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
160static cl::opt<bool> VerifySCEV(
161 "verify-scev", cl::Hidden,
162 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
163static cl::opt<bool> VerifySCEVStrict(
164 "verify-scev-strict", cl::Hidden,
165 cl::desc("Enable stricter verification with -verify-scev is passed"));
166static cl::opt<bool>
167 VerifySCEVMap("verify-scev-maps", cl::Hidden,
168 cl::desc("Verify no dangling value in ScalarEvolution's "
169 "ExprValueMap (slow)"));
170
171static cl::opt<bool> VerifyIR(
172 "scev-verify-ir", cl::Hidden,
173 cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
174 cl::init(false));
175
176static cl::opt<unsigned> MulOpsInlineThreshold(
177 "scev-mulops-inline-threshold", cl::Hidden,
178 cl::desc("Threshold for inlining multiplication operands into a SCEV"),
179 cl::init(32));
180
181static cl::opt<unsigned> AddOpsInlineThreshold(
182 "scev-addops-inline-threshold", cl::Hidden,
183 cl::desc("Threshold for inlining addition operands into a SCEV"),
184 cl::init(500));
185
186static cl::opt<unsigned> MaxSCEVCompareDepth(
187 "scalar-evolution-max-scev-compare-depth", cl::Hidden,
188 cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
189 cl::init(32));
190
191static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
192 "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
193 cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
194 cl::init(2));
195
196static cl::opt<unsigned> MaxValueCompareDepth(
197 "scalar-evolution-max-value-compare-depth", cl::Hidden,
198 cl::desc("Maximum depth of recursive value complexity comparisons"),
199 cl::init(2));
200
201static cl::opt<unsigned>
202 MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
203 cl::desc("Maximum depth of recursive arithmetics"),
204 cl::init(32));
205
206static cl::opt<unsigned> MaxConstantEvolvingDepth(
207 "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
208 cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
209
210static cl::opt<unsigned>
211 MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
212 cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
213 cl::init(8));
214
215static cl::opt<unsigned>
216 MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
217 cl::desc("Max coefficients in AddRec during evolving"),
218 cl::init(8));
219
220static cl::opt<unsigned>
221 HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
222 cl::desc("Size of the expression which is considered huge"),
223 cl::init(4096));
224
225static cl::opt<bool>
226ClassifyExpressions("scalar-evolution-classify-expressions",
227 cl::Hidden, cl::init(true),
228 cl::desc("When printing analysis, include information on every instruction"));
229
230static cl::opt<bool> UseExpensiveRangeSharpening(
231 "scalar-evolution-use-expensive-range-sharpening", cl::Hidden,
232 cl::init(false),
233 cl::desc("Use more powerful methods of sharpening expression ranges. May "
234 "be costly in terms of compile time"));
235
236//===----------------------------------------------------------------------===//
237// SCEV class definitions
238//===----------------------------------------------------------------------===//
239
240//===----------------------------------------------------------------------===//
241// Implementation of the SCEV class.
242//
243
244#if !defined(NDEBUG1) || defined(LLVM_ENABLE_DUMP)
245LLVM_DUMP_METHOD__attribute__((noinline)) void SCEV::dump() const {
246 print(dbgs());
247 dbgs() << '\n';
248}
249#endif
250
251void SCEV::print(raw_ostream &OS) const {
252 switch (getSCEVType()) {
253 case scConstant:
254 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
255 return;
256 case scPtrToInt: {
257 const SCEVPtrToIntExpr *PtrToInt = cast<SCEVPtrToIntExpr>(this);
258 const SCEV *Op = PtrToInt->getOperand();
259 OS << "(ptrtoint " << *Op->getType() << " " << *Op << " to "
260 << *PtrToInt->getType() << ")";
261 return;
262 }
263 case scTruncate: {
264 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
265 const SCEV *Op = Trunc->getOperand();
266 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
267 << *Trunc->getType() << ")";
268 return;
269 }
270 case scZeroExtend: {
271 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
272 const SCEV *Op = ZExt->getOperand();
273 OS << "(zext " << *Op->getType() << " " << *Op << " to "
274 << *ZExt->getType() << ")";
275 return;
276 }
277 case scSignExtend: {
278 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
279 const SCEV *Op = SExt->getOperand();
280 OS << "(sext " << *Op->getType() << " " << *Op << " to "
281 << *SExt->getType() << ")";
282 return;
283 }
284 case scAddRecExpr: {
285 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
286 OS << "{" << *AR->getOperand(0);
287 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
288 OS << ",+," << *AR->getOperand(i);
289 OS << "}<";
290 if (AR->hasNoUnsignedWrap())
291 OS << "nuw><";
292 if (AR->hasNoSignedWrap())
293 OS << "nsw><";
294 if (AR->hasNoSelfWrap() &&
295 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
296 OS << "nw><";
297 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
298 OS << ">";
299 return;
300 }
301 case scAddExpr:
302 case scMulExpr:
303 case scUMaxExpr:
304 case scSMaxExpr:
305 case scUMinExpr:
306 case scSMinExpr: {
307 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
308 const char *OpStr = nullptr;
309 switch (NAry->getSCEVType()) {
310 case scAddExpr: OpStr = " + "; break;
311 case scMulExpr: OpStr = " * "; break;
312 case scUMaxExpr: OpStr = " umax "; break;
313 case scSMaxExpr: OpStr = " smax "; break;
314 case scUMinExpr:
315 OpStr = " umin ";
316 break;
317 case scSMinExpr:
318 OpStr = " smin ";
319 break;
320 default:
321 llvm_unreachable("There are no other nary expression types.")__builtin_unreachable();
322 }
323 OS << "(";
324 ListSeparator LS(OpStr);
325 for (const SCEV *Op : NAry->operands())
326 OS << LS << *Op;
327 OS << ")";
328 switch (NAry->getSCEVType()) {
329 case scAddExpr:
330 case scMulExpr:
331 if (NAry->hasNoUnsignedWrap())
332 OS << "<nuw>";
333 if (NAry->hasNoSignedWrap())
334 OS << "<nsw>";
335 break;
336 default:
337 // Nothing to print for other nary expressions.
338 break;
339 }
340 return;
341 }
342 case scUDivExpr: {
343 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
344 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
345 return;
346 }
347 case scUnknown: {
348 const SCEVUnknown *U = cast<SCEVUnknown>(this);
349 Type *AllocTy;
350 if (U->isSizeOf(AllocTy)) {
351 OS << "sizeof(" << *AllocTy << ")";
352 return;
353 }
354 if (U->isAlignOf(AllocTy)) {
355 OS << "alignof(" << *AllocTy << ")";
356 return;
357 }
358
359 Type *CTy;
360 Constant *FieldNo;
361 if (U->isOffsetOf(CTy, FieldNo)) {
362 OS << "offsetof(" << *CTy << ", ";
363 FieldNo->printAsOperand(OS, false);
364 OS << ")";
365 return;
366 }
367
368 // Otherwise just print it normally.
369 U->getValue()->printAsOperand(OS, false);
370 return;
371 }
372 case scCouldNotCompute:
373 OS << "***COULDNOTCOMPUTE***";
374 return;
375 }
376 llvm_unreachable("Unknown SCEV kind!")__builtin_unreachable();
377}
378
379Type *SCEV::getType() const {
380 switch (getSCEVType()) {
381 case scConstant:
382 return cast<SCEVConstant>(this)->getType();
383 case scPtrToInt:
384 case scTruncate:
385 case scZeroExtend:
386 case scSignExtend:
387 return cast<SCEVCastExpr>(this)->getType();
388 case scAddRecExpr:
389 return cast<SCEVAddRecExpr>(this)->getType();
390 case scMulExpr:
391 return cast<SCEVMulExpr>(this)->getType();
392 case scUMaxExpr:
393 case scSMaxExpr:
394 case scUMinExpr:
395 case scSMinExpr:
396 return cast<SCEVMinMaxExpr>(this)->getType();
397 case scAddExpr:
398 return cast<SCEVAddExpr>(this)->getType();
399 case scUDivExpr:
400 return cast<SCEVUDivExpr>(this)->getType();
401 case scUnknown:
402 return cast<SCEVUnknown>(this)->getType();
403 case scCouldNotCompute:
404 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")__builtin_unreachable();
405 }
406 llvm_unreachable("Unknown SCEV kind!")__builtin_unreachable();
407}
408
409bool SCEV::isZero() const {
410 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
411 return SC->getValue()->isZero();
412 return false;
413}
414
415bool SCEV::isOne() const {
416 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
417 return SC->getValue()->isOne();
418 return false;
419}
420
421bool SCEV::isAllOnesValue() const {
422 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
423 return SC->getValue()->isMinusOne();
424 return false;
425}
426
427bool SCEV::isNonConstantNegative() const {
428 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
429 if (!Mul) return false;
430
431 // If there is a constant factor, it will be first.
432 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
433 if (!SC) return false;
434
435 // Return true if the value is negative, this matches things like (-42 * V).
436 return SC->getAPInt().isNegative();
437}
438
439SCEVCouldNotCompute::SCEVCouldNotCompute() :
440 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {}
441
442bool SCEVCouldNotCompute::classof(const SCEV *S) {
443 return S->getSCEVType() == scCouldNotCompute;
444}
445
446const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
447 FoldingSetNodeID ID;
448 ID.AddInteger(scConstant);
449 ID.AddPointer(V);
450 void *IP = nullptr;
451 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
452 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
453 UniqueSCEVs.InsertNode(S, IP);
454 return S;
455}
456
457const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
458 return getConstant(ConstantInt::get(getContext(), Val));
459}
460
461const SCEV *
462ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
463 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
464 return getConstant(ConstantInt::get(ITy, V, isSigned));
465}
466
467SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy,
468 const SCEV *op, Type *ty)
469 : SCEV(ID, SCEVTy, computeExpressionSize(op)), Ty(ty) {
470 Operands[0] = op;
471}
472
473SCEVPtrToIntExpr::SCEVPtrToIntExpr(const FoldingSetNodeIDRef ID, const SCEV *Op,
474 Type *ITy)
475 : SCEVCastExpr(ID, scPtrToInt, Op, ITy) {
476 assert(getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() &&((void)0)
477 "Must be a non-bit-width-changing pointer-to-integer cast!")((void)0);
478}
479
480SCEVIntegralCastExpr::SCEVIntegralCastExpr(const FoldingSetNodeIDRef ID,
481 SCEVTypes SCEVTy, const SCEV *op,
482 Type *ty)
483 : SCEVCastExpr(ID, SCEVTy, op, ty) {}
484
485SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, const SCEV *op,
486 Type *ty)
487 : SCEVIntegralCastExpr(ID, scTruncate, op, ty) {
488 assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((void)0)
489 "Cannot truncate non-integer value!")((void)0);
490}
491
492SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
493 const SCEV *op, Type *ty)
494 : SCEVIntegralCastExpr(ID, scZeroExtend, op, ty) {
495 assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((void)0)
496 "Cannot zero extend non-integer value!")((void)0);
497}
498
499SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
500 const SCEV *op, Type *ty)
501 : SCEVIntegralCastExpr(ID, scSignExtend, op, ty) {
502 assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((void)0)
503 "Cannot sign extend non-integer value!")((void)0);
504}
505
506void SCEVUnknown::deleted() {
507 // Clear this SCEVUnknown from various maps.
508 SE->forgetMemoizedResults(this);
509
510 // Remove this SCEVUnknown from the uniquing map.
511 SE->UniqueSCEVs.RemoveNode(this);
512
513 // Release the value.
514 setValPtr(nullptr);
515}
516
517void SCEVUnknown::allUsesReplacedWith(Value *New) {
518 // Remove this SCEVUnknown from the uniquing map.
519 SE->UniqueSCEVs.RemoveNode(this);
520
521 // Update this SCEVUnknown to point to the new value. This is needed
522 // because there may still be outstanding SCEVs which still point to
523 // this SCEVUnknown.
524 setValPtr(New);
525}
526
527bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
528 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
529 if (VCE->getOpcode() == Instruction::PtrToInt)
530 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
531 if (CE->getOpcode() == Instruction::GetElementPtr &&
532 CE->getOperand(0)->isNullValue() &&
533 CE->getNumOperands() == 2)
534 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
535 if (CI->isOne()) {
536 AllocTy = cast<GEPOperator>(CE)->getSourceElementType();
537 return true;
538 }
539
540 return false;
541}
542
543bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
544 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
545 if (VCE->getOpcode() == Instruction::PtrToInt)
546 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
547 if (CE->getOpcode() == Instruction::GetElementPtr &&
548 CE->getOperand(0)->isNullValue()) {
549 Type *Ty = cast<GEPOperator>(CE)->getSourceElementType();
550 if (StructType *STy = dyn_cast<StructType>(Ty))
551 if (!STy->isPacked() &&
552 CE->getNumOperands() == 3 &&
553 CE->getOperand(1)->isNullValue()) {
554 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
555 if (CI->isOne() &&
556 STy->getNumElements() == 2 &&
557 STy->getElementType(0)->isIntegerTy(1)) {
558 AllocTy = STy->getElementType(1);
559 return true;
560 }
561 }
562 }
563
564 return false;
565}
566
567bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
568 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
569 if (VCE->getOpcode() == Instruction::PtrToInt)
570 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
571 if (CE->getOpcode() == Instruction::GetElementPtr &&
572 CE->getNumOperands() == 3 &&
573 CE->getOperand(0)->isNullValue() &&
574 CE->getOperand(1)->isNullValue()) {
575 Type *Ty = cast<GEPOperator>(CE)->getSourceElementType();
576 // Ignore vector types here so that ScalarEvolutionExpander doesn't
577 // emit getelementptrs that index into vectors.
578 if (Ty->isStructTy() || Ty->isArrayTy()) {
579 CTy = Ty;
580 FieldNo = CE->getOperand(2);
581 return true;
582 }
583 }
584
585 return false;
586}
587
588//===----------------------------------------------------------------------===//
589// SCEV Utilities
590//===----------------------------------------------------------------------===//
591
592/// Compare the two values \p LV and \p RV in terms of their "complexity" where
593/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
594/// operands in SCEV expressions. \p EqCache is a set of pairs of values that
595/// have been previously deemed to be "equally complex" by this routine. It is
596/// intended to avoid exponential time complexity in cases like:
597///
598/// %a = f(%x, %y)
599/// %b = f(%a, %a)
600/// %c = f(%b, %b)
601///
602/// %d = f(%x, %y)
603/// %e = f(%d, %d)
604/// %f = f(%e, %e)
605///
606/// CompareValueComplexity(%f, %c)
607///
608/// Since we do not continue running this routine on expression trees once we
609/// have seen unequal values, there is no need to track them in the cache.
610static int
611CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
612 const LoopInfo *const LI, Value *LV, Value *RV,
613 unsigned Depth) {
614 if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
615 return 0;
616
617 // Order pointer values after integer values. This helps SCEVExpander form
618 // GEPs.
619 bool LIsPointer = LV->getType()->isPointerTy(),
620 RIsPointer = RV->getType()->isPointerTy();
621 if (LIsPointer != RIsPointer)
622 return (int)LIsPointer - (int)RIsPointer;
623
624 // Compare getValueID values.
625 unsigned LID = LV->getValueID(), RID = RV->getValueID();
626 if (LID != RID)
627 return (int)LID - (int)RID;
628
629 // Sort arguments by their position.
630 if (const auto *LA = dyn_cast<Argument>(LV)) {
631 const auto *RA = cast<Argument>(RV);
632 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
633 return (int)LArgNo - (int)RArgNo;
634 }
635
636 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
637 const auto *RGV = cast<GlobalValue>(RV);
638
639 const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
640 auto LT = GV->getLinkage();
641 return !(GlobalValue::isPrivateLinkage(LT) ||
642 GlobalValue::isInternalLinkage(LT));
643 };
644
645 // Use the names to distinguish the two values, but only if the
646 // names are semantically important.
647 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
648 return LGV->getName().compare(RGV->getName());
649 }
650
651 // For instructions, compare their loop depth, and their operand count. This
652 // is pretty loose.
653 if (const auto *LInst = dyn_cast<Instruction>(LV)) {
654 const auto *RInst = cast<Instruction>(RV);
655
656 // Compare loop depths.
657 const BasicBlock *LParent = LInst->getParent(),
658 *RParent = RInst->getParent();
659 if (LParent != RParent) {
660 unsigned LDepth = LI->getLoopDepth(LParent),
661 RDepth = LI->getLoopDepth(RParent);
662 if (LDepth != RDepth)
663 return (int)LDepth - (int)RDepth;
664 }
665
666 // Compare the number of operands.
667 unsigned LNumOps = LInst->getNumOperands(),
668 RNumOps = RInst->getNumOperands();
669 if (LNumOps != RNumOps)
670 return (int)LNumOps - (int)RNumOps;
671
672 for (unsigned Idx : seq(0u, LNumOps)) {
673 int Result =
674 CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
675 RInst->getOperand(Idx), Depth + 1);
676 if (Result != 0)
677 return Result;
678 }
679 }
680
681 EqCacheValue.unionSets(LV, RV);
682 return 0;
683}
684
685// Return negative, zero, or positive, if LHS is less than, equal to, or greater
686// than RHS, respectively. A three-way result allows recursive comparisons to be
687// more efficient.
688// If the max analysis depth was reached, return None, assuming we do not know
689// if they are equivalent for sure.
690static Optional<int>
691CompareSCEVComplexity(EquivalenceClasses<const SCEV *> &EqCacheSCEV,
692 EquivalenceClasses<const Value *> &EqCacheValue,
693 const LoopInfo *const LI, const SCEV *LHS,
694 const SCEV *RHS, DominatorTree &DT, unsigned Depth = 0) {
695 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
696 if (LHS == RHS)
697 return 0;
698
699 // Primarily, sort the SCEVs by their getSCEVType().
700 SCEVTypes LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
701 if (LType != RType)
702 return (int)LType - (int)RType;
703
704 if (EqCacheSCEV.isEquivalent(LHS, RHS))
705 return 0;
706
707 if (Depth > MaxSCEVCompareDepth)
708 return None;
709
710 // Aside from the getSCEVType() ordering, the particular ordering
711 // isn't very important except that it's beneficial to be consistent,
712 // so that (a + b) and (b + a) don't end up as different expressions.
713 switch (LType) {
714 case scUnknown: {
715 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
716 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
717
718 int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
719 RU->getValue(), Depth + 1);
720 if (X == 0)
721 EqCacheSCEV.unionSets(LHS, RHS);
722 return X;
723 }
724
725 case scConstant: {
726 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
727 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
728
729 // Compare constant values.
730 const APInt &LA = LC->getAPInt();
731 const APInt &RA = RC->getAPInt();
732 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
733 if (LBitWidth != RBitWidth)
734 return (int)LBitWidth - (int)RBitWidth;
735 return LA.ult(RA) ? -1 : 1;
736 }
737
738 case scAddRecExpr: {
739 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
740 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
741
742 // There is always a dominance between two recs that are used by one SCEV,
743 // so we can safely sort recs by loop header dominance. We require such
744 // order in getAddExpr.
745 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
746 if (LLoop != RLoop) {
747 const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
748 assert(LHead != RHead && "Two loops share the same header?")((void)0);
749 if (DT.dominates(LHead, RHead))
750 return 1;
751 else
752 assert(DT.dominates(RHead, LHead) &&((void)0)
753 "No dominance between recurrences used by one SCEV?")((void)0);
754 return -1;
755 }
756
757 // Addrec complexity grows with operand count.
758 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
759 if (LNumOps != RNumOps)
760 return (int)LNumOps - (int)RNumOps;
761
762 // Lexicographically compare.
763 for (unsigned i = 0; i != LNumOps; ++i) {
764 auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
765 LA->getOperand(i), RA->getOperand(i), DT,
766 Depth + 1);
767 if (X != 0)
768 return X;
769 }
770 EqCacheSCEV.unionSets(LHS, RHS);
771 return 0;
772 }
773
774 case scAddExpr:
775 case scMulExpr:
776 case scSMaxExpr:
777 case scUMaxExpr:
778 case scSMinExpr:
779 case scUMinExpr: {
780 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
781 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
782
783 // Lexicographically compare n-ary expressions.
784 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
785 if (LNumOps != RNumOps)
786 return (int)LNumOps - (int)RNumOps;
787
788 for (unsigned i = 0; i != LNumOps; ++i) {
789 auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
790 LC->getOperand(i), RC->getOperand(i), DT,
791 Depth + 1);
792 if (X != 0)
793 return X;
794 }
795 EqCacheSCEV.unionSets(LHS, RHS);
796 return 0;
797 }
798
799 case scUDivExpr: {
800 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
801 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
802
803 // Lexicographically compare udiv expressions.
804 auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
805 RC->getLHS(), DT, Depth + 1);
806 if (X != 0)
807 return X;
808 X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
809 RC->getRHS(), DT, Depth + 1);
810 if (X == 0)
811 EqCacheSCEV.unionSets(LHS, RHS);
812 return X;
813 }
814
815 case scPtrToInt:
816 case scTruncate:
817 case scZeroExtend:
818 case scSignExtend: {
819 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
820 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
821
822 // Compare cast expressions by operand.
823 auto X =
824 CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getOperand(),
825 RC->getOperand(), DT, Depth + 1);
826 if (X == 0)
827 EqCacheSCEV.unionSets(LHS, RHS);
828 return X;
829 }
830
831 case scCouldNotCompute:
832 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")__builtin_unreachable();
833 }
834 llvm_unreachable("Unknown SCEV kind!")__builtin_unreachable();
835}
836
837/// Given a list of SCEV objects, order them by their complexity, and group
838/// objects of the same complexity together by value. When this routine is
839/// finished, we know that any duplicates in the vector are consecutive and that
840/// complexity is monotonically increasing.
841///
842/// Note that we go take special precautions to ensure that we get deterministic
843/// results from this routine. In other words, we don't want the results of
844/// this to depend on where the addresses of various SCEV objects happened to
845/// land in memory.
846static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
847 LoopInfo *LI, DominatorTree &DT) {
848 if (Ops.size() < 2) return; // Noop
849
850 EquivalenceClasses<const SCEV *> EqCacheSCEV;
851 EquivalenceClasses<const Value *> EqCacheValue;
852
853 // Whether LHS has provably less complexity than RHS.
854 auto IsLessComplex = [&](const SCEV *LHS, const SCEV *RHS) {
855 auto Complexity =
856 CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT);
857 return Complexity && *Complexity < 0;
858 };
859 if (Ops.size() == 2) {
860 // This is the common case, which also happens to be trivially simple.
861 // Special case it.
862 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
863 if (IsLessComplex(RHS, LHS))
864 std::swap(LHS, RHS);
865 return;
866 }
867
868 // Do the rough sort by complexity.
869 llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) {
870 return IsLessComplex(LHS, RHS);
871 });
872
873 // Now that we are sorted by complexity, group elements of the same
874 // complexity. Note that this is, at worst, N^2, but the vector is likely to
875 // be extremely short in practice. Note that we take this approach because we
876 // do not want to depend on the addresses of the objects we are grouping.
877 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
878 const SCEV *S = Ops[i];
879 unsigned Complexity = S->getSCEVType();
880
881 // If there are any objects of the same complexity and same value as this
882 // one, group them.
883 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
884 if (Ops[j] == S) { // Found a duplicate.
885 // Move it to immediately after i'th element.
886 std::swap(Ops[i+1], Ops[j]);
887 ++i; // no need to rescan it.
888 if (i == e-2) return; // Done!
889 }
890 }
891 }
892}
893
894/// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at
895/// least HugeExprThreshold nodes).
896static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) {
897 return any_of(Ops, [](const SCEV *S) {
898 return S->getExpressionSize() >= HugeExprThreshold;
899 });
900}
901
902//===----------------------------------------------------------------------===//
903// Simple SCEV method implementations
904//===----------------------------------------------------------------------===//
905
906/// Compute BC(It, K). The result has width W. Assume, K > 0.
907static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
908 ScalarEvolution &SE,
909 Type *ResultTy) {
910 // Handle the simplest case efficiently.
911 if (K == 1)
912 return SE.getTruncateOrZeroExtend(It, ResultTy);
913
914 // We are using the following formula for BC(It, K):
915 //
916 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
917 //
918 // Suppose, W is the bitwidth of the return value. We must be prepared for
919 // overflow. Hence, we must assure that the result of our computation is
920 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
921 // safe in modular arithmetic.
922 //
923 // However, this code doesn't use exactly that formula; the formula it uses
924 // is something like the following, where T is the number of factors of 2 in
925 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
926 // exponentiation:
927 //
928 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
929 //
930 // This formula is trivially equivalent to the previous formula. However,
931 // this formula can be implemented much more efficiently. The trick is that
932 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
933 // arithmetic. To do exact division in modular arithmetic, all we have
934 // to do is multiply by the inverse. Therefore, this step can be done at
935 // width W.
936 //
937 // The next issue is how to safely do the division by 2^T. The way this
938 // is done is by doing the multiplication step at a width of at least W + T
939 // bits. This way, the bottom W+T bits of the product are accurate. Then,
940 // when we perform the division by 2^T (which is equivalent to a right shift
941 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
942 // truncated out after the division by 2^T.
943 //
944 // In comparison to just directly using the first formula, this technique
945 // is much more efficient; using the first formula requires W * K bits,
946 // but this formula less than W + K bits. Also, the first formula requires
947 // a division step, whereas this formula only requires multiplies and shifts.
948 //
949 // It doesn't matter whether the subtraction step is done in the calculation
950 // width or the input iteration count's width; if the subtraction overflows,
951 // the result must be zero anyway. We prefer here to do it in the width of
952 // the induction variable because it helps a lot for certain cases; CodeGen
953 // isn't smart enough to ignore the overflow, which leads to much less
954 // efficient code if the width of the subtraction is wider than the native
955 // register width.
956 //
957 // (It's possible to not widen at all by pulling out factors of 2 before
958 // the multiplication; for example, K=2 can be calculated as
959 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
960 // extra arithmetic, so it's not an obvious win, and it gets
961 // much more complicated for K > 3.)
962
963 // Protection from insane SCEVs; this bound is conservative,
964 // but it probably doesn't matter.
965 if (K > 1000)
966 return SE.getCouldNotCompute();
967
968 unsigned W = SE.getTypeSizeInBits(ResultTy);
969
970 // Calculate K! / 2^T and T; we divide out the factors of two before
971 // multiplying for calculating K! / 2^T to avoid overflow.
972 // Other overflow doesn't matter because we only care about the bottom
973 // W bits of the result.
974 APInt OddFactorial(W, 1);
975 unsigned T = 1;
976 for (unsigned i = 3; i <= K; ++i) {
977 APInt Mult(W, i);
978 unsigned TwoFactors = Mult.countTrailingZeros();
979 T += TwoFactors;
980 Mult.lshrInPlace(TwoFactors);
981 OddFactorial *= Mult;
982 }
983
984 // We need at least W + T bits for the multiplication step
985 unsigned CalculationBits = W + T;
986
987 // Calculate 2^T, at width T+W.
988 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
989
990 // Calculate the multiplicative inverse of K! / 2^T;
991 // this multiplication factor will perform the exact division by
992 // K! / 2^T.
993 APInt Mod = APInt::getSignedMinValue(W+1);
994 APInt MultiplyFactor = OddFactorial.zext(W+1);
995 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
996 MultiplyFactor = MultiplyFactor.trunc(W);
997
998 // Calculate the product, at width T+W
999 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1000 CalculationBits);
1001 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1002 for (unsigned i = 1; i != K; ++i) {
1003 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1004 Dividend = SE.getMulExpr(Dividend,
1005 SE.getTruncateOrZeroExtend(S, CalculationTy));
1006 }
1007
1008 // Divide by 2^T
1009 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1010
1011 // Truncate the result, and divide by K! / 2^T.
1012
1013 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1014 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1015}
1016
1017/// Return the value of this chain of recurrences at the specified iteration
1018/// number. We can evaluate this recurrence by multiplying each element in the
1019/// chain by the binomial coefficient corresponding to it. In other words, we
1020/// can evaluate {A,+,B,+,C,+,D} as:
1021///
1022/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1023///
1024/// where BC(It, k) stands for binomial coefficient.
1025const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1026 ScalarEvolution &SE) const {
1027 return evaluateAtIteration(makeArrayRef(op_begin(), op_end()), It, SE);
1028}
1029
1030const SCEV *
1031SCEVAddRecExpr::evaluateAtIteration(ArrayRef<const SCEV *> Operands,
1032 const SCEV *It, ScalarEvolution &SE) {
1033 assert(Operands.size() > 0)((void)0);
1034 const SCEV *Result = Operands[0];
1035 for (unsigned i = 1, e = Operands.size(); i != e; ++i) {
1036 // The computation is correct in the face of overflow provided that the
1037 // multiplication is performed _after_ the evaluation of the binomial
1038 // coefficient.
1039 const SCEV *Coeff = BinomialCoefficient(It, i, SE, Result->getType());
1040 if (isa<SCEVCouldNotCompute>(Coeff))
1041 return Coeff;
1042
1043 Result = SE.getAddExpr(Result, SE.getMulExpr(Operands[i], Coeff));
1044 }
1045 return Result;
1046}
1047
1048//===----------------------------------------------------------------------===//
1049// SCEV Expression folder implementations
1050//===----------------------------------------------------------------------===//
1051
1052const SCEV *ScalarEvolution::getLosslessPtrToIntExpr(const SCEV *Op,
1053 unsigned Depth) {
1054 assert(Depth <= 1 &&((void)0)
1055 "getLosslessPtrToIntExpr() should self-recurse at most once.")((void)0);
1056
1057 // We could be called with an integer-typed operands during SCEV rewrites.
1058 // Since the operand is an integer already, just perform zext/trunc/self cast.
1059 if (!Op->getType()->isPointerTy())
1060 return Op;
1061
1062 // What would be an ID for such a SCEV cast expression?
1063 FoldingSetNodeID ID;
1064 ID.AddInteger(scPtrToInt);
1065 ID.AddPointer(Op);
1066
1067 void *IP = nullptr;
1068
1069 // Is there already an expression for such a cast?
1070 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
1071 return S;
1072
1073 // It isn't legal for optimizations to construct new ptrtoint expressions
1074 // for non-integral pointers.
1075 if (getDataLayout().isNonIntegralPointerType(Op->getType()))
1076 return getCouldNotCompute();
1077
1078 Type *IntPtrTy = getDataLayout().getIntPtrType(Op->getType());
1079
1080 // We can only trivially model ptrtoint if SCEV's effective (integer) type
1081 // is sufficiently wide to represent all possible pointer values.
1082 // We could theoretically teach SCEV to truncate wider pointers, but
1083 // that isn't implemented for now.
1084 if (getDataLayout().getTypeSizeInBits(getEffectiveSCEVType(Op->getType())) !=
1085 getDataLayout().getTypeSizeInBits(IntPtrTy))
1086 return getCouldNotCompute();
1087
1088 // If not, is this expression something we can't reduce any further?
1089 if (auto *U = dyn_cast<SCEVUnknown>(Op)) {
1090 // Perform some basic constant folding. If the operand of the ptr2int cast
1091 // is a null pointer, don't create a ptr2int SCEV expression (that will be
1092 // left as-is), but produce a zero constant.
1093 // NOTE: We could handle a more general case, but lack motivational cases.
1094 if (isa<ConstantPointerNull>(U->getValue()))
1095 return getZero(IntPtrTy);
1096
1097 // Create an explicit cast node.
1098 // We can reuse the existing insert position since if we get here,
1099 // we won't have made any changes which would invalidate it.
1100 SCEV *S = new (SCEVAllocator)
1101 SCEVPtrToIntExpr(ID.Intern(SCEVAllocator), Op, IntPtrTy);
1102 UniqueSCEVs.InsertNode(S, IP);
1103 addToLoopUseLists(S);
1104 return S;
1105 }
1106
1107 assert(Depth == 0 && "getLosslessPtrToIntExpr() should not self-recurse for "((void)0)
1108 "non-SCEVUnknown's.")((void)0);
1109
1110 // Otherwise, we've got some expression that is more complex than just a
1111 // single SCEVUnknown. But we don't want to have a SCEVPtrToIntExpr of an
1112 // arbitrary expression, we want to have SCEVPtrToIntExpr of an SCEVUnknown
1113 // only, and the expressions must otherwise be integer-typed.
1114 // So sink the cast down to the SCEVUnknown's.
1115
1116 /// The SCEVPtrToIntSinkingRewriter takes a scalar evolution expression,
1117 /// which computes a pointer-typed value, and rewrites the whole expression
1118 /// tree so that *all* the computations are done on integers, and the only
1119 /// pointer-typed operands in the expression are SCEVUnknown.
1120 class SCEVPtrToIntSinkingRewriter
1121 : public SCEVRewriteVisitor<SCEVPtrToIntSinkingRewriter> {
1122 using Base = SCEVRewriteVisitor<SCEVPtrToIntSinkingRewriter>;
1123
1124 public:
1125 SCEVPtrToIntSinkingRewriter(ScalarEvolution &SE) : SCEVRewriteVisitor(SE) {}
1126
1127 static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE) {
1128 SCEVPtrToIntSinkingRewriter Rewriter(SE);
1129 return Rewriter.visit(Scev);
1130 }
1131
1132 const SCEV *visit(const SCEV *S) {
1133 Type *STy = S->getType();
1134 // If the expression is not pointer-typed, just keep it as-is.
1135 if (!STy->isPointerTy())
1136 return S;
1137 // Else, recursively sink the cast down into it.
1138 return Base::visit(S);
1139 }
1140
1141 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
1142 SmallVector<const SCEV *, 2> Operands;
1143 bool Changed = false;
1144 for (auto *Op : Expr->operands()) {
1145 Operands.push_back(visit(Op));
1146 Changed |= Op != Operands.back();
1147 }
1148 return !Changed ? Expr : SE.getAddExpr(Operands, Expr->getNoWrapFlags());
1149 }
1150
1151 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
1152 SmallVector<const SCEV *, 2> Operands;
1153 bool Changed = false;
1154 for (auto *Op : Expr->operands()) {
1155 Operands.push_back(visit(Op));
1156 Changed |= Op != Operands.back();
1157 }
1158 return !Changed ? Expr : SE.getMulExpr(Operands, Expr->getNoWrapFlags());
1159 }
1160
1161 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
1162 assert(Expr->getType()->isPointerTy() &&((void)0)
1163 "Should only reach pointer-typed SCEVUnknown's.")((void)0);
1164 return SE.getLosslessPtrToIntExpr(Expr, /*Depth=*/1);
1165 }
1166 };
1167
1168 // And actually perform the cast sinking.
1169 const SCEV *IntOp = SCEVPtrToIntSinkingRewriter::rewrite(Op, *this);
1170 assert(IntOp->getType()->isIntegerTy() &&((void)0)
1171 "We must have succeeded in sinking the cast, "((void)0)
1172 "and ending up with an integer-typed expression!")((void)0);
1173 return IntOp;
1174}
1175
1176const SCEV *ScalarEvolution::getPtrToIntExpr(const SCEV *Op, Type *Ty) {
1177 assert(Ty->isIntegerTy() && "Target type must be an integer type!")((void)0);
1178
1179 const SCEV *IntOp = getLosslessPtrToIntExpr(Op);
1180 if (isa<SCEVCouldNotCompute>(IntOp))
1181 return IntOp;
1182
1183 return getTruncateOrZeroExtend(IntOp, Ty);
1184}
1185
1186const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
1187 unsigned Depth) {
1188 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&((void)0)
1189 "This is not a truncating conversion!")((void)0);
1190 assert(isSCEVable(Ty) &&((void)0)
1191 "This is not a conversion to a SCEVable type!")((void)0);
1192 assert(!Op->getType()->isPointerTy() && "Can't truncate pointer!")((void)0);
1193 Ty = getEffectiveSCEVType(Ty);
1194
1195 FoldingSetNodeID ID;
1196 ID.AddInteger(scTruncate);
1197 ID.AddPointer(Op);
1198 ID.AddPointer(Ty);
1199 void *IP = nullptr;
1200 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1201
1202 // Fold if the operand is constant.
1203 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1204 return getConstant(
1205 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1206
1207 // trunc(trunc(x)) --> trunc(x)
1208 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1209 return getTruncateExpr(ST->getOperand(), Ty, Depth + 1);
1210
1211 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1212 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1213 return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1);
1214
1215 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1216 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1217 return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1);
1218
1219 if (Depth > MaxCastDepth) {
1220 SCEV *S =
1221 new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty);
1222 UniqueSCEVs.InsertNode(S, IP);
1223 addToLoopUseLists(S);
1224 return S;
1225 }
1226
1227 // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
1228 // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
1229 // if after transforming we have at most one truncate, not counting truncates
1230 // that replace other casts.
1231 if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
1232 auto *CommOp = cast<SCEVCommutativeExpr>(Op);
1233 SmallVector<const SCEV *, 4> Operands;
1234 unsigned numTruncs = 0;
1235 for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
1236 ++i) {
1237 const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1);
1238 if (!isa<SCEVIntegralCastExpr>(CommOp->getOperand(i)) &&
1239 isa<SCEVTruncateExpr>(S))
1240 numTruncs++;
1241 Operands.push_back(S);
1242 }
1243 if (numTruncs < 2) {
1244 if (isa<SCEVAddExpr>(Op))
1245 return getAddExpr(Operands);
1246 else if (isa<SCEVMulExpr>(Op))
1247 return getMulExpr(Operands);
1248 else
1249 llvm_unreachable("Unexpected SCEV type for Op.")__builtin_unreachable();
1250 }
1251 // Although we checked in the beginning that ID is not in the cache, it is
1252 // possible that during recursion and different modification ID was inserted
1253 // into the cache. So if we find it, just return it.
1254 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
1255 return S;
1256 }
1257
1258 // If the input value is a chrec scev, truncate the chrec's operands.
1259 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1260 SmallVector<const SCEV *, 4> Operands;
1261 for (const SCEV *Op : AddRec->operands())
1262 Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1));
1263 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1264 }
1265
1266 // Return zero if truncating to known zeros.
1267 uint32_t MinTrailingZeros = GetMinTrailingZeros(Op);
1268 if (MinTrailingZeros >= getTypeSizeInBits(Ty))
1269 return getZero(Ty);
1270
1271 // The cast wasn't folded; create an explicit cast node. We can reuse
1272 // the existing insert position since if we get here, we won't have
1273 // made any changes which would invalidate it.
1274 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1275 Op, Ty);
1276 UniqueSCEVs.InsertNode(S, IP);
1277 addToLoopUseLists(S);
1278 return S;
1279}
1280
1281// Get the limit of a recurrence such that incrementing by Step cannot cause
1282// signed overflow as long as the value of the recurrence within the
1283// loop does not exceed this limit before incrementing.
1284static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1285 ICmpInst::Predicate *Pred,
1286 ScalarEvolution *SE) {
1287 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1288 if (SE->isKnownPositive(Step)) {
1289 *Pred = ICmpInst::ICMP_SLT;
1290 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1291 SE->getSignedRangeMax(Step));
1292 }
1293 if (SE->isKnownNegative(Step)) {
1294 *Pred = ICmpInst::ICMP_SGT;
1295 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1296 SE->getSignedRangeMin(Step));
1297 }
1298 return nullptr;
1299}
1300
1301// Get the limit of a recurrence such that incrementing by Step cannot cause
1302// unsigned overflow as long as the value of the recurrence within the loop does
1303// not exceed this limit before incrementing.
1304static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1305 ICmpInst::Predicate *Pred,
1306 ScalarEvolution *SE) {
1307 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1308 *Pred = ICmpInst::ICMP_ULT;
1309
1310 return SE->getConstant(APInt::getMinValue(BitWidth) -
1311 SE->getUnsignedRangeMax(Step));
1312}
1313
1314namespace {
1315
1316struct ExtendOpTraitsBase {
1317 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
1318 unsigned);
1319};
1320
1321// Used to make code generic over signed and unsigned overflow.
1322template <typename ExtendOp> struct ExtendOpTraits {
1323 // Members present:
1324 //
1325 // static const SCEV::NoWrapFlags WrapType;
1326 //
1327 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1328 //
1329 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1330 // ICmpInst::Predicate *Pred,
1331 // ScalarEvolution *SE);
1332};
1333
1334template <>
1335struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1336 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1337
1338 static const GetExtendExprTy GetExtendExpr;
1339
1340 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1341 ICmpInst::Predicate *Pred,
1342 ScalarEvolution *SE) {
1343 return getSignedOverflowLimitForStep(Step, Pred, SE);
1344 }
1345};
1346
1347const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1348 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1349
1350template <>
1351struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1352 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1353
1354 static const GetExtendExprTy GetExtendExpr;
1355
1356 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1357 ICmpInst::Predicate *Pred,
1358 ScalarEvolution *SE) {
1359 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1360 }
1361};
1362
1363const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1364 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1365
1366} // end anonymous namespace
1367
1368// The recurrence AR has been shown to have no signed/unsigned wrap or something
1369// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1370// easily prove NSW/NUW for its preincrement or postincrement sibling. This
1371// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1372// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1373// expression "Step + sext/zext(PreIncAR)" is congruent with
1374// "sext/zext(PostIncAR)"
1375template <typename ExtendOpTy>
1376static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1377 ScalarEvolution *SE, unsigned Depth) {
1378 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1379 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1380
1381 const Loop *L = AR->getLoop();
1382 const SCEV *Start = AR->getStart();
1383 const SCEV *Step = AR->getStepRecurrence(*SE);
1384
1385 // Check for a simple looking step prior to loop entry.
1386 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1387 if (!SA)
1388 return nullptr;
1389
1390 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1391 // subtraction is expensive. For this purpose, perform a quick and dirty
1392 // difference, by checking for Step in the operand list.
1393 SmallVector<const SCEV *, 4> DiffOps;
1394 for (const SCEV *Op : SA->operands())
1395 if (Op != Step)
1396 DiffOps.push_back(Op);
1397
1398 if (DiffOps.size() == SA->getNumOperands())
1399 return nullptr;
1400
1401 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1402 // `Step`:
1403
1404 // 1. NSW/NUW flags on the step increment.
1405 auto PreStartFlags =
1406 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1407 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1408 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1409 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1410
1411 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1412 // "S+X does not sign/unsign-overflow".
1413 //
1414
1415 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1416 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1417 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1418 return PreStart;
1419
1420 // 2. Direct overflow check on the step operation's expression.
1421 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1422 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1423 const SCEV *OperandExtendedStart =
1424 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
1425 (SE->*GetExtendExpr)(Step, WideTy, Depth));
1426 if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
1427 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1428 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1429 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1430 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1431 SE->setNoWrapFlags(const_cast<SCEVAddRecExpr *>(PreAR), WrapType);
1432 }
1433 return PreStart;
1434 }
1435
1436 // 3. Loop precondition.
1437 ICmpInst::Predicate Pred;
1438 const SCEV *OverflowLimit =
1439 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1440
1441 if (OverflowLimit &&
1442 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1443 return PreStart;
1444
1445 return nullptr;
1446}
1447
1448// Get the normalized zero or sign extended expression for this AddRec's Start.
1449template <typename ExtendOpTy>
1450static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1451 ScalarEvolution *SE,
1452 unsigned Depth) {
1453 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1454
1455 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
1456 if (!PreStart)
1457 return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
1458
1459 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
1460 Depth),
1461 (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1462}
1463
1464// Try to prove away overflow by looking at "nearby" add recurrences. A
1465// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1466// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1467//
1468// Formally:
1469//
1470// {S,+,X} == {S-T,+,X} + T
1471// => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1472//
1473// If ({S-T,+,X} + T) does not overflow ... (1)
1474//
1475// RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1476//
1477// If {S-T,+,X} does not overflow ... (2)
1478//
1479// RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1480// == {Ext(S-T)+Ext(T),+,Ext(X)}
1481//
1482// If (S-T)+T does not overflow ... (3)
1483//
1484// RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1485// == {Ext(S),+,Ext(X)} == LHS
1486//
1487// Thus, if (1), (2) and (3) are true for some T, then
1488// Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1489//
1490// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1491// does not overflow" restricted to the 0th iteration. Therefore we only need
1492// to check for (1) and (2).
1493//
1494// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1495// is `Delta` (defined below).
1496template <typename ExtendOpTy>
1497bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1498 const SCEV *Step,
1499 const Loop *L) {
1500 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1501
1502 // We restrict `Start` to a constant to prevent SCEV from spending too much
1503 // time here. It is correct (but more expensive) to continue with a
1504 // non-constant `Start` and do a general SCEV subtraction to compute
1505 // `PreStart` below.
1506 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1507 if (!StartC)
1508 return false;
1509
1510 APInt StartAI = StartC->getAPInt();
1511
1512 for (unsigned Delta : {-2, -1, 1, 2}) {
1513 const SCEV *PreStart = getConstant(StartAI - Delta);
1514
1515 FoldingSetNodeID ID;
1516 ID.AddInteger(scAddRecExpr);
1517 ID.AddPointer(PreStart);
1518 ID.AddPointer(Step);
1519 ID.AddPointer(L);
1520 void *IP = nullptr;
1521 const auto *PreAR =
1522 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1523
1524 // Give up if we don't already have the add recurrence we need because
1525 // actually constructing an add recurrence is relatively expensive.
1526 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1527 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1528 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1529 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1530 DeltaS, &Pred, this);
1531 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1532 return true;
1533 }
1534 }
1535
1536 return false;
1537}
1538
1539// Finds an integer D for an expression (C + x + y + ...) such that the top
1540// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
1541// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
1542// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
1543// the (C + x + y + ...) expression is \p WholeAddExpr.
1544static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1545 const SCEVConstant *ConstantTerm,
1546 const SCEVAddExpr *WholeAddExpr) {
1547 const APInt &C = ConstantTerm->getAPInt();
1548 const unsigned BitWidth = C.getBitWidth();
1549 // Find number of trailing zeros of (x + y + ...) w/o the C first:
1550 uint32_t TZ = BitWidth;
1551 for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
1552 TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I)));
1553 if (TZ) {
1554 // Set D to be as many least significant bits of C as possible while still
1555 // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
1556 return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
1557 }
1558 return APInt(BitWidth, 0);
1559}
1560
1561// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
1562// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
1563// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
1564// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
1565static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1566 const APInt &ConstantStart,
1567 const SCEV *Step) {
1568 const unsigned BitWidth = ConstantStart.getBitWidth();
1569 const uint32_t TZ = SE.GetMinTrailingZeros(Step);
1570 if (TZ)
1571 return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
1572 : ConstantStart;
1573 return APInt(BitWidth, 0);
1574}
1575
1576const SCEV *
1577ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1578 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&((void)0)
1579 "This is not an extending conversion!")((void)0);
1580 assert(isSCEVable(Ty) &&((void)0)
1581 "This is not a conversion to a SCEVable type!")((void)0);
1582 assert(!Op->getType()->isPointerTy() && "Can't extend pointer!")((void)0);
1583 Ty = getEffectiveSCEVType(Ty);
1584
1585 // Fold if the operand is constant.
1586 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1587 return getConstant(
1588 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1589
1590 // zext(zext(x)) --> zext(x)
1591 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1592 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1593
1594 // Before doing any expensive analysis, check to see if we've already
1595 // computed a SCEV for this Op and Ty.
1596 FoldingSetNodeID ID;
1597 ID.AddInteger(scZeroExtend);
1598 ID.AddPointer(Op);
1599 ID.AddPointer(Ty);
1600 void *IP = nullptr;
1601 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1602 if (Depth > MaxCastDepth) {
1603 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1604 Op, Ty);
1605 UniqueSCEVs.InsertNode(S, IP);
1606 addToLoopUseLists(S);
1607 return S;
1608 }
1609
1610 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1611 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1612 // It's possible the bits taken off by the truncate were all zero bits. If
1613 // so, we should be able to simplify this further.
1614 const SCEV *X = ST->getOperand();
1615 ConstantRange CR = getUnsignedRange(X);
1616 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1617 unsigned NewBits = getTypeSizeInBits(Ty);
1618 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1619 CR.zextOrTrunc(NewBits)))
1620 return getTruncateOrZeroExtend(X, Ty, Depth);
1621 }
1622
1623 // If the input value is a chrec scev, and we can prove that the value
1624 // did not overflow the old, smaller, value, we can zero extend all of the
1625 // operands (often constants). This allows analysis of something like
1626 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1627 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1628 if (AR->isAffine()) {
1629 const SCEV *Start = AR->getStart();
1630 const SCEV *Step = AR->getStepRecurrence(*this);
1631 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1632 const Loop *L = AR->getLoop();
1633
1634 if (!AR->hasNoUnsignedWrap()) {
1635 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1636 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
1637 }
1638
1639 // If we have special knowledge that this addrec won't overflow,
1640 // we don't need to do any further analysis.
1641 if (AR->hasNoUnsignedWrap())
1642 return getAddRecExpr(
1643 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1644 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1645
1646 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1647 // Note that this serves two purposes: It filters out loops that are
1648 // simply not analyzable, and it covers the case where this code is
1649 // being called from within backedge-taken count analysis, such that
1650 // attempting to ask for the backedge-taken count would likely result
1651 // in infinite recursion. In the later case, the analysis code will
1652 // cope with a conservative value, and it will take care to purge
1653 // that value once it has finished.
1654 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
1655 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1656 // Manually compute the final value for AR, checking for overflow.
1657
1658 // Check whether the backedge-taken count can be losslessly casted to
1659 // the addrec's type. The count is always unsigned.
1660 const SCEV *CastedMaxBECount =
1661 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
1662 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
1663 CastedMaxBECount, MaxBECount->getType(), Depth);
1664 if (MaxBECount == RecastedMaxBECount) {
1665 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1666 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1667 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
1668 SCEV::FlagAnyWrap, Depth + 1);
1669 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
1670 SCEV::FlagAnyWrap,
1671 Depth + 1),
1672 WideTy, Depth + 1);
1673 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
1674 const SCEV *WideMaxBECount =
1675 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1676 const SCEV *OperandExtendedAdd =
1677 getAddExpr(WideStart,
1678 getMulExpr(WideMaxBECount,
1679 getZeroExtendExpr(Step, WideTy, Depth + 1),
1680 SCEV::FlagAnyWrap, Depth + 1),
1681 SCEV::FlagAnyWrap, Depth + 1);
1682 if (ZAdd == OperandExtendedAdd) {
1683 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1684 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW);
1685 // Return the expression with the addrec on the outside.
1686 return getAddRecExpr(
1687 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1688 Depth + 1),
1689 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1690 AR->getNoWrapFlags());
1691 }
1692 // Similar to above, only this time treat the step value as signed.
1693 // This covers loops that count down.
1694 OperandExtendedAdd =
1695 getAddExpr(WideStart,
1696 getMulExpr(WideMaxBECount,
1697 getSignExtendExpr(Step, WideTy, Depth + 1),
1698 SCEV::FlagAnyWrap, Depth + 1),
1699 SCEV::FlagAnyWrap, Depth + 1);
1700 if (ZAdd == OperandExtendedAdd) {
1701 // Cache knowledge of AR NW, which is propagated to this AddRec.
1702 // Negative step causes unsigned wrap, but it still can't self-wrap.
1703 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
1704 // Return the expression with the addrec on the outside.
1705 return getAddRecExpr(
1706 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1707 Depth + 1),
1708 getSignExtendExpr(Step, Ty, Depth + 1), L,
1709 AR->getNoWrapFlags());
1710 }
1711 }
1712 }
1713
1714 // Normally, in the cases we can prove no-overflow via a
1715 // backedge guarding condition, we can also compute a backedge
1716 // taken count for the loop. The exceptions are assumptions and
1717 // guards present in the loop -- SCEV is not great at exploiting
1718 // these to compute max backedge taken counts, but can still use
1719 // these to prove lack of overflow. Use this fact to avoid
1720 // doing extra work that may not pay off.
1721 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1722 !AC.assumptions().empty()) {
1723
1724 auto NewFlags = proveNoUnsignedWrapViaInduction(AR);
1725 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
1726 if (AR->hasNoUnsignedWrap()) {
1727 // Same as nuw case above - duplicated here to avoid a compile time
1728 // issue. It's not clear that the order of checks does matter, but
1729 // it's one of two issue possible causes for a change which was
1730 // reverted. Be conservative for the moment.
1731 return getAddRecExpr(
1732 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1733 Depth + 1),
1734 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1735 AR->getNoWrapFlags());
1736 }
1737
1738 // For a negative step, we can extend the operands iff doing so only
1739 // traverses values in the range zext([0,UINT_MAX]).
1740 if (isKnownNegative(Step)) {
1741 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1742 getSignedRangeMin(Step));
1743 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1744 isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
1745 // Cache knowledge of AR NW, which is propagated to this
1746 // AddRec. Negative step causes unsigned wrap, but it
1747 // still can't self-wrap.
1748 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
1749 // Return the expression with the addrec on the outside.
1750 return getAddRecExpr(
1751 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1752 Depth + 1),
1753 getSignExtendExpr(Step, Ty, Depth + 1), L,
1754 AR->getNoWrapFlags());
1755 }
1756 }
1757 }
1758
1759 // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
1760 // if D + (C - D + Step * n) could be proven to not unsigned wrap
1761 // where D maximizes the number of trailing zeros of (C - D + Step * n)
1762 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
1763 const APInt &C = SC->getAPInt();
1764 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
1765 if (D != 0) {
1766 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1767 const SCEV *SResidual =
1768 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
1769 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1770 return getAddExpr(SZExtD, SZExtR,
1771 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1772 Depth + 1);
1773 }
1774 }
1775
1776 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1777 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW);
1778 return getAddRecExpr(
1779 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1780 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1781 }
1782 }
1783
1784 // zext(A % B) --> zext(A) % zext(B)
1785 {
1786 const SCEV *LHS;
1787 const SCEV *RHS;
1788 if (matchURem(Op, LHS, RHS))
1789 return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
1790 getZeroExtendExpr(RHS, Ty, Depth + 1));
1791 }
1792
1793 // zext(A / B) --> zext(A) / zext(B).
1794 if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
1795 return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
1796 getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
1797
1798 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1799 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1800 if (SA->hasNoUnsignedWrap()) {
1801 // If the addition does not unsign overflow then we can, by definition,
1802 // commute the zero extension with the addition operation.
1803 SmallVector<const SCEV *, 4> Ops;
1804 for (const auto *Op : SA->operands())
1805 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1806 return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
1807 }
1808
1809 // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
1810 // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
1811 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1812 //
1813 // Often address arithmetics contain expressions like
1814 // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
1815 // This transformation is useful while proving that such expressions are
1816 // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
1817 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
1818 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
1819 if (D != 0) {
1820 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1821 const SCEV *SResidual =
1822 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
1823 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1824 return getAddExpr(SZExtD, SZExtR,
1825 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1826 Depth + 1);
1827 }
1828 }
1829 }
1830
1831 if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
1832 // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
1833 if (SM->hasNoUnsignedWrap()) {
1834 // If the multiply does not unsign overflow then we can, by definition,
1835 // commute the zero extension with the multiply operation.
1836 SmallVector<const SCEV *, 4> Ops;
1837 for (const auto *Op : SM->operands())
1838 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1839 return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
1840 }
1841
1842 // zext(2^K * (trunc X to iN)) to iM ->
1843 // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
1844 //
1845 // Proof:
1846 //
1847 // zext(2^K * (trunc X to iN)) to iM
1848 // = zext((trunc X to iN) << K) to iM
1849 // = zext((trunc X to i{N-K}) << K)<nuw> to iM
1850 // (because shl removes the top K bits)
1851 // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
1852 // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
1853 //
1854 if (SM->getNumOperands() == 2)
1855 if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0)))
1856 if (MulLHS->getAPInt().isPowerOf2())
1857 if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) {
1858 int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) -
1859 MulLHS->getAPInt().logBase2();
1860 Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
1861 return getMulExpr(
1862 getZeroExtendExpr(MulLHS, Ty),
1863 getZeroExtendExpr(
1864 getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty),
1865 SCEV::FlagNUW, Depth + 1);
1866 }
1867 }
1868
1869 // The cast wasn't folded; create an explicit cast node.
1870 // Recompute the insert position, as it may have been invalidated.
1871 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1872 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1873 Op, Ty);
1874 UniqueSCEVs.InsertNode(S, IP);
1875 addToLoopUseLists(S);
1876 return S;
1877}
1878
1879const SCEV *
1880ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1881 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&((void)0)
1882 "This is not an extending conversion!")((void)0);
1883 assert(isSCEVable(Ty) &&((void)0)
1884 "This is not a conversion to a SCEVable type!")((void)0);
1885 assert(!Op->getType()->isPointerTy() && "Can't extend pointer!")((void)0);
1886 Ty = getEffectiveSCEVType(Ty);
1887
1888 // Fold if the operand is constant.
1889 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1890 return getConstant(
1891 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1892
1893 // sext(sext(x)) --> sext(x)
1894 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1895 return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
1896
1897 // sext(zext(x)) --> zext(x)
1898 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1899 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1900
1901 // Before doing any expensive analysis, check to see if we've already
1902 // computed a SCEV for this Op and Ty.
1903 FoldingSetNodeID ID;
1904 ID.AddInteger(scSignExtend);
1905 ID.AddPointer(Op);
1906 ID.AddPointer(Ty);
1907 void *IP = nullptr;
1908 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1909 // Limit recursion depth.
1910 if (Depth > MaxCastDepth) {
1911 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1912 Op, Ty);
1913 UniqueSCEVs.InsertNode(S, IP);
1914 addToLoopUseLists(S);
1915 return S;
1916 }
1917
1918 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1919 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1920 // It's possible the bits taken off by the truncate were all sign bits. If
1921 // so, we should be able to simplify this further.
1922 const SCEV *X = ST->getOperand();
1923 ConstantRange CR = getSignedRange(X);
1924 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1925 unsigned NewBits = getTypeSizeInBits(Ty);
1926 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1927 CR.sextOrTrunc(NewBits)))
1928 return getTruncateOrSignExtend(X, Ty, Depth);
1929 }
1930
1931 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1932 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1933 if (SA->hasNoSignedWrap()) {
1934 // If the addition does not sign overflow then we can, by definition,
1935 // commute the sign extension with the addition operation.
1936 SmallVector<const SCEV *, 4> Ops;
1937 for (const auto *Op : SA->operands())
1938 Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
1939 return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
1940 }
1941
1942 // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
1943 // if D + (C - D + x + y + ...) could be proven to not signed wrap
1944 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1945 //
1946 // For instance, this will bring two seemingly different expressions:
1947 // 1 + sext(5 + 20 * %x + 24 * %y) and
1948 // sext(6 + 20 * %x + 24 * %y)
1949 // to the same form:
1950 // 2 + sext(4 + 20 * %x + 24 * %y)
1951 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
1952 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
1953 if (D != 0) {
1954 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
1955 const SCEV *SResidual =
1956 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
1957 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
1958 return getAddExpr(SSExtD, SSExtR,
1959 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1960 Depth + 1);
1961 }
1962 }
1963 }
1964 // If the input value is a chrec scev, and we can prove that the value
1965 // did not overflow the old, smaller, value, we can sign extend all of the
1966 // operands (often constants). This allows analysis of something like
1967 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1968 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1969 if (AR->isAffine()) {
1970 const SCEV *Start = AR->getStart();
1971 const SCEV *Step = AR->getStepRecurrence(*this);
1972 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1973 const Loop *L = AR->getLoop();
1974
1975 if (!AR->hasNoSignedWrap()) {
1976 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1977 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
1978 }
1979
1980 // If we have special knowledge that this addrec won't overflow,
1981 // we don't need to do any further analysis.
1982 if (AR->hasNoSignedWrap())
1983 return getAddRecExpr(
1984 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1985 getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
1986
1987 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1988 // Note that this serves two purposes: It filters out loops that are
1989 // simply not analyzable, and it covers the case where this code is
1990 // being called from within backedge-taken count analysis, such that
1991 // attempting to ask for the backedge-taken count would likely result
1992 // in infinite recursion. In the later case, the analysis code will
1993 // cope with a conservative value, and it will take care to purge
1994 // that value once it has finished.
1995 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
1996 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1997 // Manually compute the final value for AR, checking for
1998 // overflow.
1999
2000 // Check whether the backedge-taken count can be losslessly casted to
2001 // the addrec's type. The count is always unsigned.
2002 const SCEV *CastedMaxBECount =
2003 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
2004 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
2005 CastedMaxBECount, MaxBECount->getType(), Depth);
2006 if (MaxBECount == RecastedMaxBECount) {
2007 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
2008 // Check whether Start+Step*MaxBECount has no signed overflow.
2009 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
2010 SCEV::FlagAnyWrap, Depth + 1);
2011 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
2012 SCEV::FlagAnyWrap,
2013 Depth + 1),
2014 WideTy, Depth + 1);
2015 const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
2016 const SCEV *WideMaxBECount =
2017 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
2018 const SCEV *OperandExtendedAdd =
2019 getAddExpr(WideStart,
2020 getMulExpr(WideMaxBECount,
2021 getSignExtendExpr(Step, WideTy, Depth + 1),
2022 SCEV::FlagAnyWrap, Depth + 1),
2023 SCEV::FlagAnyWrap, Depth + 1);
2024 if (SAdd == OperandExtendedAdd) {
2025 // Cache knowledge of AR NSW, which is propagated to this AddRec.
2026 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW);
2027 // Return the expression with the addrec on the outside.
2028 return getAddRecExpr(
2029 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
2030 Depth + 1),
2031 getSignExtendExpr(Step, Ty, Depth + 1), L,
2032 AR->getNoWrapFlags());
2033 }
2034 // Similar to above, only this time treat the step value as unsigned.
2035 // This covers loops that count up with an unsigned step.
2036 OperandExtendedAdd =
2037 getAddExpr(WideStart,
2038 getMulExpr(WideMaxBECount,
2039 getZeroExtendExpr(Step, WideTy, Depth + 1),
2040 SCEV::FlagAnyWrap, Depth + 1),
2041 SCEV::FlagAnyWrap, Depth + 1);
2042 if (SAdd == OperandExtendedAdd) {
2043 // If AR wraps around then
2044 //
2045 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
2046 // => SAdd != OperandExtendedAdd
2047 //
2048 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
2049 // (SAdd == OperandExtendedAdd => AR is NW)
2050
2051 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
2052
2053 // Return the expression with the addrec on the outside.
2054 return getAddRecExpr(
2055 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
2056 Depth + 1),
2057 getZeroExtendExpr(Step, Ty, Depth + 1), L,
2058 AR->getNoWrapFlags());
2059 }
2060 }
2061 }
2062
2063 auto NewFlags = proveNoSignedWrapViaInduction(AR);
2064 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
2065 if (AR->hasNoSignedWrap()) {
2066 // Same as nsw case above - duplicated here to avoid a compile time
2067 // issue. It's not clear that the order of checks does matter, but
2068 // it's one of two issue possible causes for a change which was
2069 // reverted. Be conservative for the moment.
2070 return getAddRecExpr(
2071 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2072 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2073 }
2074
2075 // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
2076 // if D + (C - D + Step * n) could be proven to not signed wrap
2077 // where D maximizes the number of trailing zeros of (C - D + Step * n)
2078 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
2079 const APInt &C = SC->getAPInt();
2080 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
2081 if (D != 0) {
2082 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
2083 const SCEV *SResidual =
2084 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
2085 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
2086 return getAddExpr(SSExtD, SSExtR,
2087 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
2088 Depth + 1);
2089 }
2090 }
2091
2092 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
2093 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW);
2094 return getAddRecExpr(
2095 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2096 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2097 }
2098 }
2099
2100 // If the input value is provably positive and we could not simplify
2101 // away the sext build a zext instead.
2102 if (isKnownNonNegative(Op))
2103 return getZeroExtendExpr(Op, Ty, Depth + 1);
2104
2105 // The cast wasn't folded; create an explicit cast node.
2106 // Recompute the insert position, as it may have been invalidated.
2107 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2108 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
2109 Op, Ty);
2110 UniqueSCEVs.InsertNode(S, IP);
2111 addToLoopUseLists(S);
2112 return S;
2113}
2114
2115/// getAnyExtendExpr - Return a SCEV for the given operand extended with
2116/// unspecified bits out to the given type.
2117const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
2118 Type *Ty) {
2119 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&((void)0)
2120 "This is not an extending conversion!")((void)0);
2121 assert(isSCEVable(Ty) &&((void)0)
2122 "This is not a conversion to a SCEVable type!")((void)0);
2123 Ty = getEffectiveSCEVType(Ty);
2124
2125 // Sign-extend negative constants.
2126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
2127 if (SC->getAPInt().isNegative())
2128 return getSignExtendExpr(Op, Ty);
2129
2130 // Peel off a truncate cast.
2131 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
2132 const SCEV *NewOp = T->getOperand();
2133 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
2134 return getAnyExtendExpr(NewOp, Ty);
2135 return getTruncateOrNoop(NewOp, Ty);
2136 }
2137
2138 // Next try a zext cast. If the cast is folded, use it.
2139 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
2140 if (!isa<SCEVZeroExtendExpr>(ZExt))
2141 return ZExt;
2142
2143 // Next try a sext cast. If the cast is folded, use it.
2144 const SCEV *SExt = getSignExtendExpr(Op, Ty);
2145 if (!isa<SCEVSignExtendExpr>(SExt))
2146 return SExt;
2147
2148 // Force the cast to be folded into the operands of an addrec.
2149 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
2150 SmallVector<const SCEV *, 4> Ops;
2151 for (const SCEV *Op : AR->operands())
2152 Ops.push_back(getAnyExtendExpr(Op, Ty));
2153 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
2154 }
2155
2156 // If the expression is obviously signed, use the sext cast value.
2157 if (isa<SCEVSMaxExpr>(Op))
2158 return SExt;
2159
2160 // Absent any other information, use the zext cast value.
2161 return ZExt;
2162}
2163
2164/// Process the given Ops list, which is a list of operands to be added under
2165/// the given scale, update the given map. This is a helper function for
2166/// getAddRecExpr. As an example of what it does, given a sequence of operands
2167/// that would form an add expression like this:
2168///
2169/// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2170///
2171/// where A and B are constants, update the map with these values:
2172///
2173/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2174///
2175/// and add 13 + A*B*29 to AccumulatedConstant.
2176/// This will allow getAddRecExpr to produce this:
2177///
2178/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2179///
2180/// This form often exposes folding opportunities that are hidden in
2181/// the original operand list.
2182///
2183/// Return true iff it appears that any interesting folding opportunities
2184/// may be exposed. This helps getAddRecExpr short-circuit extra work in
2185/// the common case where no interesting opportunities are present, and
2186/// is also used as a check to avoid infinite recursion.
2187static bool
2188CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
2189 SmallVectorImpl<const SCEV *> &NewOps,
2190 APInt &AccumulatedConstant,
2191 const SCEV *const *Ops, size_t NumOperands,
2192 const APInt &Scale,
2193 ScalarEvolution &SE) {
2194 bool Interesting = false;
2195
2196 // Iterate over the add operands. They are sorted, with constants first.
2197 unsigned i = 0;
2198 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2199 ++i;
2200 // Pull a buried constant out to the outside.
2201 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
2202 Interesting = true;
2203 AccumulatedConstant += Scale * C->getAPInt();
2204 }
2205
2206 // Next comes everything else. We're especially interested in multiplies
2207 // here, but they're in the middle, so just visit the rest with one loop.
2208 for (; i != NumOperands; ++i) {
2209 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
2210 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
2211 APInt NewScale =
2212 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
2213 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
2214 // A multiplication of a constant with another add; recurse.
2215 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2216 Interesting |=
2217 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2218 Add->op_begin(), Add->getNumOperands(),
2219 NewScale, SE);
2220 } else {
2221 // A multiplication of a constant with some other value. Update
2222 // the map.
2223 SmallVector<const SCEV *, 4> MulOps(drop_begin(Mul->operands()));
2224 const SCEV *Key = SE.getMulExpr(MulOps);
2225 auto Pair = M.insert({Key, NewScale});
2226 if (Pair.second) {
2227 NewOps.push_back(Pair.first->first);
2228 } else {
2229 Pair.first->second += NewScale;
2230 // The map already had an entry for this value, which may indicate
2231 // a folding opportunity.
2232 Interesting = true;
2233 }
2234 }
2235 } else {
2236 // An ordinary operand. Update the map.
2237 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2238 M.insert({Ops[i], Scale});
2239 if (Pair.second) {
2240 NewOps.push_back(Pair.first->first);
2241 } else {
2242 Pair.first->second += Scale;
2243 // The map already had an entry for this value, which may indicate
2244 // a folding opportunity.
2245 Interesting = true;
2246 }
2247 }
2248 }
2249
2250 return Interesting;
2251}
2252
2253bool ScalarEvolution::willNotOverflow(Instruction::BinaryOps BinOp, bool Signed,
2254 const SCEV *LHS, const SCEV *RHS) {
2255 const SCEV *(ScalarEvolution::*Operation)(const SCEV *, const SCEV *,
2256 SCEV::NoWrapFlags, unsigned);
2257 switch (BinOp) {
2258 default:
2259 llvm_unreachable("Unsupported binary op")__builtin_unreachable();
2260 case Instruction::Add:
2261 Operation = &ScalarEvolution::getAddExpr;
2262 break;
2263 case Instruction::Sub:
2264 Operation = &ScalarEvolution::getMinusSCEV;
2265 break;
2266 case Instruction::Mul:
2267 Operation = &ScalarEvolution::getMulExpr;
2268 break;
2269 }
2270
2271 const SCEV *(ScalarEvolution::*Extension)(const SCEV *, Type *, unsigned) =
2272 Signed ? &ScalarEvolution::getSignExtendExpr
2273 : &ScalarEvolution::getZeroExtendExpr;
2274
2275 // Check ext(LHS op RHS) == ext(LHS) op ext(RHS)
2276 auto *NarrowTy = cast<IntegerType>(LHS->getType());
2277 auto *WideTy =
2278 IntegerType::get(NarrowTy->getContext(), NarrowTy->getBitWidth() * 2);
2279
2280 const SCEV *A = (this->*Extension)(
2281 (this->*Operation)(LHS, RHS, SCEV::FlagAnyWrap, 0), WideTy, 0);
2282 const SCEV *B = (this->*Operation)((this->*Extension)(LHS, WideTy, 0),
2283 (this->*Extension)(RHS, WideTy, 0),
2284 SCEV::FlagAnyWrap, 0);
2285 return A == B;
2286}
2287
2288std::pair<SCEV::NoWrapFlags, bool /*Deduced*/>
2289ScalarEvolution::getStrengthenedNoWrapFlagsFromBinOp(
2290 const OverflowingBinaryOperator *OBO) {
2291 SCEV::NoWrapFlags Flags = SCEV::NoWrapFlags::FlagAnyWrap;
2292
2293 if (OBO->hasNoUnsignedWrap())
2294 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2295 if (OBO->hasNoSignedWrap())
2296 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2297
2298 bool Deduced = false;
2299
2300 if (OBO->hasNoUnsignedWrap() && OBO->hasNoSignedWrap())
2301 return {Flags, Deduced};
2302
2303 if (OBO->getOpcode() != Instruction::Add &&
2304 OBO->getOpcode() != Instruction::Sub &&
2305 OBO->getOpcode() != Instruction::Mul)
2306 return {Flags, Deduced};
2307
2308 const SCEV *LHS = getSCEV(OBO->getOperand(0));
2309 const SCEV *RHS = getSCEV(OBO->getOperand(1));
2310
2311 if (!OBO->hasNoUnsignedWrap() &&
2312 willNotOverflow((Instruction::BinaryOps)OBO->getOpcode(),
2313 /* Signed */ false, LHS, RHS)) {
2314 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2315 Deduced = true;
2316 }
2317
2318 if (!OBO->hasNoSignedWrap() &&
2319 willNotOverflow((Instruction::BinaryOps)OBO->getOpcode(),
2320 /* Signed */ true, LHS, RHS)) {
2321 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2322 Deduced = true;
2323 }
2324
2325 return {Flags, Deduced};
2326}
2327
2328// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2329// `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2330// can't-overflow flags for the operation if possible.
2331static SCEV::NoWrapFlags
2332StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
2333 const ArrayRef<const SCEV *> Ops,
2334 SCEV::NoWrapFlags Flags) {
2335 using namespace std::placeholders;
2336
2337 using OBO = OverflowingBinaryOperator;
2338
2339 bool CanAnalyze =
2340 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2341 (void)CanAnalyze;
2342 assert(CanAnalyze && "don't call from other places!")((void)0);
2343
2344 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2345 SCEV::NoWrapFlags SignOrUnsignWrap =
2346 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2347
2348 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2349 auto IsKnownNonNegative = [&](const SCEV *S) {
2350 return SE->isKnownNonNegative(S);
2351 };
2352
2353 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2354 Flags =
2355 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2356
2357 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2358
2359 if (SignOrUnsignWrap != SignOrUnsignMask &&
2360 (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
2361 isa<SCEVConstant>(Ops[0])) {
2362
2363 auto Opcode = [&] {
2364 switch (Type) {
2365 case scAddExpr:
2366 return Instruction::Add;
2367 case scMulExpr:
2368 return Instruction::Mul;
2369 default:
2370 llvm_unreachable("Unexpected SCEV op.")__builtin_unreachable();
2371 }
2372 }();
2373
2374 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2375
2376 // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
2377 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2378 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2379 Opcode, C, OBO::NoSignedWrap);
2380 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2381 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2382 }
2383
2384 // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
2385 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2386 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2387 Opcode, C, OBO::NoUnsignedWrap);
2388 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2389 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2390 }
2391 }
2392
2393 return Flags;
2394}
2395
2396bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
2397 return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
2398}
2399
2400/// Get a canonical add expression, or something simpler if possible.
2401const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2402 SCEV::NoWrapFlags OrigFlags,
2403 unsigned Depth) {
2404 assert(!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&((void)0)
2405 "only nuw or nsw allowed")((void)0);
2406 assert(!Ops.empty() && "Cannot get empty add!")((void)0);
2407 if (Ops.size() == 1) return Ops[0];
2408#ifndef NDEBUG1
2409 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2410 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2411 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((void)0)
2412 "SCEVAddExpr operand types don't match!")((void)0);
2413 unsigned NumPtrs = count_if(
2414 Ops, [](const SCEV *Op) { return Op->getType()->isPointerTy(); });
2415 assert(NumPtrs <= 1 && "add has at most one pointer operand")((void)0);
2416#endif
2417
2418 // Sort by complexity, this groups all similar expression types together.
2419 GroupByComplexity(Ops, &LI, DT);
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())((void)0);
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 // Delay expensive flag strengthening until necessary.
2444 auto ComputeFlags = [this, OrigFlags](const ArrayRef<const SCEV *> Ops) {
2445 return StrengthenNoWrapFlags(this, scAddExpr, Ops, OrigFlags);
2446 };
2447
2448 // Limit recursion calls depth.
2449 if (Depth > MaxArithDepth || hasHugeExpression(Ops))
2450 return getOrCreateAddExpr(Ops, ComputeFlags(Ops));
2451
2452 if (SCEV *S = std::get<0>(findExistingSCEVInCache(scAddExpr, Ops))) {
2453 // Don't strengthen flags if we have no new information.
2454 SCEVAddExpr *Add = static_cast<SCEVAddExpr *>(S);
2455 if (Add->getNoWrapFlags(OrigFlags) != OrigFlags)
2456 Add->setNoWrapFlags(ComputeFlags(Ops));
2457 return S;
2458 }
2459
2460 // Okay, check to see if the same value occurs in the operand list more than
2461 // once. If so, merge them together into an multiply expression. Since we
2462 // sorted the list, these values are required to be adjacent.
2463 Type *Ty = Ops[0]->getType();
2464 bool FoundMatch = false;
2465 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2466 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2467 // Scan ahead to count how many equal operands there are.
2468 unsigned Count = 2;
2469 while (i+Count != e && Ops[i+Count] == Ops[i])
2470 ++Count;
2471 // Merge the values into a multiply.
2472 const SCEV *Scale = getConstant(Ty, Count);
2473 const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
2474 if (Ops.size() == Count)
2475 return Mul;
2476 Ops[i] = Mul;
2477 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2478 --i; e -= Count - 1;
2479 FoundMatch = true;
2480 }
2481 if (FoundMatch)
2482 return getAddExpr(Ops, OrigFlags, Depth + 1);
2483
2484 // Check for truncates. If all the operands are truncated from the same
2485 // type, see if factoring out the truncate would permit the result to be
2486 // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
2487 // if the contents of the resulting outer trunc fold to something simple.
2488 auto FindTruncSrcType = [&]() -> Type * {
2489 // We're ultimately looking to fold an addrec of truncs and muls of only
2490 // constants and truncs, so if we find any other types of SCEV
2491 // as operands of the addrec then we bail and return nullptr here.
2492 // Otherwise, we return the type of the operand of a trunc that we find.
2493 if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
2494 return T->getOperand()->getType();
2495 if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2496 const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
2497 if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
2498 return T->getOperand()->getType();
2499 }
2500 return nullptr;
2501 };
2502 if (auto *SrcType = FindTruncSrcType()) {
2503 SmallVector<const SCEV *, 8> LargeOps;
2504 bool Ok = true;
2505 // Check all the operands to see if they can be represented in the
2506 // source type of the truncate.
2507 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2508 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2509 if (T->getOperand()->getType() != SrcType) {
2510 Ok = false;
2511 break;
2512 }
2513 LargeOps.push_back(T->getOperand());
2514 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2515 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2516 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2517 SmallVector<const SCEV *, 8> LargeMulOps;
2518 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2519 if (const SCEVTruncateExpr *T =
2520 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2521 if (T->getOperand()->getType() != SrcType) {
2522 Ok = false;
2523 break;
2524 }
2525 LargeMulOps.push_back(T->getOperand());
2526 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2527 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2528 } else {
2529 Ok = false;
2530 break;
2531 }
2532 }
2533 if (Ok)
2534 LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
2535 } else {
2536 Ok = false;
2537 break;
2538 }
2539 }
2540 if (Ok) {
2541 // Evaluate the expression in the larger type.
2542 const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
2543 // If it folds to something simple, use it. Otherwise, don't.
2544 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2545 return getTruncateExpr(Fold, Ty);
2546 }
2547 }
2548
2549 if (Ops.size() == 2) {
2550 // Check if we have an expression of the form ((X + C1) - C2), where C1 and
2551 // C2 can be folded in a way that allows retaining wrapping flags of (X +
2552 // C1).
2553 const SCEV *A = Ops[0];
2554 const SCEV *B = Ops[1];
2555 auto *AddExpr = dyn_cast<SCEVAddExpr>(B);
2556 auto *C = dyn_cast<SCEVConstant>(A);
2557 if (AddExpr && C && isa<SCEVConstant>(AddExpr->getOperand(0))) {
2558 auto C1 = cast<SCEVConstant>(AddExpr->getOperand(0))->getAPInt();
2559 auto C2 = C->getAPInt();
2560 SCEV::NoWrapFlags PreservedFlags = SCEV::FlagAnyWrap;
2561
2562 APInt ConstAdd = C1 + C2;
2563 auto AddFlags = AddExpr->getNoWrapFlags();
2564 // Adding a smaller constant is NUW if the original AddExpr was NUW.
2565 if (ScalarEvolution::maskFlags(AddFlags, SCEV::FlagNUW) ==
2566 SCEV::FlagNUW &&
2567 ConstAdd.ule(C1)) {
2568 PreservedFlags =
2569 ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNUW);
2570 }
2571
2572 // Adding a constant with the same sign and small magnitude is NSW, if the
2573 // original AddExpr was NSW.
2574 if (ScalarEvolution::maskFlags(AddFlags, SCEV::FlagNSW) ==
2575 SCEV::FlagNSW &&
2576 C1.isSignBitSet() == ConstAdd.isSignBitSet() &&
2577 ConstAdd.abs().ule(C1.abs())) {
2578 PreservedFlags =
2579 ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNSW);
2580 }
2581
2582 if (PreservedFlags != SCEV::FlagAnyWrap) {
2583 SmallVector<const SCEV *, 4> NewOps(AddExpr->op_begin(),
2584 AddExpr->op_end());
2585 NewOps[0] = getConstant(ConstAdd);
2586 return getAddExpr(NewOps, PreservedFlags);
2587 }
2588 }
2589 }
2590
2591 // Skip past any other cast SCEVs.
2592 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2593 ++Idx;
2594
2595 // If there are add operands they would be next.
2596 if (Idx < Ops.size()) {
2597 bool DeletedAdd = false;
2598 // If the original flags and all inlined SCEVAddExprs are NUW, use the
2599 // common NUW flag for expression after inlining. Other flags cannot be
2600 // preserved, because they may depend on the original order of operations.
2601 SCEV::NoWrapFlags CommonFlags = maskFlags(OrigFlags, SCEV::FlagNUW);
2602 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2603 if (Ops.size() > AddOpsInlineThreshold ||
2604 Add->getNumOperands() > AddOpsInlineThreshold)
2605 break;
2606 // If we have an add, expand the add operands onto the end of the operands
2607 // list.
2608 Ops.erase(Ops.begin()+Idx);
2609 Ops.append(Add->op_begin(), Add->op_end());
2610 DeletedAdd = true;
2611 CommonFlags = maskFlags(CommonFlags, Add->getNoWrapFlags());
2612 }
2613
2614 // If we deleted at least one add, we added operands to the end of the list,
2615 // and they are not necessarily sorted. Recurse to resort and resimplify
2616 // any operands we just acquired.
2617 if (DeletedAdd)
2618 return getAddExpr(Ops, CommonFlags, Depth + 1);
2619 }
2620
2621 // Skip over the add expression until we get to a multiply.
2622 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2623 ++Idx;
2624
2625 // Check to see if there are any folding opportunities present with
2626 // operands multiplied by constant values.
2627 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2628 uint64_t BitWidth = getTypeSizeInBits(Ty);
2629 DenseMap<const SCEV *, APInt> M;
2630 SmallVector<const SCEV *, 8> NewOps;
2631 APInt AccumulatedConstant(BitWidth, 0);
2632 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2633 Ops.data(), Ops.size(),
2634 APInt(BitWidth, 1), *this)) {
2635 struct APIntCompare {
2636 bool operator()(const APInt &LHS, const APInt &RHS) const {
2637 return LHS.ult(RHS);
2638 }
2639 };
2640
2641 // Some interesting folding opportunity is present, so its worthwhile to
2642 // re-generate the operands list. Group the operands by constant scale,
2643 // to avoid multiplying by the same constant scale multiple times.
2644 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2645 for (const SCEV *NewOp : NewOps)
2646 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2647 // Re-generate the operands list.
2648 Ops.clear();
2649 if (AccumulatedConstant != 0)
2650 Ops.push_back(getConstant(AccumulatedConstant));
2651 for (auto &MulOp : MulOpLists) {
2652 if (MulOp.first == 1) {
2653 Ops.push_back(getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1));
2654 } else if (MulOp.first != 0) {
2655 Ops.push_back(getMulExpr(
2656 getConstant(MulOp.first),
2657 getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
2658 SCEV::FlagAnyWrap, Depth + 1));
2659 }
2660 }
2661 if (Ops.empty())
2662 return getZero(Ty);
2663 if (Ops.size() == 1)
2664 return Ops[0];
2665 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2666 }
2667 }
2668
2669 // If we are adding something to a multiply expression, make sure the
2670 // something is not already an operand of the multiply. If so, merge it into
2671 // the multiply.
2672 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2673 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2674 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2675 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2676 if (isa<SCEVConstant>(MulOpSCEV))
2677 continue;
2678 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2679 if (MulOpSCEV == Ops[AddOp]) {
2680 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2681 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2682 if (Mul->getNumOperands() != 2) {
2683 // If the multiply has more than two operands, we must get the
2684 // Y*Z term.
2685 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2686 Mul->op_begin()+MulOp);
2687 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2688 InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2689 }
2690 SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
2691 const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2692 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
2693 SCEV::FlagAnyWrap, Depth + 1);
2694 if (Ops.size() == 2) return OuterMul;
2695 if (AddOp < Idx) {
2696 Ops.erase(Ops.begin()+AddOp);
2697 Ops.erase(Ops.begin()+Idx-1);
2698 } else {
2699 Ops.erase(Ops.begin()+Idx);
2700 Ops.erase(Ops.begin()+AddOp-1);
2701 }
2702 Ops.push_back(OuterMul);
2703 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2704 }
2705
2706 // Check this multiply against other multiplies being added together.
2707 for (unsigned OtherMulIdx = Idx+1;
2708 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2709 ++OtherMulIdx) {
2710 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2711 // If MulOp occurs in OtherMul, we can fold the two multiplies
2712 // together.
2713 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2714 OMulOp != e; ++OMulOp)
2715 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2716 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2717 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2718 if (Mul->getNumOperands() != 2) {
2719 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2720 Mul->op_begin()+MulOp);
2721 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2722 InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2723 }
2724 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2725 if (OtherMul->getNumOperands() != 2) {
2726 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2727 OtherMul->op_begin()+OMulOp);
2728 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2729 InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2730 }
2731 SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
2732 const SCEV *InnerMulSum =
2733 getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2734 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
2735 SCEV::FlagAnyWrap, Depth + 1);
2736 if (Ops.size() == 2) return OuterMul;
2737 Ops.erase(Ops.begin()+Idx);
2738 Ops.erase(Ops.begin()+OtherMulIdx-1);
2739 Ops.push_back(OuterMul);
2740 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2741 }
2742 }
2743 }
2744 }
2745
2746 // If there are any add recurrences in the operands list, see if any other
2747 // added values are loop invariant. If so, we can fold them into the
2748 // recurrence.
2749 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2750 ++Idx;
2751
2752 // Scan over all recurrences, trying to fold loop invariants into them.
2753 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2754 // Scan all of the other operands to this add and add them to the vector if
2755 // they are loop invariant w.r.t. the recurrence.
2756 SmallVector<const SCEV *, 8> LIOps;
2757 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2758 const Loop *AddRecLoop = AddRec->getLoop();
2759 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2760 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2761 LIOps.push_back(Ops[i]);
2762 Ops.erase(Ops.begin()+i);
2763 --i; --e;
2764 }
2765
2766 // If we found some loop invariants, fold them into the recurrence.
2767 if (!LIOps.empty()) {
2768 // Compute nowrap flags for the addition of the loop-invariant ops and
2769 // the addrec. Temporarily push it as an operand for that purpose.
2770 LIOps.push_back(AddRec);
2771 SCEV::NoWrapFlags Flags = ComputeFlags(LIOps);
2772 LIOps.pop_back();
2773
2774 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2775 LIOps.push_back(AddRec->getStart());
2776
2777 SmallVector<const SCEV *, 4> AddRecOps(AddRec->operands());
2778 // This follows from the fact that the no-wrap flags on the outer add
2779 // expression are applicable on the 0th iteration, when the add recurrence
2780 // will be equal to its start value.
2781 AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
2782
2783 // Build the new addrec. Propagate the NUW and NSW flags if both the
2784 // outer add and the inner addrec are guaranteed to have no overflow.
2785 // Always propagate NW.
2786 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2787 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2788
2789 // If all of the other operands were loop invariant, we are done.
2790 if (Ops.size() == 1) return NewRec;
2791
2792 // Otherwise, add the folded AddRec by the non-invariant parts.
2793 for (unsigned i = 0;; ++i)
2794 if (Ops[i] == AddRec) {
2795 Ops[i] = NewRec;
2796 break;
2797 }
2798 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2799 }
2800
2801 // Okay, if there weren't any loop invariants to be folded, check to see if
2802 // there are multiple AddRec's with the same loop induction variable being
2803 // added together. If so, we can fold them.
2804 for (unsigned OtherIdx = Idx+1;
2805 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2806 ++OtherIdx) {
2807 // We expect the AddRecExpr's to be sorted in reverse dominance order,
2808 // so that the 1st found AddRecExpr is dominated by all others.
2809 assert(DT.dominates(((void)0)
2810 cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),((void)0)
2811 AddRec->getLoop()->getHeader()) &&((void)0)
2812 "AddRecExprs are not sorted in reverse dominance order?")((void)0);
2813 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2814 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2815 SmallVector<const SCEV *, 4> AddRecOps(AddRec->operands());
2816 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2817 ++OtherIdx) {
2818 const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2819 if (OtherAddRec->getLoop() == AddRecLoop) {
2820 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2821 i != e; ++i) {
2822 if (i >= AddRecOps.size()) {
2823 AddRecOps.append(OtherAddRec->op_begin()+i,
2824 OtherAddRec->op_end());
2825 break;
2826 }
2827 SmallVector<const SCEV *, 2> TwoOps = {
2828 AddRecOps[i], OtherAddRec->getOperand(i)};
2829 AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2830 }
2831 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2832 }
2833 }
2834 // Step size has changed, so we cannot guarantee no self-wraparound.
2835 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2836 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2837 }
2838 }
2839
2840 // Otherwise couldn't fold anything into this recurrence. Move onto the
2841 // next one.
2842 }
2843
2844 // Okay, it looks like we really DO need an add expr. Check to see if we
2845 // already have one, otherwise create a new one.
2846 return getOrCreateAddExpr(Ops, ComputeFlags(Ops));
2847}
2848
2849const SCEV *
2850ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
2851 SCEV::NoWrapFlags Flags) {
2852 FoldingSetNodeID ID;
2853 ID.AddInteger(scAddExpr);
2854 for (const SCEV *Op : Ops)
2855 ID.AddPointer(Op);
2856 void *IP = nullptr;
2857 SCEVAddExpr *S =
2858 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2859 if (!S) {
2860 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2861 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2862 S = new (SCEVAllocator)
2863 SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
2864 UniqueSCEVs.InsertNode(S, IP);
2865 addToLoopUseLists(S);
2866 }
2867 S->setNoWrapFlags(Flags);
2868 return S;
2869}
2870
2871const SCEV *
2872ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
2873 const Loop *L, SCEV::NoWrapFlags Flags) {
2874 FoldingSetNodeID ID;
2875 ID.AddInteger(scAddRecExpr);
2876 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2877 ID.AddPointer(Ops[i]);
2878 ID.AddPointer(L);
2879 void *IP = nullptr;
2880 SCEVAddRecExpr *S =
2881 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2882 if (!S) {
2883 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2884 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2885 S = new (SCEVAllocator)
2886 SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
2887 UniqueSCEVs.InsertNode(S, IP);
2888 addToLoopUseLists(S);
2889 }
2890 setNoWrapFlags(S, Flags);
2891 return S;
2892}
2893
2894const SCEV *
2895ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
2896 SCEV::NoWrapFlags Flags) {
2897 FoldingSetNodeID ID;
2898 ID.AddInteger(scMulExpr);
2899 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2900 ID.AddPointer(Ops[i]);
2901 void *IP = nullptr;
2902 SCEVMulExpr *S =
2903 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2904 if (!S) {
2905 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2906 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2907 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2908 O, Ops.size());
2909 UniqueSCEVs.InsertNode(S, IP);
2910 addToLoopUseLists(S);
2911 }
2912 S->setNoWrapFlags(Flags);
2913 return S;
2914}
2915
2916static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2917 uint64_t k = i*j;
2918 if (j > 1 && k / j != i) Overflow = true;
2919 return k;
2920}
2921
2922/// Compute the result of "n choose k", the binomial coefficient. If an
2923/// intermediate computation overflows, Overflow will be set and the return will
2924/// be garbage. Overflow is not cleared on absence of overflow.
2925static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2926 // We use the multiplicative formula:
2927 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2928 // At each iteration, we take the n-th term of the numeral and divide by the
2929 // (k-n)th term of the denominator. This division will always produce an
2930 // integral result, and helps reduce the chance of overflow in the
2931 // intermediate computations. However, we can still overflow even when the
2932 // final result would fit.
2933
2934 if (n == 0 || n == k) return 1;
2935 if (k > n) return 0;
2936
2937 if (k > n/2)
2938 k = n-k;
2939
2940 uint64_t r = 1;
2941 for (uint64_t i = 1; i <= k; ++i) {
2942 r = umul_ov(r, n-(i-1), Overflow);
2943 r /= i;
2944 }
2945 return r;
2946}
2947
2948/// Determine if any of the operands in this SCEV are a constant or if
2949/// any of the add or multiply expressions in this SCEV contain a constant.
2950static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
2951 struct FindConstantInAddMulChain {
2952 bool FoundConstant = false;
2953
2954 bool follow(const SCEV *S) {
2955 FoundConstant |= isa<SCEVConstant>(S);
2956 return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
2957 }
2958
2959 bool isDone() const {
2960 return FoundConstant;
2961 }
2962 };
2963
2964 FindConstantInAddMulChain F;
2965 SCEVTraversal<FindConstantInAddMulChain> ST(F);
2966 ST.visitAll(StartExpr);
2967 return F.FoundConstant;
2968}
2969
2970/// Get a canonical multiply expression, or something simpler if possible.
2971const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2972 SCEV::NoWrapFlags OrigFlags,
2973 unsigned Depth) {
2974 assert(OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) &&((void)0)
2975 "only nuw or nsw allowed")((void)0);
2976 assert(!Ops.empty() && "Cannot get empty mul!")((void)0);
2977 if (Ops.size() == 1) return Ops[0];
2978#ifndef NDEBUG1
2979 Type *ETy = Ops[0]->getType();
2980 assert(!ETy->isPointerTy())((void)0);
2981 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2982 assert(Ops[i]->getType() == ETy &&((void)0)
2983 "SCEVMulExpr operand types don't match!")((void)0);
2984#endif
2985
2986 // Sort by complexity, this groups all similar expression types together.
2987 GroupByComplexity(Ops, &LI, DT);
2988
2989 // If there are any constants, fold them together.
2990 unsigned Idx = 0;
2991 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2992 ++Idx;
2993 assert(Idx < Ops.size())((void)0);
2994 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2995 // We found two constants, fold them together!
2996 Ops[0] = getConstant(LHSC->getAPInt() * RHSC->getAPInt());
2997 if (Ops.size() == 2) return Ops[0];
2998 Ops.erase(Ops.begin()+1); // Erase the folded element
2999 LHSC = cast<SCEVConstant>(Ops[0]);
3000 }
3001
3002 // If we have a multiply of zero, it will always be zero.
3003 if (LHSC->getValue()->isZero())
3004 return LHSC;
3005
3006 // If we are left with a constant one being multiplied, strip it off.
3007 if (LHSC->getValue()->isOne()) {
3008 Ops.erase(Ops.begin());
3009 --Idx;
3010 }
3011
3012 if (Ops.size() == 1)
3013 return Ops[0];
3014 }
3015
3016 // Delay expensive flag strengthening until necessary.
3017 auto ComputeFlags = [this, OrigFlags](const ArrayRef<const SCEV *> Ops) {
3018 return StrengthenNoWrapFlags(this, scMulExpr, Ops, OrigFlags);
3019 };
3020
3021 // Limit recursion calls depth.
3022 if (Depth > MaxArithDepth || hasHugeExpression(Ops))
3023 return getOrCreateMulExpr(Ops, ComputeFlags(Ops));
3024
3025 if (SCEV *S = std::get<0>(findExistingSCEVInCache(scMulExpr, Ops))) {
3026 // Don't strengthen flags if we have no new information.
3027 SCEVMulExpr *Mul = static_cast<SCEVMulExpr *>(S);
3028 if (Mul->getNoWrapFlags(OrigFlags) != OrigFlags)
3029 Mul->setNoWrapFlags(ComputeFlags(Ops));
3030 return S;
3031 }
3032
3033 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3034 if (Ops.size() == 2) {
3035 // C1*(C2+V) -> C1*C2 + C1*V
3036 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
3037 // If any of Add's ops are Adds or Muls with a constant, apply this
3038 // transformation as well.
3039 //
3040 // TODO: There are some cases where this transformation is not
3041 // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
3042 // this transformation should be narrowed down.
3043 if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add))
3044 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
3045 SCEV::FlagAnyWrap, Depth + 1),
3046 getMulExpr(LHSC, Add->getOperand(1),
3047 SCEV::FlagAnyWrap, Depth + 1),
3048 SCEV::FlagAnyWrap, Depth + 1);
3049
3050 if (Ops[0]->isAllOnesValue()) {
3051 // If we have a mul by -1 of an add, try distributing the -1 among the
3052 // add operands.
3053 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
3054 SmallVector<const SCEV *, 4> NewOps;
3055 bool AnyFolded = false;
3056 for (const SCEV *AddOp : Add->operands()) {
3057 const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
3058 Depth + 1);
3059 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
3060 NewOps.push_back(Mul);
3061 }
3062 if (AnyFolded)
3063 return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
3064 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
3065 // Negation preserves a recurrence's no self-wrap property.
3066 SmallVector<const SCEV *, 4> Operands;
3067 for (const SCEV *AddRecOp : AddRec->operands())
3068 Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
3069 Depth + 1));
3070
3071 return getAddRecExpr(Operands, AddRec->getLoop(),
3072 AddRec->getNoWrapFlags(SCEV::FlagNW));
3073 }
3074 }
3075 }
3076 }
3077
3078 // Skip over the add expression until we get to a multiply.
3079 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
3080 ++Idx;
3081
3082 // If there are mul operands inline them all into this expression.
3083 if (Idx < Ops.size()) {
3084 bool DeletedMul = false;
3085 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
3086 if (Ops.size() > MulOpsInlineThreshold)
3087 break;
3088 // If we have an mul, expand the mul operands onto the end of the
3089 // operands list.
3090 Ops.erase(Ops.begin()+Idx);
3091 Ops.append(Mul->op_begin(), Mul->op_end());
3092 DeletedMul = true;
3093 }
3094
3095 // If we deleted at least one mul, we added operands to the end of the
3096 // list, and they are not necessarily sorted. Recurse to resort and
3097 // resimplify any operands we just acquired.
3098 if (DeletedMul)
3099 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3100 }
3101
3102 // If there are any add recurrences in the operands list, see if any other
3103 // added values are loop invariant. If so, we can fold them into the
3104 // recurrence.
3105 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
3106 ++Idx;
3107
3108 // Scan over all recurrences, trying to fold loop invariants into them.
3109 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
3110 // Scan all of the other operands to this mul and add them to the vector
3111 // if they are loop invariant w.r.t. the recurrence.
3112 SmallVector<const SCEV *, 8> LIOps;
3113 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
3114 const Loop *AddRecLoop = AddRec->getLoop();
3115 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3116 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
3117 LIOps.push_back(Ops[i]);
3118 Ops.erase(Ops.begin()+i);
3119 --i; --e;
3120 }
3121
3122 // If we found some loop invariants, fold them into the recurrence.
3123 if (!LIOps.empty()) {
3124 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
3125 SmallVector<const SCEV *, 4> NewOps;
3126 NewOps.reserve(AddRec->getNumOperands());
3127 const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
3128 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
3129 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
3130 SCEV::FlagAnyWrap, Depth + 1));
3131
3132 // Build the new addrec. Propagate the NUW and NSW flags if both the
3133 // outer mul and the inner addrec are guaranteed to have no overflow.
3134 //
3135 // No self-wrap cannot be guaranteed after changing the step size, but
3136 // will be inferred if either NUW or NSW is true.
3137 SCEV::NoWrapFlags Flags = ComputeFlags({Scale, AddRec});
3138 const SCEV *NewRec = getAddRecExpr(
3139 NewOps, AddRecLoop, AddRec->getNoWrapFlags(Flags));
3140
3141 // If all of the other operands were loop invariant, we are done.
3142 if (Ops.size() == 1) return NewRec;
3143
3144 // Otherwise, multiply the folded AddRec by the non-invariant parts.
3145 for (unsigned i = 0;; ++i)
3146 if (Ops[i] == AddRec) {
3147 Ops[i] = NewRec;
3148 break;
3149 }
3150 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3151 }
3152
3153 // Okay, if there weren't any loop invariants to be folded, check to see
3154 // if there are multiple AddRec's with the same loop induction variable
3155 // being multiplied together. If so, we can fold them.
3156
3157 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
3158 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
3159 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
3160 // ]]],+,...up to x=2n}.
3161 // Note that the arguments to choose() are always integers with values
3162 // known at compile time, never SCEV objects.
3163 //
3164 // The implementation avoids pointless extra computations when the two
3165 // addrec's are of different length (mathematically, it's equivalent to
3166 // an infinite stream of zeros on the right).
3167 bool OpsModified = false;
3168 for (unsigned OtherIdx = Idx+1;
3169 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
3170 ++OtherIdx) {
3171 const SCEVAddRecExpr *OtherAddRec =
3172 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
3173 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
3174 continue;
3175
3176 // Limit max number of arguments to avoid creation of unreasonably big
3177 // SCEVAddRecs with very complex operands.
3178 if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
3179 MaxAddRecSize || hasHugeExpression({AddRec, OtherAddRec}))
3180 continue;
3181
3182 bool Overflow = false;
3183 Type *Ty = AddRec->getType();
3184 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
3185 SmallVector<const SCEV*, 7> AddRecOps;
3186 for (int x = 0, xe = AddRec->getNumOperands() +
3187 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
3188 SmallVector <const SCEV *, 7> SumOps;
3189 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
3190 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
3191 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
3192 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
3193 z < ze && !Overflow; ++z) {
3194 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
3195 uint64_t Coeff;
3196 if (LargerThan64Bits)
3197 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
3198 else
3199 Coeff = Coeff1*Coeff2;
3200 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
3201 const SCEV *Term1 = AddRec->getOperand(y-z);
3202 const SCEV *Term2 = OtherAddRec->getOperand(z);
3203 SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
3204 SCEV::FlagAnyWrap, Depth + 1));
3205 }
3206 }
3207 if (SumOps.empty())
3208 SumOps.push_back(getZero(Ty));
3209 AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
3210 }
3211 if (!Overflow) {
3212 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRecLoop,
3213 SCEV::FlagAnyWrap);
3214 if (Ops.size() == 2) return NewAddRec;
3215 Ops[Idx] = NewAddRec;
3216 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
3217 OpsModified = true;
3218 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
3219 if (!AddRec)
3220 break;
3221 }
3222 }
3223 if (OpsModified)
3224 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3225
3226 // Otherwise couldn't fold anything into this recurrence. Move onto the
3227 // next one.
3228 }
3229
3230 // Okay, it looks like we really DO need an mul expr. Check to see if we
3231 // already have one, otherwise create a new one.
3232 return getOrCreateMulExpr(Ops, ComputeFlags(Ops));
3233}
3234
3235/// Represents an unsigned remainder expression based on unsigned division.
3236const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
3237 const SCEV *RHS) {
3238 assert(getEffectiveSCEVType(LHS->getType()) ==((void)0)
3239 getEffectiveSCEVType(RHS->getType()) &&((void)0)
3240 "SCEVURemExpr operand types don't match!")((void)0);
3241
3242 // Short-circuit easy cases
3243 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3244 // If constant is one, the result is trivial
3245 if (RHSC->getValue()->isOne())
3246 return getZero(LHS->getType()); // X urem 1 --> 0
3247
3248 // If constant is a power of two, fold into a zext(trunc(LHS)).
3249 if (RHSC->getAPInt().isPowerOf2()) {
3250 Type *FullTy = LHS->getType();
3251 Type *TruncTy =
3252 IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
3253 return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
3254 }
3255 }
3256
3257 // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
3258 const SCEV *UDiv = getUDivExpr(LHS, RHS);
3259 const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
3260 return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
3261}
3262
3263/// Get a canonical unsigned division expression, or something simpler if
3264/// possible.
3265const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
3266 const SCEV *RHS) {
3267 assert(!LHS->getType()->isPointerTy() &&((void)0)
3268 "SCEVUDivExpr operand can't be pointer!")((void)0);
3269 assert(LHS->getType() == RHS->getType() &&((void)0)
3270 "SCEVUDivExpr operand types don't match!")((void)0);
3271
3272 FoldingSetNodeID ID;
3273 ID.AddInteger(scUDivExpr);
3274 ID.AddPointer(LHS);
3275 ID.AddPointer(RHS);
3276 void *IP = nullptr;
3277 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
3278 return S;
3279
3280 // 0 udiv Y == 0
3281 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS))
3282 if (LHSC->getValue()->isZero())
3283 return LHS;
3284
3285 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3286 if (RHSC->getValue()->isOne())
3287 return LHS; // X udiv 1 --> x
3288 // If the denominator is zero, the result of the udiv is undefined. Don't
3289 // try to analyze it, because the resolution chosen here may differ from
3290 // the resolution chosen in other parts of the compiler.
3291 if (!RHSC->getValue()->isZero()) {
3292 // Determine if the division can be folded into the operands of
3293 // its operands.
3294 // TODO: Generalize this to non-constants by using known-bits information.
3295 Type *Ty = LHS->getType();
3296 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
3297 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
3298 // For non-power-of-two values, effectively round the value up to the
3299 // nearest power of two.
3300 if (!RHSC->getAPInt().isPowerOf2())
3301 ++MaxShiftAmt;
3302 IntegerType *ExtTy =
3303 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
3304 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
3305 if (const SCEVConstant *Step =
3306 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
3307 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
3308 const APInt &StepInt = Step->getAPInt();
3309 const APInt &DivInt = RHSC->getAPInt();
3310 if (!StepInt.urem(DivInt) &&
3311 getZeroExtendExpr(AR, ExtTy) ==
3312 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3313 getZeroExtendExpr(Step, ExtTy),
3314 AR->getLoop(), SCEV::FlagAnyWrap)) {
3315 SmallVector<const SCEV *, 4> Operands;
3316 for (const SCEV *Op : AR->operands())
3317 Operands.push_back(getUDivExpr(Op, RHS));
3318 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
3319 }
3320 /// Get a canonical UDivExpr for a recurrence.
3321 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
3322 // We can currently only fold X%N if X is constant.
3323 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
3324 if (StartC && !DivInt.urem(StepInt) &&
3325 getZeroExtendExpr(AR, ExtTy) ==
3326 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3327 getZeroExtendExpr(Step, ExtTy),
3328 AR->getLoop(), SCEV::FlagAnyWrap)) {
3329 const APInt &StartInt = StartC->getAPInt();
3330 const APInt &StartRem = StartInt.urem(StepInt);
3331 if (StartRem != 0) {
3332 const SCEV *NewLHS =
3333 getAddRecExpr(getConstant(StartInt - StartRem), Step,
3334 AR->getLoop(), SCEV::FlagNW);
3335 if (LHS != NewLHS) {
3336 LHS = NewLHS;
3337
3338 // Reset the ID to include the new LHS, and check if it is
3339 // already cached.
3340 ID.clear();
3341 ID.AddInteger(scUDivExpr);
3342 ID.AddPointer(LHS);
3343 ID.AddPointer(RHS);
3344 IP = nullptr;
3345 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
3346 return S;
3347 }
3348 }
3349 }
3350 }
3351 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
3352 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
3353 SmallVector<const SCEV *, 4> Operands;
3354 for (const SCEV *Op : M->operands())
3355 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3356 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
3357 // Find an operand that's safely divisible.
3358 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
3359 const SCEV *Op = M->getOperand(i);
3360 const SCEV *Div = getUDivExpr(Op, RHSC);
3361 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
3362 Operands = SmallVector<const SCEV *, 4>(M->operands());
3363 Operands[i] = Div;
3364 return getMulExpr(Operands);
3365 }
3366 }
3367 }
3368
3369 // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
3370 if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
3371 if (auto *DivisorConstant =
3372 dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
3373 bool Overflow = false;
3374 APInt NewRHS =
3375 DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
3376 if (Overflow) {
3377 return getConstant(RHSC->getType(), 0, false);
3378 }
3379 return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
3380 }
3381 }
3382
3383 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
3384 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
3385 SmallVector<const SCEV *, 4> Operands;
3386 for (const SCEV *Op : A->operands())
3387 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3388 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
3389 Operands.clear();
3390 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
3391 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
3392 if (isa<SCEVUDivExpr>(Op) ||
3393 getMulExpr(Op, RHS) != A->getOperand(i))
3394 break;
3395 Operands.push_back(Op);
3396 }
3397 if (Operands.size() == A->getNumOperands())
3398 return getAddExpr(Operands);
3399 }
3400 }
3401
3402 // Fold if both operands are constant.
3403 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
3404 Constant *LHSCV = LHSC->getValue();
3405 Constant *RHSCV = RHSC->getValue();
3406 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
3407 RHSCV)));
3408 }
3409 }
3410 }
3411
3412 // The Insertion Point (IP) might be invalid by now (due to UniqueSCEVs
3413 // changes). Make sure we get a new one.
3414 IP = nullptr;
3415 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3416 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
3417 LHS, RHS);
3418 UniqueSCEVs.InsertNode(S, IP);
3419 addToLoopUseLists(S);
3420 return S;
3421}
3422
3423static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
3424 APInt A = C1->getAPInt().abs();
3425 APInt B = C2->getAPInt().abs();
3426 uint32_t ABW = A.getBitWidth();
3427 uint32_t BBW = B.getBitWidth();
3428
3429 if (ABW > BBW)
3430 B = B.zext(ABW);
3431 else if (ABW < BBW)
3432 A = A.zext(BBW);
3433
3434 return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
3435}
3436
3437/// Get a canonical unsigned division expression, or something simpler if
3438/// possible. There is no representation for an exact udiv in SCEV IR, but we
3439/// can attempt to remove factors from the LHS and RHS. We can't do this when
3440/// it's not exact because the udiv may be clearing bits.
3441const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
3442 const SCEV *RHS) {
3443 // TODO: we could try to find factors in all sorts of things, but for now we
3444 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
3445 // end of this file for inspiration.
3446
3447 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
3448 if (!Mul || !Mul->hasNoUnsignedWrap())
3449 return getUDivExpr(LHS, RHS);
3450
3451 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
3452 // If the mulexpr multiplies by a constant, then that constant must be the
3453 // first element of the mulexpr.
3454 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
3455 if (LHSCst == RHSCst) {
3456 SmallVector<const SCEV *, 2> Operands(drop_begin(Mul->operands()));
3457 return getMulExpr(Operands);
3458 }
3459
3460 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
3461 // that there's a factor provided by one of the other terms. We need to
3462 // check.
3463 APInt Factor = gcd(LHSCst, RHSCst);
3464 if (!Factor.isIntN(1)) {
3465 LHSCst =
3466 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
3467 RHSCst =
3468 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
3469 SmallVector<const SCEV *, 2> Operands;
3470 Operands.push_back(LHSCst);
3471 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3472 LHS = getMulExpr(Operands);
3473 RHS = RHSCst;
3474 Mul = dyn_cast<SCEVMulExpr>(LHS);
3475 if (!Mul)
3476 return getUDivExactExpr(LHS, RHS);
3477 }
3478 }
3479 }
3480
3481 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
3482 if (Mul->getOperand(i) == RHS) {
3483 SmallVector<const SCEV *, 2> Operands;
3484 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
3485 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
3486 return getMulExpr(Operands);
3487 }
3488 }
3489
3490 return getUDivExpr(LHS, RHS);
3491}
3492
3493/// Get an add recurrence expression for the specified loop. Simplify the
3494/// expression as much as possible.
3495const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
3496 const Loop *L,
3497 SCEV::NoWrapFlags Flags) {
3498 SmallVector<const SCEV *, 4> Operands;
3499 Operands.push_back(Start);
3500 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
3501 if (StepChrec->getLoop() == L) {
3502 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
3503 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
3504 }
3505
3506 Operands.push_back(Step);
3507 return getAddRecExpr(Operands, L, Flags);
3508}
3509
3510/// Get an add recurrence expression for the specified loop. Simplify the
3511/// expression as much as possible.
3512const SCEV *
3513ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
3514 const Loop *L, SCEV::NoWrapFlags Flags) {
3515 if (Operands.size() == 1) return Operands[0];
3516#ifndef NDEBUG1
3517 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
3518 for (unsigned i = 1, e = Operands.size(); i != e; ++i) {
3519 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&((void)0)
3520 "SCEVAddRecExpr operand types don't match!")((void)0);
3521 assert(!Operands[i]->getType()->isPointerTy() && "Step must be integer")((void)0);
3522 }
3523 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3524 assert(isLoopInvariant(Operands[i], L) &&((void)0)
3525 "SCEVAddRecExpr operand is not loop-invariant!")((void)0);
3526#endif
3527
3528 if (Operands.back()->isZero()) {
3529 Operands.pop_back();
3530 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
3531 }
3532
3533 // It's tempting to want to call getConstantMaxBackedgeTakenCount count here and
3534 // use that information to infer NUW and NSW flags. However, computing a
3535 // BE count requires calling getAddRecExpr, so we may not yet have a
3536 // meaningful BE count at this point (and if we don't, we'd be stuck
3537 // with a SCEVCouldNotCompute as the cached BE count).
3538
3539 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
3540
3541 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
3542 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
3543 const Loop *NestedLoop = NestedAR->getLoop();
3544 if (L->contains(NestedLoop)
3545 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
3546 : (!NestedLoop->contains(L) &&
3547 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
3548 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->operands());
3549 Operands[0] = NestedAR->getStart();
3550 // AddRecs require their operands be loop-invariant with respect to their
3551 // loops. Don't perform this transformation if it would break this
3552 // requirement.
3553 bool AllInvariant = all_of(
3554 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
3555
3556 if (AllInvariant) {
3557 // Create a recurrence for the outer loop with the same step size.
3558 //
3559 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3560 // inner recurrence has the same property.
3561 SCEV::NoWrapFlags OuterFlags =
3562 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3563
3564 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3565 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3566 return isLoopInvariant(Op, NestedLoop);
3567 });
3568
3569 if (AllInvariant) {
3570 // Ok, both add recurrences are valid after the transformation.
3571 //
3572 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3573 // the outer recurrence has the same property.
3574 SCEV::NoWrapFlags InnerFlags =
3575 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3576 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3577 }
3578 }
3579 // Reset Operands to its original state.
3580 Operands[0] = NestedAR;
3581 }
3582 }
3583
3584 // Okay, it looks like we really DO need an addrec expr. Check to see if we
3585 // already have one, otherwise create a new one.
3586 return getOrCreateAddRecExpr(Operands, L, Flags);
3587}
3588
3589const SCEV *
3590ScalarEvolution::getGEPExpr(GEPOperator *GEP,
3591 const SmallVectorImpl<const SCEV *> &IndexExprs) {
3592 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3593 // getSCEV(Base)->getType() has the same address space as Base->getType()
3594 // because SCEV::getType() preserves the address space.
3595 Type *IntIdxTy = getEffectiveSCEVType(BaseExpr->getType());
3596 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3597 // instruction to its SCEV, because the Instruction may be guarded by control
3598 // flow and the no-overflow bits may not be valid for the expression in any
3599 // context. This can be fixed similarly to how these flags are handled for
3600 // adds.
3601 SCEV::NoWrapFlags OffsetWrap =
3602 GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3603
3604 Type *CurTy = GEP->getType();
3605 bool FirstIter = true;
3606 SmallVector<const SCEV *, 4> Offsets;
3607 for (const SCEV *IndexExpr : IndexExprs) {
3608 // Compute the (potentially symbolic) offset in bytes for this index.
3609 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3610 // For a struct, add the member offset.
3611 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3612 unsigned FieldNo = Index->getZExtValue();
3613 const SCEV *FieldOffset = getOffsetOfExpr(IntIdxTy, STy, FieldNo);
3614 Offsets.push_back(FieldOffset);
3615
3616 // Update CurTy to the type of the field at Index.
3617 CurTy = STy->getTypeAtIndex(Index);
3618 } else {
3619 // Update CurTy to its element type.
3620 if (FirstIter) {
3621 assert(isa<PointerType>(CurTy) &&((void)0)
3622 "The first index of a GEP indexes a pointer")((void)0);
3623 CurTy = GEP->getSourceElementType();
3624 FirstIter = false;
3625 } else {
3626 CurTy = GetElementPtrInst::getTypeAtIndex(CurTy, (uint64_t)0);
3627 }
3628 // For an array, add the element offset, explicitly scaled.
3629 const SCEV *ElementSize = getSizeOfExpr(IntIdxTy, CurTy);
3630 // Getelementptr indices are signed.
3631 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntIdxTy);
3632
3633 // Multiply the index by the element size to compute the element offset.
3634 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, OffsetWrap);
3635 Offsets.push_back(LocalOffset);
3636 }
3637 }
3638
3639 // Handle degenerate case of GEP without offsets.
3640 if (Offsets.empty())
3641 return BaseExpr;
3642
3643 // Add the offsets together, assuming nsw if inbounds.
3644 const SCEV *Offset = getAddExpr(Offsets, OffsetWrap);
3645 // Add the base address and the offset. We cannot use the nsw flag, as the
3646 // base address is unsigned. However, if we know that the offset is
3647 // non-negative, we can use nuw.
3648 SCEV::NoWrapFlags BaseWrap = GEP->isInBounds() && isKnownNonNegative(Offset)
3649 ? SCEV::FlagNUW : SCEV::FlagAnyWrap;
3650 return getAddExpr(BaseExpr, Offset, BaseWrap);
3651}
3652
3653std::tuple<SCEV *, FoldingSetNodeID, void *>
3654ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType,
3655 ArrayRef<const SCEV *> Ops) {
3656 FoldingSetNodeID ID;
3657 void *IP = nullptr;
3658 ID.AddInteger(SCEVType);
3659 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3660 ID.AddPointer(Ops[i]);
3661 return std::tuple<SCEV *, FoldingSetNodeID, void *>(
3662 UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP);
3663}
3664
3665const SCEV *ScalarEvolution::getAbsExpr(const SCEV *Op, bool IsNSW) {
3666 SCEV::NoWrapFlags Flags = IsNSW ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3667 return getSMaxExpr(Op, getNegativeSCEV(Op, Flags));
3668}
3669
3670const SCEV *ScalarEvolution::getMinMaxExpr(SCEVTypes Kind,
3671 SmallVectorImpl<const SCEV *> &Ops) {
3672 assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!")((void)0);
3673 if (Ops.size() == 1) return Ops[0];
3674#ifndef NDEBUG1
3675 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3676 for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
3677 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((void)0)
3678 "Operand types don't match!")((void)0);
3679 assert(Ops[0]->getType()->isPointerTy() ==((void)0)
3680 Ops[i]->getType()->isPointerTy() &&((void)0)
3681 "min/max should be consistently pointerish")((void)0);
3682 }
3683#endif
3684
3685 bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
3686 bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;
3687
3688 // Sort by complexity, this groups all similar expression types together.
3689 GroupByComplexity(Ops, &LI, DT);
3690
3691 // Check if we have created the same expression before.
3692 if (const SCEV *S = std::get<0>(findExistingSCEVInCache(Kind, Ops))) {
3693 return S;
3694 }
3695
3696 // If there are any constants, fold them together.
3697 unsigned Idx = 0;
3698 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3699 ++Idx;
3700 assert(Idx < Ops.size())((void)0);
3701 auto FoldOp = [&](const APInt &LHS, const APInt &RHS) {
3702 if (Kind == scSMaxExpr)
3703 return APIntOps::smax(LHS, RHS);
3704 else if (Kind == scSMinExpr)
3705 return APIntOps::smin(LHS, RHS);
3706 else if (Kind == scUMaxExpr)
3707 return APIntOps::umax(LHS, RHS);
3708 else if (Kind == scUMinExpr)
3709 return APIntOps::umin(LHS, RHS);
3710 llvm_unreachable("Unknown SCEV min/max opcode")__builtin_unreachable();
3711 };
3712
3713 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3714 // We found two constants, fold them together!
3715 ConstantInt *Fold = ConstantInt::get(
3716 getContext(), FoldOp(LHSC->getAPInt(), RHSC->getAPInt()));
3717 Ops[0] = getConstant(Fold);
3718 Ops.erase(Ops.begin()+1); // Erase the folded element
3719 if (Ops.size() == 1) return Ops[0];
3720 LHSC = cast<SCEVConstant>(Ops[0]);
3721 }
3722
3723 bool IsMinV = LHSC->getValue()->isMinValue(IsSigned);
3724 bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned);
3725
3726 if (IsMax ? IsMinV : IsMaxV) {
3727 // If we are left with a constant minimum(/maximum)-int, strip it off.
3728 Ops.erase(Ops.begin());
3729 --Idx;
3730 } else if (IsMax ? IsMaxV : IsMinV) {
3731 // If we have a max(/min) with a constant maximum(/minimum)-int,
3732 // it will always be the extremum.
3733 return LHSC;
3734 }
3735
3736 if (Ops.size() == 1) return Ops[0];
3737 }
3738
3739 // Find the first operation of the same kind
3740 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
3741 ++Idx;
3742
3743 // Check to see if one of the operands is of the same kind. If so, expand its
3744 // operands onto our operand list, and recurse to simplify.
3745 if (Idx < Ops.size()) {
3746 bool DeletedAny = false;
3747 while (Ops[Idx]->getSCEVType() == Kind) {
3748 const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]);
3749 Ops.erase(Ops.begin()+Idx);
3750 Ops.append(SMME->op_begin(), SMME->op_end());
3751 DeletedAny = true;
3752 }
3753
3754 if (DeletedAny)
3755 return getMinMaxExpr(Kind, Ops);
3756 }
3757
3758 // Okay, check to see if the same value occurs in the operand list twice. If
3759 // so, delete one. Since we sorted the list, these values are required to
3760 // be adjacent.
3761 llvm::CmpInst::Predicate GEPred =
3762 IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
3763 llvm::CmpInst::Predicate LEPred =
3764 IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
3765 llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
3766 llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
3767 for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
3768 if (Ops[i] == Ops[i + 1] ||
3769 isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) {
3770 // X op Y op Y --> X op Y
3771 // X op Y --> X, if we know X, Y are ordered appropriately
3772 Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
3773 --i;
3774 --e;
3775 } else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i],
3776 Ops[i + 1])) {
3777 // X op Y --> Y, if we know X, Y are ordered appropriately
3778 Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
3779 --i;
3780 --e;
3781 }
3782 }
3783
3784 if (Ops.size() == 1) return Ops[0];
3785
3786 assert(!Ops.empty() && "Reduced smax down to nothing!")((void)0);
3787
3788 // Okay, it looks like we really DO need an expr. Check to see if we
3789 // already have one, otherwise create a new one.
3790 const SCEV *ExistingSCEV;
3791 FoldingSetNodeID ID;
3792 void *IP;
3793 std::tie(ExistingSCEV, ID, IP) = findExistingSCEVInCache(Kind, Ops);
3794 if (ExistingSCEV)
3795 return ExistingSCEV;
3796 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3797 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3798 SCEV *S = new (SCEVAllocator)
3799 SCEVMinMaxExpr(ID.Intern(SCEVAllocator), Kind, O, Ops.size());
3800
3801 UniqueSCEVs.InsertNode(S, IP);
3802 addToLoopUseLists(S);
3803 return S;
3804}
3805
3806const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) {
3807 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3808 return getSMaxExpr(Ops);
3809}
3810
3811const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3812 return getMinMaxExpr(scSMaxExpr, Ops);
3813}
3814
3815const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) {
3816 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3817 return getUMaxExpr(Ops);
3818}
3819
3820const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3821 return getMinMaxExpr(scUMaxExpr, Ops);
3822}
3823
3824const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3825 const SCEV *RHS) {
3826 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3827 return getSMinExpr(Ops);
3828}
3829
3830const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3831 return getMinMaxExpr(scSMinExpr, Ops);
3832}
3833
3834const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3835 const SCEV *RHS) {
3836 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3837 return getUMinExpr(Ops);
3838}
3839
3840const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3841 return getMinMaxExpr(scUMinExpr, Ops);
3842}
3843
3844const SCEV *
3845ScalarEvolution::getSizeOfScalableVectorExpr(Type *IntTy,
3846 ScalableVectorType *ScalableTy) {
3847 Constant *NullPtr = Constant::getNullValue(ScalableTy->getPointerTo());
3848 Constant *One = ConstantInt::get(IntTy, 1);
3849 Constant *GEP = ConstantExpr::getGetElementPtr(ScalableTy, NullPtr, One);
3850 // Note that the expression we created is the final expression, we don't
3851 // want to simplify it any further Also, if we call a normal getSCEV(),
3852 // we'll end up in an endless recursion. So just create an SCEVUnknown.
3853 return getUnknown(ConstantExpr::getPtrToInt(GEP, IntTy));
3854}
3855
3856const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3857 if (auto *ScalableAllocTy = dyn_cast<ScalableVectorType>(AllocTy))
3858 return getSizeOfScalableVectorExpr(IntTy, ScalableAllocTy);
3859 // We can bypass creating a target-independent constant expression and then
3860 // folding it back into a ConstantInt. This is just a compile-time
3861 // optimization.
3862 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3863}
3864
3865const SCEV *ScalarEvolution::getStoreSizeOfExpr(Type *IntTy, Type *StoreTy) {
3866 if (auto *ScalableStoreTy = dyn_cast<ScalableVectorType>(StoreTy))
3867 return getSizeOfScalableVectorExpr(IntTy, ScalableStoreTy);
3868 // We can bypass creating a target-independent constant expression and then
3869 // folding it back into a ConstantInt. This is just a compile-time
3870 // optimization.
3871 return getConstant(IntTy, getDataLayout().getTypeStoreSize(StoreTy));
3872}
3873
3874const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3875 StructType *STy,
3876 unsigned FieldNo) {
3877 // We can bypass creating a target-independent constant expression and then
3878 // folding it back into a ConstantInt. This is just a compile-time
3879 // optimization.
3880 return getConstant(
3881 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3882}
3883
3884const SCEV *ScalarEvolution::getUnknown(Value *V) {
3885 // Don't attempt to do anything other than create a SCEVUnknown object
3886 // here. createSCEV only calls getUnknown after checking for all other
3887 // interesting possibilities, and any other code that calls getUnknown
3888 // is doing so in order to hide a value from SCEV canonicalization.
3889
3890 FoldingSetNodeID ID;
3891 ID.AddInteger(scUnknown);
3892 ID.AddPointer(V);
3893 void *IP = nullptr;
3894 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3895 assert(cast<SCEVUnknown>(S)->getValue() == V &&((void)0)
3896 "Stale SCEVUnknown in uniquing map!")((void)0);
3897 return S;
3898 }
3899 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3900 FirstUnknown);
3901 FirstUnknown = cast<SCEVUnknown>(S);
3902 UniqueSCEVs.InsertNode(S, IP);
3903 return S;
3904}
3905
3906//===----------------------------------------------------------------------===//
3907// Basic SCEV Analysis and PHI Idiom Recognition Code
3908//
3909
3910/// Test if values of the given type are analyzable within the SCEV
3911/// framework. This primarily includes integer types, and it can optionally
3912/// include pointer types if the ScalarEvolution class has access to
3913/// target-specific information.
3914bool ScalarEvolution::isSCEVable(Type *Ty) const {
3915 // Integers and pointers are always SCEVable.
3916 return Ty->isIntOrPtrTy();
3917}
3918
3919/// Return the size in bits of the specified type, for which isSCEVable must
3920/// return true.
3921uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3922 assert(isSCEVable(Ty) && "Type is not SCEVable!")((void)0);
3923 if (Ty->isPointerTy())
3924 return getDataLayout().getIndexTypeSizeInBits(Ty);
3925 return getDataLayout().getTypeSizeInBits(Ty);
3926}
3927
3928/// Return a type with the same bitwidth as the given type and which represents
3929/// how SCEV will treat the given type, for which isSCEVable must return
3930/// true. For pointer types, this is the pointer index sized integer type.
3931Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3932 assert(isSCEVable(Ty) && "Type is not SCEVable!")((void)0);
3933
3934 if (Ty->isIntegerTy())
3935 return Ty;
3936
3937 // The only other support type is pointer.
3938 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!")((void)0);
3939 return getDataLayout().getIndexType(Ty);
3940}
3941
3942Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
3943 return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
3944}
3945
3946const SCEV *ScalarEvolution::getCouldNotCompute() {
3947 return CouldNotCompute.get();
3948}
3949
3950bool ScalarEvolution::checkValidity(const SCEV *S) const {
3951 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3952 auto *SU = dyn_cast<SCEVUnknown>(S);
3953 return SU && SU->getValue() == nullptr;
3954 });
3955
3956 return !ContainsNulls;
3957}
3958
3959bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3960 HasRecMapType::iterator I = HasRecMap.find(S);
3961 if (I != HasRecMap.end())
3962 return I->second;
3963
3964 bool FoundAddRec =
3965 SCEVExprContains(S, [](const SCEV *S) { return isa<SCEVAddRecExpr>(S); });
3966 HasRecMap.insert({S, FoundAddRec});
3967 return FoundAddRec;
3968}
3969
3970/// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3971/// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3972/// offset I, then return {S', I}, else return {\p S, nullptr}.
3973static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3974 const auto *Add = dyn_cast<SCEVAddExpr>(S);
3975 if (!Add)
3976 return {S, nullptr};
3977
3978 if (Add->getNumOperands() != 2)
3979 return {S, nullptr};
3980
3981 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3982 if (!ConstOp)
3983 return {S, nullptr};
3984
3985 return {Add->getOperand(1), ConstOp->getValue()};
3986}
3987
3988/// Return the ValueOffsetPair set for \p S. \p S can be represented
3989/// by the value and offset from any ValueOffsetPair in the set.
3990ScalarEvolution::ValueOffsetPairSetVector *
3991ScalarEvolution::getSCEVValues(const SCEV *S) {
3992 ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3993 if (SI == ExprValueMap.end())
3994 return nullptr;
3995#ifndef NDEBUG1
3996 if (VerifySCEVMap) {
3997 // Check there is no dangling Value in the set returned.
3998 for (const auto &VE : SI->second)
3999 assert(ValueExprMap.count(VE.first))((void)0);
4000 }
4001#endif
4002 return &SI->second;
4003}
4004
4005/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
4006/// cannot be used separately. eraseValueFromMap should be used to remove
4007/// V from ValueExprMap and ExprValueMap at the same time.
4008void ScalarEvolution::eraseValueFromMap(Value *V) {
4009 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
4010 if (I != ValueExprMap.end()) {
4011 const SCEV *S = I->second;
4012 // Remove {V, 0} from the set of ExprValueMap[S]
4013 if (auto *SV = getSCEVValues(S))
4014 SV->remove({V, nullptr});
4015
4016 // Remove {V, Offset} from the set of ExprValueMap[Stripped]
4017 const SCEV *Stripped;
4018 ConstantInt *Offset;
4019 std::tie(Stripped, Offset) = splitAddExpr(S);
4020 if (Offset != nullptr) {
4021 if (auto *SV = getSCEVValues(Stripped))
4022 SV->remove({V, Offset});
4023 }
4024 ValueExprMap.erase(V);
4025 }
4026}
4027
4028/// Check whether value has nuw/nsw/exact set but SCEV does not.
4029/// TODO: In reality it is better to check the poison recursively
4030/// but this is better than nothing.
4031static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) {
4032 if (auto *I = dyn_cast<Instruction>(V)) {
4033 if (isa<OverflowingBinaryOperator>(I)) {
4034 if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) {
4035 if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap())
4036 return true;
4037 if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap())
4038 return true;
4039 }
4040 } else if (isa<PossiblyExactOperator>(I) && I->isExact())
4041 return true;
4042 }
4043 return false;
4044}
4045
4046/// Return an existing SCEV if it exists, otherwise analyze the expression and
4047/// create a new one.
4048const SCEV *ScalarEvolution::getSCEV(Value *V) {
4049 assert(isSCEVable(V->getType()) && "Value is not SCEVable!")((void)0);
4050
4051 const SCEV *S = getExistingSCEV(V);
4052 if (S == nullptr) {
4053 S = createSCEV(V);
4054 // During PHI resolution, it is possible to create two SCEVs for the same
4055 // V, so it is needed to double check whether V->S is inserted into
4056 // ValueExprMap before insert S->{V, 0} into ExprValueMap.
4057 std::pair<ValueExprMapType::iterator, bool> Pair =
4058 ValueExprMap.insert({SCEVCallbackVH(V, this), S});
4059 if (Pair.second && !SCEVLostPoisonFlags(S, V)) {
4060 ExprValueMap[S].insert({V, nullptr});
4061
4062 // If S == Stripped + Offset, add Stripped -> {V, Offset} into
4063 // ExprValueMap.
4064 const SCEV *Stripped = S;
4065 ConstantInt *Offset = nullptr;
4066 std::tie(Stripped, Offset) = splitAddExpr(S);
4067 // If stripped is SCEVUnknown, don't bother to save
4068 // Stripped -> {V, offset}. It doesn't simplify and sometimes even
4069 // increase the complexity of the expansion code.
4070 // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
4071 // because it may generate add/sub instead of GEP in SCEV expansion.
4072 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
4073 !isa<GetElementPtrInst>(V))
4074 ExprValueMap[Stripped].insert({V, Offset});
4075 }
4076 }
4077 return S;
4078}
4079
4080const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
4081 assert(isSCEVable(V->getType()) && "Value is not SCEVable!")((void)0);
4082
4083 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
4084 if (I != ValueExprMap.end()) {
4085 const SCEV *S = I->second;
4086 if (checkValidity(S))
4087 return S;
4088 eraseValueFromMap(V);
4089 forgetMemoizedResults(S);
4090 }
4091 return nullptr;
4092}
4093
4094/// Return a SCEV corresponding to -V = -1*V
4095const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
4096 SCEV::NoWrapFlags Flags) {
4097 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
4098 return getConstant(
4099 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
4100
4101 Type *Ty = V->getType();
4102 Ty = getEffectiveSCEVType(Ty);
4103 return getMulExpr(V, getMinusOne(Ty), Flags);
4104}
4105
4106/// If Expr computes ~A, return A else return nullptr
4107static const SCEV *MatchNotExpr(const SCEV *Expr) {
4108 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
4109 if (!Add || Add->getNumOperands() != 2 ||
4110 !Add->getOperand(0)->isAllOnesValue())
4111 return nullptr;
4112
4113 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
4114 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
4115 !AddRHS->getOperand(0)->isAllOnesValue())
4116 return nullptr;
4117
4118 return AddRHS->getOperand(1);
4119}
4120
4121/// Return a SCEV corresponding to ~V = -1-V
4122const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
4123 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
4124 return getConstant(
4125 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
4126
4127 // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
4128 if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) {
4129 auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
4130 SmallVector<const SCEV *, 2> MatchedOperands;
4131 for (const SCEV *Operand : MME->operands()) {
4132 const SCEV *Matched = MatchNotExpr(Operand);
4133 if (!Matched)
4134 return (const SCEV *)nullptr;
4135 MatchedOperands.push_back(Matched);
4136 }
4137 return getMinMaxExpr(SCEVMinMaxExpr::negate(MME->getSCEVType()),
4138 MatchedOperands);
4139 };
4140 if (const SCEV *Replaced = MatchMinMaxNegation(MME))
4141 return Replaced;
4142 }
4143
4144 Type *Ty = V->getType();
4145 Ty = getEffectiveSCEVType(Ty);
4146 return getMinusSCEV(getMinusOne(Ty), V);
4147}
4148
4149/// Compute an expression equivalent to S - getPointerBase(S).
4150static const SCEV *removePointerBase(ScalarEvolution *SE, const SCEV *P) {
4151 assert(P->getType()->isPointerTy())((void)0);
4152
4153 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(P)) {
4154 // The base of an AddRec is the first operand.
4155 SmallVector<const SCEV *> Ops{AddRec->operands()};
4156 Ops[0] = removePointerBase(SE, Ops[0]);
4157 // Don't try to transfer nowrap flags for now. We could in some cases
4158 // (for example, if pointer operand of the AddRec is a SCEVUnknown).
4159 return SE->getAddRecExpr(Ops, AddRec->getLoop(), SCEV::FlagAnyWrap);
4160 }
4161 if (auto *Add = dyn_cast<SCEVAddExpr>(P)) {
4162 // The base of an Add is the pointer operand.
4163 SmallVector<const SCEV *> Ops{Add->operands()};
4164 const SCEV **PtrOp = nullptr;
4165 for (const SCEV *&AddOp : Ops) {
4166 if (AddOp->getType()->isPointerTy()) {
4167 // If we find an Add with multiple pointer operands, treat it as a
4168 // pointer base to be consistent with getPointerBase. Eventually
4169 // we should be able to assert this is impossible.
4170 if (PtrOp)
4171 return SE->getZero(P->getType());
4172 PtrOp = &AddOp;
4173 }
4174 }
4175 *PtrOp = removePointerBase(SE, *PtrOp);
4176 // Don't try to transfer nowrap flags for now. We could in some cases
4177 // (for example, if the pointer operand of the Add is a SCEVUnknown).
4178 return SE->getAddExpr(Ops);
4179 }
4180 // Any other expression must be a pointer base.
4181 return SE->getZero(P->getType());
4182}
4183
4184const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
4185 SCEV::NoWrapFlags Flags,
4186 unsigned Depth) {
4187 // Fast path: X - X --> 0.
4188 if (LHS == RHS)
4189 return getZero(LHS->getType());
4190
4191 // If we subtract two pointers with different pointer bases, bail.
4192 // Eventually, we're going to add an assertion to getMulExpr that we
4193 // can't multiply by a pointer.
4194 if (RHS->getType()->isPointerTy()) {
4195 if (!LHS->getType()->isPointerTy() ||
4196 getPointerBase(LHS) != getPointerBase(RHS))
4197 return getCouldNotCompute();
4198 LHS = removePointerBase(this, LHS);
4199 RHS = removePointerBase(this, RHS);
4200 }
4201
4202 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
4203 // makes it so that we cannot make much use of NUW.
4204 auto AddFlags = SCEV::FlagAnyWrap;
4205 const bool RHSIsNotMinSigned =
4206 !getSignedRangeMin(RHS).isMinSignedValue();
4207 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
4208 // Let M be the minimum representable signed value. Then (-1)*RHS
4209 // signed-wraps if and only if RHS is M. That can happen even for
4210 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
4211 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
4212 // (-1)*RHS, we need to prove that RHS != M.
4213 //
4214 // If LHS is non-negative and we know that LHS - RHS does not
4215 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
4216 // either by proving that RHS > M or that LHS >= 0.
4217 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
4218 AddFlags = SCEV::FlagNSW;
4219 }
4220 }
4221
4222 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
4223 // RHS is NSW and LHS >= 0.
4224 //
4225 // The difficulty here is that the NSW flag may have been proven
4226 // relative to a loop that is to be found in a recurrence in LHS and
4227 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
4228 // larger scope than intended.
4229 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
4230
4231 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
4232}
4233
4234const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
4235 unsigned Depth) {
4236 Type *SrcTy = V->getType();
4237 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((void)0)
4238 "Cannot truncate or zero extend with non-integer arguments!")((void)0);
4239 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4240 return V; // No conversion
4241 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
4242 return getTruncateExpr(V, Ty, Depth);
4243 return getZeroExtendExpr(V, Ty, Depth);
4244}
4245
4246const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
4247 unsigned Depth) {
4248 Type *SrcTy = V->getType();
4249 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((void)0)
4250 "Cannot truncate or zero extend with non-integer arguments!")((void)0);
4251 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4252 return V; // No conversion
4253 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
4254 return getTruncateExpr(V, Ty, Depth);
4255 return getSignExtendExpr(V, Ty, Depth);
4256}
4257
4258const SCEV *
4259ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
4260 Type *SrcTy = V->getType();
4261 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((void)0)
4262 "Cannot noop or zero extend with non-integer arguments!")((void)0);
4263 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&((void)0)
4264 "getNoopOrZeroExtend cannot truncate!")((void)0);
4265 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4266 return V; // No conversion
4267 return getZeroExtendExpr(V, Ty);
4268}
4269
4270const SCEV *
4271ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
4272 Type *SrcTy = V->getType();
4273 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((void)0)
4274 "Cannot noop or sign extend with non-integer arguments!")((void)0);
4275 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&((void)0)
4276 "getNoopOrSignExtend cannot truncate!")((void)0);
4277 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4278 return V; // No conversion
4279 return getSignExtendExpr(V, Ty);
4280}
4281
4282const SCEV *
4283ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
4284 Type *SrcTy = V->getType();
4285 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((void)0)
4286 "Cannot noop or any extend with non-integer arguments!")((void)0);
4287 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&((void)0)
4288 "getNoopOrAnyExtend cannot truncate!")((void)0);
4289 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4290 return V; // No conversion
4291 return getAnyExtendExpr(V, Ty);
4292}
4293
4294const SCEV *
4295ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
4296 Type *SrcTy = V->getType();
4297 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((void)0)
4298 "Cannot truncate or noop with non-integer arguments!")((void)0);
4299 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&((void)0)
4300 "getTruncateOrNoop cannot extend!")((void)0);
4301 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
4302 return V; // No conversion
4303 return getTruncateExpr(V, Ty);
4304}
4305
4306const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
4307 const SCEV *RHS) {
4308 const SCEV *PromotedLHS = LHS;
4309 const SCEV *PromotedRHS = RHS;
4310
4311 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
4312 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
4313 else
4314 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
4315
4316 return getUMaxExpr(PromotedLHS, PromotedRHS);
4317}
4318
4319const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
4320 const SCEV *RHS) {
4321 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
4322 return getUMinFromMismatchedTypes(Ops);
4323}
4324
4325const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(
4326 SmallVectorImpl<const SCEV *> &Ops) {
4327 assert(!Ops.empty() && "At least one operand must be!")((void)0);
4328 // Trivial case.
4329 if (Ops.size() == 1)
4330 return Ops[0];
4331
4332 // Find the max type first.
4333 Type *MaxType = nullptr;
4334 for (auto *S : Ops)
4335 if (MaxType)
4336 MaxType = getWiderType(MaxType, S->getType());
4337 else
4338 MaxType = S->getType();
4339 assert(MaxType && "Failed to find maximum type!")((void)0);
4340
4341 // Extend all ops to max type.
4342 SmallVector<const SCEV *, 2> PromotedOps;
4343 for (auto *S : Ops)
4344 PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
4345
4346 // Generate umin.
4347 return getUMinExpr(PromotedOps);
4348}
4349
4350const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
4351 // A pointer operand may evaluate to a nonpointer expression, such as null.
4352 if (!V->getType()->isPointerTy())
4353 return V;
4354
4355 while (true) {
4356 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4357 V = AddRec->getStart();
4358 } else if (auto *Add = dyn_cast<SCEVAddExpr>(V)) {
4359 const SCEV *PtrOp = nullptr;
4360 for (const SCEV *AddOp : Add->operands()) {
4361 if (AddOp->getType()->isPointerTy()) {
4362 // Cannot find the base of an expression with multiple pointer ops.
4363 if (PtrOp)
4364 return V;
4365 PtrOp = AddOp;
4366 }
4367 }
4368 if (!PtrOp) // All operands were non-pointer.
4369 return V;
4370 V = PtrOp;
4371 } else // Not something we can look further into.
4372 return V;
4373 }
4374}
4375
4376/// Push users of the given Instruction onto the given Worklist.
4377static void
4378PushDefUseChildren(Instruction *I,
4379 SmallVectorImpl<Instruction *> &Worklist) {
4380 // Push the def-use children onto the Worklist stack.
4381 for (User *U : I->users())
4382 Worklist.push_back(cast<Instruction>(U));
4383}
4384
4385void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
4386 SmallVector<Instruction *, 16> Worklist;
4387 PushDefUseChildren(PN, Worklist);
4388
4389 SmallPtrSet<Instruction *, 8> Visited;
4390 Visited.insert(PN);
4391 while (!Worklist.empty()) {
4392 Instruction *I = Worklist.pop_back_val();
4393 if (!Visited.insert(I).second)
4394 continue;
4395
4396 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
4397 if (It != ValueExprMap.end()) {
4398 const SCEV *Old = It->second;
4399
4400 // Short-circuit the def-use traversal if the symbolic name
4401 // ceases to appear in expressions.
4402 if (Old != SymName && !hasOperand(Old, SymName))
4403 continue;
4404
4405 // SCEVUnknown for a PHI either means that it has an unrecognized
4406 // structure, it's a PHI that's in the progress of being computed
4407 // by createNodeForPHI, or it's a single-value PHI. In the first case,
4408 // additional loop trip count information isn't going to change anything.
4409 // In the second case, createNodeForPHI will perform the necessary
4410 // updates on its own when it gets to that point. In the third, we do
4411 // want to forget the SCEVUnknown.
4412 if (!isa<PHINode>(I) ||
4413 !isa<SCEVUnknown>(Old) ||
4414 (I != PN && Old == SymName)) {
4415 eraseValueFromMap(It->first);
4416 forgetMemoizedResults(Old);
4417 }
4418 }
4419
4420 PushDefUseChildren(I, Worklist);
4421 }
4422}
4423
4424namespace {
4425
4426/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
4427/// expression in case its Loop is L. If it is not L then
4428/// if IgnoreOtherLoops is true then use AddRec itself
4429/// otherwise rewrite cannot be done.
4430/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4431class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4432public:
4433 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
4434 bool IgnoreOtherLoops = true) {
4435 SCEVInitRewriter Rewriter(L, SE);
4436 const SCEV *Result = Rewriter.visit(S);
4437 if (Rewriter.hasSeenLoopVariantSCEVUnknown())
4438 return SE.getCouldNotCompute();
4439 return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
4440 ? SE.getCouldNotCompute()
4441 : Result;
4442 }
4443
4444 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4445 if (!SE.isLoopInvariant(Expr, L))
4446 SeenLoopVariantSCEVUnknown = true;
4447 return Expr;
4448 }
4449
4450 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4451 // Only re-write AddRecExprs for this loop.
4452 if (Expr->getLoop() == L)
4453 return Expr->getStart();
4454 SeenOtherLoops = true;
4455 return Expr;
4456 }
4457
4458 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4459
4460 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4461
4462private:
4463 explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
4464 : SCEVRewriteVisitor(SE), L(L) {}
4465
4466 const Loop *L;
4467 bool SeenLoopVariantSCEVUnknown = false;
4468 bool SeenOtherLoops = false;
4469};
4470
4471/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
4472/// increment expression in case its Loop is L. If it is not L then
4473/// use AddRec itself.
4474/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4475class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
4476public:
4477 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
4478 SCEVPostIncRewriter Rewriter(L, SE);
4479 const SCEV *Result = Rewriter.visit(S);
4480 return Rewriter.hasSeenLoopVariantSCEVUnknown()
4481 ? SE.getCouldNotCompute()
4482 : Result;
4483 }
4484
4485 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4486 if (!SE.isLoopInvariant(Expr, L))
4487 SeenLoopVariantSCEVUnknown = true;
4488 return Expr;
4489 }
4490
4491 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4492 // Only re-write AddRecExprs for this loop.
4493 if (Expr->getLoop() == L)
4494 return Expr->getPostIncExpr(SE);
4495 SeenOtherLoops = true;
4496 return Expr;
4497 }
4498
4499 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4500
4501 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4502
4503private:
4504 explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
4505 : SCEVRewriteVisitor(SE), L(L) {}
4506
4507 const Loop *L;
4508 bool SeenLoopVariantSCEVUnknown = false;
4509 bool SeenOtherLoops = false;
4510};
4511
4512/// This class evaluates the compare condition by matching it against the
4513/// condition of loop latch. If there is a match we assume a true value
4514/// for the condition while building SCEV nodes.
4515class SCEVBackedgeConditionFolder
4516 : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4517public:
4518 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4519 ScalarEvolution &SE) {
4520 bool IsPosBECond = false;
4521 Value *BECond = nullptr;
4522 if (BasicBlock *Latch = L->getLoopLatch()) {
4523 BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
4524 if (BI && BI->isConditional()) {
4525 assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&((void)0)
4526 "Both outgoing branches should not target same header!")((void)0);
4527 BECond = BI->getCondition();
4528 IsPosBECond = BI->getSuccessor(0) == L->getHeader();
4529 } else {
4530 return S;
4531 }
4532 }
4533 SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
4534 return Rewriter.visit(S);
4535 }
4536
4537 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4538 const SCEV *Result = Expr;
4539 bool InvariantF = SE.isLoopInvariant(Expr, L);
4540
4541 if (!InvariantF) {
4542 Instruction *I = cast<Instruction>(Expr->getValue());
4543 switch (I->getOpcode()) {
4544 case Instruction::Select: {
4545 SelectInst *SI = cast<SelectInst>(I);
4546 Optional<const SCEV *> Res =
4547 compareWithBackedgeCondition(SI->getCondition());
4548 if (Res.hasValue()) {
4549 bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
4550 Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
4551 }
4552 break;
4553 }
4554 default: {
4555 Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
4556 if (Res.hasValue())
4557 Result = Res.getValue();
4558 break;
4559 }
4560 }
4561 }
4562 return Result;
4563 }
4564
4565private:
4566 explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
4567 bool IsPosBECond, ScalarEvolution &SE)
4568 : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
4569 IsPositiveBECond(IsPosBECond) {}
4570
4571 Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
4572
4573 const Loop *L;
4574 /// Loop back condition.
4575 Value *BackedgeCond = nullptr;
4576 /// Set to true if loop back is on positive branch condition.
4577 bool IsPositiveBECond;
4578};
4579
4580Optional<const SCEV *>
4581SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
4582
4583 // If value matches the backedge condition for loop latch,
4584 // then return a constant evolution node based on loopback
4585 // branch taken.
4586 if (BackedgeCond == IC)
4587 return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
4588 : SE.getZero(Type::getInt1Ty(SE.getContext()));
4589 return None;
4590}
4591
4592class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4593public:
4594 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4595 ScalarEvolution &SE) {
4596 SCEVShiftRewriter Rewriter(L, SE);
4597 const SCEV *Result = Rewriter.visit(S);
4598 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4599 }
4600
4601 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4602 // Only allow AddRecExprs for this loop.
4603 if (!SE.isLoopInvariant(Expr, L))
4604 Valid = false;
4605 return Expr;
4606 }
4607
4608 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4609 if (Expr->getLoop() == L && Expr->isAffine())
4610 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
4611 Valid = false;
4612 return Expr;
4613 }
4614
4615 bool isValid() { return Valid; }
4616
4617private:
4618 explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
4619 : SCEVRewriteVisitor(SE), L(L) {}
4620
4621 const Loop *L;
4622 bool Valid = true;
4623};
4624
4625} // end anonymous namespace
4626
4627SCEV::NoWrapFlags
4628ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
4629 if (!AR->isAffine())
4630 return SCEV::FlagAnyWrap;
4631
4632 using OBO = OverflowingBinaryOperator;
4633
4634 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
4635
4636 if (!AR->hasNoSignedWrap()) {
4637 ConstantRange AddRecRange = getSignedRange(AR);
4638 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
4639
4640 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4641 Instruction::Add, IncRange, OBO::NoSignedWrap);
4642 if (NSWRegion.contains(AddRecRange))
4643 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
4644 }
4645
4646 if (!AR->hasNoUnsignedWrap()) {
4647 ConstantRange AddRecRange = getUnsignedRange(AR);
4648 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
4649
4650 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4651 Instruction::Add, IncRange, OBO::NoUnsignedWrap);
4652 if (NUWRegion.contains(AddRecRange))
4653 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
4654 }
4655
4656 return Result;
4657}
4658
4659SCEV::NoWrapFlags
4660ScalarEvolution::proveNoSignedWrapViaInduction(const SCEVAddRecExpr *AR) {
4661 SCEV::NoWrapFlags Result = AR->getNoWrapFlags();
4662
4663 if (AR->hasNoSignedWrap())
4664 return Result;
4665
4666 if (!AR->isAffine())
4667 return Result;
4668
4669 const SCEV *Step = AR->getStepRecurrence(*this);
4670 const Loop *L = AR->getLoop();
4671
4672 // Check whether the backedge-taken count is SCEVCouldNotCompute.
4673 // Note that this serves two purposes: It filters out loops that are
4674 // simply not analyzable, and it covers the case where this code is
4675 // being called from within backedge-taken count analysis, such that
4676 // attempting to ask for the backedge-taken count would likely result
4677 // in infinite recursion. In the later case, the analysis code will
4678 // cope with a conservative value, and it will take care to purge
4679 // that value once it has finished.
4680 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
4681
4682 // Normally, in the cases we can prove no-overflow via a
4683 // backedge guarding condition, we can also compute a backedge
4684 // taken count for the loop. The exceptions are assumptions and
4685 // guards present in the loop -- SCEV is not great at exploiting
4686 // these to compute max backedge taken counts, but can still use
4687 // these to prove lack of overflow. Use this fact to avoid
4688 // doing extra work that may not pay off.
4689
4690 if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards &&
4691 AC.assumptions().empty())
4692 return Result;
4693
4694 // If the backedge is guarded by a comparison with the pre-inc value the
4695 // addrec is safe. Also, if the entry is guarded by a comparison with the
4696 // start value and the backedge is guarded by a comparison with the post-inc
4697 // value, the addrec is safe.
4698 ICmpInst::Predicate Pred;
4699 const SCEV *OverflowLimit =
4700 getSignedOverflowLimitForStep(Step, &Pred, this);
4701 if (OverflowLimit &&
4702 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
4703 isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
4704 Result = setFlags(Result, SCEV::FlagNSW);
4705 }
4706 return Result;
4707}
4708SCEV::NoWrapFlags
4709ScalarEvolution::proveNoUnsignedWrapViaInduction(const SCEVAddRecExpr *AR) {
4710 SCEV::NoWrapFlags Result = AR->getNoWrapFlags();
4711
4712 if (AR->hasNoUnsignedWrap())
4713 return Result;
4714
4715 if (!AR->isAffine())
4716 return Result;
4717
4718 const SCEV *Step = AR->getStepRecurrence(*this);
4719 unsigned BitWidth = getTypeSizeInBits(AR->getType());
4720 const Loop *L = AR->getLoop();
4721
4722 // Check whether the backedge-taken count is SCEVCouldNotCompute.
4723 // Note that this serves two purposes: It filters out loops that are
4724 // simply not analyzable, and it covers the case where this code is
4725 // being called from within backedge-taken count analysis, such that
4726 // attempting to ask for the backedge-taken count would likely result
4727 // in infinite recursion. In the later case, the analysis code will
4728 // cope with a conservative value, and it will take care to purge
4729 // that value once it has finished.
4730 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
4731
4732 // Normally, in the cases we can prove no-overflow via a
4733 // backedge guarding condition, we can also compute a backedge
4734 // taken count for the loop. The exceptions are assumptions and
4735 // guards present in the loop -- SCEV is not great at exploiting
4736 // these to compute max backedge taken counts, but can still use
4737 // these to prove lack of overflow. Use this fact to avoid
4738 // doing extra work that may not pay off.
4739
4740 if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards &&
4741 AC.assumptions().empty())
4742 return Result;
4743
4744 // If the backedge is guarded by a comparison with the pre-inc value the
4745 // addrec is safe. Also, if the entry is guarded by a comparison with the
4746 // start value and the backedge is guarded by a comparison with the post-inc
4747 // value, the addrec is safe.
4748 if (isKnownPositive(Step)) {
4749 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
4750 getUnsignedRangeMax(Step));
4751 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
4752 isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
4753 Result = setFlags(Result, SCEV::FlagNUW);
4754 }
4755 }
4756
4757 return Result;
4758}
4759
4760namespace {
4761
4762/// Represents an abstract binary operation. This may exist as a
4763/// normal instruction or constant expression, or may have been
4764/// derived from an expression tree.
4765struct BinaryOp {
4766 unsigned Opcode;
4767 Value *LHS;
4768 Value *RHS;
4769 bool IsNSW = false;
4770 bool IsNUW = false;
4771
4772 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
4773 /// constant expression.
4774 Operator *Op = nullptr;
4775
4776 explicit BinaryOp(Operator *Op)
4777 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
4778 Op(Op) {
4779 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
4780 IsNSW = OBO->hasNoSignedWrap();
4781 IsNUW = OBO->hasNoUnsignedWrap();
4782 }
4783 }
4784
4785 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
4786 bool IsNUW = false)
4787 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
4788};
4789
4790} // end anonymous namespace
4791
4792/// Try to map \p V into a BinaryOp, and return \c None on failure.
4793static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
4794 auto *Op = dyn_cast<Operator>(V);
4795 if (!Op)
4796 return None;
4797
4798 // Implementation detail: all the cleverness here should happen without
4799 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
4800 // SCEV expressions when possible, and we should not break that.
4801
4802 switch (Op->getOpcode()) {
4803 case Instruction::Add:
4804 case Instruction::Sub:
4805 case Instruction::Mul:
4806 case Instruction::UDiv:
4807 case Instruction::URem:
4808 case Instruction::And:
4809 case Instruction::Or:
4810 case Instruction::AShr:
4811 case Instruction::Shl:
4812 return BinaryOp(Op);
4813
4814 case Instruction::Xor:
4815 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
4816 // If the RHS of the xor is a signmask, then this is just an add.
4817 // Instcombine turns add of signmask into xor as a strength reduction step.
4818 if (RHSC->getValue().isSignMask())
4819 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
4820 return BinaryOp(Op);
4821
4822 case Instruction::LShr:
4823 // Turn logical shift right of a constant into a unsigned divide.
4824 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
4825 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
4826
4827 // If the shift count is not less than the bitwidth, the result of
4828 // the shift is undefined. Don't try to analyze it, because the
4829 // resolution chosen here may differ from the resolution chosen in
4830 // other parts of the compiler.
4831 if (SA->getValue().ult(BitWidth)) {
4832 Constant *X =
4833 ConstantInt::get(SA->getContext(),
4834 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4835 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
4836 }
4837 }
4838 return BinaryOp(Op);
4839
4840 case Instruction::ExtractValue: {
4841 auto *EVI = cast<ExtractValueInst>(Op);
4842 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
4843 break;
4844
4845 auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand());
4846 if (!WO)
4847 break;
4848
4849 Instruction::BinaryOps BinOp = WO->getBinaryOp();
4850 bool Signed = WO->isSigned();
4851 // TODO: Should add nuw/nsw flags for mul as well.
4852 if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
4853 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());
4854
4855 // Now that we know that all uses of the arithmetic-result component of
4856 // CI are guarded by the overflow check, we can go ahead and pretend
4857 // that the arithmetic is non-overflowing.
4858 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
4859 /* IsNSW = */ Signed, /* IsNUW = */ !Signed);
4860 }
4861
4862 default:
4863 break;
4864 }
4865
4866 // Recognise intrinsic loop.decrement.reg, and as this has exactly the same
4867 // semantics as a Sub, return a binary sub expression.
4868 if (auto *II = dyn_cast<IntrinsicInst>(V))
4869 if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg)
4870 return BinaryOp(Instruction::Sub, II->getOperand(0), II->getOperand(1));
4871
4872 return None;
4873}
4874
4875/// Helper function to createAddRecFromPHIWithCasts. We have a phi
4876/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
4877/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
4878/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
4879/// follows one of the following patterns:
4880/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4881/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4882/// If the SCEV expression of \p Op conforms with one of the expected patterns
4883/// we return the type of the truncation operation, and indicate whether the
4884/// truncated type should be treated as signed/unsigned by setting
4885/// \p Signed to true/false, respectively.
4886static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
4887 bool &Signed, ScalarEvolution &SE) {
4888 // The case where Op == SymbolicPHI (that is, with no type conversions on
4889 // the way) is handled by the regular add recurrence creating logic and
4890 // would have already been triggered in createAddRecForPHI. Reaching it here
4891 // means that createAddRecFromPHI had failed for this PHI before (e.g.,
4892 // because one of the other operands of the SCEVAddExpr updating this PHI is
4893 // not invariant).
4894 //
4895 // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
4896 // this case predicates that allow us to prove that Op == SymbolicPHI will
4897 // be added.
4898 if (Op == SymbolicPHI)
4899 return nullptr;
4900
4901 unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
4902 unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
4903 if (SourceBits != NewBits)
4904 return nullptr;
4905
4906 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
4907 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
4908 if (!SExt && !ZExt)
4909 return nullptr;
4910 const SCEVTruncateExpr *Trunc =
4911 SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
4912 : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
4913 if (!Trunc)
4914 return nullptr;
4915 const SCEV *X = Trunc->getOperand();
4916 if (X != SymbolicPHI)
4917 return nullptr;
4918 Signed = SExt != nullptr;
4919 return Trunc->getType();
4920}
4921
4922static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
4923 if (!PN->getType()->isIntegerTy())
4924 return nullptr;
4925 const Loop *L = LI.getLoopFor(PN->getParent());
4926 if (!L || L->getHeader() != PN->getParent())
4927 return nullptr;
4928 return L;
4929}
4930
4931// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
4932// computation that updates the phi follows the following pattern:
4933// (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
4934// which correspond to a phi->trunc->sext/zext->add->phi update chain.
4935// If so, try to see if it can be rewritten as an AddRecExpr under some
4936// Predicates. If successful, return them as a pair. Also cache the results
4937// of the analysis.
4938//
4939// Example usage scenario:
4940// Say the Rewriter is called for the following SCEV:
4941// 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4942// where:
4943// %X = phi i64 (%Start, %BEValue)
4944// It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
4945// and call this function with %SymbolicPHI = %X.
4946//
4947// The analysis will find that the value coming around the backedge has
4948// the following SCEV:
4949// BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4950// Upon concluding that this matches the desired pattern, the function
4951// will return the pair {NewAddRec, SmallPredsVec} where:
4952// NewAddRec = {%Start,+,%Step}
4953// SmallPredsVec = {P1, P2, P3} as follows:
4954// P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
4955// P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
4956// P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
4957// The returned pair means that SymbolicPHI can be rewritten into NewAddRec
4958// under the predicates {P1,P2,P3}.
4959// This predicated rewrite will be cached in PredicatedSCEVRewrites:
4960// PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
4961//
4962// TODO's:
4963//
4964// 1) Extend the Induction descriptor to also support inductions that involve
4965// casts: When needed (namely, when we are called in the context of the
4966// vectorizer induction analysis), a Set of cast instructions will be
4967// populated by this method, and provided back to isInductionPHI. This is
4968// needed to allow the vectorizer to properly record them to be ignored by
4969// the cost model and to avoid vectorizing them (otherwise these casts,
4970// which are redundant under the runtime overflow checks, will be
4971// vectorized, which can be costly).
4972//
4973// 2) Support additional induction/PHISCEV patterns: We also want to support
4974// inductions where the sext-trunc / zext-trunc operations (partly) occur
4975// after the induction update operation (the induction increment):
4976//
4977// (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
4978// which correspond to a phi->add->trunc->sext/zext->phi update chain.
4979//
4980// (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
4981// which correspond to a phi->trunc->add->sext/zext->phi update chain.
4982//
4983// 3) Outline common code with createAddRecFromPHI to avoid duplication.
4984Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4985ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
4986 SmallVector<const SCEVPredicate *, 3> Predicates;
4987
4988 // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
4989 // return an AddRec expression under some predicate.
4990
4991 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4992 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4993 assert(L && "Expecting an integer loop header phi")((void)0);
4994
4995 // The loop may have multiple entrances or multiple exits; we can analyze
4996 // this phi as an addrec if it has a unique entry value and a unique
4997 // backedge value.
4998 Value *BEValueV = nullptr, *StartValueV = nullptr;
4999 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5000 Value *V = PN->getIncomingValue(i);
5001 if (L->contains(PN->getIncomingBlock(i))) {
5002 if (!BEValueV) {
5003 BEValueV = V;
5004 } else if (BEValueV != V) {
5005 BEValueV = nullptr;
5006 break;
5007 }
5008 } else if (!StartValueV) {
5009 StartValueV = V;
5010 } else if (StartValueV != V) {
5011 StartValueV = nullptr;
5012 break;
5013 }
5014 }
5015 if (!BEValueV || !StartValueV)
5016 return None;
5017
5018 const SCEV *BEValue = getSCEV(BEValueV);
5019
5020 // If the value coming around the backedge is an add with the symbolic
5021 // value we just inserted, possibly with casts that we can ignore under
5022 // an appropriate runtime guard, then we found a simple induction variable!
5023 const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
5024 if (!Add)
5025 return None;
5026
5027 // If there is a single occurrence of the symbolic value, possibly
5028 // casted, replace it with a recurrence.
5029 unsigned FoundIndex = Add->getNumOperands();
5030 Type *TruncTy = nullptr;
5031 bool Signed;
5032 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5033 if ((TruncTy =
5034 isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
5035 if (FoundIndex == e) {
5036 FoundIndex = i;
5037 break;
5038 }
5039
5040 if (FoundIndex == Add->getNumOperands())
5041 return None;
5042
5043 // Create an add with everything but the specified operand.
5044 SmallVector<const SCEV *, 8> Ops;
5045 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5046 if (i != FoundIndex)
5047 Ops.push_back(Add->getOperand(i));
5048 const SCEV *Accum = getAddExpr(Ops);
5049
5050 // The runtime checks will not be valid if the step amount is
5051 // varying inside the loop.
5052 if (!isLoopInvariant(Accum, L))
5053 return None;
5054
5055 // *** Part2: Create the predicates
5056
5057 // Analysis was successful: we have a phi-with-cast pattern for which we
5058 // can return an AddRec expression under the following predicates:
5059 //
5060 // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
5061 // fits within the truncated type (does not overflow) for i = 0 to n-1.
5062 // P2: An Equal predicate that guarantees that
5063 // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
5064 // P3: An Equal predicate that guarantees that
5065 // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
5066 //
5067 // As we next prove, the above predicates guarantee that:
5068 // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
5069 //
5070 //
5071 // More formally, we want to prove that:
5072 // Expr(i+1) = Start + (i+1) * Accum
5073 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
5074 //
5075 // Given that:
5076 // 1) Expr(0) = Start
5077 // 2) Expr(1) = Start + Accum
5078 // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
5079 // 3) Induction hypothesis (step i):
5080 // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
5081 //
5082 // Proof:
5083 // Expr(i+1) =
5084 // = Start + (i+1)*Accum
5085 // = (Start + i*Accum) + Accum
5086 // = Expr(i) + Accum
5087 // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
5088 // :: from step i
5089 //
5090 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
5091 //
5092 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
5093 // + (Ext ix (Trunc iy (Accum) to ix) to iy)
5094 // + Accum :: from P3
5095 //
5096 // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
5097 // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
5098 //
5099 // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
5100 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
5101 //
5102 // By induction, the same applies to all iterations 1<=i<n:
5103 //
5104
5105 // Create a truncated addrec for which we will add a no overflow check (P1).
5106 const SCEV *StartVal = getSCEV(StartValueV);
5107 const SCEV *PHISCEV =
5108 getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
5109 getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
5110
5111 // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
5112 // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
5113 // will be constant.
5114 //
5115 // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
5116 // add P1.
5117 if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
5118 SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
5119 Signed ? SCEVWrapPredicate::IncrementNSSW
5120 : SCEVWrapPredicate::IncrementNUSW;
5121 const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
5122 Predicates.push_back(AddRecPred);
5123 }
5124
5125 // Create the Equal Predicates P2,P3:
5126
5127 // It is possible that the predicates P2 and/or P3 are computable at
5128 // compile time due to StartVal and/or Accum being constants.
5129 // If either one is, then we can check that now and escape if either P2
5130 // or P3 is false.
5131
5132 // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
5133 // for each of StartVal and Accum
5134 auto getExtendedExpr = [&](const SCEV *Expr,
5135 bool CreateSignExtend) -> const SCEV * {
5136 assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant")((void)0);
5137 const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
5138 const SCEV *ExtendedExpr =
5139 CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
5140 : getZeroExtendExpr(TruncatedExpr, Expr->getType());
5141 return ExtendedExpr;
5142 };
5143
5144 // Given:
5145 // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
5146 // = getExtendedExpr(Expr)
5147 // Determine whether the predicate P: Expr == ExtendedExpr
5148 // is known to be false at compile time
5149 auto PredIsKnownFalse = [&](const SCEV *Expr,
5150 const SCEV *ExtendedExpr) -> bool {
5151 return Expr != ExtendedExpr &&
5152 isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
5153 };
5154
5155 const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
5156 if (PredIsKnownFalse(StartVal, StartExtended)) {
5157 LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";)do { } while (false);
5158 return None;
5159 }
5160
5161 // The Step is always Signed (because the overflow checks are either
5162 // NSSW or NUSW)
5163 const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
5164 if (PredIsKnownFalse(Accum, AccumExtended)) {
5165 LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";)do { } while (false);
5166 return None;
5167 }
5168
5169 auto AppendPredicate = [&](const SCEV *Expr,
5170 const SCEV *ExtendedExpr) -> void {
5171 if (Expr != ExtendedExpr &&
5172 !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
5173 const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
5174 LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred)do { } while (false);
5175 Predicates.push_back(Pred);
5176 }
5177 };
5178
5179 AppendPredicate(StartVal, StartExtended);
5180 AppendPredicate(Accum, AccumExtended);
5181
5182 // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
5183 // which the casts had been folded away. The caller can rewrite SymbolicPHI
5184 // into NewAR if it will also add the runtime overflow checks specified in
5185 // Predicates.
5186 auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
5187
5188 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
5189 std::make_pair(NewAR, Predicates);
5190 // Remember the result of the analysis for this SCEV at this locayyytion.
5191 PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
5192 return PredRewrite;
5193}
5194
5195Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
5196ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
5197 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
5198 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
5199 if (!L)
5200 return None;
5201
5202 // Check to see if we already analyzed this PHI.
5203 auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
5204 if (I != PredicatedSCEVRewrites.end()) {
5205 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
5206 I->second;
5207 // Analysis was done before and failed to create an AddRec:
5208 if (Rewrite.first == SymbolicPHI)
5209 return None;
5210 // Analysis was done before and succeeded to create an AddRec under
5211 // a predicate:
5212 assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec")((void)0);
5213 assert(!(Rewrite.second).empty() && "Expected to find Predicates")((void)0);
5214 return Rewrite;
5215 }
5216
5217 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
5218 Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
5219
5220 // Record in the cache that the analysis failed
5221 if (!Rewrite) {
5222 SmallVector<const SCEVPredicate *, 3> Predicates;
5223 PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
5224 return None;
5225 }
5226
5227 return Rewrite;
5228}
5229
5230// FIXME: This utility is currently required because the Rewriter currently
5231// does not rewrite this expression:
5232// {0, +, (sext ix (trunc iy to ix) to iy)}
5233// into {0, +, %step},
5234// even when the following Equal predicate exists:
5235// "%step == (sext ix (trunc iy to ix) to iy)".
5236bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
5237 const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
5238 if (AR1 == AR2)
5239 return true;
5240
5241 auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
5242 if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
5243 !Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
5244 return false;
5245 return true;
5246 };
5247
5248 if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
5249 !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
5250 return false;
5251 return true;
5252}
5253
5254/// A helper function for createAddRecFromPHI to handle simple cases.
5255///
5256/// This function tries to find an AddRec expression for the simplest (yet most
5257/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
5258/// If it fails, createAddRecFromPHI will use a more general, but slow,
5259/// technique for finding the AddRec expression.
5260const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
5261 Value *BEValueV,
5262 Value *StartValueV) {
5263 const Loop *L = LI.getLoopFor(PN->getParent());
5264 assert(L && L->getHeader() == PN->getParent())((void)0);
5265 assert(BEValueV && StartValueV)((void)0);
5266
5267 auto BO = MatchBinaryOp(BEValueV, DT);
5268 if (!BO)
5269 return nullptr;
5270
5271 if (BO->Opcode != Instruction::Add)
5272 return nullptr;
5273
5274 const SCEV *Accum = nullptr;
5275 if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
5276 Accum = getSCEV(BO->RHS);
5277 else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
5278 Accum = getSCEV(BO->LHS);
5279
5280 if (!Accum)
5281 return nullptr;
5282
5283 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5284 if (BO->IsNUW)
5285 Flags = setFlags(Flags, SCEV::FlagNUW);
5286 if (BO->IsNSW)
5287 Flags = setFlags(Flags, SCEV::FlagNSW);
5288
5289 const SCEV *StartVal = getSCEV(StartValueV);
5290 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
5291
5292 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
5293
5294 // We can add Flags to the post-inc expression only if we
5295 // know that it is *undefined behavior* for BEValueV to
5296 // overflow.
5297 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
5298 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
5299 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
5300
5301 return PHISCEV;
5302}
5303
5304const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
5305 const Loop *L = LI.getLoopFor(PN->getParent());
5306 if (!L || L->getHeader() != PN->getParent())
5307 return nullptr;
5308
5309 // The loop may have multiple entrances or multiple exits; we can analyze
5310 // this phi as an addrec if it has a unique entry value and a unique
5311 // backedge value.
5312 Value *BEValueV = nullptr, *StartValueV = nullptr;
5313 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5314 Value *V = PN->getIncomingValue(i);
5315 if (L->contains(PN->getIncomingBlock(i))) {
5316 if (!BEValueV) {
5317 BEValueV = V;
5318 } else if (BEValueV != V) {
5319 BEValueV = nullptr;
5320 break;
5321 }
5322 } else if (!StartValueV) {
5323 StartValueV = V;
5324 } else if (StartValueV != V) {
5325 StartValueV = nullptr;
5326 break;
5327 }
5328 }
5329 if (!BEValueV || !StartValueV)
5330 return nullptr;
5331
5332 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&((void)0)
5333 "PHI node already processed?")((void)0);
5334
5335 // First, try to find AddRec expression without creating a fictituos symbolic
5336 // value for PN.
5337 if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
5338 return S;
5339
5340 // Handle PHI node value symbolically.
5341 const SCEV *SymbolicName = getUnknown(PN);
5342 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
5343
5344 // Using this symbolic name for the PHI, analyze the value coming around
5345 // the back-edge.
5346 const SCEV *BEValue = getSCEV(BEValueV);
5347
5348 // NOTE: If BEValue is loop invariant, we know that the PHI node just
5349 // has a special value for the first iteration of the loop.
5350
5351 // If the value coming around the backedge is an add with the symbolic
5352 // value we just inserted, then we found a simple induction variable!
5353 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
5354 // If there is a single occurrence of the symbolic value, replace it
5355 // with a recurrence.
5356 unsigned FoundIndex = Add->getNumOperands();
5357 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5358 if (Add->getOperand(i) == SymbolicName)
5359 if (FoundIndex == e) {
5360 FoundIndex = i;
5361 break;
5362 }
5363
5364 if (FoundIndex != Add->getNumOperands()) {
5365 // Create an add with everything but the specified operand.
5366 SmallVector<const SCEV *, 8> Ops;
5367 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
5368 if (i != FoundIndex)
5369 Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
5370 L, *this));
5371 const SCEV *Accum = getAddExpr(Ops);
5372
5373 // This is not a valid addrec if the step amount is varying each
5374 // loop iteration, but is not itself an addrec in this loop.
5375 if (isLoopInvariant(Accum, L) ||
5376 (isa<SCEVAddRecExpr>(Accum) &&
5377 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
5378 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5379
5380 if (auto BO = MatchBinaryOp(BEValueV, DT)) {
5381 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
5382 if (BO->IsNUW)
5383 Flags = setFlags(Flags, SCEV::FlagNUW);
5384 if (BO->IsNSW)
5385 Flags = setFlags(Flags, SCEV::FlagNSW);
5386 }
5387 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
5388 // If the increment is an inbounds GEP, then we know the address
5389 // space cannot be wrapped around. We cannot make any guarantee
5390 // about signed or unsigned overflow because pointers are
5391 // unsigned but we may have a negative index from the base
5392 // pointer. We can guarantee that no unsigned wrap occurs if the
5393 // indices form a positive value.
5394 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
5395 Flags = setFlags(Flags, SCEV::FlagNW);
5396
5397 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
5398 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
5399 Flags = setFlags(Flags, SCEV::FlagNUW);
5400 }
5401
5402 // We cannot transfer nuw and nsw flags from subtraction
5403 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
5404 // for instance.
5405 }
5406
5407 const SCEV *StartVal = getSCEV(StartValueV);
5408 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
5409
5410 // Okay, for the entire analysis of this edge we assumed the PHI
5411 // to be symbolic. We now need to go back and purge all of the
5412 // entries for the scalars that use the symbolic expression.
5413 forgetSymbolicName(PN, SymbolicName);
5414 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
5415
5416 // We can add Flags to the post-inc expression only if we
5417 // know that it is *undefined behavior* for BEValueV to
5418 // overflow.
5419 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
5420 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
5421 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
5422
5423 return PHISCEV;
5424 }
5425 }
5426 } else {
5427 // Otherwise, this could be a loop like this:
5428 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
5429 // In this case, j = {1,+,1} and BEValue is j.
5430 // Because the other in-value of i (0) fits the evolution of BEValue
5431 // i really is an addrec evolution.
5432 //
5433 // We can generalize this saying that i is the shifted value of BEValue
5434 // by one iteration:
5435 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
5436 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
5437 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
5438 if (Shifted != getCouldNotCompute() &&
5439 Start != getCouldNotCompute()) {
5440 const SCEV *StartVal = getSCEV(StartValueV);
5441 if (Start == StartVal) {
5442 // Okay, for the entire analysis of this edge we assumed the PHI
5443 // to be symbolic. We now need to go back and purge all of the
5444 // entries for the scalars that use the symbolic expression.
5445 forgetSymbolicName(PN, SymbolicName);
5446 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
5447 return Shifted;
5448 }
5449 }
5450 }
5451
5452 // Remove the temporary PHI node SCEV that has been inserted while intending
5453 // to create an AddRecExpr for this PHI node. We can not keep this temporary
5454 // as it will prevent later (possibly simpler) SCEV expressions to be added
5455 // to the ValueExprMap.
5456 eraseValueFromMap(PN);
5457
5458 return nullptr;
5459}
5460
5461// Checks if the SCEV S is available at BB. S is considered available at BB
5462// if S can be materialized at BB without introducing a fault.
5463static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
5464 BasicBlock *BB) {
5465 struct CheckAvailable {
5466 bool TraversalDone = false;
5467 bool Available = true;
5468
5469 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
5470 BasicBlock *BB = nullptr;
5471 DominatorTree &DT;
5472
5473 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
5474 : L(L), BB(BB), DT(DT) {}
5475
5476 bool setUnavailable() {
5477 TraversalDone = true;
5478 Available = false;
5479 return false;
5480 }
5481
5482 bool follow(const SCEV *S) {
5483 switch (S->getSCEVType()) {
5484 case scConstant:
5485 case scPtrToInt:
5486 case scTruncate:
5487 case scZeroExtend:
5488 case scSignExtend:
5489 case scAddExpr:
5490 case scMulExpr:
5491 case scUMaxExpr:
5492 case scSMaxExpr:
5493 case scUMinExpr:
5494 case scSMinExpr:
5495 // These expressions are available if their operand(s) is/are.
5496 return true;
5497
5498 case scAddRecExpr: {
5499 // We allow add recurrences that are on the loop BB is in, or some
5500 // outer loop. This guarantees availability because the value of the
5501 // add recurrence at BB is simply the "current" value of the induction
5502 // variable. We can relax this in the future; for instance an add
5503 // recurrence on a sibling dominating loop is also available at BB.
5504 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
5505 if (L && (ARLoop == L || ARLoop->contains(L)))
5506 return true;
5507
5508 return setUnavailable();
5509 }
5510
5511 case scUnknown: {
5512 // For SCEVUnknown, we check for simple dominance.
5513 const auto *SU = cast<SCEVUnknown>(S);
5514 Value *V = SU->getValue();
5515
5516 if (isa<Argument>(V))
5517 return false;
5518
5519 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
5520 return false;
5521
5522 return setUnavailable();
5523 }
5524
5525 case scUDivExpr:
5526 case scCouldNotCompute:
5527 // We do not try to smart about these at all.
5528 return setUnavailable();
5529 }
5530 llvm_unreachable("Unknown SCEV kind!")__builtin_unreachable();
5531 }
5532
5533 bool isDone() { return TraversalDone; }
5534 };
5535
5536 CheckAvailable CA(L, BB, DT);
5537 SCEVTraversal<CheckAvailable> ST(CA);
5538
5539 ST.visitAll(S);
5540 return CA.Available;
5541}
5542
5543// Try to match a control flow sequence that branches out at BI and merges back
5544// at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
5545// match.
5546static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
5547 Value *&C, Value *&LHS, Value *&RHS) {
5548 C = BI->getCondition();
5549
5550 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
5551 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
5552
5553 if (!LeftEdge.isSingleEdge())
5554 return false;
5555
5556 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()")((void)0);
5557
5558 Use &LeftUse = Merge->getOperandUse(0);
5559 Use &RightUse = Merge->getOperandUse(1);
5560
5561 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
5562 LHS = LeftUse;
5563 RHS = RightUse;
5564 return true;
5565 }
5566
5567 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
5568 LHS = RightUse;
5569 RHS = LeftUse;
5570 return true;
5571 }
5572
5573 return false;
5574}
5575
5576const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
5577 auto IsReachable =
5578 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
5579 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
5580 const Loop *L = LI.getLoopFor(PN->getParent());
5581
5582 // We don't want to break LCSSA, even in a SCEV expression tree.
5583 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
5584 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
5585 return nullptr;
5586
5587 // Try to match
5588 //
5589 // br %cond, label %left, label %right
5590 // left:
5591 // br label %merge
5592 // right:
5593 // br label %merge
5594 // merge:
5595 // V = phi [ %x, %left ], [ %y, %right ]
5596 //
5597 // as "select %cond, %x, %y"
5598
5599 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
5600 assert(IDom && "At least the entry block should dominate PN")((void)0);
5601
5602 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
5603 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
5604
5605 if (BI && BI->isConditional() &&
5606 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
5607 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
5608 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
5609 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
5610 }
5611
5612 return nullptr;
5613}
5614
5615const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
5616 if (const SCEV *S = createAddRecFromPHI(PN))
5617 return S;
5618
5619 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
5620 return S;
5621
5622 // If the PHI has a single incoming value, follow that value, unless the
5623 // PHI's incoming blocks are in a different loop, in which case doing so
5624 // risks breaking LCSSA form. Instcombine would normally zap these, but
5625 // it doesn't have DominatorTree information, so it may miss cases.
5626 if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
5627 if (LI.replacementPreservesLCSSAForm(PN, V))
5628 return getSCEV(V);
5629
5630 // If it's not a loop phi, we can't handle it yet.
5631 return getUnknown(PN);
5632}
5633
5634const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
5635 Value *Cond,
5636 Value *TrueVal,
5637 Value *FalseVal) {
5638 // Handle "constant" branch or select. This can occur for instance when a
5639 // loop pass transforms an inner loop and moves on to process the outer loop.
5640 if (auto *CI = dyn_cast<ConstantInt>(Cond))
5641 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
5642
5643 // Try to match some simple smax or umax patterns.
5644 auto *ICI = dyn_cast<ICmpInst>(Cond);
5645 if (!ICI)
5646 return getUnknown(I);
5647
5648 Value *LHS = ICI->getOperand(0);
5649 Value *RHS = ICI->getOperand(1);
5650
5651 switch (ICI->getPredicate()) {
5652 case ICmpInst::ICMP_SLT:
5653 case ICmpInst::ICMP_SLE:
5654 case ICmpInst::ICMP_ULT:
5655 case ICmpInst::ICMP_ULE:
5656 std::swap(LHS, RHS);
5657 LLVM_FALLTHROUGH[[gnu::fallthrough]];
5658 case ICmpInst::ICMP_SGT:
5659 case ICmpInst::ICMP_SGE:
5660 case ICmpInst::ICMP_UGT:
5661 case ICmpInst::ICMP_UGE:
5662 // a > b ? a+x : b+x -> max(a, b)+x
5663 // a > b ? b+x : a+x -> min(a, b)+x
5664 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5665 bool Signed = ICI->isSigned();
5666 const SCEV *LA = getSCEV(TrueVal);
5667 const SCEV *RA = getSCEV(FalseVal);
5668 const SCEV *LS = getSCEV(LHS);
5669 const SCEV *RS = getSCEV(RHS);
5670 if (LA->getType()->isPointerTy()) {
5671 // FIXME: Handle cases where LS/RS are pointers not equal to LA/RA.
5672 // Need to make sure we can't produce weird expressions involving
5673 // negated pointers.
5674 if (LA == LS && RA == RS)
5675 return Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS);
5676 if (LA == RS && RA == LS)
5677 return Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS);
5678 }
5679 auto CoerceOperand = [&](const SCEV *Op) -> const SCEV * {
5680 if (Op->getType()->isPointerTy()) {
5681 Op = getLosslessPtrToIntExpr(Op);
5682 if (isa<SCEVCouldNotCompute>(Op))
5683 return Op;
5684 }
5685 if (Signed)
5686 Op = getNoopOrSignExtend(Op, I->getType());
5687 else
5688 Op = getNoopOrZeroExtend(Op, I->getType());
5689 return Op;
5690 };
5691 LS = CoerceOperand(LS);
5692 RS = CoerceOperand(RS);
5693 if (isa<SCEVCouldNotCompute>(LS) || isa<SCEVCouldNotCompute>(RS))
5694 break;
5695 const SCEV *LDiff = getMinusSCEV(LA, LS);
5696 const SCEV *RDiff = getMinusSCEV(RA, RS);
5697 if (LDiff == RDiff)
5698 return getAddExpr(Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS),
5699 LDiff);
5700 LDiff = getMinusSCEV(LA, RS);
5701 RDiff = getMinusSCEV(RA, LS);
5702 if (LDiff == RDiff)
5703 return getAddExpr(Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS),
5704 LDiff);
5705 }
5706 break;
5707 case ICmpInst::ICMP_NE:
5708 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
5709 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5710 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5711 const SCEV *One = getOne(I->getType());
5712 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5713 const SCEV *LA = getSCEV(TrueVal);
5714 const SCEV *RA = getSCEV(FalseVal);
5715 const SCEV *LDiff = getMinusSCEV(LA, LS);
5716 const SCEV *RDiff = getMinusSCEV(RA, One);
5717 if (LDiff == RDiff)
5718 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5719 }
5720 break;
5721 case ICmpInst::ICMP_EQ:
5722 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
5723 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5724 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5725 const SCEV *One = getOne(I->getType());
5726 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5727 const SCEV *LA = getSCEV(TrueVal);
5728 const SCEV *RA = getSCEV(FalseVal);
5729 const SCEV *LDiff = getMinusSCEV(LA, One);
5730 const SCEV *RDiff = getMinusSCEV(RA, LS);
5731 if (LDiff == RDiff)
5732 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5733 }
5734 break;
5735 default:
5736 break;
5737 }
5738
5739 return getUnknown(I);
5740}
5741
5742/// Expand GEP instructions into add and multiply operations. This allows them
5743/// to be analyzed by regular SCEV code.
5744const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
5745 // Don't attempt to analyze GEPs over unsized objects.
5746 if (!GEP->getSourceElementType()->isSized())
5747 return getUnknown(GEP);
5748
5749 SmallVector<const SCEV *, 4> IndexExprs;
5750 for (Value *Index : GEP->indices())
5751 IndexExprs.push_back(getSCEV(Index));
5752 return getGEPExpr(GEP, IndexExprs);
5753}
5754
5755uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
5756 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5757 return C->getAPInt().countTrailingZeros();
5758
5759 if (const SCEVPtrToIntExpr *I = dyn_cast<SCEVPtrToIntExpr>(S))
5760 return GetMinTrailingZeros(I->getOperand());
5761
5762 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
5763 return std::min(GetMinTrailingZeros(T->getOperand()),
5764 (uint32_t)getTypeSizeInBits(T->getType()));
5765
5766 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
5767 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5768 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5769 ? getTypeSizeInBits(E->getType())
5770 : OpRes;
5771 }
5772
5773 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
5774 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5775 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5776 ? getTypeSizeInBits(E->getType())
5777 : OpRes;
5778 }
5779
5780 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
5781 // The result is the min of all operands results.
5782 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5783 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5784 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5785 return MinOpRes;
5786 }
5787
5788 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
5789 // The result is the sum of all operands results.
5790 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
5791 uint32_t BitWidth = getTypeSizeInBits(M->getType());
5792 for (unsigned i = 1, e = M->getNumOperands();
5793 SumOpRes != BitWidth && i != e; ++i)
5794 SumOpRes =
5795 std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
5796 return SumOpRes;
5797 }
5798
5799 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
5800 // The result is the min of all operands results.
5801 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5802 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5803 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5804 return MinOpRes;
5805 }
5806
5807 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
5808 // The result is the min of all operands results.
5809 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5810 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5811 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5812 return MinOpRes;
5813 }
5814
5815 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
5816 // The result is the min of all operands results.
5817 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5818 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5819 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5820 return MinOpRes;
5821 }
5822
5823 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5824 // For a SCEVUnknown, ask ValueTracking.
5825 KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
5826 return Known.countMinTrailingZeros();
5827 }
5828
5829 // SCEVUDivExpr
5830 return 0;
5831}
5832
5833uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
5834 auto I = MinTrailingZerosCache.find(S);
5835 if (I != MinTrailingZerosCache.end())
5836 return I->second;
5837
5838 uint32_t Result = GetMinTrailingZerosImpl(S);
5839 auto InsertPair = MinTrailingZerosCache.insert({S, Result});
5840 assert(InsertPair.second && "Should insert a new key")((void)0);
5841 return InsertPair.first->second;
5842}
5843
5844/// Helper method to assign a range to V from metadata present in the IR.
5845static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
5846 if (Instruction *I = dyn_cast<Instruction>(V))
5847 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
5848 return getConstantRangeFromMetadata(*MD);
5849
5850 return None;
5851}
5852
5853void ScalarEvolution::setNoWrapFlags(SCEVAddRecExpr *AddRec,
5854 SCEV::NoWrapFlags Flags) {
5855 if (AddRec->getNoWrapFlags(Flags) != Flags) {
5856 AddRec->setNoWrapFlags(Flags);
5857 UnsignedRanges.erase(AddRec);
5858 SignedRanges.erase(AddRec);
5859 }
5860}
5861
5862ConstantRange ScalarEvolution::
5863getRangeForUnknownRecurrence(const SCEVUnknown *U) {
5864 const DataLayout &DL = getDataLayout();
5865
5866 unsigned BitWidth = getTypeSizeInBits(U->getType());
5867 const ConstantRange FullSet(BitWidth, /*isFullSet=*/true);
5868
5869 // Match a simple recurrence of the form: <start, ShiftOp, Step>, and then
5870 // use information about the trip count to improve our available range. Note
5871 // that the trip count independent cases are already handled by known bits.
5872 // WARNING: The definition of recurrence used here is subtly different than
5873 // the one used by AddRec (and thus most of this file). Step is allowed to
5874 // be arbitrarily loop varying here, where AddRec allows only loop invariant
5875 // and other addrecs in the same loop (for non-affine addrecs). The code
5876 // below intentionally handles the case where step is not loop invariant.
5877 auto *P = dyn_cast<PHINode>(U->getValue());
5878 if (!P)
5879 return FullSet;
5880
5881 // Make sure that no Phi input comes from an unreachable block. Otherwise,
5882 // even the values that are not available in these blocks may come from them,
5883 // and this leads to false-positive recurrence test.
5884 for (auto *Pred : predecessors(P->getParent()))
5885 if (!DT.isReachableFromEntry(Pred))
5886 return FullSet;
5887
5888 BinaryOperator *BO;
5889 Value *Start, *Step;
5890 if (!matchSimpleRecurrence(P, BO, Start, Step))
5891 return FullSet;
5892
5893 // If we found a recurrence in reachable code, we must be in a loop. Note
5894 // that BO might be in some subloop of L, and that's completely okay.
5895 auto *L = LI.getLoopFor(P->getParent());
5896 assert(L && L->getHeader() == P->getParent())((void)0);
5897 if (!L->contains(BO->getParent()))
5898 // NOTE: This bailout should be an assert instead. However, asserting
5899 // the condition here exposes a case where LoopFusion is querying SCEV
5900 // with malformed loop information during the midst of the transform.
5901 // There doesn't appear to be an obvious fix, so for the moment bailout
5902 // until the caller issue can be fixed. PR49566 tracks the bug.
5903 return FullSet;
5904
5905 // TODO: Extend to other opcodes such as mul, and div
5906 switch (BO->getOpcode()) {
5907 default:
5908 return FullSet;
5909 case Instruction::AShr:
5910 case Instruction::LShr:
5911 case Instruction::Shl:
5912 break;
5913 };
5914
5915 if (BO->getOperand(0) != P)
5916 // TODO: Handle the power function forms some day.
5917 return FullSet;
5918
5919 unsigned TC = getSmallConstantMaxTripCount(L);
5920 if (!TC || TC >= BitWidth)
5921 return FullSet;
5922
5923 auto KnownStart = computeKnownBits(Start, DL, 0, &AC, nullptr, &DT);
5924 auto KnownStep = computeKnownBits(Step, DL, 0, &AC, nullptr, &DT);
5925 assert(KnownStart.getBitWidth() == BitWidth &&((void)0)
5926 KnownStep.getBitWidth() == BitWidth)((void)0);
5927
5928 // Compute total shift amount, being careful of overflow and bitwidths.
5929 auto MaxShiftAmt = KnownStep.getMaxValue();
5930 APInt TCAP(BitWidth, TC-1);
5931 bool Overflow = false;
5932 auto TotalShift = MaxShiftAmt.umul_ov(TCAP, Overflow);
5933 if (Overflow)
5934 return FullSet;
5935
5936 switch (BO->getOpcode()) {
5937 default:
5938 llvm_unreachable("filtered out above")__builtin_unreachable();
5939 case Instruction::AShr: {
5940 // For each ashr, three cases:
5941 // shift = 0 => unchanged value
5942 // saturation => 0 or -1
5943 // other => a value closer to zero (of the same sign)
5944 // Thus, the end value is closer to zero than the start.
5945 auto KnownEnd = KnownBits::ashr(KnownStart,
5946 KnownBits::makeConstant(TotalShift));
5947 if (KnownStart.isNonNegative())
5948 // Analogous to lshr (simply not yet canonicalized)
5949 return ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
5950 KnownStart.getMaxValue() + 1);
5951 if (KnownStart.isNegative())
5952 // End >=u Start && End <=s Start
5953 return ConstantRange::getNonEmpty(KnownStart.getMinValue(),
5954 KnownEnd.getMaxValue() + 1);
5955 break;
5956 }
5957 case Instruction::LShr: {
5958 // For each lshr, three cases:
5959 // shift = 0 => unchanged value
5960 // saturation => 0
5961 // other => a smaller positive number
5962 // Thus, the low end of the unsigned range is the last value produced.
5963 auto KnownEnd = KnownBits::lshr(KnownStart,
5964 KnownBits::makeConstant(TotalShift));
5965 return ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
5966 KnownStart.getMaxValue() + 1);
5967 }
5968 case Instruction::Shl: {
5969 // Iff no bits are shifted out, value increases on every shift.
5970 auto KnownEnd = KnownBits::shl(KnownStart,
5971 KnownBits::makeConstant(TotalShift));
5972 if (TotalShift.ult(KnownStart.countMinLeadingZeros()))
5973 return ConstantRange(KnownStart.getMinValue(),
5974 KnownEnd.getMaxValue() + 1);
5975 break;
5976 }
5977 };
5978 return FullSet;
5979}
5980
5981/// Determine the range for a particular SCEV. If SignHint is
5982/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
5983/// with a "cleaner" unsigned (resp. signed) representation.
5984const ConstantRange &
5985ScalarEvolution::getRangeRef(const SCEV *S,
5986 ScalarEvolution::RangeSignHint SignHint) {
5987 DenseMap<const SCEV *, ConstantRange> &Cache =
5988 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
5989 : SignedRanges;
5990 ConstantRange::PreferredRangeType RangeType =
5991 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED
5992 ? ConstantRange::Unsigned : ConstantRange::Signed;
5993
5994 // See if we've computed this range already.
5995 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
5996 if (I != Cache.end())
5997 return I->second;
5998
5999 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
6000 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
6001
6002 unsigned BitWidth = getTypeSizeInBits(S->getType());
6003 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
6004 using OBO = OverflowingBinaryOperator;
6005
6006 // If the value has known zeros, the maximum value will have those known zeros
6007 // as well.
6008 uint32_t TZ = GetMinTrailingZeros(S);
6009 if (TZ != 0) {
6010 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
6011 ConservativeResult =
6012 ConstantRange(APInt::getMinValue(BitWidth),
6013 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
6014 else
6015 ConservativeResult = ConstantRange(
6016 APInt::getSignedMinValue(BitWidth),
6017 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
6018 }
6019
6020 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
6021 ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
6022 unsigned WrapType = OBO::AnyWrap;
6023 if (Add->hasNoSignedWrap())
6024 WrapType |= OBO::NoSignedWrap;
6025 if (Add->hasNoUnsignedWrap())
6026 WrapType |= OBO::NoUnsignedWrap;
6027 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
6028 X = X.addWithNoWrap(getRangeRef(Add->getOperand(i), SignHint),
6029 WrapType, RangeType);
6030 return setRange(Add, SignHint,
6031 ConservativeResult.intersectWith(X, RangeType));
6032 }
6033
6034 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
6035 ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
6036 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
6037 X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
6038 return setRange(Mul, SignHint,
6039 ConservativeResult.intersectWith(X, RangeType));
6040 }
6041
6042 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
6043 ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
6044 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
6045 X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
6046 return setRange(SMax, SignHint,
6047 ConservativeResult.intersectWith(X, RangeType));
6048 }
6049
6050 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
6051 ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
6052 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
6053 X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
6054 return setRange(UMax, SignHint,
6055 ConservativeResult.intersectWith(X, RangeType));
6056 }
6057
6058 if (const SCEVSMinExpr *SMin = dyn_cast<SCEVSMinExpr>(S)) {
6059 ConstantRange X = getRangeRef(SMin->getOperand(0), SignHint);
6060 for (unsigned i = 1, e = SMin->getNumOperands(); i != e; ++i)
6061 X = X.smin(getRangeRef(SMin->getOperand(i), SignHint));
6062 return setRange(SMin, SignHint,
6063 ConservativeResult.intersectWith(X, RangeType));
6064 }
6065
6066 if (const SCEVUMinExpr *UMin = dyn_cast<SCEVUMinExpr>(S)) {
6067 ConstantRange X = getRangeRef(UMin->getOperand(0), SignHint);
6068 for (unsigned i = 1, e = UMin->getNumOperands(); i != e; ++i)
6069 X = X.umin(getRangeRef(UMin->getOperand(i), SignHint));
6070 return setRange(UMin, SignHint,
6071 ConservativeResult.intersectWith(X, RangeType));
6072 }
6073
6074 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
6075 ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
6076 ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
6077 return setRange(UDiv, SignHint,
6078 ConservativeResult.intersectWith(X.udiv(Y), RangeType));
6079 }
6080
6081 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
6082 ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
6083 return setRange(ZExt, SignHint,
6084 ConservativeResult.intersectWith(X.zeroExtend(BitWidth),
6085 RangeType));
6086 }
6087
6088 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
6089 ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
6090 return setRange(SExt, SignHint,
6091 ConservativeResult.intersectWith(X.signExtend(BitWidth),
6092 RangeType));
6093 }
6094
6095 if (const SCEVPtrToIntExpr *PtrToInt = dyn_cast<SCEVPtrToIntExpr>(S)) {
6096 ConstantRange X = getRangeRef(PtrToInt->getOperand(), SignHint);
6097 return setRange(PtrToInt, SignHint, X);
6098 }
6099
6100 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
6101 ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
6102 return setRange(Trunc, SignHint,
6103 ConservativeResult.intersectWith(X.truncate(BitWidth),
6104 RangeType));
6105 }
6106
6107 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
6108 // If there's no unsigned wrap, the value will never be less than its
6109 // initial value.
6110 if (AddRec->hasNoUnsignedWrap()) {
6111 APInt UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart());
6112 if (!UnsignedMinValue.isNullValue())
6113 ConservativeResult = ConservativeResult.intersectWith(
6114 ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType);
6115 }
6116
6117 // If there's no signed wrap, and all the operands except initial value have
6118 // the same sign or zero, the value won't ever be:
6119 // 1: smaller than initial value if operands are non negative,
6120 // 2: bigger than initial value if operands are non positive.
6121 // For both cases, value can not cross signed min/max boundary.
6122 if (AddRec->hasNoSignedWrap()) {
6123 bool AllNonNeg = true;
6124 bool AllNonPos = true;
6125 for (unsigned i = 1, e = AddRec->getNumOperands(); i != e; ++i) {
6126 if (!isKnownNonNegative(AddRec->getOperand(i)))
6127 AllNonNeg = false;
6128 if (!isKnownNonPositive(AddRec->getOperand(i)))
6129 AllNonPos = false;
6130 }
6131 if (AllNonNeg)
6132 ConservativeResult = ConservativeResult.intersectWith(
6133 ConstantRange::getNonEmpty(getSignedRangeMin(AddRec->getStart()),
6134 APInt::getSignedMinValue(BitWidth)),
6135 RangeType);
6136 else if (AllNonPos)
6137 ConservativeResult = ConservativeResult.intersectWith(
6138 ConstantRange::getNonEmpty(
6139 APInt::getSignedMinValue(BitWidth),
6140 getSignedRangeMax(AddRec->getStart()) + 1),
6141 RangeType);
6142 }
6143
6144 // TODO: non-affine addrec
6145 if (AddRec->isAffine()) {
6146 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(AddRec->getLoop());
6147 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
6148 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
6149 auto RangeFromAffine = getRangeForAffineAR(
6150 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
6151 BitWidth);
6152 ConservativeResult =
6153 ConservativeResult.intersectWith(RangeFromAffine, RangeType);
6154
6155 auto RangeFromFactoring = getRangeViaFactoring(
6156 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
6157 BitWidth);
6158 ConservativeResult =
6159 ConservativeResult.intersectWith(RangeFromFactoring, RangeType);
6160 }
6161
6162 // Now try symbolic BE count and more powerful methods.
6163 if (UseExpensiveRangeSharpening) {
6164 const SCEV *SymbolicMaxBECount =
6165 getSymbolicMaxBackedgeTakenCount(AddRec->getLoop());
6166 if (!isa<SCEVCouldNotCompute>(SymbolicMaxBECount) &&
6167 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
6168 AddRec->hasNoSelfWrap()) {
6169 auto RangeFromAffineNew = getRangeForAffineNoSelfWrappingAR(
6170 AddRec, SymbolicMaxBECount, BitWidth, SignHint);
6171 ConservativeResult =
6172 ConservativeResult.intersectWith(RangeFromAffineNew, RangeType);
6173 }
6174 }
6175 }
6176
6177 return setRange(AddRec, SignHint, std::move(ConservativeResult));
6178 }
6179
6180 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
6181
6182 // Check if the IR explicitly contains !range metadata.
6183 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
6184 if (MDRange.hasValue())
6185 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue(),
6186 RangeType);
6187
6188 // Use facts about recurrences in the underlying IR. Note that add
6189 // recurrences are AddRecExprs and thus don't hit this path. This
6190 // primarily handles shift recurrences.
6191 auto CR = getRangeForUnknownRecurrence(U);
6192 ConservativeResult = ConservativeResult.intersectWith(CR);
6193
6194 // See if ValueTracking can give us a useful range.
6195 const DataLayout &DL = getDataLayout();
6196 KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
6197 if (Known.getBitWidth() != BitWidth)
6198 Known = Known.zextOrTrunc(BitWidth);
6199
6200 // ValueTracking may be able to compute a tighter result for the number of
6201 // sign bits than for the value of those sign bits.
6202 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
6203 if (U->getType()->isPointerTy()) {
6204 // If the pointer size is larger than the index size type, this can cause
6205 // NS to be larger than BitWidth. So compensate for this.
6206 unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType());
6207 int ptrIdxDiff = ptrSize - BitWidth;
6208 if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff)
6209 NS -= ptrIdxDiff;
6210 }
6211
6212 if (NS > 1) {
6213 // If we know any of the sign bits, we know all of the sign bits.
6214 if (!Known.Zero.getHiBits(NS).isNullValue())
6215 Known.Zero.setHighBits(NS);
6216 if (!Known.One.getHiBits(NS).isNullValue())
6217 Known.One.setHighBits(NS);
6218 }
6219
6220 if (Known.getMinValue() != Known.getMaxValue() + 1)
6221 ConservativeResult = ConservativeResult.intersectWith(
6222 ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1),
6223 RangeType);
6224 if (NS > 1)
6225 ConservativeResult = ConservativeResult.intersectWith(
6226 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
6227 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1),
6228 RangeType);
6229
6230 // A range of Phi is a subset of union of all ranges of its input.
6231 if (const PHINode *Phi = dyn_cast<PHINode>(U->getValue())) {
6232 // Make sure that we do not run over cycled Phis.
6233 if (PendingPhiRanges.insert(Phi).second) {
6234 ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
6235 for (auto &Op : Phi->operands()) {
6236 auto OpRange = getRangeRef(getSCEV(Op), SignHint);
6237 RangeFromOps = RangeFromOps.unionWith(OpRange);
6238 // No point to continue if we already have a full set.
6239 if (RangeFromOps.isFullSet())
6240 break;
6241 }
6242 ConservativeResult =
6243 ConservativeResult.intersectWith(RangeFromOps, RangeType);
6244 bool Erased = PendingPhiRanges.erase(Phi);
6245 assert(Erased && "Failed to erase Phi properly?")((void)0);
6246 (void) Erased;
6247 }
6248 }
6249
6250 return setRange(U, SignHint, std::move(ConservativeResult));
6251 }
6252
6253 return setRange(S, SignHint, std::move(ConservativeResult));
6254}
6255
6256// Given a StartRange, Step and MaxBECount for an expression compute a range of
6257// values that the expression can take. Initially, the expression has a value
6258// from StartRange and then is changed by Step up to MaxBECount times. Signed
6259// argument defines if we treat Step as signed or unsigned.
6260static ConstantRange getRangeForAffineARHelper(APInt Step,
6261 const ConstantRange &StartRange,
6262 const APInt &MaxBECount,
6263 unsigned BitWidth, bool Signed) {
6264 // If either Step or MaxBECount is 0, then the expression won't change, and we
6265 // just need to return the initial range.
6266 if (Step == 0 || MaxBECount == 0)
6267 return StartRange;
6268
6269 // If we don't know anything about the initial value (i.e. StartRange is
6270 // FullRange), then we don't know anything about the final range either.
6271 // Return FullRange.
6272 if (StartRange.isFullSet())
6273 return ConstantRange::getFull(BitWidth);
6274
6275 // If Step is signed and negative, then we use its absolute value, but we also
6276 // note that we're moving in the opposite direction.
6277 bool Descending = Signed && Step.isNegative();
6278
6279 if (Signed)
6280 // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
6281 // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
6282 // This equations hold true due to the well-defined wrap-around behavior of
6283 // APInt.
6284 Step = Step.abs();
6285
6286 // Check if Offset is more than full span of BitWidth. If it is, the
6287 // expression is guaranteed to overflow.
6288 if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
6289 return ConstantRange::getFull(BitWidth);
6290
6291 // Offset is by how much the expression can change. Checks above guarantee no
6292 // overflow here.
6293 APInt Offset = Step * MaxBECount;
6294
6295 // Minimum value of the final range will match the minimal value of StartRange
6296 // if the expression is increasing and will be decreased by Offset otherwise.
6297 // Maximum value of the final range will match the maximal value of StartRange
6298 // if the expression is decreasing and will be increased by Offset otherwise.
6299 APInt StartLower = StartRange.getLower();
6300 APInt StartUpper = StartRange.getUpper() - 1;
6301 APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
6302 : (StartUpper + std::move(Offset));
6303
6304 // It's possible that the new minimum/maximum value will fall into the initial
6305 // range (due to wrap around). This means that the expression can take any
6306 // value in this bitwidth, and we have to return full range.
6307 if (StartRange.contains(MovedBoundary))
6308 return ConstantRange::getFull(BitWidth);
6309
6310 APInt NewLower =
6311 Descending ? std::move(MovedBoundary) : std::move(StartLower);
6312 APInt NewUpper =
6313 Descending ? std::move(StartUpper) : std::move(MovedBoundary);
6314 NewUpper += 1;
6315
6316 // No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
6317 return ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper));
6318}
6319
6320ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
6321 const SCEV *Step,
6322 const SCEV *MaxBECount,
6323 unsigned BitWidth) {
6324 assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&((void)0)
6325 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&((void)0)
6326 "Precondition!")((void)0);
6327
6328 MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
6329 APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount);
6330
6331 // First, consider step signed.
6332 ConstantRange StartSRange = getSignedRange(Start);
6333 ConstantRange StepSRange = getSignedRange(Step);
6334
6335 // If Step can be both positive and negative, we need to find ranges for the
6336 // maximum absolute step values in both directions and union them.
6337 ConstantRange SR =
6338 getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange,
6339 MaxBECountValue, BitWidth, /* Signed = */ true);
6340 SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(),
6341 StartSRange, MaxBECountValue,
6342 BitWidth, /* Signed = */ true));
6343
6344 // Next, consider step unsigned.
6345 ConstantRange UR = getRangeForAffineARHelper(
6346 getUnsignedRangeMax(Step), getUnsignedRange(Start),
6347 MaxBECountValue, BitWidth, /* Signed = */ false);
6348
6349 // Finally, intersect signed and unsigned ranges.
6350 return SR.intersectWith(UR, ConstantRange::Smallest);
6351}
6352
6353ConstantRange ScalarEvolution::getRangeForAffineNoSelfWrappingAR(
6354 const SCEVAddRecExpr *AddRec, const SCEV *MaxBECount, unsigned BitWidth,
6355 ScalarEvolution::RangeSignHint SignHint) {
6356 assert(AddRec->isAffine() && "Non-affine AddRecs are not suppored!\n")((void)0);
6357 assert(AddRec->hasNoSelfWrap() &&((void)0)
6358 "This only works for non-self-wrapping AddRecs!")((void)0);
6359 const bool IsSigned = SignHint == HINT_RANGE_SIGNED;
6360 const SCEV *Step = AddRec->getStepRecurrence(*this);
6361 // Only deal with constant step to save compile time.
6362 if (!isa<SCEVConstant>(Step))
6363 return ConstantRange::getFull(BitWidth);
6364 // Let's make sure that we can prove that we do not self-wrap during
6365 // MaxBECount iterations. We need this because MaxBECount is a maximum
6366 // iteration count estimate, and we might infer nw from some exit for which we
6367 // do not know max exit count (or any other side reasoning).
6368 // TODO: Turn into assert at some point.
6369 if (getTypeSizeInBits(MaxBECount->getType()) >
6370 getTypeSizeInBits(AddRec->getType()))
6371 return ConstantRange::getFull(BitWidth);
6372 MaxBECount = getNoopOrZeroExtend(MaxBECount, AddRec->getType());
6373 const SCEV *RangeWidth = getMinusOne(AddRec->getType());
6374 const SCEV *StepAbs = getUMinExpr(Step, getNegativeSCEV(Step));
6375 const SCEV *MaxItersWithoutWrap = getUDivExpr(RangeWidth, StepAbs);
6376 if (!isKnownPredicateViaConstantRanges(ICmpInst::ICMP_ULE, MaxBECount,
6377 MaxItersWithoutWrap))
6378 return ConstantRange::getFull(BitWidth);
6379
6380 ICmpInst::Predicate LEPred =
6381 IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
6382 ICmpInst::Predicate GEPred =
6383 IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
6384 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
6385
6386 // We know that there is no self-wrap. Let's take Start and End values and
6387 // look at all intermediate values V1, V2, ..., Vn that IndVar takes during
6388 // the iteration. They either lie inside the range [Min(Start, End),
6389 // Max(Start, End)] or outside it:
6390 //
6391 // Case 1: RangeMin ... Start V1 ... VN End ... RangeMax;
6392 // Case 2: RangeMin Vk ... V1 Start ... End Vn ... Vk + 1 RangeMax;
6393 //
6394 // No self wrap flag guarantees that the intermediate values cannot be BOTH
6395 // outside and inside the range [Min(Start, End), Max(Start, End)]. Using that
6396 // knowledge, let's try to prove that we are dealing with Case 1. It is so if
6397 // Start <= End and step is positive, or Start >= End and step is negative.
6398 const SCEV *Start = AddRec->getStart();
6399 ConstantRange StartRange = getRangeRef(Start, SignHint);
6400 ConstantRange EndRange = getRangeRef(End, SignHint);
6401 ConstantRange RangeBetween = StartRange.unionWith(EndRange);
6402 // If they already cover full iteration space, we will know nothing useful
6403 // even if we prove what we want to prove.
6404 if (RangeBetween.isFullSet())
6405 return RangeBetween;
6406 // Only deal with ranges that do not wrap (i.e. RangeMin < RangeMax).
6407 bool IsWrappedSet = IsSigned ? RangeBetween.isSignWrappedSet()
6408 : RangeBetween.isWrappedSet();
6409 if (IsWrappedSet)
6410 return ConstantRange::getFull(BitWidth);
6411
6412 if (isKnownPositive(Step) &&
6413 isKnownPredicateViaConstantRanges(LEPred, Start, End))
6414 return RangeBetween;
6415 else if (isKnownNegative(Step) &&
6416 isKnownPredicateViaConstantRanges(GEPred, Start, End))
6417 return RangeBetween;
6418 return ConstantRange::getFull(BitWidth);
6419}
6420
6421ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
6422 const SCEV *Step,
6423 const SCEV *MaxBECount,
6424 unsigned BitWidth) {
6425 // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
6426 // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
6427
6428 struct SelectPattern {
6429 Value *Condition = nullptr;
6430 APInt TrueValue;
6431 APInt FalseValue;
6432
6433 explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
6434 const SCEV *S) {
6435 Optional<unsigned> CastOp;
6436 APInt Offset(BitWidth, 0);
6437
6438 assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&((void)0)
6439 "Should be!")((void)0);
6440
6441 // Peel off a constant offset:
6442 if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
6443 // In the future we could consider being smarter here and handle
6444 // {Start+Step,+,Step} too.
6445 if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
6446 return;
6447
6448 Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
6449 S = SA->getOperand(1);
6450 }
6451
6452 // Peel off a cast operation
6453 if (auto *SCast = dyn_cast<SCEVIntegralCastExpr>(S)) {
6454 CastOp = SCast->getSCEVType();
6455 S = SCast->getOperand();
6456 }
6457
6458 using namespace llvm::PatternMatch;
6459
6460 auto *SU = dyn_cast<SCEVUnknown>(S);
6461 const APInt *TrueVal, *FalseVal;
6462 if (!SU ||
6463 !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
6464 m_APInt(FalseVal)))) {
6465 Condition = nullptr;
6466 return;
6467 }
6468
6469 TrueValue = *TrueVal;
6470 FalseValue = *FalseVal;
6471
6472 // Re-apply the cast we peeled off earlier
6473 if (CastOp.hasValue())
6474 switch (*CastOp) {
6475 default:
6476 llvm_unreachable("Unknown SCEV cast type!")__builtin_unreachable();
6477
6478 case scTruncate:
6479 TrueValue = TrueValue.trunc(BitWidth);
6480 FalseValue = FalseValue.trunc(BitWidth);
6481 break;
6482 case scZeroExtend:
6483 TrueValue = TrueValue.zext(BitWidth);
6484 FalseValue = FalseValue.zext(BitWidth);
6485 break;
6486 case scSignExtend:
6487 TrueValue = TrueValue.sext(BitWidth);
6488 FalseValue = FalseValue.sext(BitWidth);
6489 break;
6490 }
6491
6492 // Re-apply the constant offset we peeled off earlier
6493 TrueValue += Offset;
6494 FalseValue += Offset;
6495 }
6496
6497 bool isRecognized() { return Condition != nullptr; }
6498 };
6499
6500 SelectPattern StartPattern(*this, BitWidth, Start);
6501 if (!StartPattern.isRecognized())
6502 return ConstantRange::getFull(BitWidth);
6503
6504 SelectPattern StepPattern(*this, BitWidth, Step);
6505 if (!StepPattern.isRecognized())
6506 return ConstantRange::getFull(BitWidth);
6507
6508 if (StartPattern.Condition != StepPattern.Condition) {
6509 // We don't handle this case today; but we could, by considering four
6510 // possibilities below instead of two. I'm not sure if there are cases where
6511 // that will help over what getRange already does, though.
6512 return ConstantRange::getFull(BitWidth);
6513 }
6514
6515 // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
6516 // construct arbitrary general SCEV expressions here. This function is called
6517 // from deep in the call stack, and calling getSCEV (on a sext instruction,
6518 // say) can end up caching a suboptimal value.
6519
6520 // FIXME: without the explicit `this` receiver below, MSVC errors out with
6521 // C2352 and C2512 (otherwise it isn't needed).
6522
6523 const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
6524 const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
6525 const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
6526 const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
6527
6528 ConstantRange TrueRange =
6529 this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
6530 ConstantRange FalseRange =
6531 this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
6532
6533 return TrueRange.unionWith(FalseRange);
6534}
6535
6536SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
6537 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
6538 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
6539
6540 // Return early if there are no flags to propagate to the SCEV.
6541 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
6542 if (BinOp->hasNoUnsignedWrap())
6543 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
6544 if (BinOp->hasNoSignedWrap())
6545 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
6546 if (Flags == SCEV::FlagAnyWrap)
6547 return SCEV::FlagAnyWrap;
6548
6549 return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
6550}
6551
6552bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
6553 // Here we check that I is in the header of the innermost loop containing I,
6554 // since we only deal with instructions in the loop header. The actual loop we
6555 // need to check later will come from an add recurrence, but getting that
6556 // requires computing the SCEV of the operands, which can be expensive. This
6557 // check we can do cheaply to rule out some cases early.
6558 Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
6559 if (InnermostContainingLoop == nullptr ||
6560 InnermostContainingLoop->getHeader() != I->getParent())
6561 return false;
6562
6563 // Only proceed if we can prove that I does not yield poison.
6564 if (!programUndefinedIfPoison(I))
6565 return false;
6566
6567 // At this point we know that if I is executed, then it does not wrap
6568 // according to at least one of NSW or NUW. If I is not executed, then we do
6569 // not know if the calculation that I represents would wrap. Multiple
6570 // instructions can map to the same SCEV. If we apply NSW or NUW from I to
6571 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
6572 // derived from other instructions that map to the same SCEV. We cannot make
6573 // that guarantee for cases where I is not executed. So we need to find the
6574 // loop that I is considered in relation to and prove that I is executed for
6575 // every iteration of that loop. That implies that the value that I
6576 // calculates does not wrap anywhere in the loop, so then we can apply the
6577 // flags to the SCEV.
6578 //
6579 // We check isLoopInvariant to disambiguate in case we are adding recurrences
6580 // from different loops, so that we know which loop to prove that I is
6581 // executed in.
6582 for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
6583 // I could be an extractvalue from a call to an overflow intrinsic.
6584 // TODO: We can do better here in some cases.
6585 if (!isSCEVable(I->getOperand(OpIndex)->getType()))
6586 return false;
6587 const SCEV *Op = getSCEV(I->getOperand(OpIndex));
6588 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
6589 bool AllOtherOpsLoopInvariant = true;
6590 for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
6591 ++OtherOpIndex) {
6592 if (OtherOpIndex != OpIndex) {
6593 const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
6594 if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
6595 AllOtherOpsLoopInvariant = false;
6596 break;
6597 }
6598 }
6599 }
6600 if (AllOtherOpsLoopInvariant &&
6601 isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
6602 return true;
6603 }
6604 }
6605 return false;
6606}
6607
6608bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
6609 // If we know that \c I can never be poison period, then that's enough.
6610 if (isSCEVExprNeverPoison(I))
6611 return true;
6612
6613 // For an add recurrence specifically, we assume that infinite loops without
6614 // side effects are undefined behavior, and then reason as follows:
6615 //
6616 // If the add recurrence is poison in any iteration, it is poison on all
6617 // future iterations (since incrementing poison yields poison). If the result
6618 // of the add recurrence is fed into the loop latch condition and the loop
6619 // does not contain any throws or exiting blocks other than the latch, we now
6620 // have the ability to "choose" whether the backedge is taken or not (by
6621 // choosing a sufficiently evil value for the poison feeding into the branch)
6622 // for every iteration including and after the one in which \p I first became
6623 // poison. There are two possibilities (let's call the iteration in which \p
6624 // I first became poison as K):
6625 //
6626 // 1. In the set of iterations including and after K, the loop body executes
6627 // no side effects. In this case executing the backege an infinte number
6628 // of times will yield undefined behavior.
6629 //
6630 // 2. In the set of iterations including and after K, the loop body executes
6631 // at least one side effect. In this case, that specific instance of side
6632 // effect is control dependent on poison, which also yields undefined
6633 // behavior.
6634
6635 auto *ExitingBB = L->getExitingBlock();
6636 auto *LatchBB = L->getLoopLatch();
6637 if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
6638 return false;
6639
6640 SmallPtrSet<const Instruction *, 16> Pushed;
6641 SmallVector<const Instruction *, 8> PoisonStack;
6642
6643 // We start by assuming \c I, the post-inc add recurrence, is poison. Only
6644 // things that are known to be poison under that assumption go on the
6645 // PoisonStack.
6646 Pushed.insert(I);
6647 PoisonStack.push_back(I);
6648
6649 bool LatchControlDependentOnPoison = false;
6650 while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
6651 const Instruction *Poison = PoisonStack.pop_back_val();
6652
6653 for (auto *PoisonUser : Poison->users()) {
6654 if (propagatesPoison(cast<Operator>(PoisonUser))) {
6655 if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
6656 PoisonStack.push_back(cast<Instruction>(PoisonUser));
6657 } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
6658 assert(BI->isConditional() && "Only possibility!")((void)0);
6659 if (BI->getParent() == LatchBB) {
6660 LatchControlDependentOnPoison = true;
6661 break;
6662 }
6663 }
6664 }
6665 }
6666
6667 return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
6668}
6669
6670ScalarEvolution::LoopProperties
6671ScalarEvolution::getLoopProperties(const Loop *L) {
6672 using LoopProperties = ScalarEvolution::LoopProperties;
6673
6674 auto Itr = LoopPropertiesCache.find(L);
6675 if (Itr == LoopPropertiesCache.end()) {
6676 auto HasSideEffects = [](Instruction *I) {
6677 if (auto *SI = dyn_cast<StoreInst>(I))
6678 return !SI->isSimple();
6679
6680 return I->mayThrow() || I->mayWriteToMemory();
6681 };
6682
6683 LoopProperties LP = {/* HasNoAbnormalExits */ true,
6684 /*HasNoSideEffects*/ true};
6685
6686 for (auto *BB : L->getBlocks())
6687 for (auto &I : *BB) {
6688 if (!isGuaranteedToTransferExecutionToSuccessor(&I))
6689 LP.HasNoAbnormalExits = false;
6690 if (HasSideEffects(&I))
6691 LP.HasNoSideEffects = false;
6692 if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
6693 break; // We're already as pessimistic as we can get.
6694 }
6695
6696 auto InsertPair = LoopPropertiesCache.insert({L, LP});
6697 assert(InsertPair.second && "We just checked!")((void)0);
6698 Itr = InsertPair.first;
6699 }
6700
6701 return Itr->second;
6702}
6703
6704bool ScalarEvolution::loopIsFiniteByAssumption(const Loop *L) {
6705 // A mustprogress loop without side effects must be finite.
6706 // TODO: The check used here is very conservative. It's only *specific*
6707 // side effects which are well defined in infinite loops.
6708 return isMustProgress(L) && loopHasNoSideEffects(L);
6709}
6710
6711const SCEV *ScalarEvolution::createSCEV(Value *V) {
6712 if (!isSCEVable(V->getType()))
6713 return getUnknown(V);
6714
6715 if (Instruction *I = dyn_cast<Instruction>(V)) {
6716 // Don't attempt to analyze instructions in blocks that aren't
6717 // reachable. Such instructions don't matter, and they aren't required
6718 // to obey basic rules for definitions dominating uses which this
6719 // analysis depends on.
6720 if (!DT.isReachableFromEntry(I->getParent()))
6721 return getUnknown(UndefValue::get(V->getType()));
6722 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
6723 return getConstant(CI);
6724 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
6725 return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
6726 else if (!isa<ConstantExpr>(V))
6727 return getUnknown(V);
6728
6729 Operator *U = cast<Operator>(V);
6730 if (auto BO = MatchBinaryOp(U, DT)) {
6731 switch (BO->Opcode) {
6732 case Instruction::Add: {
6733 // The simple thing to do would be to just call getSCEV on both operands
6734 // and call getAddExpr with the result. However if we're looking at a
6735 // bunch of things all added together, this can be quite inefficient,
6736 // because it leads to N-1 getAddExpr calls for N ultimate operands.
6737 // Instead, gather up all the operands and make a single getAddExpr call.
6738 // LLVM IR canonical form means we need only traverse the left operands.
6739 SmallVector<const SCEV *, 4> AddOps;
6740 do {
6741 if (BO->Op) {
6742 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
6743 AddOps.push_back(OpSCEV);
6744 break;
6745 }
6746
6747 // If a NUW or NSW flag can be applied to the SCEV for this
6748 // addition, then compute the SCEV for this addition by itself
6749 // with a separate call to getAddExpr. We need to do that
6750 // instead of pushing the operands of the addition onto AddOps,
6751 // since the flags are only known to apply to this particular
6752 // addition - they may not apply to other additions that can be
6753 // formed with operands from AddOps.
6754 const SCEV *RHS = getSCEV(BO->RHS);
6755 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
6756 if (Flags != SCEV::FlagAnyWrap) {
6757 const SCEV *LHS = getSCEV(BO->LHS);
6758 if (BO->Opcode == Instruction::Sub)
6759 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
6760 else
6761 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
6762 break;
6763 }
6764 }
6765
6766 if (BO->Opcode == Instruction::Sub)
6767 AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
6768 else
6769 AddOps.push_back(getSCEV(BO->RHS));
6770
6771 auto NewBO = MatchBinaryOp(BO->LHS, DT);
6772 if (!NewBO || (NewBO->Opcode != Instruction::Add &&
6773 NewBO->Opcode != Instruction::Sub)) {
6774 AddOps.push_back(getSCEV(BO->LHS));
6775 break;
6776 }
6777 BO = NewBO;
6778 } while (true);
6779
6780 return getAddExpr(AddOps);
6781 }
6782
6783 case Instruction::Mul: {
6784 SmallVector<const SCEV *, 4> MulOps;
6785 do {
6786 if (BO->Op) {
6787 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
6788 MulOps.push_back(OpSCEV);
6789 break;
6790 }
6791
6792 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
6793 if (Flags != SCEV::FlagAnyWrap) {
6794 MulOps.push_back(
6795 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
6796 break;
6797 }
6798 }
6799
6800 MulOps.push_back(getSCEV(BO->RHS));
6801 auto NewBO = MatchBinaryOp(BO->LHS, DT);
6802 if (!NewBO || NewBO->Opcode != Instruction::Mul) {
6803 MulOps.push_back(getSCEV(BO->LHS));
6804 break;
6805 }
6806 BO = NewBO;
6807 } while (true);
6808
6809 return getMulExpr(MulOps);
6810 }
6811 case Instruction::UDiv:
6812 return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
6813 case Instruction::URem:
6814 return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
6815 case Instruction::Sub: {
6816 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
6817 if (BO->Op)
6818 Flags = getNoWrapFlagsFromUB(BO->Op);
6819 return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
6820 }
6821 case Instruction::And:
6822 // For an expression like x&255 that merely masks off the high bits,
6823 // use zext(trunc(x)) as the SCEV expression.
6824 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
6825 if (CI->isZero())
6826 return getSCEV(BO->RHS);
6827 if (CI->isMinusOne())
6828 return getSCEV(BO->LHS);
6829 const APInt &A = CI->getValue();
6830
6831 // Instcombine's ShrinkDemandedConstant may strip bits out of
6832 // constants, obscuring what would otherwise be a low-bits mask.
6833 // Use computeKnownBits to compute what ShrinkDemandedConstant
6834 // knew about to reconstruct a low-bits mask value.
6835 unsigned LZ = A.countLeadingZeros();
6836 unsigned TZ = A.countTrailingZeros();
6837 unsigned BitWidth = A.getBitWidth();
6838 KnownBits Known(BitWidth);
6839 computeKnownBits(BO->LHS, Known, getDataLayout(),
6840 0, &AC, nullptr, &DT);
6841
6842 APInt EffectiveMask =
6843 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
6844 if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
6845 const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ));
6846 const SCEV *LHS = getSCEV(BO->LHS);
6847 const SCEV *ShiftedLHS = nullptr;
6848 if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) {
6849 if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) {
6850 // For an expression like (x * 8) & 8, simplify the multiply.
6851 unsigned MulZeros = OpC->getAPInt().countTrailingZeros();
6852 unsigned GCD = std::min(MulZeros, TZ);
6853 APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD);
6854 SmallVector<const SCEV*, 4> MulOps;
6855 MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD)));
6856 MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end());
6857 auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags());
6858 ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt));
6859 }
6860 }
6861 if (!ShiftedLHS)
6862 ShiftedLHS = getUDivExpr(LHS, MulCount);
6863 return getMulExpr(
6864 getZeroExtendExpr(
6865 getTruncateExpr(ShiftedLHS,
6866 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
6867 BO->LHS->getType()),
6868 MulCount);
6869 }
6870 }
6871 break;
6872
6873 case Instruction::Or:
6874 // If the RHS of the Or is a constant, we may have something like:
6875 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
6876 // optimizations will transparently handle this case.
6877 //
6878 // In order for this transformation to be safe, the LHS must be of the
6879 // form X*(2^n) and the Or constant must be less than 2^n.
6880 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
6881 const SCEV *LHS = getSCEV(BO->LHS);
6882 const APInt &CIVal = CI->getValue();
6883 if (GetMinTrailingZeros(LHS) >=
6884 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
6885 // Build a plain add SCEV.
6886 return getAddExpr(LHS, getSCEV(CI),
6887 (SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNSW));
6888 }
6889 }
6890 break;
6891
6892 case Instruction::Xor:
6893 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
6894 // If the RHS of xor is -1, then this is a not operation.
6895 if (CI->isMinusOne())
6896 return getNotSCEV(getSCEV(BO->LHS));
6897
6898 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
6899 // This is a variant of the check for xor with -1, and it handles
6900 // the case where instcombine has trimmed non-demanded bits out
6901 // of an xor with -1.
6902 if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
6903 if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
6904 if (LBO->getOpcode() == Instruction::And &&
6905 LCI->getValue() == CI->getValue())
6906 if (const SCEVZeroExtendExpr *Z =
6907 dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
6908 Type *UTy = BO->LHS->getType();
6909 const SCEV *Z0 = Z->getOperand();
6910 Type *Z0Ty = Z0->getType();
6911 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
6912
6913 // If C is a low-bits mask, the zero extend is serving to
6914 // mask off the high bits. Complement the operand and
6915 // re-apply the zext.
6916 if (CI->getValue().isMask(Z0TySize))
6917 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
6918
6919 // If C is a single bit, it may be in the sign-bit position
6920 // before the zero-extend. In this case, represent the xor
6921 // using an add, which is equivalent, and re-apply the zext.
6922 APInt Trunc = CI->getValue().trunc(Z0TySize);
6923 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
6924 Trunc.isSignMask())
6925 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
6926 UTy);
6927 }
6928 }
6929 break;
6930
6931 case Instruction::Shl:
6932 // Turn shift left of a constant amount into a multiply.
6933 if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
6934 uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
6935
6936 // If the shift count is not less than the bitwidth, the result of
6937 // the shift is undefined. Don't try to analyze it, because the
6938 // resolution chosen here may differ from the resolution chosen in
6939 // other parts of the compiler.
6940 if (SA->getValue().uge(BitWidth))
6941 break;
6942
6943 // We can safely preserve the nuw flag in all cases. It's also safe to
6944 // turn a nuw nsw shl into a nuw nsw mul. However, nsw in isolation
6945 // requires special handling. It can be preserved as long as we're not
6946 // left shifting by bitwidth - 1.
6947 auto Flags = SCEV::FlagAnyWrap;
6948 if (BO->Op) {
6949 auto MulFlags = getNoWrapFlagsFromUB(BO->Op);
6950 if ((MulFlags & SCEV::FlagNSW) &&
6951 ((MulFlags & SCEV::FlagNUW) || SA->getValue().ult(BitWidth - 1)))
6952 Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNSW);
6953 if (MulFlags & SCEV::FlagNUW)
6954 Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNUW);
6955 }
6956
6957 Constant *X = ConstantInt::get(
6958 getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
6959 return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
6960 }
6961 break;
6962
6963 case Instruction::AShr: {
6964 // AShr X, C, where C is a constant.
6965 ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS);
6966 if (!CI)
6967 break;
6968
6969 Type *OuterTy = BO->LHS->getType();
6970 uint64_t BitWidth = getTypeSizeInBits(OuterTy);
6971 // If the shift count is not less than the bitwidth, the result of
6972 // the shift is undefined. Don't try to analyze it, because the
6973 // resolution chosen here may differ from the resolution chosen in
6974 // other parts of the compiler.
6975 if (CI->getValue().uge(BitWidth))
6976 break;
6977
6978 if (CI->isZero())
6979 return getSCEV(BO->LHS); // shift by zero --> noop
6980
6981 uint64_t AShrAmt = CI->getZExtValue();
6982 Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt);
6983
6984 Operator *L = dyn_cast<Operator>(BO->LHS);
6985 if (L && L->getOpcode() == Instruction::Shl) {
6986 // X = Shl A, n
6987 // Y = AShr X, m
6988 // Both n and m are constant.
6989
6990 const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0));
6991 if (L->getOperand(1) == BO->RHS)
6992 // For a two-shift sext-inreg, i.e. n = m,
6993 // use sext(trunc(x)) as the SCEV expression.
6994 return getSignExtendExpr(
6995 getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy);
6996
6997 ConstantInt *ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1));
6998 if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) {
6999 uint64_t ShlAmt = ShlAmtCI->getZExtValue();
7000 if (ShlAmt > AShrAmt) {
7001 // When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
7002 // expression. We already checked that ShlAmt < BitWidth, so
7003 // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
7004 // ShlAmt - AShrAmt < Amt.
7005 APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt,
7006 ShlAmt - AShrAmt);
7007 return getSignExtendExpr(
7008 getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy),
7009 getConstant(Mul)), OuterTy);
7010 }
7011 }
7012 }
7013 break;
7014 }
7015 }
7016 }
7017
7018 switch (U->getOpcode()) {
7019 case Instruction::Trunc:
7020 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
7021
7022 case Instruction::ZExt:
7023 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
7024
7025 case Instruction::SExt:
7026 if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) {
7027 // The NSW flag of a subtract does not always survive the conversion to
7028 // A + (-1)*B. By pushing sign extension onto its operands we are much
7029 // more likely to preserve NSW and allow later AddRec optimisations.
7030 //
7031 // NOTE: This is effectively duplicating this logic from getSignExtend:
7032 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
7033 // but by that point the NSW information has potentially been lost.
7034 if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
7035 Type *Ty = U->getType();
7036 auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
7037 auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
7038 return getMinusSCEV(V1, V2, SCEV::FlagNSW);
7039 }
7040 }
7041 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
7042
7043 case Instruction::BitCast:
7044 // BitCasts are no-op casts so we just eliminate the cast.
7045 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
7046 return getSCEV(U->getOperand(0));
7047 break;
7048
7049 case Instruction::PtrToInt: {
7050 // Pointer to integer cast is straight-forward, so do model it.
7051 const SCEV *Op = getSCEV(U->getOperand(0));
7052 Type *DstIntTy = U->getType();
7053 // But only if effective SCEV (integer) type is wide enough to represent
7054 // all possible pointer values.
7055 const SCEV *IntOp = getPtrToIntExpr(Op, DstIntTy);
7056 if (isa<SCEVCouldNotCompute>(IntOp))
7057 return getUnknown(V);
7058 return IntOp;
7059 }
7060 case Instruction::IntToPtr:
7061 // Just don't deal with inttoptr casts.
7062 return getUnknown(V);
7063
7064 case Instruction::SDiv:
7065 // If both operands are non-negative, this is just an udiv.
7066 if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
7067 isKnownNonNegative(getSCEV(U->getOperand(1))))
7068 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
7069 break;
7070
7071 case Instruction::SRem:
7072 // If both operands are non-negative, this is just an urem.
7073 if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
7074 isKnownNonNegative(getSCEV(U->getOperand(1))))
7075 return getURemExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
7076 break;
7077
7078 case Instruction::GetElementPtr:
7079 return createNodeForGEP(cast<GEPOperator>(U));
7080
7081 case Instruction::PHI:
7082 return createNodeForPHI(cast<PHINode>(U));
7083
7084 case Instruction::Select:
7085 // U can also be a select constant expr, which let fall through. Since
7086 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
7087 // constant expressions cannot have instructions as operands, we'd have
7088 // returned getUnknown for a select constant expressions anyway.
7089 if (isa<Instruction>(U))
7090 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
7091 U->getOperand(1), U->getOperand(2));
7092 break;
7093
7094 case Instruction::Call:
7095 case Instruction::Invoke:
7096 if (Value *RV = cast<CallBase>(U)->getReturnedArgOperand())
7097 return getSCEV(RV);
7098
7099 if (auto *II = dyn_cast<IntrinsicInst>(U)) {
7100 switch (II->getIntrinsicID()) {
7101 case Intrinsic::abs:
7102 return getAbsExpr(
7103 getSCEV(II->getArgOperand(0)),
7104 /*IsNSW=*/cast<ConstantInt>(II->getArgOperand(1))->isOne());
7105 case Intrinsic::umax:
7106 return getUMaxExpr(getSCEV(II->getArgOperand(0)),
7107 getSCEV(II->getArgOperand(1)));
7108 case Intrinsic::umin:
7109 return getUMinExpr(getSCEV(II->getArgOperand(0)),
7110 getSCEV(II->getArgOperand(1)));
7111 case Intrinsic::smax:
7112 return getSMaxExpr(getSCEV(II->getArgOperand(0)),
7113 getSCEV(II->getArgOperand(1)));
7114 case Intrinsic::smin:
7115 return getSMinExpr(getSCEV(II->getArgOperand(0)),
7116 getSCEV(II->getArgOperand(1)));
7117 case Intrinsic::usub_sat: {
7118 const SCEV *X = getSCEV(II->getArgOperand(0));
7119 const SCEV *Y = getSCEV(II->getArgOperand(1));
7120 const SCEV *ClampedY = getUMinExpr(X, Y);
7121 return getMinusSCEV(X, ClampedY, SCEV::FlagNUW);
7122 }
7123 case Intrinsic::uadd_sat: {
7124 const SCEV *X = getSCEV(II->getArgOperand(0));
7125 const SCEV *Y = getSCEV(II->getArgOperand(1));
7126 const SCEV *ClampedX = getUMinExpr(X, getNotSCEV(Y));
7127 return getAddExpr(ClampedX, Y, SCEV::FlagNUW);
7128 }
7129 case Intrinsic::start_loop_iterations:
7130 // A start_loop_iterations is just equivalent to the first operand for
7131 // SCEV purposes.
7132 return getSCEV(II->getArgOperand(0));
7133 default:
7134 break;
7135 }
7136 }
7137 break;
7138 }
7139
7140 return getUnknown(V);
7141}
7142
7143//===----------------------------------------------------------------------===//
7144// Iteration Count Computation Code
7145//
7146
7147const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount) {
7148 // Get the trip count from the BE count by adding 1. Overflow, results
7149 // in zero which means "unknown".
7150 return getAddExpr(ExitCount, getOne(ExitCount->getType()));
7151}
7152
7153static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
7154 if (!ExitCount)
7155 return 0;
7156
7157 ConstantInt *ExitConst = ExitCount->getValue();
7158
7159 // Guard against huge trip counts.
7160 if (ExitConst->getValue().getActiveBits() > 32)
7161 return 0;
7162
7163 // In case of integer overflow, this returns 0, which is correct.
7164 return ((unsigned)ExitConst->getZExtValue()) + 1;
7165}
7166
7167unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
7168 auto *ExitCount = dyn_cast<SCEVConstant>(getBackedgeTakenCount(L, Exact));
7169 return getConstantTripCount(ExitCount);
7170}
7171
7172unsigned
7173ScalarEvolution::getSmallConstantTripCount(const Loop *L,
7174 const BasicBlock *ExitingBlock) {
7175 assert(ExitingBlock && "Must pass a non-null exiting block!")((void)0);
7176 assert(L->isLoopExiting(ExitingBlock) &&((void)0)
7177 "Exiting block must actually branch out of the loop!")((void)0);
7178 const SCEVConstant *ExitCount =
7179 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
7180 return getConstantTripCount(ExitCount);
7181}
7182
7183unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) {
7184 const auto *MaxExitCount =
7185 dyn_cast<SCEVConstant>(getConstantMaxBackedgeTakenCount(L));
7186 return getConstantTripCount(MaxExitCount);
7187}
7188
7189unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
7190 SmallVector<BasicBlock *, 8> ExitingBlocks;
7191 L->getExitingBlocks(ExitingBlocks);
7192
7193 Optional<unsigned> Res = None;
7194 for (auto *ExitingBB : ExitingBlocks) {
7195 unsigned Multiple = getSmallConstantTripMultiple(L, ExitingBB);
7196 if (!Res)
7197 Res = Multiple;
7198 Res = (unsigned)GreatestCommonDivisor64(*Res, Multiple);
7199 }
7200 return Res.getValueOr(1);
7201}
7202
7203unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
7204 const SCEV *ExitCount) {
7205 if (ExitCount == getCouldNotCompute())
7206 return 1;
7207
7208 // Get the trip count
7209 const SCEV *TCExpr = getTripCountFromExitCount(ExitCount);
7210
7211 const SCEVConstant *TC = dyn_cast<SCEVConstant>(TCExpr);
7212 if (!TC)
7213 // Attempt to factor more general cases. Returns the greatest power of
7214 // two divisor. If overflow happens, the trip count expression is still
7215 // divisible by the greatest power of 2 divisor returned.
7216 return 1U << std::min((uint32_t)31,
7217 GetMinTrailingZeros(applyLoopGuards(TCExpr, L)));
7218
7219 ConstantInt *Result = TC->getValue();
7220
7221 // Guard against huge trip counts (this requires checking
7222 // for zero to handle the case where the trip count == -1 and the
7223 // addition wraps).
7224 if (!Result || Result->getValue().getActiveBits() > 32 ||
7225 Result->getValue().getActiveBits() == 0)
7226 return 1;
7227
7228 return (unsigned)Result->getZExtValue();
7229}
7230
7231/// Returns the largest constant divisor of the trip count of this loop as a
7232/// normal unsigned value, if possible. This means that the actual trip count is
7233/// always a multiple of the returned value (don't forget the trip count could
7234/// very well be zero as well!).
7235///
7236/// Returns 1 if the trip count is unknown or not guaranteed to be the
7237/// multiple of a constant (which is also the case if the trip count is simply
7238/// constant, use getSmallConstantTripCount for that case), Will also return 1
7239/// if the trip count is very large (>= 2^32).
7240///
7241/// As explained in the comments for getSmallConstantTripCount, this assumes
7242/// that control exits the loop via ExitingBlock.
7243unsigned
7244ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
7245 const BasicBlock *ExitingBlock) {
7246 assert(ExitingBlock && "Must pass a non-null exiting block!")((void)0);
7247 assert(L->isLoopExiting(ExitingBlock) &&((void)0)
7248 "Exiting block must actually branch out of the loop!")((void)0);
7249 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
7250 return getSmallConstantTripMultiple(L, ExitCount);
7251}
7252
7253const SCEV *ScalarEvolution::getExitCount(const Loop *L,
7254 const BasicBlock *ExitingBlock,
7255 ExitCountKind Kind) {
7256 switch (Kind) {
7257 case Exact:
7258 case SymbolicMaximum:
7259 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
7260 case ConstantMaximum:
7261 return getBackedgeTakenInfo(L).getConstantMax(ExitingBlock, this);
7262 };
7263 llvm_unreachable("Invalid ExitCountKind!")__builtin_unreachable();
7264}
7265
7266const SCEV *
7267ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
7268 SCEVUnionPredicate &Preds) {
7269 return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds);
7270}
7271
7272const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L,
7273 ExitCountKind Kind) {
7274 switch (Kind) {
7275 case Exact:
7276 return getBackedgeTakenInfo(L).getExact(L, this);
7277 case ConstantMaximum:
7278 return getBackedgeTakenInfo(L).getConstantMax(this);
7279 case SymbolicMaximum:
7280 return getBackedgeTakenInfo(L).getSymbolicMax(L, this);
7281 };
7282 llvm_unreachable("Invalid ExitCountKind!")__builtin_unreachable();
7283}
7284
7285bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
7286 return getBackedgeTakenInfo(L).isConstantMaxOrZero(this);
7287}
7288
7289/// Push PHI nodes in the header of the given loop onto the given Worklist.
7290static void
7291PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
7292 BasicBlock *Header = L->getHeader();
7293
7294 // Push all Loop-header PHIs onto the Worklist stack.
7295 for (PHINode &PN : Header->phis())
7296 Worklist.push_back(&PN);
7297}
7298
7299const ScalarEvolution::BackedgeTakenInfo &
7300ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
7301 auto &BTI = getBackedgeTakenInfo(L);
7302 if (BTI.hasFullInfo())
7303 return BTI;
7304
7305 auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
7306
7307 if (!Pair.second)
7308 return Pair.first->second;
7309
7310 BackedgeTakenInfo Result =
7311 computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
7312
7313 return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
7314}
7315
7316ScalarEvolution::BackedgeTakenInfo &
7317ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
7318 // Initially insert an invalid entry for this loop. If the insertion
7319 // succeeds, proceed to actually compute a backedge-taken count and
7320 // update the value. The temporary CouldNotCompute value tells SCEV
7321 // code elsewhere that it shouldn't attempt to request a new
7322 // backedge-taken count, which could result in infinite recursion.
7323 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
7324 BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
7325 if (!Pair.second)
7326 return Pair.first->second;
7327
7328 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
7329 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
7330 // must be cleared in this scope.
7331 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
7332
7333 // In product build, there are no usage of statistic.
7334 (void)NumTripCountsComputed;
7335 (void)NumTripCountsNotComputed;
7336#if LLVM_ENABLE_STATS0 || !defined(NDEBUG1)
7337 const SCEV *BEExact = Result.getExact(L, this);
7338 if (BEExact != getCouldNotCompute()) {
7339 assert(isLoopInvariant(BEExact, L) &&((void)0)
7340 isLoopInvariant(Result.getConstantMax(this), L) &&((void)0)
7341 "Computed backedge-taken count isn't loop invariant for loop!")((void)0);
7342 ++NumTripCountsComputed;
7343 } else if (Result.getConstantMax(this) == getCouldNotCompute() &&
7344 isa<PHINode>(L->getHeader()->begin())) {
7345 // Only count loops that have phi nodes as not being computable.
7346 ++NumTripCountsNotComputed;
7347 }
7348#endif // LLVM_ENABLE_STATS || !defined(NDEBUG)
7349
7350 // Now that we know more about the trip count for this loop, forget any
7351 // existing SCEV values for PHI nodes in this loop since they are only
7352 // conservative estimates made without the benefit of trip count
7353 // information. This is similar to the code in forgetLoop, except that
7354 // it handles SCEVUnknown PHI nodes specially.
7355 if (Result.hasAnyInfo()) {
7356 SmallVector<Instruction *, 16> Worklist;
7357 PushLoopPHIs(L, Worklist);
7358
7359 SmallPtrSet<Instruction *, 8> Discovered;
7360 while (!Worklist.empty()) {
7361 Instruction *I = Worklist.pop_back_val();
7362
7363 ValueExprMapType::iterator It =
7364 ValueExprMap.find_as(static_cast<Value *>(I));
7365 if (It != ValueExprMap.end()) {
7366 const SCEV *Old = It->second;
7367
7368 // SCEVUnknown for a PHI either means that it has an unrecognized
7369 // structure, or it's a PHI that's in the progress of being computed
7370 // by createNodeForPHI. In the former case, additional loop trip
7371 // count information isn't going to change anything. In the later
7372 // case, createNodeForPHI will perform the necessary updates on its
7373 // own when it gets to that point.
7374 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
7375 eraseValueFromMap(It->first);
7376 forgetMemoizedResults(Old);
7377 }
7378 if (PHINode *PN = dyn_cast<PHINode>(I))
7379 ConstantEvolutionLoopExitValue.erase(PN);
7380 }
7381
7382 // Since we don't need to invalidate anything for correctness and we're
7383 // only invalidating to make SCEV's results more precise, we get to stop
7384 // early to avoid invalidating too much. This is especially important in
7385 // cases like:
7386 //
7387 // %v = f(pn0, pn1) // pn0 and pn1 used through some other phi node
7388 // loop0:
7389 // %pn0 = phi
7390 // ...
7391 // loop1:
7392 // %pn1 = phi
7393 // ...
7394 //
7395 // where both loop0 and loop1's backedge taken count uses the SCEV
7396 // expression for %v. If we don't have the early stop below then in cases
7397 // like the above, getBackedgeTakenInfo(loop1) will clear out the trip
7398 // count for loop0 and getBackedgeTakenInfo(loop0) will clear out the trip
7399 // count for loop1, effectively nullifying SCEV's trip count cache.
7400 for (auto *U : I->users())
7401 if (auto *I = dyn_cast<Instruction>(U)) {
7402 auto *LoopForUser = LI.getLoopFor(I->getParent());
7403 if (LoopForUser && L->contains(LoopForUser) &&
7404 Discovered.insert(I).second)
7405 Worklist.push_back(I);
7406 }
7407 }
7408 }
7409
7410 // Re-lookup the insert position, since the call to
7411 // computeBackedgeTakenCount above could result in a
7412 // recusive call to getBackedgeTakenInfo (on a different
7413 // loop), which would invalidate the iterator computed
7414 // earlier.
7415 return BackedgeTakenCounts.find(L)->second = std::move(Result);
7416}
7417
7418void ScalarEvolution::forgetAllLoops() {
7419 // This method is intended to forget all info about loops. It should
7420 // invalidate caches as if the following happened:
7421 // - The trip counts of all loops have changed arbitrarily
7422 // - Every llvm::Value has been updated in place to produce a different
7423 // result.
7424 BackedgeTakenCounts.clear();
7425 PredicatedBackedgeTakenCounts.clear();
7426 LoopPropertiesCache.clear();
7427 ConstantEvolutionLoopExitValue.clear();
7428 ValueExprMap.clear();
7429 ValuesAtScopes.clear();
7430 LoopDispositions.clear();
7431 BlockDispositions.clear();
7432 UnsignedRanges.clear();
7433 SignedRanges.clear();
7434 ExprValueMap.clear();
7435 HasRecMap.clear();
7436 MinTrailingZerosCache.clear();
7437 PredicatedSCEVRewrites.clear();
7438}
7439
7440void ScalarEvolution::forgetLoop(const Loop *L) {
7441 SmallVector<const Loop *, 16> LoopWorklist(1, L);
7442 SmallVector<Instruction *, 32> Worklist;
7443 SmallPtrSet<Instruction *, 16> Visited;
7444
7445 // Iterate over all the loops and sub-loops to drop SCEV information.
7446 while (!LoopWorklist.empty()) {
7447 auto *CurrL = LoopWorklist.pop_back_val();
7448
7449 // Drop any stored trip count value.
7450 BackedgeTakenCounts.erase(CurrL);
7451 PredicatedBackedgeTakenCounts.erase(CurrL);
7452
7453 // Drop information about predicated SCEV rewrites for this loop.
7454 for (auto I = PredicatedSCEVRewrites.begin();
7455 I != PredicatedSCEVRewrites.end();) {
7456 std::pair<const SCEV *, const Loop *> Entry = I->first;
7457 if (Entry.second == CurrL)
7458 PredicatedSCEVRewrites.erase(I++);
7459 else
7460 ++I;
7461 }
7462
7463 auto LoopUsersItr = LoopUsers.find(CurrL);
7464 if (LoopUsersItr != LoopUsers.end()) {
7465 for (auto *S : LoopUsersItr->second)
7466 forgetMemoizedResults(S);
7467 LoopUsers.erase(LoopUsersItr);
7468 }
7469
7470 // Drop information about expressions based on loop-header PHIs.
7471 PushLoopPHIs(CurrL, Worklist);
7472
7473 while (!Worklist.empty()) {
7474 Instruction *I = Worklist.pop_back_val();
7475 if (!Visited.insert(I).second)
7476 continue;
7477
7478 ValueExprMapType::iterator It =
7479 ValueExprMap.find_as(static_cast<Value *>(I));
7480 if (It != ValueExprMap.end()) {
7481 eraseValueFromMap(It->first);
7482 forgetMemoizedResults(It->second);
7483 if (PHINode *PN = dyn_cast<PHINode>(I))
7484 ConstantEvolutionLoopExitValue.erase(PN);
7485 }
7486
7487 PushDefUseChildren(I, Worklist);
7488 }
7489
7490 LoopPropertiesCache.erase(CurrL);
7491 // Forget all contained loops too, to avoid dangling entries in the
7492 // ValuesAtScopes map.
7493 LoopWorklist.append(CurrL->begin(), CurrL->end());
7494 }
7495}
7496
7497void ScalarEvolution::forgetTopmostLoop(const Loop *L) {
7498 while (Loop *Parent = L->getParentLoop())
7499 L = Parent;
7500 forgetLoop(L);
7501}
7502
7503void ScalarEvolution::forgetValue(Value *V) {
7504 Instruction *I = dyn_cast<Instruction>(V);
7505 if (!I) return;
7506
7507 // Drop information about expressions based on loop-header PHIs.
7508 SmallVector<Instruction *, 16> Worklist;
7509 Worklist.push_back(I);
7510
7511 SmallPtrSet<Instruction *, 8> Visited;
7512 while (!Worklist.empty()) {
7513 I = Worklist.pop_back_val();
7514 if (!Visited.insert(I).second)
7515 continue;
7516
7517 ValueExprMapType::iterator It =
7518 ValueExprMap.find_as(static_cast<Value *>(I));
7519 if (It != ValueExprMap.end()) {
7520 eraseValueFromMap(It->first);
7521 forgetMemoizedResults(It->second);
7522 if (PHINode *PN = dyn_cast<PHINode>(I))
7523 ConstantEvolutionLoopExitValue.erase(PN);
7524 }
7525
7526 PushDefUseChildren(I, Worklist);
7527 }
7528}
7529
7530void ScalarEvolution::forgetLoopDispositions(const Loop *L) {
7531 LoopDispositions.clear();
7532}
7533
7534/// Get the exact loop backedge taken count considering all loop exits. A
7535/// computable result can only be returned for loops with all exiting blocks
7536/// dominating the latch. howFarToZero assumes that the limit of each loop test
7537/// is never skipped. This is a valid assumption as long as the loop exits via
7538/// that test. For precise results, it is the caller's responsibility to specify
7539/// the relevant loop exiting block using getExact(ExitingBlock, SE).
7540const SCEV *
7541ScalarEvolution::BackedgeTakenInfo::getExact(const Loop *L, ScalarEvolution *SE,
7542 SCEVUnionPredicate *Preds) const {
7543 // If any exits were not computable, the loop is not computable.
7544 if (!isComplete() || ExitNotTaken.empty())
7545 return SE->getCouldNotCompute();
7546
7547 const BasicBlock *Latch = L->getLoopLatch();
7548 // All exiting blocks we have collected must dominate the only backedge.
7549 if (!Latch)
7550 return SE->getCouldNotCompute();
7551
7552 // All exiting blocks we have gathered dominate loop's latch, so exact trip
7553 // count is simply a minimum out of all these calculated exit counts.
7554 SmallVector<const SCEV *, 2> Ops;
7555 for (auto &ENT : ExitNotTaken) {
7556 const SCEV *BECount = ENT.ExactNotTaken;
7557 assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!")((void)0);
7558 assert(SE->DT.dominates(ENT.ExitingBlock, Latch) &&((void)0)
7559 "We should only have known counts for exiting blocks that dominate "((void)0)
7560 "latch!")((void)0);
7561
7562 Ops.push_back(BECount);
7563
7564 if (Preds && !ENT.hasAlwaysTruePredicate())
7565 Preds->add(ENT.Predicate.get());
7566
7567 assert((Preds || ENT.hasAlwaysTruePredicate()) &&((void)0)
7568 "Predicate should be always true!")((void)0);
7569 }
7570
7571 return SE->getUMinFromMismatchedTypes(Ops);
7572}
7573
7574/// Get the exact not taken count for this loop exit.
7575const SCEV *
7576ScalarEvolution::BackedgeTakenInfo::getExact(const BasicBlock *ExitingBlock,
7577 ScalarEvolution *SE) const {
7578 for (auto &ENT : ExitNotTaken)
7579 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
7580 return ENT.ExactNotTaken;
7581
7582 return SE->getCouldNotCompute();
7583}
7584
7585const SCEV *ScalarEvolution::BackedgeTakenInfo::getConstantMax(
7586 const BasicBlock *ExitingBlock, ScalarEvolution *SE) const {
7587 for (auto &ENT : ExitNotTaken)
7588 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
7589 return ENT.MaxNotTaken;
7590
7591 return SE->getCouldNotCompute();
7592}
7593
7594/// getConstantMax - Get the constant max backedge taken count for the loop.
7595const SCEV *
7596ScalarEvolution::BackedgeTakenInfo::getConstantMax(ScalarEvolution *SE) const {
7597 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
7598 return !ENT.hasAlwaysTruePredicate();
7599 };
7600
7601 if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getConstantMax())
7602 return SE->getCouldNotCompute();
7603
7604 assert((isa<SCEVCouldNotCompute>(getConstantMax()) ||((void)0)
7605 isa<SCEVConstant>(getConstantMax())) &&((void)0)
7606 "No point in having a non-constant max backedge taken count!")((void)0);
7607 return getConstantMax();
7608}
7609
7610const SCEV *
7611ScalarEvolution::BackedgeTakenInfo::getSymbolicMax(const Loop *L,
7612 ScalarEvolution *SE) {
7613 if (!SymbolicMax)
7614 SymbolicMax = SE->computeSymbolicMaxBackedgeTakenCount(L);
7615 return SymbolicMax;
7616}
7617
7618bool ScalarEvolution::BackedgeTakenInfo::isConstantMaxOrZero(
7619 ScalarEvolution *SE) const {
7620 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
7621 return !ENT.hasAlwaysTruePredicate();
7622 };
7623 return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
7624}
7625
7626bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S) const {
7627 return Operands.contains(S);
7628}
7629
7630ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
7631 : ExitLimit(E, E, false, None) {
7632}
7633
7634ScalarEvolution::ExitLimit::ExitLimit(
7635 const SCEV *E, const SCEV *M, bool MaxOrZero,
7636 ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList)
7637 : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) {
7638 assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||((void)0)
7639 !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&((void)0)
7640 "Exact is not allowed to be less precise than Max")((void)0);
7641 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||((void)0)
7642 isa<SCEVConstant>(MaxNotTaken)) &&((void)0)
7643 "No point in having a non-constant max backedge taken count!")((void)0);
7644 for (auto *PredSet : PredSetList)
7645 for (auto *P : *PredSet)
7646 addPredicate(P);
7647 assert((isa<SCEVCouldNotCompute>(E) || !E->getType()->isPointerTy()) &&((void)0)
7648 "Backedge count should be int")((void)0);
7649 assert((isa<SCEVCouldNotCompute>(M) || !M->getType()->isPointerTy()) &&((void)0)
7650 "Max backedge count should be int")((void)0);
7651}
7652
7653ScalarEvolution::ExitLimit::ExitLimit(
7654 const SCEV *E, const SCEV *M, bool MaxOrZero,
7655 const SmallPtrSetImpl<const SCEVPredicate *> &PredSet)
7656 : ExitLimit(E, M, MaxOrZero, {&PredSet}) {
7657}
7658
7659ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M,
7660 bool MaxOrZero)
7661 : ExitLimit(E, M, MaxOrZero, None) {
7662}
7663
7664class SCEVRecordOperands {
7665 SmallPtrSetImpl<const SCEV *> &Operands;
7666
7667public:
7668 SCEVRecordOperands(SmallPtrSetImpl<const SCEV *> &Operands)
7669 : Operands(Operands) {}
7670 bool follow(const SCEV *S) {
7671 Operands.insert(S);
7672 return true;
7673 }
7674 bool isDone() { return false; }
7675};
7676
7677/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
7678/// computable exit into a persistent ExitNotTakenInfo array.
7679ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
7680 ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo> ExitCounts,
7681 bool IsComplete, const SCEV *ConstantMax, bool MaxOrZero)
7682 : ConstantMax(ConstantMax), IsComplete(IsComplete), MaxOrZero(MaxOrZero) {
7683 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
7684
7685 ExitNotTaken.reserve(ExitCounts.size());
7686 std::transform(
7687 ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken),
7688 [&](const EdgeExitInfo &EEI) {
7689 BasicBlock *ExitBB = EEI.first;
7690 const ExitLimit &EL = EEI.second;
7691 if (EL.Predicates.empty())
7692 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
7693 nullptr);
7694
7695 std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate);
7696 for (auto *Pred : EL.Predicates)
7697 Predicate->add(Pred);
7698
7699 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
7700 std::move(Predicate));
7701 });
7702 assert((isa<SCEVCouldNotCompute>(ConstantMax) ||((void)0)
7703 isa<SCEVConstant>(ConstantMax)) &&((void)0)
7704 "No point in having a non-constant max backedge taken count!")((void)0);
7705
7706 SCEVRecordOperands RecordOperands(Operands);
7707 SCEVTraversal<SCEVRecordOperands> ST(RecordOperands);
7708 if (!isa<SCEVCouldNotCompute>(ConstantMax))
7709 ST.visitAll(ConstantMax);
7710 for (auto &ENT : ExitNotTaken)
7711 if (!isa<SCEVCouldNotCompute>(ENT.ExactNotTaken))
7712 ST.visitAll(ENT.ExactNotTaken);
7713}
7714
7715/// Compute the number of times the backedge of the specified loop will execute.
7716ScalarEvolution::BackedgeTakenInfo
7717ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
7718 bool AllowPredicates) {
7719 SmallVector<BasicBlock *, 8> ExitingBlocks;
7720 L->getExitingBlocks(ExitingBlocks);
7721
7722 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
7723
7724 SmallVector<EdgeExitInfo, 4> ExitCounts;
7725 bool CouldComputeBECount = true;
7726 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
7727 const SCEV *MustExitMaxBECount = nullptr;
7728 const SCEV *MayExitMaxBECount = nullptr;
7729 bool MustExitMaxOrZero = false;
7730
7731 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
7732 // and compute maxBECount.
7733 // Do a union of all the predicates here.
7734 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
7735 BasicBlock *ExitBB = ExitingBlocks[i];
7736
7737 // We canonicalize untaken exits to br (constant), ignore them so that
7738 // proving an exit untaken doesn't negatively impact our ability to reason
7739 // about the loop as whole.
7740 if (auto *BI = dyn_cast<BranchInst>(ExitBB->getTerminator()))
7741 if (auto *CI = dyn_cast<ConstantInt>(BI->getCondition())) {
7742 bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
7743 if ((ExitIfTrue && CI->isZero()) || (!ExitIfTrue && CI->isOne()))
7744 continue;
7745 }
7746
7747 ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
7748
7749 assert((AllowPredicates || EL.Predicates.empty()) &&((void)0)
7750 "Predicated exit limit when predicates are not allowed!")((void)0);
7751
7752 // 1. For each exit that can be computed, add an entry to ExitCounts.
7753 // CouldComputeBECount is true only if all exits can be computed.
7754 if (EL.ExactNotTaken == getCouldNotCompute())
7755 // We couldn't compute an exact value for this exit, so
7756 // we won't be able to compute an exact value for the loop.
7757 CouldComputeBECount = false;
7758 else
7759 ExitCounts.emplace_back(ExitBB, EL);
7760
7761 // 2. Derive the loop's MaxBECount from each exit's max number of
7762 // non-exiting iterations. Partition the loop exits into two kinds:
7763 // LoopMustExits and LoopMayExits.
7764 //
7765 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
7766 // is a LoopMayExit. If any computable LoopMustExit is found, then
7767 // MaxBECount is the minimum EL.MaxNotTaken of computable
7768 // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
7769 // EL.MaxNotTaken, where CouldNotCompute is considered greater than any
7770 // computable EL.MaxNotTaken.
7771 if (EL.MaxNotTaken != getCouldNotCompute() && Latch &&
7772 DT.dominates(ExitBB, Latch)) {
7773 if (!MustExitMaxBECount) {
7774 MustExitMaxBECount = EL.MaxNotTaken;
7775 MustExitMaxOrZero = EL.MaxOrZero;
7776 } else {
7777 MustExitMaxBECount =
7778 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken);
7779 }
7780 } else if (MayExitMaxBECount != getCouldNotCompute()) {
7781 if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute())
7782 MayExitMaxBECount = EL.MaxNotTaken;
7783 else {
7784 MayExitMaxBECount =
7785 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken);
7786 }
7787 }
7788 }
7789 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
7790 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
7791 // The loop backedge will be taken the maximum or zero times if there's
7792 // a single exit that must be taken the maximum or zero times.
7793 bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
7794 return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
7795 MaxBECount, MaxOrZero);
7796}
7797
7798ScalarEvolution::ExitLimit
7799ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
7800 bool AllowPredicates) {
7801 assert(L->contains(ExitingBlock) && "Exit count for non-loop block?")((void)0);
7802 // If our exiting block does not dominate the latch, then its connection with
7803 // loop's exit limit may be far from trivial.
7804 const BasicBlock *Latch = L->getLoopLatch();
7805 if (!Latch || !DT.dominates(ExitingBlock, Latch))
7806 return getCouldNotCompute();
7807
7808 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
7809 Instruction *Term = ExitingBlock->getTerminator();
7810 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
7811 assert(BI->isConditional() && "If unconditional, it can't be in loop!")((void)0);
7812 bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
7813 assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) &&((void)0)
7814 "It should have one successor in loop and one exit block!")((void)0);
7815 // Proceed to the next level to examine the exit condition expression.
7816 return computeExitLimitFromCond(
7817 L, BI->getCondition(), ExitIfTrue,
7818 /*ControlsExit=*/IsOnlyExit, AllowPredicates);
7819 }
7820
7821 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) {
7822 // For switch, make sure that there is a single exit from the loop.
7823 BasicBlock *Exit = nullptr;
7824 for (auto *SBB : successors(ExitingBlock))
7825 if (!L->contains(SBB)) {
7826 if (Exit) // Multiple exit successors.
7827 return getCouldNotCompute();
7828 Exit = SBB;
7829 }
7830 assert(Exit && "Exiting block must have at least one exit")((void)0);
7831 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
7832 /*ControlsExit=*/IsOnlyExit);
7833 }
7834
7835 return getCouldNotCompute();
7836}
7837
7838ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
7839 const Loop *L, Value *ExitCond, bool ExitIfTrue,
7840 bool ControlsExit, bool AllowPredicates) {
7841 ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates);
7842 return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue,
7843 ControlsExit, AllowPredicates);
7844}
7845
7846Optional<ScalarEvolution::ExitLimit>
7847ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
7848 bool ExitIfTrue, bool ControlsExit,
7849 bool AllowPredicates) {
7850 (void)this->L;
7851 (void)this->ExitIfTrue;
7852 (void)this->AllowPredicates;
7853
7854 assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&((void)0)
7855 this->AllowPredicates == AllowPredicates &&((void)0)
7856 "Variance in assumed invariant key components!")((void)0);
7857 auto Itr = TripCountMap.find({ExitCond, ControlsExit});
7858 if (Itr == TripCountMap.end())
7859 return None;
7860 return Itr->second;
7861}
7862
7863void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
7864 bool ExitIfTrue,
7865 bool ControlsExit,
7866 bool AllowPredicates,
7867 const ExitLimit &EL) {
7868 assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&((void)0)
7869 this->AllowPredicates == AllowPredicates &&((void)0)
7870 "Variance in assumed invariant key components!")((void)0);
7871
7872 auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL});
7873 assert(InsertResult.second && "Expected successful insertion!")((void)0);
7874 (void)InsertResult;
7875 (void)ExitIfTrue;
7876}
7877
7878ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
7879 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
7880 bool ControlsExit, bool AllowPredicates) {
7881
7882 if (auto MaybeEL =
7883 Cache.find(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates))
7884 return *MaybeEL;
7885
7886 ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, ExitIfTrue,
7887 ControlsExit, AllowPredicates);
7888 Cache.insert(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates, EL);
7889 return EL;
7890}
7891
7892ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
7893 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
7894 bool ControlsExit, bool AllowPredicates) {
7895 // Handle BinOp conditions (And, Or).
7896 if (auto LimitFromBinOp = computeExitLimitFromCondFromBinOp(
7897 Cache, L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates))
7898 return *LimitFromBinOp;
7899
7900 // With an icmp, it may be feasible to compute an exact backedge-taken count.
7901 // Proceed to the next level to examine the icmp.
7902 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
7903 ExitLimit EL =
7904 computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit);
7905 if (EL.hasFullInfo() || !AllowPredicates)
7906 return EL;
7907
7908 // Try again, but use SCEV predicates this time.
7909 return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit,
7910 /*AllowPredicates=*/true);
7911 }
7912
7913 // Check for a constant condition. These are normally stripped out by
7914 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
7915 // preserve the CFG and is temporarily leaving constant conditions
7916 // in place.
7917 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
7918 if (ExitIfTrue == !CI->getZExtValue())
7919 // The backedge is always taken.
7920 return getCouldNotCompute();
7921 else
7922 // The backedge is never taken.
7923 return getZero(CI->getType());
7924 }
7925
7926 // If it's not an integer or pointer comparison then compute it the hard way.
7927 return computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
7928}
7929
7930Optional<ScalarEvolution::ExitLimit>
7931ScalarEvolution::computeExitLimitFromCondFromBinOp(
7932 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
7933 bool ControlsExit, bool AllowPredicates) {
7934 // Check if the controlling expression for this loop is an And or Or.
7935 Value *Op0, *Op1;
7936 bool IsAnd = false;
7937 if (match(ExitCond, m_LogicalAnd(m_Value(Op0), m_Value(Op1))))
7938 IsAnd = true;
7939 else if (match(ExitCond, m_LogicalOr(m_Value(Op0), m_Value(Op1))))
7940 IsAnd = false;
7941 else
7942 return None;
7943
7944 // EitherMayExit is true in these two cases:
7945 // br (and Op0 Op1), loop, exit
7946 // br (or Op0 Op1), exit, loop
7947 bool EitherMayExit = IsAnd ^ ExitIfTrue;
7948 ExitLimit EL0 = computeExitLimitFromCondCached(Cache, L, Op0, ExitIfTrue,
7949 ControlsExit && !EitherMayExit,
7950 AllowPredicates);
7951 ExitLimit EL1 = computeExitLimitFromCondCached(Cache, L, Op1, ExitIfTrue,
7952 ControlsExit && !EitherMayExit,
7953 AllowPredicates);
7954
7955 // Be robust against unsimplified IR for the form "op i1 X, NeutralElement"
7956 const Constant *NeutralElement = ConstantInt::get(ExitCond->getType(), IsAnd);
7957 if (isa<ConstantInt>(Op1))
7958 return Op1 == NeutralElement ? EL0 : EL1;
7959 if (isa<ConstantInt>(Op0))
7960 return Op0 == NeutralElement ? EL1 : EL0;
7961
7962 const SCEV *BECount = getCouldNotCompute();
7963 const SCEV *MaxBECount = getCouldNotCompute();
7964 if (EitherMayExit) {
7965 // Both conditions must be same for the loop to continue executing.
7966 // Choose the less conservative count.
7967 // If ExitCond is a short-circuit form (select), using
7968 // umin(EL0.ExactNotTaken, EL1.ExactNotTaken) is unsafe in general.
7969 // To see the detailed examples, please see
7970 // test/Analysis/ScalarEvolution/exit-count-select.ll
7971 bool PoisonSafe = isa<BinaryOperator>(ExitCond);
7972 if (!PoisonSafe)
7973 // Even if ExitCond is select, we can safely derive BECount using both
7974 // EL0 and EL1 in these cases:
7975 // (1) EL0.ExactNotTaken is non-zero
7976 // (2) EL1.ExactNotTaken is non-poison
7977 // (3) EL0.ExactNotTaken is zero (BECount should be simply zero and
7978 // it cannot be umin(0, ..))
7979 // The PoisonSafe assignment below is simplified and the assertion after
7980 // BECount calculation fully guarantees the condition (3).
7981 PoisonSafe = isa<SCEVConstant>(EL0.ExactNotTaken) ||
7982 isa<SCEVConstant>(EL1.ExactNotTaken);
7983 if (EL0.ExactNotTaken != getCouldNotCompute() &&
7984 EL1.ExactNotTaken != getCouldNotCompute() && PoisonSafe) {
7985 BECount =
7986 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
7987
7988 // If EL0.ExactNotTaken was zero and ExitCond was a short-circuit form,
7989 // it should have been simplified to zero (see the condition (3) above)
7990 assert(!isa<BinaryOperator>(ExitCond) || !EL0.ExactNotTaken->isZero() ||((void)0)
7991 BECount->isZero())((void)0);
7992 }
7993 if (EL0.MaxNotTaken == getCouldNotCompute())
7994 MaxBECount = EL1.MaxNotTaken;
7995 else if (EL1.MaxNotTaken == getCouldNotCompute())
7996 MaxBECount = EL0.MaxNotTaken;
7997 else
7998 MaxBECount = getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
7999 } else {
8000 // Both conditions must be same at the same time for the loop to exit.
8001 // For now, be conservative.
8002 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
8003 BECount = EL0.ExactNotTaken;
8004 }
8005
8006 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
8007 // to be more aggressive when computing BECount than when computing
8008 // MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
8009 // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
8010 // to not.
8011 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
8012 !isa<SCEVCouldNotCompute>(BECount))
8013 MaxBECount = getConstant(getUnsignedRangeMax(BECount));
8014
8015 return ExitLimit(BECount, MaxBECount, false,
8016 { &EL0.Predicates, &EL1.Predicates });
8017}
8018
8019ScalarEvolution::ExitLimit
8020ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
8021 ICmpInst *ExitCond,
8022 bool ExitIfTrue,
8023 bool ControlsExit,
8024 bool AllowPredicates) {
8025 // If the condition was exit on true, convert the condition to exit on false
8026 ICmpInst::Predicate Pred;
8027 if (!ExitIfTrue)
8028 Pred = ExitCond->getPredicate();
8029 else
8030 Pred = ExitCond->getInversePredicate();
8031 const ICmpInst::Predicate OriginalPred = Pred;
8032
8033 // Handle common loops like: for (X = "string"; *X; ++X)
8034 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
8035 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
8036 ExitLimit ItCnt =
8037 computeLoadConstantCompareExitLimit(LI, RHS, L, Pred);
8038 if (ItCnt.hasAnyInfo())
8039 return ItCnt;
8040 }
8041
8042 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
8043 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
8044
8045 // Try to evaluate any dependencies out of the loop.
8046 LHS = getSCEVAtScope(LHS, L);
8047 RHS = getSCEVAtScope(RHS, L);
8048
8049 // At this point, we would like to compute how many iterations of the
8050 // loop the predicate will return true for these inputs.
8051 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
8052 // If there is a loop-invariant, force it into the RHS.
8053 std::swap(LHS, RHS);
8054 Pred = ICmpInst::getSwappedPredicate(Pred);
8055 }
8056
8057 // Simplify the operands before analyzing them.
8058 (void)SimplifyICmpOperands(Pred, LHS, RHS);
8059
8060 // If we have a comparison of a chrec against a constant, try to use value
8061 // ranges to answer this query.
8062 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
8063 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
8064 if (AddRec->getLoop() == L) {
8065 // Form the constant range.
8066 ConstantRange CompRange =
8067 ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt());
8068
8069 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
8070 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
8071 }
8072
8073 switch (Pred) {
8074 case ICmpInst::ICMP_NE: { // while (X != Y)
8075 // Convert to: while (X-Y != 0)
8076 if (LHS->getType()->isPointerTy()) {
8077 LHS = getLosslessPtrToIntExpr(LHS);
8078 if (isa<SCEVCouldNotCompute>(LHS))
8079 return LHS;
8080 }
8081 if (RHS->getType()->isPointerTy()) {
8082 RHS = getLosslessPtrToIntExpr(RHS);
8083 if (isa<SCEVCouldNotCompute>(RHS))
8084 return RHS;
8085 }
8086 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
8087 AllowPredicates);
8088 if (EL.hasAnyInfo()) return EL;
8089 break;
8090 }
8091 case ICmpInst::ICMP_EQ: { // while (X == Y)
8092 // Convert to: while (X-Y == 0)
8093 if (LHS->getType()->isPointerTy()) {
8094 LHS = getLosslessPtrToIntExpr(LHS);
8095 if (isa<SCEVCouldNotCompute>(LHS))
8096 return LHS;
8097 }
8098 if (RHS->getType()->isPointerTy()) {
8099 RHS = getLosslessPtrToIntExpr(RHS);
8100 if (isa<SCEVCouldNotCompute>(RHS))
8101 return RHS;
8102 }
8103 ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
8104 if (EL.hasAnyInfo()) return EL;
8105 break;
8106 }
8107 case ICmpInst::ICMP_SLT:
8108 case ICmpInst::ICMP_ULT: { // while (X < Y)
8109 bool IsSigned = Pred == ICmpInst::ICMP_SLT;
8110 ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
8111 AllowPredicates);
8112 if (EL.hasAnyInfo()) return EL;
8113 break;
8114 }
8115 case ICmpInst::ICMP_SGT:
8116 case ICmpInst::ICMP_UGT: { // while (X > Y)
8117 bool IsSigned = Pred == ICmpInst::ICMP_SGT;
8118 ExitLimit EL =
8119 howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
8120 AllowPredicates);
8121 if (EL.hasAnyInfo()) return EL;
8122 break;
8123 }
8124 default:
8125 break;
8126 }
8127
8128 auto *ExhaustiveCount =
8129 computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
8130
8131 if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
8132 return ExhaustiveCount;
8133
8134 return computeShiftCompareExitLimit(ExitCond->getOperand(0),
8135 ExitCond->getOperand(1), L, OriginalPred);
8136}
8137
8138ScalarEvolution::ExitLimit
8139ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
8140 SwitchInst *Switch,
8141 BasicBlock *ExitingBlock,
8142 bool ControlsExit) {
8143 assert(!L->contains(ExitingBlock) && "Not an exiting block!")((void)0);
8144
8145 // Give up if the exit is the default dest of a switch.
8146 if (Switch->getDefaultDest() == ExitingBlock)
8147 return getCouldNotCompute();
8148
8149 assert(L->contains(Switch->getDefaultDest()) &&((void)0)
8150 "Default case must not exit the loop!")((void)0);
8151 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
8152 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
8153
8154 // while (X != Y) --> while (X-Y != 0)
8155 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
8156 if (EL.hasAnyInfo())
8157 return EL;
8158
8159 return getCouldNotCompute();
8160}
8161
8162static ConstantInt *
8163EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
8164 ScalarEvolution &SE) {
8165 const SCEV *InVal = SE.getConstant(C);
8166 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
8167 assert(isa<SCEVConstant>(Val) &&((void)0)
8168 "Evaluation of SCEV at constant didn't fold correctly?")((void)0);
8169 return cast<SCEVConstant>(Val)->getValue();
8170}
8171
8172/// Given an exit condition of 'icmp op load X, cst', try to see if we can
8173/// compute the backedge execution count.
8174ScalarEvolution::ExitLimit
8175ScalarEvolution::computeLoadConstantCompareExitLimit(
8176 LoadInst *LI,
8177 Constant *RHS,
8178 const Loop *L,
8179 ICmpInst::Predicate predicate) {
8180 if (LI->isVolatile()) return getCouldNotCompute();
8181
8182 // Check to see if the loaded pointer is a getelementptr of a global.
8183 // TODO: Use SCEV instead of manually grubbing with GEPs.
8184 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
8185 if (!GEP) return getCouldNotCompute();
8186
8187 // Make sure that it is really a constant global we are gepping, with an
8188 // initializer, and make sure the first IDX is really 0.
8189 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
8190 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
8191 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
8192 !cast<Constant>(GEP->getOperand(1))->isNullValue())
8193 return getCouldNotCompute();
8194
8195 // Okay, we allow one non-constant index into the GEP instruction.
8196 Value *VarIdx = nullptr;
8197 std::vector<Constant*> Indexes;
8198 unsigned VarIdxNum = 0;
8199 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
8200 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
8201 Indexes.push_back(CI);
8202 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
8203 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
8204 VarIdx = GEP->getOperand(i);
8205 VarIdxNum = i-2;
8206 Indexes.push_back(nullptr);
8207 }
8208
8209 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
8210 if (!VarIdx)
8211 return getCouldNotCompute();
8212
8213 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
8214 // Check to see if X is a loop variant variable value now.
8215 const SCEV *Idx = getSCEV(VarIdx);
8216 Idx = getSCEVAtScope(Idx, L);
8217
8218 // We can only recognize very limited forms of loop index expressions, in
8219 // particular, only affine AddRec's like {C1,+,C2}<L>.
8220 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
8221 if (!IdxExpr || IdxExpr->getLoop() != L || !IdxExpr->isAffine() ||
8222 isLoopInvariant(IdxExpr, L) ||
8223 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
8224 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
8225 return getCouldNotCompute();
8226
8227 unsigned MaxSteps = MaxBruteForceIterations;
8228 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
8229 ConstantInt *ItCst = ConstantInt::get(
8230 cast<IntegerType>(IdxExpr->getType()), IterationNum);
8231 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
8232
8233 // Form the GEP offset.
8234 Indexes[VarIdxNum] = Val;
8235
8236 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
8237 Indexes);
8238 if (!Result) break; // Cannot compute!
8239
8240 // Evaluate the condition for this iteration.
8241 Result = ConstantExpr::getICmp(predicate, Result, RHS);
8242 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
8243 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
8244 ++NumArrayLenItCounts;
8245 return getConstant(ItCst); // Found terminating iteration!
8246 }
8247 }
8248 return getCouldNotCompute();
8249}
8250
8251ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
8252 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
8253 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
8254 if (!RHS)
8255 return getCouldNotCompute();
8256
8257 const BasicBlock *Latch = L->getLoopLatch();
8258 if (!Latch)
8259 return getCouldNotCompute();
8260
8261 const BasicBlock *Predecessor = L->getLoopPredecessor();
8262 if (!Predecessor)
8263 return getCouldNotCompute();
8264
8265 // Return true if V is of the form "LHS `shift_op` <positive constant>".
8266 // Return LHS in OutLHS and shift_opt in OutOpCode.
8267 auto MatchPositiveShift =
8268 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
8269
8270 using namespace PatternMatch;
8271
8272 ConstantInt *ShiftAmt;
8273 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
8274 OutOpCode = Instruction::LShr;
8275 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
8276 OutOpCode = Instruction::AShr;
8277 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
8278 OutOpCode = Instruction::Shl;
8279 else
8280 return false;
8281
8282 return ShiftAmt->getValue().isStrictlyPositive();
8283 };
8284
8285 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
8286 //
8287 // loop:
8288 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
8289 // %iv.shifted = lshr i32 %iv, <positive constant>
8290 //
8291 // Return true on a successful match. Return the corresponding PHI node (%iv
8292 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
8293 auto MatchShiftRecurrence =
8294 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
8295 Optional<Instruction::BinaryOps> PostShiftOpCode;
8296
8297 {
8298 Instruction::BinaryOps OpC;
8299 Value *V;
8300
8301 // If we encounter a shift instruction, "peel off" the shift operation,
8302 // and remember that we did so. Later when we inspect %iv's backedge
8303 // value, we will make sure that the backedge value uses the same
8304 // operation.
8305 //
8306 // Note: the peeled shift operation does not have to be the same
8307 // instruction as the one feeding into the PHI's backedge value. We only
8308 // really care about it being the same *kind* of shift instruction --
8309 // that's all that is required for our later inferences to hold.
8310 if (MatchPositiveShift(LHS, V, OpC)) {
8311 PostShiftOpCode = OpC;
8312 LHS = V;
8313 }
8314 }
8315
8316 PNOut = dyn_cast<PHINode>(LHS);
8317 if (!PNOut || PNOut->getParent() != L->getHeader())
8318 return false;
8319
8320 Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
8321 Value *OpLHS;
8322
8323 return
8324 // The backedge value for the PHI node must be a shift by a positive
8325 // amount
8326 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
8327
8328 // of the PHI node itself
8329 OpLHS == PNOut &&
8330
8331 // and the kind of shift should be match the kind of shift we peeled
8332 // off, if any.
8333 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
8334 };
8335
8336 PHINode *PN;
8337 Instruction::BinaryOps OpCode;
8338 if (!MatchShiftRecurrence(LHS, PN, OpCode))
8339 return getCouldNotCompute();
8340
8341 const DataLayout &DL = getDataLayout();
8342
8343 // The key rationale for this optimization is that for some kinds of shift
8344 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
8345 // within a finite number of iterations. If the condition guarding the
8346 // backedge (in the sense that the backedge is taken if the condition is true)
8347 // is false for the value the shift recurrence stabilizes to, then we know
8348 // that the backedge is taken only a finite number of times.
8349
8350 ConstantInt *StableValue = nullptr;
8351 switch (OpCode) {
8352 default:
8353 llvm_unreachable("Impossible case!")__builtin_unreachable();
8354
8355 case Instruction::AShr: {
8356 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
8357 // bitwidth(K) iterations.
8358 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
8359 KnownBits Known = computeKnownBits(FirstValue, DL, 0, &AC,
8360 Predecessor->getTerminator(), &DT);
8361 auto *Ty = cast<IntegerType>(RHS->getType());
8362 if (Known.isNonNegative())
8363 StableValue = ConstantInt::get(Ty, 0);
8364 else if (Known.isNegative())
8365 StableValue = ConstantInt::get(Ty, -1, true);
8366 else
8367 return getCouldNotCompute();
8368
8369 break;
8370 }
8371 case Instruction::LShr:
8372 case Instruction::Shl:
8373 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
8374 // stabilize to 0 in at most bitwidth(K) iterations.
8375 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
8376 break;
8377 }
8378
8379 auto *Result =
8380 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
8381 assert(Result->getType()->isIntegerTy(1) &&((void)0)
8382 "Otherwise cannot be an operand to a branch instruction")((void)0);
8383
8384 if (Result->isZeroValue()) {
8385 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8386 const SCEV *UpperBound =
8387 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
8388 return ExitLimit(getCouldNotCompute(), UpperBound, false);
8389 }
8390
8391 return getCouldNotCompute();
8392}
8393
8394/// Return true if we can constant fold an instruction of the specified type,
8395/// assuming that all operands were constants.
8396static bool CanConstantFold(const Instruction *I) {
8397 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
8398 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
8399 isa<LoadInst>(I) || isa<ExtractValueInst>(I))
8400 return true;
8401
8402 if (const CallInst *CI = dyn_cast<CallInst>(I))
8403 if (const Function *F = CI->getCalledFunction())
8404 return canConstantFoldCallTo(CI, F);
8405 return false;
8406}
8407
8408/// Determine whether this instruction can constant evolve within this loop
8409/// assuming its operands can all constant evolve.
8410static bool canConstantEvolve(Instruction *I, const Loop *L) {
8411 // An instruction outside of the loop can't be derived from a loop PHI.
8412 if (!L->contains(I)) return false;
8413
8414 if (isa<PHINode>(I)) {
8415 // We don't currently keep track of the control flow needed to evaluate
8416 // PHIs, so we cannot handle PHIs inside of loops.
8417 return L->getHeader() == I->getParent();
8418 }
8419
8420 // If we won't be able to constant fold this expression even if the operands
8421 // are constants, bail early.
8422 return CanConstantFold(I);
8423}
8424
8425/// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
8426/// recursing through each instruction operand until reaching a loop header phi.
8427static PHINode *
8428getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
8429 DenseMap<Instruction *, PHINode *> &PHIMap,
8430 unsigned Depth) {
8431 if (Depth > MaxConstantEvolvingDepth)
8432 return nullptr;
8433
8434 // Otherwise, we can evaluate this instruction if all of its operands are
8435 // constant or derived from a PHI node themselves.
8436 PHINode *PHI = nullptr;
8437 for (Value *Op : UseInst->operands()) {
8438 if (isa<Constant>(Op)) continue;
8439
8440 Instruction *OpInst = dyn_cast<Instruction>(Op);
8441 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
8442
8443 PHINode *P = dyn_cast<PHINode>(OpInst);
8444 if (!P)
8445 // If this operand is already visited, reuse the prior result.
8446 // We may have P != PHI if this is the deepest point at which the
8447 // inconsistent paths meet.
8448 P = PHIMap.lookup(OpInst);
8449 if (!P) {
8450 // Recurse and memoize the results, whether a phi is found or not.
8451 // This recursive call invalidates pointers into PHIMap.
8452 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1);
8453 PHIMap[OpInst] = P;
8454 }
8455 if (!P)
8456 return nullptr; // Not evolving from PHI
8457 if (PHI && PHI != P)
8458 return nullptr; // Evolving from multiple different PHIs.
8459 PHI = P;
8460 }
8461 // This is a expression evolving from a constant PHI!
8462 return PHI;
8463}
8464
8465/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
8466/// in the loop that V is derived from. We allow arbitrary operations along the
8467/// way, but the operands of an operation must either be constants or a value
8468/// derived from a constant PHI. If this expression does not fit with these
8469/// constraints, return null.
8470static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
8471 Instruction *I = dyn_cast<Instruction>(V);
8472 if (!I || !canConstantEvolve(I, L)) return nullptr;
8473
8474 if (PHINode *PN = dyn_cast<PHINode>(I))
8475 return PN;
8476
8477 // Record non-constant instructions contained by the loop.
8478 DenseMap<Instruction *, PHINode *> PHIMap;
8479 return getConstantEvolvingPHIOperands(I, L, PHIMap, 0);
8480}
8481
8482/// EvaluateExpression - Given an expression that passes the
8483/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
8484/// in the loop has the value PHIVal. If we can't fold this expression for some
8485/// reason, return null.
8486static Constant *EvaluateExpression(Value *V, const Loop *L,
8487 DenseMap<Instruction *, Constant *> &Vals,
8488 const DataLayout &DL,
8489 const TargetLibraryInfo *TLI) {
8490 // Convenient constant check, but redundant for recursive calls.
8491 if (Constant *C = dyn_cast<Constant>(V)) return C;
8492 Instruction *I = dyn_cast<Instruction>(V);
8493 if (!I) return nullptr;
8494
8495 if (Constant *C = Vals.lookup(I)) return C;
8496
8497 // An instruction inside the loop depends on a value outside the loop that we
8498 // weren't given a mapping for, or a value such as a call inside the loop.
8499 if (!canConstantEvolve(I, L)) return nullptr;
8500
8501 // An unmapped PHI can be due to a branch or another loop inside this loop,
8502 // or due to this not being the initial iteration through a loop where we
8503 // couldn't compute the evolution of this particular PHI last time.
8504 if (isa<PHINode>(I)) return nullptr;
8505
8506 std::vector<Constant*> Operands(I->getNumOperands());
8507
8508 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
8509 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
8510 if (!Operand) {
8511 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
8512 if (!Operands[i]) return nullptr;
8513 continue;
8514 }
8515 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
8516 Vals[Operand] = C;
8517 if (!C) return nullptr;
8518 Operands[i] = C;
8519 }
8520
8521 if (CmpInst *CI = dyn_cast<CmpInst>(I))
8522 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
8523 Operands[1], DL, TLI);
8524 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
8525 if (!LI->isVolatile())
8526 return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
8527 }
8528 return ConstantFoldInstOperands(I, Operands, DL, TLI);
8529}
8530
8531
8532// If every incoming value to PN except the one for BB is a specific Constant,
8533// return that, else return nullptr.
8534static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
8535 Constant *IncomingVal = nullptr;
8536
8537 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
8538 if (PN->getIncomingBlock(i) == BB)
8539 continue;
8540
8541 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
8542 if (!CurrentVal)
8543 return nullptr;
8544
8545 if (IncomingVal != CurrentVal) {
8546 if (IncomingVal)
8547 return nullptr;
8548 IncomingVal = CurrentVal;
8549 }
8550 }
8551
8552 return IncomingVal;
8553}
8554
8555/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
8556/// in the header of its containing loop, we know the loop executes a
8557/// constant number of times, and the PHI node is just a recurrence
8558/// involving constants, fold it.
8559Constant *
8560ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
8561 const APInt &BEs,
8562 const Loop *L) {
8563 auto I = ConstantEvolutionLoopExitValue.find(PN);
8564 if (I != ConstantEvolutionLoopExitValue.end())
8565 return I->second;
8566
8567 if (BEs.ugt(MaxBruteForceIterations))
8568 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
8569
8570 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
8571
8572 DenseMap<Instruction *, Constant *> CurrentIterVals;
8573 BasicBlock *Header = L->getHeader();
8574 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!")((void)0);
8575
8576 BasicBlock *Latch = L->getLoopLatch();
8577 if (!Latch)
8578 return nullptr;
8579
8580 for (PHINode &PHI : Header->phis()) {
8581 if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
8582 CurrentIterVals[&PHI] = StartCST;
8583 }
8584 if (!CurrentIterVals.count(PN))
8585 return RetVal = nullptr;
8586
8587 Value *BEValue = PN->getIncomingValueForBlock(Latch);
8588
8589 // Execute the loop symbolically to determine the exit value.
8590 assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&((void)0)
8591 "BEs is <= MaxBruteForceIterations which is an 'unsigned'!")((void)0);
8592
8593 unsigned NumIterations = BEs.getZExtValue(); // must be in range
8594 unsigned IterationNum = 0;
8595 const DataLayout &DL = getDataLayout();
8596 for (; ; ++IterationNum) {
8597 if (IterationNum == NumIterations)
8598 return RetVal = CurrentIterVals[PN]; // Got exit value!
8599
8600 // Compute the value of the PHIs for the next iteration.
8601 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
8602 DenseMap<Instruction *, Constant *> NextIterVals;
8603 Constant *NextPHI =
8604 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
8605 if (!NextPHI)
8606 return nullptr; // Couldn't evaluate!
8607 NextIterVals[PN] = NextPHI;
8608
8609 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
8610
8611 // Also evaluate the other PHI nodes. However, we don't get to stop if we
8612 // cease to be able to evaluate one of them or if they stop evolving,
8613 // because that doesn't necessarily prevent us from computing PN.
8614 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
8615 for (const auto &I : CurrentIterVals) {
8616 PHINode *PHI = dyn_cast<PHINode>(I.first);
8617 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
8618 PHIsToCompute.emplace_back(PHI, I.second);
8619 }
8620 // We use two distinct loops because EvaluateExpression may invalidate any
8621 // iterators into CurrentIterVals.
8622 for (const auto &I : PHIsToCompute) {
8623 PHINode *PHI = I.first;
8624 Constant *&NextPHI = NextIterVals[PHI];
8625 if (!NextPHI) { // Not already computed.
8626 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
8627 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
8628 }
8629 if (NextPHI != I.second)
8630 StoppedEvolving = false;
8631 }
8632
8633 // If all entries in CurrentIterVals == NextIterVals then we can stop
8634 // iterating, the loop can't continue to change.
8635 if (StoppedEvolving)
8636 return RetVal = CurrentIterVals[PN];
8637
8638 CurrentIterVals.swap(NextIterVals);
8639 }
8640}
8641
8642const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
8643 Value *Cond,
8644 bool ExitWhen) {
8645 PHINode *PN = getConstantEvolvingPHI(Cond, L);
8646 if (!PN) return getCouldNotCompute();
8647
8648 // If the loop is canonicalized, the PHI will have exactly two entries.
8649 // That's the only form we support here.
8650 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
8651
8652 DenseMap<Instruction *, Constant *> CurrentIterVals;
8653 BasicBlock *Header = L->getHeader();
8654 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!")((void)0);
8655
8656 BasicBlock *Latch = L->getLoopLatch();
8657 assert(Latch && "Should follow from NumIncomingValues == 2!")((void)0);
8658
8659 for (PHINode &PHI : Header->phis()) {
8660 if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
8661 CurrentIterVals[&PHI] = StartCST;
8662 }
8663 if (!CurrentIterVals.count(PN))
8664 return getCouldNotCompute();
8665
8666 // Okay, we find a PHI node that defines the trip count of this loop. Execute
8667 // the loop symbolically to determine when the condition gets a value of
8668 // "ExitWhen".
8669 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
8670 const DataLayout &DL = getDataLayout();
8671 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
8672 auto *CondVal = dyn_cast_or_null<ConstantInt>(
8673 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
8674
8675 // Couldn't symbolically evaluate.
8676 if (!CondVal) return getCouldNotCompute();
8677
8678 if (CondVal->getValue() == uint64_t(ExitWhen)) {
8679 ++NumBruteForceTripCountsComputed;
8680 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
8681 }
8682
8683 // Update all the PHI nodes for the next iteration.
8684 DenseMap<Instruction *, Constant *> NextIterVals;
8685
8686 // Create a list of which PHIs we need to compute. We want to do this before
8687 // calling EvaluateExpression on them because that may invalidate iterators
8688 // into CurrentIterVals.
8689 SmallVector<PHINode *, 8> PHIsToCompute;
8690 for (const auto &I : CurrentIterVals) {
8691 PHINode *PHI = dyn_cast<PHINode>(I.first);
8692 if (!PHI || PHI->getParent() != Header) continue;
8693 PHIsToCompute.push_back(PHI);
8694 }
8695 for (PHINode *PHI : PHIsToCompute) {
8696 Constant *&NextPHI = NextIterVals[PHI];
8697 if (NextPHI) continue; // Already computed!
8698
8699 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
8700 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
8701 }
8702 CurrentIterVals.swap(NextIterVals);
8703 }
8704
8705 // Too many iterations were needed to evaluate.
8706 return getCouldNotCompute();
8707}
8708
8709const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
8710 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
8711 ValuesAtScopes[V];
8712 // Check to see if we've folded this expression at this loop before.
8713 for (auto &LS : Values)
8714 if (LS.first == L)
8715 return LS.second ? LS.second : V;
8716
8717 Values.emplace_back(L, nullptr);
8718
8719 // Otherwise compute it.
8720 const SCEV *C = computeSCEVAtScope(V, L);
8721 for (auto &LS : reverse(ValuesAtScopes[V]))
8722 if (LS.first == L) {
8723 LS.second = C;
8724 break;
8725 }
8726 return C;
8727}
8728
8729/// This builds up a Constant using the ConstantExpr interface. That way, we
8730/// will return Constants for objects which aren't represented by a
8731/// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
8732/// Returns NULL if the SCEV isn't representable as a Constant.
8733static Constant *BuildConstantFromSCEV(const SCEV *V) {
8734 switch (V->getSCEVType()) {
8735 case scCouldNotCompute:
8736 case scAddRecExpr:
8737 return nullptr;
8738 case scConstant:
8739 return cast<SCEVConstant>(V)->getValue();
8740 case scUnknown:
8741 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
8742 case scSignExtend: {
8743 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
8744 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
8745 return ConstantExpr::getSExt(CastOp, SS->getType());
8746 return nullptr;
8747 }
8748 case scZeroExtend: {
8749 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
8750 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
8751 return ConstantExpr::getZExt(CastOp, SZ->getType());
8752 return nullptr;
8753 }
8754 case scPtrToInt: {
8755 const SCEVPtrToIntExpr *P2I = cast<SCEVPtrToIntExpr>(V);
8756 if (Constant *CastOp = BuildConstantFromSCEV(P2I->getOperand()))
8757 return ConstantExpr::getPtrToInt(CastOp, P2I->getType());
8758
8759 return nullptr;
8760 }
8761 case scTruncate: {
8762 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
8763 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
8764 return ConstantExpr::getTrunc(CastOp, ST->getType());
8765 return nullptr;
8766 }
8767 case scAddExpr: {
8768 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
8769 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
8770 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
8771 unsigned AS = PTy->getAddressSpace();
8772 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
8773 C = ConstantExpr::getBitCast(C, DestPtrTy);
8774 }
8775 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
8776 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
8777 if (!C2)
8778 return nullptr;
8779
8780 // First pointer!
8781 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
8782 unsigned AS = C2->getType()->getPointerAddressSpace();
8783 std::swap(C, C2);
8784 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
8785 // The offsets have been converted to bytes. We can add bytes to an
8786 // i8* by GEP with the byte count in the first index.
8787 C = ConstantExpr::getBitCast(C, DestPtrTy);
8788 }
8789
8790 // Don't bother trying to sum two pointers. We probably can't
8791 // statically compute a load that results from it anyway.
8792 if (C2->getType()->isPointerTy())
8793 return nullptr;
8794
8795 if (C->getType()->isPointerTy()) {
8796 C = ConstantExpr::getGetElementPtr(Type::getInt8Ty(C->getContext()),
8797 C, C2);
8798 } else {
8799 C = ConstantExpr::getAdd(C, C2);
8800 }
8801 }
8802 return C;
8803 }
8804 return nullptr;
8805 }
8806 case scMulExpr: {
8807 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
8808 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
8809 // Don't bother with pointers at all.
8810 if (C->getType()->isPointerTy())
8811 return nullptr;
8812 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
8813 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
8814 if (!C2 || C2->getType()->isPointerTy())
8815 return nullptr;
8816 C = ConstantExpr::getMul(C, C2);
8817 }
8818 return C;
8819 }
8820 return nullptr;
8821 }
8822 case scUDivExpr: {
8823 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
8824 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
8825 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
8826 if (LHS->getType() == RHS->getType())
8827 return ConstantExpr::getUDiv(LHS, RHS);
8828 return nullptr;
8829 }
8830 case scSMaxExpr:
8831 case scUMaxExpr:
8832 case scSMinExpr:
8833 case scUMinExpr:
8834 return nullptr; // TODO: smax, umax, smin, umax.
8835 }
8836 llvm_unreachable("Unknown SCEV kind!")__builtin_unreachable();
8837}
8838
8839const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
8840 if (isa<SCEVConstant>(V)) return V;
8841
8842 // If this instruction is evolved from a constant-evolving PHI, compute the
8843 // exit value from the loop without using SCEVs.
8844 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
8845 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
8846 if (PHINode *PN = dyn_cast<PHINode>(I)) {
8847 const Loop *CurrLoop = this->LI[I->getParent()];
8848 // Looking for loop exit value.
8849 if (CurrLoop && CurrLoop->getParentLoop() == L &&
8850 PN->getParent() == CurrLoop->getHeader()) {
8851 // Okay, there is no closed form solution for the PHI node. Check
8852 // to see if the loop that contains it has a known backedge-taken
8853 // count. If so, we may be able to force computation of the exit
8854 // value.
8855 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(CurrLoop);
8856 // This trivial case can show up in some degenerate cases where
8857 // the incoming IR has not yet been fully simplified.
8858 if (BackedgeTakenCount->isZero()) {
8859 Value *InitValue = nullptr;
8860 bool MultipleInitValues = false;
8861 for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
8862 if (!CurrLoop->contains(PN->getIncomingBlock(i))) {
8863 if (!InitValue)
8864 InitValue = PN->getIncomingValue(i);
8865 else if (InitValue != PN->getIncomingValue(i)) {
8866 MultipleInitValues = true;
8867 break;
8868 }
8869 }
8870 }
8871 if (!MultipleInitValues && InitValue)
8872 return getSCEV(InitValue);
8873 }
8874 // Do we have a loop invariant value flowing around the backedge
8875 // for a loop which must execute the backedge?
8876 if (!isa<SCEVCouldNotCompute>(BackedgeTakenCount) &&
8877 isKnownPositive(BackedgeTakenCount) &&
8878 PN->getNumIncomingValues() == 2) {
8879
8880 unsigned InLoopPred =
8881 CurrLoop->contains(PN->getIncomingBlock(0)) ? 0 : 1;
8882 Value *BackedgeVal = PN->getIncomingValue(InLoopPred);
8883 if (CurrLoop->isLoopInvariant(BackedgeVal))
8884 return getSCEV(BackedgeVal);
8885 }
8886 if (auto *BTCC = dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
8887 // Okay, we know how many times the containing loop executes. If
8888 // this is a constant evolving PHI node, get the final value at
8889 // the specified iteration number.
8890 Constant *RV = getConstantEvolutionLoopExitValue(
8891 PN, BTCC->getAPInt(), CurrLoop);
8892 if (RV) return getSCEV(RV);
8893 }
8894 }
8895
8896 // If there is a single-input Phi, evaluate it at our scope. If we can
8897 // prove that this replacement does not break LCSSA form, use new value.
8898 if (PN->getNumOperands() == 1) {
8899 const SCEV *Input = getSCEV(PN->getOperand(0));
8900 const SCEV *InputAtScope = getSCEVAtScope(Input, L);
8901 // TODO: We can generalize it using LI.replacementPreservesLCSSAForm,
8902 // for the simplest case just support constants.
8903 if (isa<SCEVConstant>(InputAtScope)) return InputAtScope;
8904 }
8905 }
8906
8907 // Okay, this is an expression that we cannot symbolically evaluate
8908 // into a SCEV. Check to see if it's possible to symbolically evaluate
8909 // the arguments into constants, and if so, try to constant propagate the
8910 // result. This is particularly useful for computing loop exit values.
8911 if (CanConstantFold(I)) {
8912 SmallVector<Constant *, 4> Operands;
8913 bool MadeImprovement = false;
8914 for (Value *Op : I->operands()) {
8915 if (Constant *C = dyn_cast<Constant>(Op)) {
8916 Operands.push_back(C);
8917 continue;
8918 }
8919
8920 // If any of the operands is non-constant and if they are
8921 // non-integer and non-pointer, don't even try to analyze them
8922 // with scev techniques.
8923 if (!isSCEVable(Op->getType()))
8924 return V;
8925
8926 const SCEV *OrigV = getSCEV(Op);
8927 const SCEV *OpV = getSCEVAtScope(OrigV, L);
8928 MadeImprovement |= OrigV != OpV;
8929
8930 Constant *C = BuildConstantFromSCEV(OpV);
8931 if (!C) return V;
8932 if (C->getType() != Op->getType())
8933 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
8934 Op->getType(),
8935 false),
8936 C, Op->getType());
8937 Operands.push_back(C);
8938 }
8939
8940 // Check to see if getSCEVAtScope actually made an improvement.
8941 if (MadeImprovement) {
8942 Constant *C = nullptr;
8943 const DataLayout &DL = getDataLayout();
8944 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
8945 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
8946 Operands[1], DL, &TLI);
8947 else if (const LoadInst *Load = dyn_cast<LoadInst>(I)) {
8948 if (!Load->isVolatile())
8949 C = ConstantFoldLoadFromConstPtr(Operands[0], Load->getType(),
8950 DL);
8951 } else
8952 C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
8953 if (!C) return V;
8954 return getSCEV(C);
8955 }
8956 }
8957 }
8958
8959 // This is some other type of SCEVUnknown, just return it.
8960 return V;
8961 }
8962
8963 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
8964 // Avoid performing the look-up in the common case where the specified
8965 // expression has no loop-variant portions.
8966 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
8967 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
8968 if (OpAtScope != Comm->getOperand(i)) {
8969 // Okay, at least one of these operands is loop variant but might be
8970 // foldable. Build a new instance of the folded commutative expression.
8971 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
8972 Comm->op_begin()+i);
8973 NewOps.push_back(OpAtScope);
8974
8975 for (++i; i != e; ++i) {
8976 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
8977 NewOps.push_back(OpAtScope);
8978 }
8979 if (isa<SCEVAddExpr>(Comm))
8980 return getAddExpr(NewOps, Comm->getNoWrapFlags());
8981 if (isa<SCEVMulExpr>(Comm))
8982 return getMulExpr(NewOps, Comm->getNoWrapFlags());
8983 if (isa<SCEVMinMaxExpr>(Comm))
8984 return getMinMaxExpr(Comm->getSCEVType(), NewOps);
8985 llvm_unreachable("Unknown commutative SCEV type!")__builtin_unreachable();
8986 }
8987 }
8988 // If we got here, all operands are loop invariant.
8989 return Comm;
8990 }
8991
8992 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
8993 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
8994 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
8995 if (LHS == Div->getLHS() && RHS == Div->getRHS())
8996 return Div; // must be loop invariant
8997 return getUDivExpr(LHS, RHS);
8998 }
8999
9000 // If this is a loop recurrence for a loop that does not contain L, then we
9001 // are dealing with the final value computed by the loop.
9002 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
9003 // First, attempt to evaluate each operand.
9004 // Avoid performing the look-up in the common case where the specified
9005 // expression has no loop-variant portions.
9006 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
9007 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
9008 if (OpAtScope == AddRec->getOperand(i))
9009 continue;
9010
9011 // Okay, at least one of these operands is loop variant but might be
9012 // foldable. Build a new instance of the folded commutative expression.
9013 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
9014 AddRec->op_begin()+i);
9015 NewOps.push_back(OpAtScope);
9016 for (++i; i != e; ++i)
9017 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
9018
9019 const SCEV *FoldedRec =
9020 getAddRecExpr(NewOps, AddRec->getLoop(),
9021 AddRec->getNoWrapFlags(SCEV::FlagNW));
9022 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
9023 // The addrec may be folded to a nonrecurrence, for example, if the
9024 // induction variable is multiplied by zero after constant folding. Go
9025 // ahead and return the folded value.
9026 if (!AddRec)
9027 return FoldedRec;
9028 break;
9029 }
9030
9031 // If the scope is outside the addrec's loop, evaluate it by using the
9032 // loop exit value of the addrec.
9033 if (!AddRec->getLoop()->contains(L)) {
9034 // To evaluate this recurrence, we need to know how many times the AddRec
9035 // loop iterates. Compute this now.
9036 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
9037 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
9038
9039 // Then, evaluate the AddRec.
9040 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
9041 }
9042
9043 return AddRec;
9044 }
9045
9046 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
9047 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
9048 if (Op == Cast->getOperand())
9049 return Cast; // must be loop invariant
9050 return getZeroExtendExpr(Op, Cast->getType());
9051 }
9052
9053 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
9054 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
9055 if (Op == Cast->getOperand())
9056 return Cast; // must be loop invariant
9057 return getSignExtendExpr(Op, Cast->getType());
9058 }
9059
9060 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
9061 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
9062 if (Op == Cast->getOperand())
9063 return Cast; // must be loop invariant
9064 return getTruncateExpr(Op, Cast->getType());
9065 }
9066
9067 if (const SCEVPtrToIntExpr *Cast = dyn_cast<SCEVPtrToIntExpr>(V)) {
9068 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
9069 if (Op == Cast->getOperand())
9070 return Cast; // must be loop invariant
9071 return getPtrToIntExpr(Op, Cast->getType());
9072 }
9073
9074 llvm_unreachable("Unknown SCEV type!")__builtin_unreachable();
9075}
9076
9077const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
9078 return getSCEVAtScope(getSCEV(V), L);
9079}
9080
9081const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const {
9082 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S))
9083 return stripInjectiveFunctions(ZExt->getOperand());
9084 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S))
9085 return stripInjectiveFunctions(SExt->getOperand());
9086 return S;
9087}
9088
9089/// Finds the minimum unsigned root of the following equation:
9090///
9091/// A * X = B (mod N)
9092///
9093/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
9094/// A and B isn't important.
9095///
9096/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
9097static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
9098 ScalarEvolution &SE) {
9099 uint32_t BW = A.getBitWidth();
9100 assert(BW == SE.getTypeSizeInBits(B->getType()))((void)0);
9101 assert(A != 0 && "A must be non-zero.")((void)0);
9102
9103 // 1. D = gcd(A, N)
9104 //
9105 // The gcd of A and N may have only one prime factor: 2. The number of
9106 // trailing zeros in A is its multiplicity
9107 uint32_t Mult2 = A.countTrailingZeros();
9108 // D = 2^Mult2
9109
9110 // 2. Check if B is divisible by D.
9111 //
9112 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
9113 // is not less than multiplicity of this prime factor for D.
9114 if (SE.GetMinTrailingZeros(B) < Mult2)
9115 return SE.getCouldNotCompute();
9116
9117 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
9118 // modulo (N / D).
9119 //
9120 // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
9121 // (N / D) in general. The inverse itself always fits into BW bits, though,
9122 // so we immediately truncate it.
9123 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
9124 APInt Mod(BW + 1, 0);
9125 Mod.setBit(BW - Mult2); // Mod = N / D
9126 APInt I = AD.multiplicativeInverse(Mod).trunc(BW);
9127
9128 // 4. Compute the minimum unsigned root of the equation:
9129 // I * (B / D) mod (N / D)
9130 // To simplify the computation, we factor out the divide by D:
9131 // (I * B mod N) / D
9132 const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
9133 return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
9134}
9135
9136/// For a given quadratic addrec, generate coefficients of the corresponding
9137/// quadratic equation, multiplied by a common value to ensure that they are
9138/// integers.
9139/// The returned value is a tuple { A, B, C, M, BitWidth }, where
9140/// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C
9141/// were multiplied by, and BitWidth is the bit width of the original addrec
9142/// coefficients.
9143/// This function returns None if the addrec coefficients are not compile-
9144/// time constants.
9145static Optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>>
9146GetQuadraticEquation(const SCEVAddRecExpr *AddRec) {
9147 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!")((void)0);
9148 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
9149 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
9150 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
9151 LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: "do { } while (false)
9152 << *AddRec << '\n')do { } while (false);
9153
9154 // We currently can only solve this if the coefficients are constants.
9155 if (!LC || !MC || !NC) {
9156 LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n")do { } while (false);
9157 return None;
9158 }
9159
9160 APInt L = LC->getAPInt();
9161 APInt M = MC->getAPInt();
9162 APInt N = NC->getAPInt();
9163 assert(!N.isNullValue() && "This is not a quadratic addrec")((void)0);
9164
9165 unsigned BitWidth = LC->getAPInt().getBitWidth();
9166 unsigned NewWidth = BitWidth + 1;
9167 LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: "do { } while (false)
9168 << BitWidth << '\n')do { } while (false);
9169 // The sign-extension (as opposed to a zero-extension) here matches the
9170 // extension used in SolveQuadraticEquationWrap (with the same motivation).
9171 N = N.sext(NewWidth);
9172 M = M.sext(NewWidth);
9173 L = L.sext(NewWidth);
9174
9175 // The increments are M, M+N, M+2N, ..., so the accumulated values are
9176 // L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is,
9177 // L+M, L+2M+N, L+3M+3N, ...
9178 // After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N.
9179 //
9180 // The equation Acc = 0 is then
9181 // L + nM + n(n-1)/2 N = 0, or 2L + 2M n + n(n-1) N = 0.
9182 // In a quadratic form it becomes:
9183 // N n^2 + (2M-N) n + 2L = 0.
9184
9185 APInt A = N;
9186 APInt B = 2 * M - A;
9187 APInt C = 2 * L;
9188 APInt T = APInt(NewWidth, 2);
9189 LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << Bdo { } while (false)
9190 << "x + " << C << ", coeff bw: " << NewWidthdo { } while (false)
9191 << ", multiplied by " << T << '\n')do { } while (false);
9192 return std::make_tuple(A, B, C, T, BitWidth);
9193}
9194
9195/// Helper function to compare optional APInts:
9196/// (a) if X and Y both exist, return min(X, Y),
9197/// (b) if neither X nor Y exist, return None,
9198/// (c) if exactly one of X and Y exists, return that value.
9199static Optional<APInt> MinOptional(Optional<APInt> X, Optional<APInt> Y) {
9200 if (X.hasValue() && Y.hasValue()) {
9201 unsigned W = std::max(X->getBitWidth(), Y->getBitWidth());
9202 APInt XW = X->sextOrSelf(W);
9203 APInt YW = Y->sextOrSelf(W);
9204 return XW.slt(YW) ? *X : *Y;
9205 }
9206 if (!X.hasValue() && !Y.hasValue())
9207 return None;
9208 return X.hasValue() ? *X : *Y;
9209}
9210
9211/// Helper function to truncate an optional APInt to a given BitWidth.
9212/// When solving addrec-related equations, it is preferable to return a value
9213/// that has the same bit width as the original addrec's coefficients. If the
9214/// solution fits in the original bit width, truncate it (except for i1).
9215/// Returning a value of a different bit width may inhibit some optimizations.
9216///
9217/// In general, a solution to a quadratic equation generated from an addrec
9218/// may require BW+1 bits, where BW is the bit width of the addrec's
9219/// coefficients. The reason is that the coefficients of the quadratic
9220/// equation are BW+1 bits wide (to avoid truncation when converting from
9221/// the addrec to the equation).
9222static Optional<APInt> TruncIfPossible(Optional<APInt> X, unsigned BitWidth) {
9223 if (!X.hasValue())
9224 return None;
9225 unsigned W = X->getBitWidth();
9226 if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth))
9227 return X->trunc(BitWidth);
9228 return X;
9229}
9230
9231/// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n
9232/// iterations. The values L, M, N are assumed to be signed, and they
9233/// should all have the same bit widths.
9234/// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW,
9235/// where BW is the bit width of the addrec's coefficients.
9236/// If the calculated value is a BW-bit integer (for BW > 1), it will be
9237/// returned as such, otherwise the bit width of the returned value may
9238/// be greater than BW.
9239///
9240/// This function returns None if
9241/// (a) the addrec coefficients are not constant, or
9242/// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases
9243/// like x^2 = 5, no integer solutions exist, in other cases an integer
9244/// solution may exist, but SolveQuadraticEquationWrap may fail to find it.
9245static Optional<APInt>
9246SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
9247 APInt A, B, C, M;
9248 unsigned BitWidth;
9249 auto T = GetQuadraticEquation(AddRec);
9250 if (!T.hasValue())
9251 return None;
9252
9253 std::tie(A, B, C, M, BitWidth) = *T;
9254 LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n")do { } while (false);
9255 Optional<APInt> X = APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth+1);
9256 if (!X.hasValue())
9257 return None;
9258
9259 ConstantInt *CX = ConstantInt::get(SE.getContext(), *X);
9260 ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE);
9261 if (!V->isZero())
9262 return None;
9263
9264 return TruncIfPossible(X, BitWidth);
9265}
9266
9267/// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n
9268/// iterations. The values M, N are assumed to be signed, and they
9269/// should all have the same bit widths.
9270/// Find the least n such that c(n) does not belong to the given range,
9271/// while c(n-1) does.
9272///
9273/// This function returns None if
9274/// (a) the addrec coefficients are not constant, or
9275/// (b) SolveQuadraticEquationWrap was unable to find a solution for the
9276/// bounds of the range.
9277static Optional<APInt>
9278SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec,
9279 const ConstantRange &Range, ScalarEvolution &SE) {
9280 assert(AddRec->getOperand(0)->isZero() &&((void)0)
9281 "Starting value of addrec should be 0")((void)0);
9282 LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range "do { } while (false)
9283 << Range << ", addrec " << *AddRec << '\n')do { } while (false);
9284 // This case is handled in getNumIterationsInRange. Here we can assume that
9285 // we start in the range.
9286 assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) &&((void)0)
9287 "Addrec's initial value should be in range")((void)0);
9288
9289 APInt A, B, C, M;
9290 unsigned BitWidth;
9291 auto T = GetQuadraticEquation(AddRec);
9292 if (!T.hasValue())
9293 return None;
9294
9295 // Be careful about the return value: there can be two reasons for not
9296 // returning an actual number. First, if no solutions to the equations
9297 // were found, and second, if the solutions don't leave the given range.
9298 // The first case means that the actual solution is "unknown", the second
9299 // means that it's known, but not valid. If the solution is unknown, we
9300 // cannot make any conclusions.
9301 // Return a pair: the optional solution and a flag indicating if the
9302 // solution was found.
9303 auto SolveForBoundary = [&](APInt Bound) -> std::pair<Optional<APInt>,bool> {
9304 // Solve for signed overflow and unsigned overflow, pick the lower
9305 // solution.
9306 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary "do { } while (false)
9307 << Bound << " (before multiplying by " << M << ")\n")do { } while (false);
9308 Bound *= M; // The quadratic equation multiplier.
9309
9310 Optional<APInt> SO = None;
9311 if (BitWidth > 1) {
9312 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "do { } while (false)
9313 "signed overflow\n")do { } while (false);
9314 SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth);
9315 }
9316 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "do { } while (false)
9317 "unsigned overflow\n")do { } while (false);
9318 Optional<APInt> UO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound,
9319 BitWidth+1);
9320
9321 auto LeavesRange = [&] (const APInt &X) {
9322 ConstantInt *C0 = ConstantInt::get(SE.getContext(), X);
9323 ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE);
9324 if (Range.contains(V0->getValue()))
9325 return false;
9326 // X should be at least 1, so X-1 is non-negative.
9327 ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1);
9328 ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE);
9329 if (Range.contains(V1->getValue()))
9330 return true;
9331 return false;
9332 };
9333
9334 // If SolveQuadraticEquationWrap returns None, it means that there can
9335 // be a solution, but the function failed to find it. We cannot treat it
9336 // as "no solution".
9337 if (!SO.hasValue() || !UO.hasValue())
9338 return { None, false };
9339
9340 // Check the smaller value first to see if it leaves the range.
9341 // At this point, both SO and UO must have values.
9342 Optional<APInt> Min = MinOptional(SO, UO);
9343 if (LeavesRange(*Min))
9344 return { Min, true };
9345 Optional<APInt> Max = Min == SO ? UO : SO;
9346 if (LeavesRange(*Max))
9347 return { Max, true };
9348
9349 // Solutions were found, but were eliminated, hence the "true".
9350 return { None, true };
9351 };
9352
9353 std::tie(A, B, C, M, BitWidth) = *T;
9354 // Lower bound is inclusive, subtract 1 to represent the exiting value.
9355 APInt Lower = Range.getLower().sextOrSelf(A.getBitWidth()) - 1;
9356 APInt Upper = Range.getUpper().sextOrSelf(A.getBitWidth());
9357 auto SL = SolveForBoundary(Lower);
9358 auto SU = SolveForBoundary(Upper);
9359 // If any of the solutions was unknown, no meaninigful conclusions can
9360 // be made.
9361 if (!SL.second || !SU.second)
9362 return None;
9363
9364 // Claim: The correct solution is not some value between Min and Max.
9365 //
9366 // Justification: Assuming that Min and Max are different values, one of
9367 // them is when the first signed overflow happens, the other is when the
9368 // first unsigned overflow happens. Crossing the range boundary is only
9369 // possible via an overflow (treating 0 as a special case of it, modeling
9370 // an overflow as crossing k*2^W for some k).
9371 //
9372 // The interesting case here is when Min was eliminated as an invalid
9373 // solution, but Max was not. The argument is that if there was another
9374 // overflow between Min and Max, it would also have been eliminated if
9375 // it was considered.
9376 //
9377 // For a given boundary, it is possible to have two overflows of the same
9378 // type (signed/unsigned) without having the other type in between: this
9379 // can happen when the vertex of the parabola is between the iterations
9380 // corresponding to the overflows. This is only possible when the two
9381 // overflows cross k*2^W for the same k. In such case, if the second one
9382 // left the range (and was the first one to do so), the first overflow
9383 // would have to enter the range, which would mean that either we had left
9384 // the range before or that we started outside of it. Both of these cases
9385 // are contradictions.
9386 //
9387 // Claim: In the case where SolveForBoundary returns None, the correct
9388 // solution is not some value between the Max for this boundary and the
9389 // Min of the other boundary.
9390 //
9391 // Justification: Assume that we had such Max_A and Min_B corresponding
9392 // to range boundaries A and B and such that Max_A < Min_B. If there was
9393 // a solution between Max_A and Min_B, it would have to be caused by an
9394 // overflow corresponding to either A or B. It cannot correspond to B,
9395 // since Min_B is the first occurrence of such an overflow. If it
9396 // corresponded to A, it would have to be either a signed or an unsigned
9397 // overflow that is larger than both eliminated overflows for A. But
9398 // between the eliminated overflows and this overflow, the values would
9399 // cover the entire value space, thus crossing the other boundary, which
9400 // is a contradiction.
9401
9402 return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth);
9403}
9404
9405ScalarEvolution::ExitLimit
9406ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
9407 bool AllowPredicates) {
9408
9409 // This is only used for loops with a "x != y" exit test. The exit condition
9410 // is now expressed as a single expression, V = x-y. So the exit test is
9411 // effectively V != 0. We know and take advantage of the fact that this
9412 // expression only being used in a comparison by zero context.
9413
9414 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
9415 // If the value is a constant
9416 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
9417 // If the value is already zero, the branch will execute zero times.
9418 if (C->getValue()->isZero()) return C;
9419 return getCouldNotCompute(); // Otherwise it will loop infinitely.
9420 }
9421
9422 const SCEVAddRecExpr *AddRec =
9423 dyn_cast<SCEVAddRecExpr>(stripInjectiveFunctions(V));
9424
9425 if (!AddRec && AllowPredicates)
9426 // Try to make this an AddRec using runtime tests, in the first X
9427 // iterations of this loop, where X is the SCEV expression found by the
9428 // algorithm below.
9429 AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
9430
9431 if (!AddRec || AddRec->getLoop() != L)
9432 return getCouldNotCompute();
9433
9434 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
9435 // the quadratic equation to solve it.
9436 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
9437 // We can only use this value if the chrec ends up with an exact zero
9438 // value at this index. When solving for "X*X != 5", for example, we
9439 // should not accept a root of 2.
9440 if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) {
9441 const auto *R = cast<SCEVConstant>(getConstant(S.getValue()));
9442 return ExitLimit(R, R, false, Predicates);
9443 }
9444 return getCouldNotCompute();
9445 }
9446
9447 // Otherwise we can only handle this if it is affine.
9448 if (!AddRec->isAffine())
9449 return getCouldNotCompute();
9450
9451 // If this is an affine expression, the execution count of this branch is
9452 // the minimum unsigned root of the following equation:
9453 //
9454 // Start + Step*N = 0 (mod 2^BW)
9455 //
9456 // equivalent to:
9457 //
9458 // Step*N = -Start (mod 2^BW)
9459 //
9460 // where BW is the common bit width of Start and Step.
9461
9462 // Get the initial value for the loop.
9463 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
9464 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
9465
9466 // For now we handle only constant steps.
9467 //
9468 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
9469 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
9470 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
9471 // We have not yet seen any such cases.
9472 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
9473 if (!StepC || StepC->getValue()->isZero())
9474 return getCouldNotCompute();
9475
9476 // For positive steps (counting up until unsigned overflow):
9477 // N = -Start/Step (as unsigned)
9478 // For negative steps (counting down to zero):
9479 // N = Start/-Step
9480 // First compute the unsigned distance from zero in the direction of Step.
9481 bool CountDown = StepC->getAPInt().isNegative();
9482 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
9483
9484 // Handle unitary steps, which cannot wraparound.
9485 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
9486 // N = Distance (as unsigned)
9487 if (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne()) {
9488 APInt MaxBECount = getUnsignedRangeMax(applyLoopGuards(Distance, L));
9489 APInt MaxBECountBase = getUnsignedRangeMax(Distance);
9490 if (MaxBECountBase.ult(MaxBECount))
9491 MaxBECount = MaxBECountBase;
9492
9493 // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
9494 // we end up with a loop whose backedge-taken count is n - 1. Detect this
9495 // case, and see if we can improve the bound.
9496 //
9497 // Explicitly handling this here is necessary because getUnsignedRange
9498 // isn't context-sensitive; it doesn't know that we only care about the
9499 // range inside the loop.
9500 const SCEV *Zero = getZero(Distance->getType());
9501 const SCEV *One = getOne(Distance->getType());
9502 const SCEV *DistancePlusOne = getAddExpr(Distance, One);
9503 if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
9504 // If Distance + 1 doesn't overflow, we can compute the maximum distance
9505 // as "unsigned_max(Distance + 1) - 1".
9506 ConstantRange CR = getUnsignedRange(DistancePlusOne);
9507 MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
9508 }
9509 return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
9510 }
9511
9512 // If the condition controls loop exit (the loop exits only if the expression
9513 // is true) and the addition is no-wrap we can use unsigned divide to
9514 // compute the backedge count. In this case, the step may not divide the
9515 // distance, but we don't care because if the condition is "missed" the loop
9516 // will have undefined behavior due to wrapping.
9517 if (ControlsExit && AddRec->hasNoSelfWrap() &&
9518 loopHasNoAbnormalExits(AddRec->getLoop())) {
9519 const SCEV *Exact =
9520 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
9521 const SCEV *Max = getCouldNotCompute();
9522 if (Exact != getCouldNotCompute()) {
9523 APInt MaxInt = getUnsignedRangeMax(applyLoopGuards(Exact, L));
9524 APInt BaseMaxInt = getUnsignedRangeMax(Exact);
9525 if (BaseMaxInt.ult(MaxInt))
9526 Max = getConstant(BaseMaxInt);
9527 else
9528 Max = getConstant(MaxInt);
9529 }
9530 return ExitLimit(Exact, Max, false, Predicates);
9531 }
9532
9533 // Solve the general equation.
9534 const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(),
9535 getNegativeSCEV(Start), *this);
9536 const SCEV *M = E == getCouldNotCompute()
9537 ? E
9538 : getConstant(getUnsignedRangeMax(E));
9539 return ExitLimit(E, M, false, Predicates);
9540}
9541
9542ScalarEvolution::ExitLimit
9543ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
9544 // Loops that look like: while (X == 0) are very strange indeed. We don't
9545 // handle them yet except for the trivial case. This could be expanded in the
9546 // future as needed.
9547
9548 // If the value is a constant, check to see if it is known to be non-zero
9549 // already. If so, the backedge will execute zero times.
9550 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
9551 if (!C->getValue()->isZero())
9552 return getZero(C->getType());
9553 return getCouldNotCompute(); // Otherwise it will loop infinitely.
9554 }
9555
9556 // We could implement others, but I really doubt anyone writes loops like
9557 // this, and if they did, they would already be constant folded.
9558 return getCouldNotCompute();
9559}
9560
9561std::pair<const BasicBlock *, const BasicBlock *>
9562ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(const BasicBlock *BB)
9563 const {
9564 // If the block has a unique predecessor, then there is no path from the
9565 // predecessor to the block that does not go through the direct edge
9566 // from the predecessor to the block.
9567 if (const BasicBlock *Pred = BB->getSinglePredecessor())
9568 return {Pred, BB};
9569
9570 // A loop's header is defined to be a block that dominates the loop.
9571 // If the header has a unique predecessor outside the loop, it must be
9572 // a block that has exactly one successor that can reach the loop.
9573 if (const Loop *L = LI.getLoopFor(BB))
9574 return {L->getLoopPredecessor(), L->getHeader()};
9575
9576 return {nullptr, nullptr};
9577}
9578
9579/// SCEV structural equivalence is usually sufficient for testing whether two
9580/// expressions are equal, however for the purposes of looking for a condition
9581/// guarding a loop, it can be useful to be a little more general, since a
9582/// front-end may have replicated the controlling expression.
9583static bool HasSameValue(const SCEV *A, const SCEV *B) {
9584 // Quick check to see if they are the same SCEV.
9585 if (A == B) return true;
9586
9587 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
9588 // Not all instructions that are "identical" compute the same value. For
9589 // instance, two distinct alloca instructions allocating the same type are
9590 // identical and do not read memory; but compute distinct values.
9591 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
9592 };
9593
9594 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
9595 // two different instructions with the same value. Check for this case.
9596 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
9597 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
9598 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
9599 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
9600 if (ComputesEqualValues(AI, BI))
9601 return true;
9602
9603 // Otherwise assume they may have a different value.
9604 return false;
9605}
9606
9607bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
9608 const SCEV *&LHS, const SCEV *&RHS,
9609 unsigned Depth) {
9610 bool Changed = false;
9611 // Simplifies ICMP to trivial true or false by turning it into '0 == 0' or
9612 // '0 != 0'.
9613 auto TrivialCase = [&](bool TriviallyTrue) {
9614 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
9615 Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE;
9616 return true;
9617 };
9618 // If we hit the max recursion limit bail out.
9619 if (Depth >= 3)
9620 return false;
9621
9622 // Canonicalize a constant to the right side.
9623 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
9624 // Check for both operands constant.
9625 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
9626 if (ConstantExpr::getICmp(Pred,
9627 LHSC->getValue(),
9628 RHSC->getValue())->isNullValue())
9629 return TrivialCase(false);
9630 else
9631 return TrivialCase(true);
9632 }
9633 // Otherwise swap the operands to put the constant on the right.
9634 std::swap(LHS, RHS);
9635 Pred = ICmpInst::getSwappedPredicate(Pred);
9636 Changed = true;
9637 }
9638
9639 // If we're comparing an addrec with a value which is loop-invariant in the
9640 // addrec's loop, put the addrec on the left. Also make a dominance check,
9641 // as both operands could be addrecs loop-invariant in each other's loop.
9642 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
9643 const Loop *L = AR->getLoop();
9644 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
9645 std::swap(LHS, RHS);
9646 Pred = ICmpInst::getSwappedPredicate(Pred);
9647 Changed = true;
9648 }
9649 }
9650
9651 // If there's a constant operand, canonicalize comparisons with boundary
9652 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
9653 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
9654 const APInt &RA = RC->getAPInt();
9655
9656 bool SimplifiedByConstantRange = false;
9657
9658 if (!ICmpInst::isEquality(Pred)) {
9659 ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
9660 if (ExactCR.isFullSet())
9661 return TrivialCase(true);
9662 else if (ExactCR.isEmptySet())
9663 return TrivialCase(false);
9664
9665 APInt NewRHS;
9666 CmpInst::Predicate NewPred;
9667 if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
9668 ICmpInst::isEquality(NewPred)) {
9669 // We were able to convert an inequality to an equality.
9670 Pred = NewPred;
9671 RHS = getConstant(NewRHS);
9672 Changed = SimplifiedByConstantRange = true;
9673 }
9674 }
9675
9676 if (!SimplifiedByConstantRange) {
9677 switch (Pred) {
9678 default:
9679 break;
9680 case ICmpInst::ICMP_EQ:
9681 case ICmpInst::ICMP_NE:
9682 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
9683 if (!RA)
9684 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
9685 if (const SCEVMulExpr *ME =
9686 dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
9687 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
9688 ME->getOperand(0)->isAllOnesValue()) {
9689 RHS = AE->getOperand(1);
9690 LHS = ME->getOperand(1);
9691 Changed = true;
9692 }
9693 break;
9694
9695
9696 // The "Should have been caught earlier!" messages refer to the fact
9697 // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
9698 // should have fired on the corresponding cases, and canonicalized the
9699 // check to trivial case.
9700
9701 case ICmpInst::ICMP_UGE:
9702 assert(!RA.isMinValue() && "Should have been caught earlier!")((void)0);
9703 Pred = ICmpInst::ICMP_UGT;
9704 RHS = getConstant(RA - 1);
9705 Changed = true;
9706 break;
9707 case ICmpInst::ICMP_ULE:
9708 assert(!RA.isMaxValue() && "Should have been caught earlier!")((void)0);
9709 Pred = ICmpInst::ICMP_ULT;
9710 RHS = getConstant(RA + 1);
9711 Changed = true;
9712 break;
9713 case ICmpInst::ICMP_SGE:
9714 assert(!RA.isMinSignedValue() && "Should have been caught earlier!")((void)0);
9715 Pred = ICmpInst::ICMP_SGT;
9716 RHS = getConstant(RA - 1);
9717 Changed = true;
9718 break;
9719 case ICmpInst::ICMP_SLE:
9720 assert(!RA.isMaxSignedValue() && "Should have been caught earlier!")((void)0);
9721 Pred = ICmpInst::ICMP_SLT;
9722 RHS = getConstant(RA + 1);
9723 Changed = true;
9724 break;
9725 }
9726 }
9727 }
9728
9729 // Check for obvious equality.
9730 if (HasSameValue(LHS, RHS)) {
9731 if (ICmpInst::isTrueWhenEqual(Pred))
9732 return TrivialCase(true);
9733 if (ICmpInst::isFalseWhenEqual(Pred))
9734 return TrivialCase(false);
9735 }
9736
9737 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
9738 // adding or subtracting 1 from one of the operands.
9739 switch (Pred) {
9740 case ICmpInst::ICMP_SLE:
9741 if (!getSignedRangeMax(RHS).isMaxSignedValue()) {
9742 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
9743 SCEV::FlagNSW);
9744 Pred = ICmpInst::ICMP_SLT;
9745 Changed = true;
9746 } else if (!getSignedRangeMin(LHS).isMinSignedValue()) {
9747 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
9748 SCEV::FlagNSW);
9749 Pred = ICmpInst::ICMP_SLT;
9750 Changed = true;
9751 }
9752 break;
9753 case ICmpInst::ICMP_SGE:
9754 if (!getSignedRangeMin(RHS).isMinSignedValue()) {
9755 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
9756 SCEV::FlagNSW);
9757 Pred = ICmpInst::ICMP_SGT;
9758 Changed = true;
9759 } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) {
9760 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
9761 SCEV::FlagNSW);
9762 Pred = ICmpInst::ICMP_SGT;
9763 Changed = true;
9764 }
9765 break;
9766 case ICmpInst::ICMP_ULE:
9767 if (!getUnsignedRangeMax(RHS).isMaxValue()) {
9768 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
9769 SCEV::FlagNUW);
9770 Pred = ICmpInst::ICMP_ULT;
9771 Changed = true;
9772 } else if (!getUnsignedRangeMin(LHS).isMinValue()) {
9773 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
9774 Pred = ICmpInst::ICMP_ULT;
9775 Changed = true;
9776 }
9777 break;
9778 case ICmpInst::ICMP_UGE:
9779 if (!getUnsignedRangeMin(RHS).isMinValue()) {
9780 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
9781 Pred = ICmpInst::ICMP_UGT;
9782 Changed = true;
9783 } else if (!getUnsignedRangeMax(LHS).isMaxValue()) {
9784 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
9785 SCEV::FlagNUW);
9786 Pred = ICmpInst::ICMP_UGT;
9787 Changed = true;
9788 }
9789 break;
9790 default:
9791 break;
9792 }
9793
9794 // TODO: More simplifications are possible here.
9795
9796 // Recursively simplify until we either hit a recursion limit or nothing
9797 // changes.
9798 if (Changed)
9799 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
9800
9801 return Changed;
9802}
9803
9804bool ScalarEvolution::isKnownNegative(const SCEV *S) {
9805 return getSignedRangeMax(S).isNegative();
9806}
9807
9808bool ScalarEvolution::isKnownPositive(const SCEV *S) {
9809 return getSignedRangeMin(S).isStrictlyPositive();
9810}
9811
9812bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
9813 return !getSignedRangeMin(S).isNegative();
9814}
9815
9816bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
9817 return !getSignedRangeMax(S).isStrictlyPositive();
9818}
9819
9820bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
9821 return getUnsignedRangeMin(S) != 0;
9822}
9823
9824std::pair<const SCEV *, const SCEV *>
9825ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) {
9826 // Compute SCEV on entry of loop L.
9827 const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this);
9828 if (Start == getCouldNotCompute())
9829 return { Start, Start };
9830 // Compute post increment SCEV for loop L.
9831 const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this);
9832 assert(PostInc != getCouldNotCompute() && "Unexpected could not compute")((void)0);
9833 return { Start, PostInc };
9834}
9835
9836bool ScalarEvolution::isKnownViaInduction(ICmpInst::Predicate Pred,
9837 const SCEV *LHS, const SCEV *RHS) {
9838 // First collect all loops.
9839 SmallPtrSet<const Loop *, 8> LoopsUsed;
9840 getUsedLoops(LHS, LoopsUsed);
9841 getUsedLoops(RHS, LoopsUsed);
9842
9843 if (LoopsUsed.empty())
9844 return false;
9845
9846 // Domination relationship must be a linear order on collected loops.
9847#ifndef NDEBUG1
9848 for (auto *L1 : LoopsUsed)
9849 for (auto *L2 : LoopsUsed)
9850 assert((DT.dominates(L1->getHeader(), L2->getHeader()) ||((void)0)
9851 DT.dominates(L2->getHeader(), L1->getHeader())) &&((void)0)
9852 "Domination relationship is not a linear order")((void)0);
9853#endif
9854
9855 const Loop *MDL =
9856 *std::max_element(LoopsUsed.begin(), LoopsUsed.end(),
9857 [&](const Loop *L1, const Loop *L2) {
9858 return DT.properlyDominates(L1->getHeader(), L2->getHeader());
9859 });
9860
9861 // Get init and post increment value for LHS.
9862 auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS);
9863 // if LHS contains unknown non-invariant SCEV then bail out.
9864 if (SplitLHS.first == getCouldNotCompute())
9865 return false;
9866 assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC")((void)0);
9867 // Get init and post increment value for RHS.
9868 auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS);
9869 // if RHS contains unknown non-invariant SCEV then bail out.
9870 if (SplitRHS.first == getCouldNotCompute())
9871 return false;
9872 assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC")((void)0);
9873 // It is possible that init SCEV contains an invariant load but it does
9874 // not dominate MDL and is not available at MDL loop entry, so we should
9875 // check it here.
9876 if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) ||
9877 !isAvailableAtLoopEntry(SplitRHS.first, MDL))
9878 return false;
9879
9880 // It seems backedge guard check is faster than entry one so in some cases
9881 // it can speed up whole estimation by short circuit
9882 return isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second,
9883 SplitRHS.second) &&
9884 isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first);
9885}
9886
9887bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
9888 const SCEV *LHS, const SCEV *RHS) {
9889 // Canonicalize the inputs first.
9890 (void)SimplifyICmpOperands(Pred, LHS, RHS);
9891
9892 if (isKnownViaInduction(Pred, LHS, RHS))
9893 return true;
9894
9895 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
9896 return true;
9897
9898 // Otherwise see what can be done with some simple reasoning.
9899 return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS);
9900}
9901
9902Optional<bool> ScalarEvolution::evaluatePredicate(ICmpInst::Predicate Pred,
9903 const SCEV *LHS,
9904 const SCEV *RHS) {
9905 if (isKnownPredicate(Pred, LHS, RHS))
9906 return true;
9907 else if (isKnownPredicate(ICmpInst::getInversePredicate(Pred), LHS, RHS))
9908 return false;
9909 return None;
9910}
9911
9912bool ScalarEvolution::isKnownPredicateAt(ICmpInst::Predicate Pred,
9913 const SCEV *LHS, const SCEV *RHS,
9914 const Instruction *Context) {
9915 // TODO: Analyze guards and assumes from Context's block.
9916 return isKnownPredicate(Pred, LHS, RHS) ||
9917 isBasicBlockEntryGuardedByCond(Context->getParent(), Pred, LHS, RHS);
9918}
9919
9920Optional<bool>
9921ScalarEvolution::evaluatePredicateAt(ICmpInst::Predicate Pred, const SCEV *LHS,
9922 const SCEV *RHS,
9923 const Instruction *Context) {
9924 Optional<bool> KnownWithoutContext = evaluatePredicate(Pred, LHS, RHS);
9925 if (KnownWithoutContext)
1
Calling 'Optional::operator bool'
9
Returning from 'Optional::operator bool'
10
Taking false branch
9926 return KnownWithoutContext;
9927
9928 if (isBasicBlockEntryGuardedByCond(Context->getParent(), Pred, LHS, RHS))
11
Passing value via 1st parameter 'BB'
12
Calling 'ScalarEvolution::isBasicBlockEntryGuardedByCond'
9929 return true;
9930 else if (isBasicBlockEntryGuardedByCond(Context->getParent(),
9931 ICmpInst::getInversePredicate(Pred),
9932 LHS, RHS))
9933 return false;
9934 return None;
9935}
9936
9937bool ScalarEvolution::isKnownOnEveryIteration(ICmpInst::Predicate Pred,
9938 const SCEVAddRecExpr *LHS,
9939 const SCEV *RHS) {
9940 const Loop *L = LHS->getLoop();
9941 return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) &&
9942 isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS);
9943}
9944
9945Optional<ScalarEvolution::MonotonicPredicateType>
9946ScalarEvolution::getMonotonicPredicateType(const SCEVAddRecExpr *LHS,
9947 ICmpInst::Predicate Pred) {
9948 auto Result = getMonotonicPredicateTypeImpl(LHS, Pred);
9949
9950#ifndef NDEBUG1
9951 // Verify an invariant: inverting the predicate should turn a monotonically
9952 // increasing change to a monotonically decreasing one, and vice versa.
9953 if (Result) {
9954 auto ResultSwapped =
9955 getMonotonicPredicateTypeImpl(LHS, ICmpInst::getSwappedPredicate(Pred));
9956
9957 assert(ResultSwapped.hasValue() && "should be able to analyze both!")((void)0);
9958 assert(ResultSwapped.getValue() != Result.getValue() &&((void)0)
9959 "monotonicity should flip as we flip the predicate")((void)0);
9960 }
9961#endif
9962
9963 return Result;
9964}
9965
9966Optional<ScalarEvolution::MonotonicPredicateType>
9967ScalarEvolution::getMonotonicPredicateTypeImpl(const SCEVAddRecExpr *LHS,
9968 ICmpInst::Predicate Pred) {
9969 // A zero step value for LHS means the induction variable is essentially a
9970 // loop invariant value. We don't really depend on the predicate actually
9971 // flipping from false to true (for increasing predicates, and the other way
9972 // around for decreasing predicates), all we care about is that *if* the
9973 // predicate changes then it only changes from false to true.
9974 //
9975 // A zero step value in itself is not very useful, but there may be places
9976 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
9977 // as general as possible.
9978
9979 // Only handle LE/LT/GE/GT predicates.
9980 if (!ICmpInst::isRelational(Pred))
9981 return None;
9982
9983 bool IsGreater = ICmpInst::isGE(Pred) || ICmpInst::isGT(Pred);
9984 assert((IsGreater || ICmpInst::isLE(Pred) || ICmpInst::isLT(Pred)) &&((void)0)
9985 "Should be greater or less!")((void)0);
9986
9987 // Check that AR does not wrap.
9988 if (ICmpInst::isUnsigned(Pred)) {
9989 if (!LHS->hasNoUnsignedWrap())
9990 return None;
9991 return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
9992 } else {
9993 assert(ICmpInst::isSigned(Pred) &&((void)0)
9994 "Relational predicate is either signed or unsigned!")((void)0);
9995 if (!LHS->hasNoSignedWrap())
9996 return None;
9997
9998 const SCEV *Step = LHS->getStepRecurrence(*this);
9999
10000 if (isKnownNonNegative(Step))
10001 return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
10002
10003 if (isKnownNonPositive(Step))
10004 return !IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
10005
10006 return None;
10007 }
10008}
10009
10010Optional<ScalarEvolution::LoopInvariantPredicate>
10011ScalarEvolution::getLoopInvariantPredicate(ICmpInst::Predicate Pred,
10012 const SCEV *LHS, const SCEV *RHS,
10013 const Loop *L) {
10014
10015 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
10016 if (!isLoopInvariant(RHS, L)) {
10017 if (!isLoopInvariant(LHS, L))
10018 return None;
10019
10020 std::swap(LHS, RHS);
10021 Pred = ICmpInst::getSwappedPredicate(Pred);
10022 }
10023
10024 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
10025 if (!ArLHS || ArLHS->getLoop() != L)
10026 return None;
10027
10028 auto MonotonicType = getMonotonicPredicateType(ArLHS, Pred);
10029 if (!MonotonicType)
10030 return None;
10031 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
10032 // true as the loop iterates, and the backedge is control dependent on
10033 // "ArLHS `Pred` RHS" == true then we can reason as follows:
10034 //
10035 // * if the predicate was false in the first iteration then the predicate
10036 // is never evaluated again, since the loop exits without taking the
10037 // backedge.
10038 // * if the predicate was true in the first iteration then it will
10039 // continue to be true for all future iterations since it is
10040 // monotonically increasing.
10041 //
10042 // For both the above possibilities, we can replace the loop varying
10043 // predicate with its value on the first iteration of the loop (which is
10044 // loop invariant).
10045 //
10046 // A similar reasoning applies for a monotonically decreasing predicate, by
10047 // replacing true with false and false with true in the above two bullets.
10048 bool Increasing = *MonotonicType == ScalarEvolution::MonotonicallyIncreasing;
10049 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
10050
10051 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
10052 return None;
10053
10054 return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(), RHS);
10055}
10056
10057Optional<ScalarEvolution::LoopInvariantPredicate>
10058ScalarEvolution::getLoopInvariantExitCondDuringFirstIterations(
10059 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
10060 const Instruction *Context, const SCEV *MaxIter) {
10061 // Try to prove the following set of facts:
10062 // - The predicate is monotonic in the iteration space.
10063 // - If the check does not fail on the 1st iteration:
10064 // - No overflow will happen during first MaxIter iterations;
10065 // - It will not fail on the MaxIter'th iteration.
10066 // If the check does fail on the 1st iteration, we leave the loop and no
10067 // other checks matter.
10068
10069 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
10070 if (!isLoopInvariant(RHS, L)) {
10071 if (!isLoopInvariant(LHS, L))
10072 return None;
10073
10074 std::swap(LHS, RHS);
10075 Pred = ICmpInst::getSwappedPredicate(Pred);
10076 }
10077
10078 auto *AR = dyn_cast<SCEVAddRecExpr>(LHS);
10079 if (!AR || AR->getLoop() != L)
10080 return None;
10081
10082 // The predicate must be relational (i.e. <, <=, >=, >).
10083 if (!ICmpInst::isRelational(Pred))
10084 return None;
10085
10086 // TODO: Support steps other than +/- 1.
10087 const SCEV *Step = AR->getStepRecurrence(*this);
10088 auto *One = getOne(Step->getType());
10089 auto *MinusOne = getNegativeSCEV(One);
10090 if (Step != One && Step != MinusOne)
10091 return None;
10092
10093 // Type mismatch here means that MaxIter is potentially larger than max
10094 // unsigned value in start type, which mean we cannot prove no wrap for the
10095 // indvar.
10096 if (AR->getType() != MaxIter->getType())
10097 return None;
10098
10099 // Value of IV on suggested last iteration.
10100 const SCEV *Last = AR->evaluateAtIteration(MaxIter, *this);
10101 // Does it still meet the requirement?
10102 if (!isLoopBackedgeGuardedByCond(L, Pred, Last, RHS))
10103 return None;
10104 // Because step is +/- 1 and MaxIter has same type as Start (i.e. it does
10105 // not exceed max unsigned value of this type), this effectively proves
10106 // that there is no wrap during the iteration. To prove that there is no
10107 // signed/unsigned wrap, we need to check that
10108 // Start <= Last for step = 1 or Start >= Last for step = -1.
10109 ICmpInst::Predicate NoOverflowPred =
10110 CmpInst::isSigned(Pred) ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
10111 if (Step == MinusOne)
10112 NoOverflowPred = CmpInst::getSwappedPredicate(NoOverflowPred);
10113 const SCEV *Start = AR->getStart();
10114 if (!isKnownPredicateAt(NoOverflowPred, Start, Last, Context))
10115 return None;
10116
10117 // Everything is fine.
10118 return ScalarEvolution::LoopInvariantPredicate(Pred, Start, RHS);
10119}
10120
10121bool ScalarEvolution::isKnownPredicateViaConstantRanges(
10122 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
10123 if (HasSameValue(LHS, RHS))
10124 return ICmpInst::isTrueWhenEqual(Pred);
10125
10126 // This code is split out from isKnownPredicate because it is called from
10127 // within isLoopEntryGuardedByCond.
10128
10129 auto CheckRanges = [&](const ConstantRange &RangeLHS,
10130 const ConstantRange &RangeRHS) {
10131 return RangeLHS.icmp(Pred, RangeRHS);
10132 };
10133
10134 // The check at the top of the function catches the case where the values are
10135 // known to be equal.
10136 if (Pred == CmpInst::ICMP_EQ)
10137 return false;
10138
10139 if (Pred == CmpInst::ICMP_NE) {
10140 if (CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
10141 CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)))
10142 return true;
10143 auto *Diff = getMinusSCEV(LHS, RHS);
10144 return !isa<SCEVCouldNotCompute>(Diff) && isKnownNonZero(Diff);
10145 }
10146
10147 if (CmpInst::isSigned(Pred))
10148 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
10149
10150 return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
10151}
10152
10153bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
10154 const SCEV *LHS,
10155 const SCEV *RHS) {
10156 // Match X to (A + C1)<ExpectedFlags> and Y to (A + C2)<ExpectedFlags>, where
10157 // C1 and C2 are constant integers. If either X or Y are not add expressions,
10158 // consider them as X + 0 and Y + 0 respectively. C1 and C2 are returned via
10159 // OutC1 and OutC2.
10160 auto MatchBinaryAddToConst = [this](const SCEV *X, const SCEV *Y,
10161 APInt &OutC1, APInt &OutC2,
10162 SCEV::NoWrapFlags ExpectedFlags) {
10163 const SCEV *XNonConstOp, *XConstOp;
10164 const SCEV *YNonConstOp, *YConstOp;
10165 SCEV::NoWrapFlags XFlagsPresent;
10166 SCEV::NoWrapFlags YFlagsPresent;
10167
10168 if (!splitBinaryAdd(X, XConstOp, XNonConstOp, XFlagsPresent)) {
10169 XConstOp = getZero(X->getType());
10170 XNonConstOp = X;
10171 XFlagsPresent = ExpectedFlags;
10172 }
10173 if (!isa<SCEVConstant>(XConstOp) ||
10174 (XFlagsPresent & ExpectedFlags) != ExpectedFlags)
10175 return false;
10176
10177 if (!splitBinaryAdd(Y, YConstOp, YNonConstOp, YFlagsPresent)) {
10178 YConstOp = getZero(Y->getType());
10179 YNonConstOp = Y;
10180 YFlagsPresent = ExpectedFlags;
10181 }
10182
10183 if (!isa<SCEVConstant>(YConstOp) ||
10184 (YFlagsPresent & ExpectedFlags) != ExpectedFlags)
10185 return false;
10186
10187 if (YNonConstOp != XNonConstOp)
10188 return false;
10189
10190 OutC1 = cast<SCEVConstant>(XConstOp)->getAPInt();
10191 OutC2 = cast<SCEVConstant>(YConstOp)->getAPInt();
10192
10193 return true;
10194 };
10195
10196 APInt C1;
10197 APInt C2;
10198
10199 switch (Pred) {
10200 default:
10201 break;
10202
10203 case ICmpInst::ICMP_SGE:
10204 std::swap(LHS, RHS);
10205 LLVM_FALLTHROUGH[[gnu::fallthrough]];
10206 case ICmpInst::ICMP_SLE:
10207 // (X + C1)<nsw> s<= (X + C2)<nsw> if C1 s<= C2.
10208 if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.sle(C2))
10209 return true;
10210
10211 break;
10212
10213 case ICmpInst::ICMP_SGT:
10214 std::swap(LHS, RHS);
10215 LLVM_FALLTHROUGH[[gnu::fallthrough]];
10216 case ICmpInst::ICMP_SLT:
10217 // (X + C1)<nsw> s< (X + C2)<nsw> if C1 s< C2.
10218 if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.slt(C2))
10219 return true;
10220
10221 break;
10222
10223 case ICmpInst::ICMP_UGE:
10224 std::swap(LHS, RHS);
10225 LLVM_FALLTHROUGH[[gnu::fallthrough]];
10226 case ICmpInst::ICMP_ULE:
10227 // (X + C1)<nuw> u<= (X + C2)<nuw> for C1 u<= C2.
10228 if (MatchBinaryAddToConst(RHS, LHS, C2, C1, SCEV::FlagNUW) && C1.ule(C2))
10229 return true;
10230
10231 break;
10232
10233 case ICmpInst::ICMP_UGT:
10234 std::swap(LHS, RHS);
10235 LLVM_FALLTHROUGH[[gnu::fallthrough]];
10236 case ICmpInst::ICMP_ULT:
10237 // (X + C1)<nuw> u< (X + C2)<nuw> if C1 u< C2.
10238 if (MatchBinaryAddToConst(RHS, LHS, C2, C1, SCEV::FlagNUW) && C1.ult(C2))
10239 return true;
10240 break;
10241 }
10242
10243 return false;
10244}
10245
10246bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
10247 const SCEV *LHS,
10248 const SCEV *RHS) {
10249 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
10250 return false;
10251
10252 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
10253 // the stack can result in exponential time complexity.
10254 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
10255
10256 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
10257 //
10258 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
10259 // isKnownPredicate. isKnownPredicate is more powerful, but also more
10260 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
10261 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
10262 // use isKnownPredicate later if needed.
10263 return isKnownNonNegative(RHS) &&
10264 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
10265 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
10266}
10267
10268bool ScalarEvolution::isImpliedViaGuard(const BasicBlock *BB,
10269 ICmpInst::Predicate Pred,
10270 const SCEV *LHS, const SCEV *RHS) {
10271 // No need to even try if we know the module has no guards.
10272 if (!HasGuards)
10273 return false;
10274
10275 return any_of(*BB, [&](const Instruction &I) {
10276 using namespace llvm::PatternMatch;
10277
10278 Value *Condition;
10279 return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
10280 m_Value(Condition))) &&
10281 isImpliedCond(Pred, LHS, RHS, Condition, false);
10282 });
10283}
10284
10285/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
10286/// protected by a conditional between LHS and RHS. This is used to
10287/// to eliminate casts.
10288bool
10289ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
10290 ICmpInst::Predicate Pred,
10291 const SCEV *LHS, const SCEV *RHS) {
10292 // Interpret a null as meaning no loop, where there is obviously no guard
10293 // (interprocedural conditions notwithstanding).
10294 if (!L) return true;
10295
10296 if (VerifyIR)
10297 assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&((void)0)
10298 "This cannot be done on broken IR!")((void)0);
10299
10300
10301 if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
10302 return true;
10303
10304 BasicBlock *Latch = L->getLoopLatch();
10305 if (!Latch)
10306 return false;
10307
10308 BranchInst *LoopContinuePredicate =
10309 dyn_cast<BranchInst>(Latch->getTerminator());
10310 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
10311 isImpliedCond(Pred, LHS, RHS,
10312 LoopContinuePredicate->getCondition(),
10313 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
10314 return true;
10315
10316 // We don't want more than one activation of the following loops on the stack
10317 // -- that can lead to O(n!) time complexity.
10318 if (WalkingBEDominatingConds)
10319 return false;
10320
10321 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
10322
10323 // See if we can exploit a trip count to prove the predicate.
10324 const auto &BETakenInfo = getBackedgeTakenInfo(L);
10325 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
10326 if (LatchBECount != getCouldNotCompute()) {
10327 // We know that Latch branches back to the loop header exactly
10328 // LatchBECount times. This means the backdege condition at Latch is
10329 // equivalent to "{0,+,1} u< LatchBECount".
10330 Type *Ty = LatchBECount->getType();
10331 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
10332 const SCEV *LoopCounter =
10333 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
10334 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
10335 LatchBECount))
10336 return true;
10337 }
10338
10339 // Check conditions due to any @llvm.assume intrinsics.
10340 for (auto &AssumeVH : AC.assumptions()) {
10341 if (!AssumeVH)
10342 continue;
10343 auto *CI = cast<CallInst>(AssumeVH);
10344 if (!DT.dominates(CI, Latch->getTerminator()))
10345 continue;
10346
10347 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
10348 return true;
10349 }
10350
10351 // If the loop is not reachable from the entry block, we risk running into an
10352 // infinite loop as we walk up into the dom tree. These loops do not matter
10353 // anyway, so we just return a conservative answer when we see them.
10354 if (!DT.isReachableFromEntry(L->getHeader()))
10355 return false;
10356
10357 if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
10358 return true;
10359
10360 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
10361 DTN != HeaderDTN; DTN = DTN->getIDom()) {
10362 assert(DTN && "should reach the loop header before reaching the root!")((void)0);
10363
10364 BasicBlock *BB = DTN->getBlock();
10365 if (isImpliedViaGuard(BB, Pred, LHS, RHS))
10366 return true;
10367
10368 BasicBlock *PBB = BB->getSinglePredecessor();
10369 if (!PBB)
10370 continue;
10371
10372 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
10373 if (!ContinuePredicate || !ContinuePredicate->isConditional())
10374 continue;
10375
10376 Value *Condition = ContinuePredicate->getCondition();
10377
10378 // If we have an edge `E` within the loop body that dominates the only
10379 // latch, the condition guarding `E` also guards the backedge. This
10380 // reasoning works only for loops with a single latch.
10381
10382 BasicBlockEdge DominatingEdge(PBB, BB);
10383 if (DominatingEdge.isSingleEdge()) {
10384 // We're constructively (and conservatively) enumerating edges within the
10385 // loop body that dominate the latch. The dominator tree better agree
10386 // with us on this:
10387 assert(DT.dominates(DominatingEdge, Latch) && "should be!")((void)0);
10388
10389 if (isImpliedCond(Pred, LHS, RHS, Condition,
10390 BB != ContinuePredicate->getSuccessor(0)))
10391 return true;
10392 }
10393 }
10394
10395 return false;
10396}
10397
10398bool ScalarEvolution::isBasicBlockEntryGuardedByCond(const BasicBlock *BB,
10399 ICmpInst::Predicate Pred,
10400 const SCEV *LHS,
10401 const SCEV *RHS) {
10402 if (VerifyIR)
13
Assuming the condition is false
14
Taking false branch
10403 assert(!verifyFunction(*BB->getParent(), &dbgs()) &&((void)0)
10404 "This cannot be done on broken IR!")((void)0);
10405
10406 // If we cannot prove strict comparison (e.g. a > b), maybe we can prove
10407 // the facts (a >= b && a != b) separately. A typical situation is when the
10408 // non-strict comparison is known from ranges and non-equality is known from
10409 // dominating predicates. If we are proving strict comparison, we always try
10410 // to prove non-equality and non-strict comparison separately.
10411 auto NonStrictPredicate = ICmpInst::getNonStrictPredicate(Pred);
10412 const bool ProvingStrictComparison = (Pred != NonStrictPredicate);
15
Assuming 'Pred' is equal to 'NonStrictPredicate'
10413 bool ProvedNonStrictComparison = false;
10414 bool ProvedNonEquality = false;
10415
10416 auto SplitAndProve =
10417 [&](std::function<bool(ICmpInst::Predicate)> Fn) -> bool {
10418 if (!ProvedNonStrictComparison)
10419 ProvedNonStrictComparison = Fn(NonStrictPredicate);
10420 if (!ProvedNonEquality)
10421 ProvedNonEquality = Fn(ICmpInst::ICMP_NE);
10422 if (ProvedNonStrictComparison && ProvedNonEquality)
10423 return true;
10424 return false;
10425 };
10426
10427 if (ProvingStrictComparison
15.1
'ProvingStrictComparison' is false
15.1
'ProvingStrictComparison' is false
) {
16
Taking false branch
10428 auto ProofFn = [&](ICmpInst::Predicate P) {
10429 return isKnownViaNonRecursiveReasoning(P, LHS, RHS);
10430 };
10431 if (SplitAndProve(ProofFn))
10432 return true;
10433 }
10434
10435 // Try to prove (Pred, LHS, RHS) using isImpliedViaGuard.
10436 auto ProveViaGuard = [&](const BasicBlock *Block) {
10437 if (isImpliedViaGuard(Block, Pred, LHS, RHS))
10438 return true;
10439 if (ProvingStrictComparison) {
10440 auto ProofFn = [&](ICmpInst::Predicate P) {
10441 return isImpliedViaGuard(Block, P, LHS, RHS);
10442 };
10443 if (SplitAndProve(ProofFn))
10444 return true;
10445 }
10446 return false;
10447 };
10448
10449 // Try to prove (Pred, LHS, RHS) using isImpliedCond.
10450 auto ProveViaCond = [&](const Value *Condition, bool Inverse) {
10451 const Instruction *Context = &BB->front();
26
Called C++ object pointer is null
10452 if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse, Context))
10453 return true;
10454 if (ProvingStrictComparison) {
10455 auto ProofFn = [&](ICmpInst::Predicate P) {
10456 return isImpliedCond(P, LHS, RHS, Condition, Inverse, Context);
10457 };
10458 if (SplitAndProve(ProofFn))
10459 return true;
10460 }
10461 return false;
10462 };
10463
10464 // Starting at the block's predecessor, climb up the predecessor chain, as long
10465 // as there are predecessors that can be found that have unique successors
10466 // leading to the original block.
10467 const Loop *ContainingLoop = LI.getLoopFor(BB);
10468 const BasicBlock *PredBB;
10469 if (ContainingLoop && ContainingLoop->getHeader() == BB)
17
Assuming 'ContainingLoop' is non-null
18
Assuming the condition is true
19
Taking true branch
10470 PredBB = ContainingLoop->getLoopPredecessor();
10471 else
10472 PredBB = BB->getSinglePredecessor();
10473 for (std::pair<const BasicBlock *, const BasicBlock *> Pair(PredBB, BB);
20
Loop condition is true. Entering loop body
10474 Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
10475 if (ProveViaGuard(Pair.first))
21
Taking false branch
10476 return true;
10477
10478 const BranchInst *LoopEntryPredicate =
10479 dyn_cast<BranchInst>(Pair.first->getTerminator());
22
Assuming the object is a 'BranchInst'
10480 if (!LoopEntryPredicate
22.1
'LoopEntryPredicate' is non-null
22.1
'LoopEntryPredicate' is non-null
||
23
Taking false branch
10481 LoopEntryPredicate->isUnconditional())
10482 continue;
10483
10484 if (ProveViaCond(LoopEntryPredicate->getCondition(),
25
Calling 'operator()'
10485 LoopEntryPredicate->getSuccessor(0) != Pair.second))
24
Assuming pointer value is null
10486 return true;
10487 }
10488
10489 // Check conditions due to any @llvm.assume intrinsics.
10490 for (auto &AssumeVH : AC.assumptions()) {
10491 if (!AssumeVH)
10492 continue;
10493 auto *CI = cast<CallInst>(AssumeVH);
10494 if (!DT.dominates(CI, BB))
10495 continue;
10496
10497 if (ProveViaCond(CI->getArgOperand(0), false))
10498 return true;
10499 }
10500
10501 return false;
10502}
10503
10504bool ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
10505 ICmpInst::Predicate Pred,
10506 const SCEV *LHS,
10507 const SCEV *RHS) {
10508 // Interpret a null as meaning no loop, where there is obviously no guard
10509 // (interprocedural conditions notwithstanding).
10510 if (!L)
10511 return false;
10512
10513 // Both LHS and RHS must be available at loop entry.
10514 assert(isAvailableAtLoopEntry(LHS, L) &&((void)0)
10515 "LHS is not available at Loop Entry")((void)0);
10516 assert(isAvailableAtLoopEntry(RHS, L) &&((void)0)
10517 "RHS is not available at Loop Entry")((void)0);
10518
10519 if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
10520 return true;
10521
10522 return isBasicBlockEntryGuardedByCond(L->getHeader(), Pred, LHS, RHS);
10523}
10524
10525bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
10526 const SCEV *RHS,
10527 const Value *FoundCondValue, bool Inverse,
10528 const Instruction *Context) {
10529 // False conditions implies anything. Do not bother analyzing it further.
10530 if (FoundCondValue ==
10531 ConstantInt::getBool(FoundCondValue->getContext(), Inverse))
10532 return true;
10533
10534 if (!PendingLoopPredicates.insert(FoundCondValue).second)
10535 return false;
10536
10537 auto ClearOnExit =
10538 make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); });
10539
10540 // Recursively handle And and Or conditions.
10541 const Value *Op0, *Op1;
10542 if (match(FoundCondValue, m_LogicalAnd(m_Value(Op0), m_Value(Op1)))) {
10543 if (!Inverse)
10544 return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, Context) ||
10545 isImpliedCond(Pred, LHS, RHS, Op1, Inverse, Context);
10546 } else if (match(FoundCondValue, m_LogicalOr(m_Value(Op0), m_Value(Op1)))) {
10547 if (Inverse)
10548 return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, Context) ||
10549 isImpliedCond(Pred, LHS, RHS, Op1, Inverse, Context);
10550 }
10551
10552 const ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
10553 if (!ICI) return false;
10554
10555 // Now that we found a conditional branch that dominates the loop or controls
10556 // the loop latch. Check to see if it is the comparison we are looking for.
10557 ICmpInst::Predicate FoundPred;
10558 if (Inverse)
10559 FoundPred = ICI->getInversePredicate();
10560 else
10561 FoundPred = ICI->getPredicate();
10562
10563 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
10564 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
10565
10566 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS, Context);
10567}
10568
10569bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
10570 const SCEV *RHS,
10571 ICmpInst::Predicate FoundPred,
10572 const SCEV *FoundLHS, const SCEV *FoundRHS,
10573 const Instruction *Context) {
10574 // Balance the types.
10575 if (getTypeSizeInBits(LHS->getType()) <
10576 getTypeSizeInBits(FoundLHS->getType())) {
10577 // For unsigned and equality predicates, try to prove that both found
10578 // operands fit into narrow unsigned range. If so, try to prove facts in
10579 // narrow types.
10580 if (!CmpInst::isSigned(FoundPred) && !FoundLHS->getType()->isPointerTy()) {
10581 auto *NarrowType = LHS->getType();
10582 auto *WideType = FoundLHS->getType();
10583 auto BitWidth = getTypeSizeInBits(NarrowType);
10584 const SCEV *MaxValue = getZeroExtendExpr(
10585 getConstant(APInt::getMaxValue(BitWidth)), WideType);
10586 if (isKnownPredicate(ICmpInst::ICMP_ULE, FoundLHS, MaxValue) &&
10587 isKnownPredicate(ICmpInst::ICMP_ULE, FoundRHS, MaxValue)) {
10588 const SCEV *TruncFoundLHS = getTruncateExpr(FoundLHS, NarrowType);
10589 const SCEV *TruncFoundRHS = getTruncateExpr(FoundRHS, NarrowType);
10590 if (isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, TruncFoundLHS,
10591 TruncFoundRHS, Context))
10592 return true;
10593 }
10594 }
10595
10596 if (LHS->getType()->isPointerTy())
10597 return false;
10598 if (CmpInst::isSigned(Pred)) {
10599 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
10600 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
10601 } else {
10602 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
10603 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
10604 }
10605 } else if (getTypeSizeInBits(LHS->getType()) >
10606 getTypeSizeInBits(FoundLHS->getType())) {
10607 if (FoundLHS->getType()->isPointerTy())
10608 return false;
10609 if (CmpInst::isSigned(FoundPred)) {
10610 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
10611 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
10612 } else {
10613 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
10614 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
10615 }
10616 }
10617 return isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, FoundLHS,
10618 FoundRHS, Context);
10619}
10620
10621bool ScalarEvolution::isImpliedCondBalancedTypes(
10622 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
10623 ICmpInst::Predicate FoundPred, const SCEV *FoundLHS, const SCEV *FoundRHS,
10624 const Instruction *Context) {
10625 assert(getTypeSizeInBits(LHS->getType()) ==((void)0)
10626 getTypeSizeInBits(FoundLHS->getType()) &&((void)0)
10627 "Types should be balanced!")((void)0);
10628 // Canonicalize the query to match the way instcombine will have
10629 // canonicalized the comparison.
10630 if (SimplifyICmpOperands(Pred, LHS, RHS))
10631 if (LHS == RHS)
10632 return CmpInst::isTrueWhenEqual(Pred);
10633 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
10634 if (FoundLHS == FoundRHS)
10635 return CmpInst::isFalseWhenEqual(FoundPred);
10636
10637 // Check to see if we can make the LHS or RHS match.
10638 if (LHS == FoundRHS || RHS == FoundLHS) {
10639 if (isa<SCEVConstant>(RHS)) {
10640 std::swap(FoundLHS, FoundRHS);
10641 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
10642 } else {
10643 std::swap(LHS, RHS);
10644 Pred = ICmpInst::getSwappedPredicate(Pred);
10645 }
10646 }
10647
10648 // Check whether the found predicate is the same as the desired predicate.
10649 if (FoundPred == Pred)
10650 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context);
10651
10652 // Check whether swapping the found predicate makes it the same as the
10653 // desired predicate.
10654 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
10655 // We can write the implication
10656 // 0. LHS Pred RHS <- FoundLHS SwapPred FoundRHS
10657 // using one of the following ways:
10658 // 1. LHS Pred RHS <- FoundRHS Pred FoundLHS
10659 // 2. RHS SwapPred LHS <- FoundLHS SwapPred FoundRHS
10660 // 3. LHS Pred RHS <- ~FoundLHS Pred ~FoundRHS
10661 // 4. ~LHS SwapPred ~RHS <- FoundLHS SwapPred FoundRHS
10662 // Forms 1. and 2. require swapping the operands of one condition. Don't
10663 // do this if it would break canonical constant/addrec ordering.
10664 if (!isa<SCEVConstant>(RHS) && !isa<SCEVAddRecExpr>(LHS))
10665 return isImpliedCondOperands(FoundPred, RHS, LHS, FoundLHS, FoundRHS,
10666 Context);
10667 if (!isa<SCEVConstant>(FoundRHS) && !isa<SCEVAddRecExpr>(FoundLHS))
10668 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS, Context);
10669
10670 // Don't try to getNotSCEV pointers.
10671 if (LHS->getType()->isPointerTy() || FoundLHS->getType()->isPointerTy())
10672 return false;
10673
10674 // There's no clear preference between forms 3. and 4., try both.
10675 return isImpliedCondOperands(FoundPred, getNotSCEV(LHS), getNotSCEV(RHS),
10676 FoundLHS, FoundRHS, Context) ||
10677 isImpliedCondOperands(Pred, LHS, RHS, getNotSCEV(FoundLHS),
10678 getNotSCEV(FoundRHS), Context);
10679 }
10680
10681 // Unsigned comparison is the same as signed comparison when both the operands
10682 // are non-negative.
10683 if (CmpInst::isUnsigned(FoundPred) &&
10684 CmpInst::getSignedPredicate(FoundPred) == Pred &&
10685 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
10686 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context);
10687
10688 // Check if we can make progress by sharpening ranges.
10689 if (FoundPred == ICmpInst::ICMP_NE &&
10690 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
10691
10692 const SCEVConstant *C = nullptr;
10693 const SCEV *V = nullptr;
10694
10695 if (isa<SCEVConstant>(FoundLHS)) {
10696 C = cast<SCEVConstant>(FoundLHS);
10697 V = FoundRHS;
10698 } else {
10699 C = cast<SCEVConstant>(FoundRHS);
10700 V = FoundLHS;
10701 }
10702
10703 // The guarding predicate tells us that C != V. If the known range
10704 // of V is [C, t), we can sharpen the range to [C + 1, t). The
10705 // range we consider has to correspond to same signedness as the
10706 // predicate we're interested in folding.
10707
10708 APInt Min = ICmpInst::isSigned(Pred) ?
10709 getSignedRangeMin(V) : getUnsignedRangeMin(V);
10710
10711 if (Min == C->getAPInt()) {
10712 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
10713 // This is true even if (Min + 1) wraps around -- in case of
10714 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
10715
10716 APInt SharperMin = Min + 1;
10717
10718 switch (Pred) {
10719 case ICmpInst::ICMP_SGE:
10720 case ICmpInst::ICMP_UGE:
10721 // We know V `Pred` SharperMin. If this implies LHS `Pred`
10722 // RHS, we're done.
10723 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(SharperMin),
10724 Context))
10725 return true;
10726 LLVM_FALLTHROUGH[[gnu::fallthrough]];
10727
10728 case ICmpInst::ICMP_SGT:
10729 case ICmpInst::ICMP_UGT:
10730 // We know from the range information that (V `Pred` Min ||
10731 // V == Min). We know from the guarding condition that !(V
10732 // == Min). This gives us
10733 //
10734 // V `Pred` Min || V == Min && !(V == Min)
10735 // => V `Pred` Min
10736 //
10737 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
10738
10739 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min),
10740 Context))
10741 return true;
10742 break;
10743
10744 // `LHS < RHS` and `LHS <= RHS` are handled in the same way as `RHS > LHS` and `RHS >= LHS` respectively.
10745 case ICmpInst::ICMP_SLE:
10746 case ICmpInst::ICMP_ULE:
10747 if (isImpliedCondOperands(CmpInst::getSwappedPredicate(Pred), RHS,
10748 LHS, V, getConstant(SharperMin), Context))
10749 return true;
10750 LLVM_FALLTHROUGH[[gnu::fallthrough]];
10751
10752 case ICmpInst::ICMP_SLT:
10753 case ICmpInst::ICMP_ULT:
10754 if (isImpliedCondOperands(CmpInst::getSwappedPredicate(Pred), RHS,
10755 LHS, V, getConstant(Min), Context))
10756 return true;
10757 break;
10758
10759 default:
10760 // No change
10761 break;
10762 }
10763 }
10764 }
10765
10766 // Check whether the actual condition is beyond sufficient.
10767 if (FoundPred == ICmpInst::ICMP_EQ)
10768 if (ICmpInst::isTrueWhenEqual(Pred))
10769 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context))
10770 return true;
10771 if (Pred == ICmpInst::ICMP_NE)
10772 if (!ICmpInst::isTrueWhenEqual(FoundPred))
10773 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS,
10774 Context))
10775 return true;
10776
10777 // Otherwise assume the worst.
10778 return false;
10779}
10780
10781bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
10782 const SCEV *&L, const SCEV *&R,
10783 SCEV::NoWrapFlags &Flags) {
10784 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
10785 if (!AE || AE->getNumOperands() != 2)
10786 return false;
10787
10788 L = AE->getOperand(0);
10789 R = AE->getOperand(1);
10790 Flags = AE->getNoWrapFlags();
10791 return true;
10792}
10793
10794Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More,
10795 const SCEV *Less) {
10796 // We avoid subtracting expressions here because this function is usually
10797 // fairly deep in the call stack (i.e. is called many times).
10798
10799 // X - X = 0.
10800 if (More == Less)
10801 return APInt(getTypeSizeInBits(More->getType()), 0);
10802
10803 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
10804 const auto *LAR = cast<SCEVAddRecExpr>(Less);
10805 const auto *MAR = cast<SCEVAddRecExpr>(More);
10806
10807 if (LAR->getLoop() != MAR->getLoop())
10808 return None;
10809
10810 // We look at affine expressions only; not for correctness but to keep
10811 // getStepRecurrence cheap.
10812 if (!LAR->isAffine() || !MAR->isAffine())
10813 return None;
10814
10815 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
10816 return None;
10817
10818 Less = LAR->getStart();
10819 More = MAR->getStart();
10820
10821 // fall through
10822 }
10823
10824 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
10825 const auto &M = cast<SCEVConstant>(More)->getAPInt();
10826 const auto &L = cast<SCEVConstant>(Less)->getAPInt();
10827 return M - L;
10828 }
10829
10830 SCEV::NoWrapFlags Flags;
10831 const SCEV *LLess = nullptr, *RLess = nullptr;
10832 const SCEV *LMore = nullptr, *RMore = nullptr;
10833 const SCEVConstant *C1 = nullptr, *C2 = nullptr;
10834 // Compare (X + C1) vs X.
10835 if (splitBinaryAdd(Less, LLess, RLess, Flags))
10836 if ((C1 = dyn_cast<SCEVConstant>(LLess)))
10837 if (RLess == More)
10838 return -(C1->getAPInt());
10839
10840 // Compare X vs (X + C2).
10841 if (splitBinaryAdd(More, LMore, RMore, Flags))
10842 if ((C2 = dyn_cast<SCEVConstant>(LMore)))
10843 if (RMore == Less)
10844 return C2->getAPInt();
10845
10846 // Compare (X + C1) vs (X + C2).
10847 if (C1 && C2 && RLess == RMore)
10848 return C2->getAPInt() - C1->getAPInt();
10849
10850 return None;
10851}
10852
10853bool ScalarEvolution::isImpliedCondOperandsViaAddRecStart(
10854 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
10855 const SCEV *FoundLHS, const SCEV *FoundRHS, const Instruction *Context) {
10856 // Try to recognize the following pattern:
10857 //
10858 // FoundRHS = ...
10859 // ...
10860 // loop:
10861 // FoundLHS = {Start,+,W}
10862 // context_bb: // Basic block from the same loop
10863 // known(Pred, FoundLHS, FoundRHS)
10864 //
10865 // If some predicate is known in the context of a loop, it is also known on
10866 // each iteration of this loop, including the first iteration. Therefore, in
10867 // this case, `FoundLHS Pred FoundRHS` implies `Start Pred FoundRHS`. Try to
10868 // prove the original pred using this fact.
10869 if (!Context)
10870 return false;
10871 const BasicBlock *ContextBB = Context->getParent();
10872 // Make sure AR varies in the context block.
10873 if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundLHS)) {
10874 const Loop *L = AR->getLoop();
10875 // Make sure that context belongs to the loop and executes on 1st iteration
10876 // (if it ever executes at all).
10877 if (!L->contains(ContextBB) || !DT.dominates(ContextBB, L->getLoopLatch()))
10878 return false;
10879 if (!isAvailableAtLoopEntry(FoundRHS, AR->getLoop()))
10880 return false;
10881 return isImpliedCondOperands(Pred, LHS, RHS, AR->getStart(), FoundRHS);
10882 }
10883
10884 if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundRHS)) {
10885 const Loop *L = AR->getLoop();
10886 // Make sure that context belongs to the loop and executes on 1st iteration
10887 // (if it ever executes at all).
10888 if (!L->contains(ContextBB) || !DT.dominates(ContextBB, L->getLoopLatch()))
10889 return false;
10890 if (!isAvailableAtLoopEntry(FoundLHS, AR->getLoop()))
10891 return false;
10892 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, AR->getStart());
10893 }
10894
10895 return false;
10896}
10897
10898bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
10899 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
10900 const SCEV *FoundLHS, const SCEV *FoundRHS) {
10901 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
10902 return false;
10903
10904 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
10905 if (!AddRecLHS)
10906 return false;
10907
10908 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
10909 if (!AddRecFoundLHS)
10910 return false;
10911
10912 // We'd like to let SCEV reason about control dependencies, so we constrain
10913 // both the inequalities to be about add recurrences on the same loop. This
10914 // way we can use isLoopEntryGuardedByCond later.
10915
10916 const Loop *L = AddRecFoundLHS->getLoop();
10917 if (L != AddRecLHS->getLoop())
10918 return false;
10919
10920 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
10921 //
10922 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
10923 // ... (2)
10924 //
10925 // Informal proof for (2), assuming (1) [*]:
10926 //
10927 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
10928 //
10929 // Then
10930 //
10931 // FoundLHS s< FoundRHS s< INT_MIN - C
10932 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
10933 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
10934 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
10935 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
10936 // <=> FoundLHS + C s< FoundRHS + C
10937 //
10938 // [*]: (1) can be proved by ruling out overflow.
10939 //
10940 // [**]: This can be proved by analyzing all the four possibilities:
10941 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
10942 // (A s>= 0, B s>= 0).
10943 //
10944 // Note:
10945 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
10946 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
10947 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
10948 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
10949 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
10950 // C)".
10951
10952 Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
10953 Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
10954 if (!LDiff || !RDiff || *LDiff != *RDiff)
10955 return false;
10956
10957 if (LDiff->isMinValue())
10958 return true;
10959
10960 APInt FoundRHSLimit;
10961
10962 if (Pred == CmpInst::ICMP_ULT) {
10963 FoundRHSLimit = -(*RDiff);
10964 } else {
10965 assert(Pred == CmpInst::ICMP_SLT && "Checked above!")((void)0);
10966 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
10967 }
10968
10969 // Try to prove (1) or (2), as needed.
10970 return isAvailableAtLoopEntry(FoundRHS, L) &&
10971 isLoopEntryGuardedByCond(L, Pred, FoundRHS,
10972 getConstant(FoundRHSLimit));
10973}
10974
10975bool ScalarEvolution::isImpliedViaMerge(ICmpInst::Predicate Pred,
10976 const SCEV *LHS, const SCEV *RHS,
10977 const SCEV *FoundLHS,
10978 const SCEV *FoundRHS, unsigned Depth) {
10979 const PHINode *LPhi = nullptr, *RPhi = nullptr;
10980
10981 auto ClearOnExit = make_scope_exit([&]() {
10982 if (LPhi) {
10983 bool Erased = PendingMerges.erase(LPhi);
10984 assert(Erased && "Failed to erase LPhi!")((void)0);
10985 (void)Erased;
10986 }
10987 if (RPhi) {
10988 bool Erased = PendingMerges.erase(RPhi);
10989 assert(Erased && "Failed to erase RPhi!")((void)0);
10990 (void)Erased;
10991 }
10992 });
10993
10994 // Find respective Phis and check that they are not being pending.
10995 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS))
10996 if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) {
10997 if (!PendingMerges.insert(Phi).second)
10998 return false;
10999 LPhi = Phi;
11000 }
11001 if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS))
11002 if (auto *Phi = dyn_cast<PHINode>(RU->getValue())) {
11003 // If we detect a loop of Phi nodes being processed by this method, for
11004 // example:
11005 //
11006 // %a = phi i32 [ %some1, %preheader ], [ %b, %latch ]
11007 // %b = phi i32 [ %some2, %preheader ], [ %a, %latch ]
11008 //
11009 // we don't want to deal with a case that complex, so return conservative
11010 // answer false.
11011 if (!PendingMerges.insert(Phi).second)
11012 return false;
11013 RPhi = Phi;
11014 }
11015
11016 // If none of LHS, RHS is a Phi, nothing to do here.
11017 if (!LPhi && !RPhi)
11018 return false;
11019
11020 // If there is a SCEVUnknown Phi we are interested in, make it left.
11021 if (!LPhi) {
11022 std::swap(LHS, RHS);
11023 std::swap(FoundLHS, FoundRHS);
11024 std::swap(LPhi, RPhi);
11025 Pred = ICmpInst::getSwappedPredicate(Pred);
11026 }
11027
11028 assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!")((void)0);
11029 const BasicBlock *LBB = LPhi->getParent();
11030 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
11031
11032 auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) {
11033 return isKnownViaNonRecursiveReasoning(Pred, S1, S2) ||
11034 isImpliedCondOperandsViaRanges(Pred, S1, S2, FoundLHS, FoundRHS) ||
11035 isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth);
11036 };
11037
11038 if (RPhi && RPhi->getParent() == LBB) {
11039 // Case one: RHS is also a SCEVUnknown Phi from the same basic block.
11040 // If we compare two Phis from the same block, and for each entry block
11041 // the predicate is true for incoming values from this block, then the
11042 // predicate is also true for the Phis.
11043 for (const BasicBlock *IncBB : predecessors(LBB)) {
11044 const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
11045 const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB));
11046 if (!ProvedEasily(L, R))
11047 return false;
11048 }
11049 } else if (RAR && RAR->getLoop()->getHeader() == LBB) {
11050 // Case two: RHS is also a Phi from the same basic block, and it is an
11051 // AddRec. It means that there is a loop which has both AddRec and Unknown
11052 // PHIs, for it we can compare incoming values of AddRec from above the loop
11053 // and latch with their respective incoming values of LPhi.
11054 // TODO: Generalize to handle loops with many inputs in a header.
11055 if (LPhi->getNumIncomingValues() != 2) return false;
11056
11057 auto *RLoop = RAR->getLoop();
11058 auto *Predecessor = RLoop->getLoopPredecessor();
11059 assert(Predecessor && "Loop with AddRec with no predecessor?")((void)0);
11060 const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor));
11061 if (!ProvedEasily(L1, RAR->getStart()))
11062 return false;
11063 auto *Latch = RLoop->getLoopLatch();
11064 assert(Latch && "Loop with AddRec with no latch?")((void)0);
11065 const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch));
11066 if (!ProvedEasily(L2, RAR->getPostIncExpr(*this)))
11067 return false;
11068 } else {
11069 // In all other cases go over inputs of LHS and compare each of them to RHS,
11070 // the predicate is true for (LHS, RHS) if it is true for all such pairs.
11071 // At this point RHS is either a non-Phi, or it is a Phi from some block
11072 // different from LBB.
11073 for (const BasicBlock *IncBB : predecessors(LBB)) {
11074 // Check that RHS is available in this block.
11075 if (!dominates(RHS, IncBB))
11076 return false;
11077 const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
11078 // Make sure L does not refer to a value from a potentially previous
11079 // iteration of a loop.
11080 if (!properlyDominates(L, IncBB))
11081 return false;
11082 if (!ProvedEasily(L, RHS))
11083 return false;
11084 }
11085 }
11086 return true;
11087}
11088
11089bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
11090 const SCEV *LHS, const SCEV *RHS,
11091 const SCEV *FoundLHS,
11092 const SCEV *FoundRHS,
11093 const Instruction *Context) {
11094 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
11095 return true;
11096
11097 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
11098 return true;
11099
11100 if (isImpliedCondOperandsViaAddRecStart(Pred, LHS, RHS, FoundLHS, FoundRHS,
11101 Context))
11102 return true;
11103
11104 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
11105 FoundLHS, FoundRHS);
11106}
11107
11108/// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values?
11109template <typename MinMaxExprType>
11110static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr,
11111 const SCEV *Candidate) {
11112 const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr);
11113 if (!MinMaxExpr)
11114 return false;
11115
11116 return is_contained(MinMaxExpr->operands(), Candidate);
11117}
11118
11119static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
11120 ICmpInst::Predicate Pred,
11121 const SCEV *LHS, const SCEV *RHS) {
11122 // If both sides are affine addrecs for the same loop, with equal
11123 // steps, and we know the recurrences don't wrap, then we only
11124 // need to check the predicate on the starting values.
11125
11126 if (!ICmpInst::isRelational(Pred))
11127 return false;
11128
11129 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
11130 if (!LAR)
11131 return false;
11132 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
11133 if (!RAR)
11134 return false;
11135 if (LAR->getLoop() != RAR->getLoop())
11136 return false;
11137 if (!LAR->isAffine() || !RAR->isAffine())
11138 return false;
11139
11140 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
11141 return false;
11142
11143 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
11144 SCEV::FlagNSW : SCEV::FlagNUW;
11145 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
11146 return false;
11147
11148 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
11149}
11150
11151/// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
11152/// expression?
11153static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
11154 ICmpInst::Predicate Pred,
11155 const SCEV *LHS, const SCEV *RHS) {
11156 switch (Pred) {
11157 default:
11158 return false;
11159
11160 case ICmpInst::ICMP_SGE:
11161 std::swap(LHS, RHS);
11162 LLVM_FALLTHROUGH[[gnu::fallthrough]];
11163 case ICmpInst::ICMP_SLE:
11164 return
11165 // min(A, ...) <= A
11166 IsMinMaxConsistingOf<SCEVSMinExpr>(LHS, RHS) ||
11167 // A <= max(A, ...)
11168 IsMinMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
11169
11170 case ICmpInst::ICMP_UGE:
11171 std::swap(LHS, RHS);
11172 LLVM_FALLTHROUGH[[gnu::fallthrough]];
11173 case ICmpInst::ICMP_ULE:
11174 return
11175 // min(A, ...) <= A
11176 IsMinMaxConsistingOf<SCEVUMinExpr>(LHS, RHS) ||
11177 // A <= max(A, ...)
11178 IsMinMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
11179 }
11180
11181 llvm_unreachable("covered switch fell through?!")__builtin_unreachable();
11182}
11183
11184bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred,
11185 const SCEV *LHS, const SCEV *RHS,
11186 const SCEV *FoundLHS,
11187 const SCEV *FoundRHS,
11188 unsigned Depth) {
11189 assert(getTypeSizeInBits(LHS->getType()) ==((void)0)
11190 getTypeSizeInBits(RHS->getType()) &&((void)0)
11191 "LHS and RHS have different sizes?")((void)0);
11192 assert(getTypeSizeInBits(FoundLHS->getType()) ==((void)0)
11193 getTypeSizeInBits(FoundRHS->getType()) &&((void)0)
11194 "FoundLHS and FoundRHS have different sizes?")((void)0);
11195 // We want to avoid hurting the compile time with analysis of too big trees.
11196 if (Depth > MaxSCEVOperationsImplicationDepth)
11197 return false;
11198
11199 // We only want to work with GT comparison so far.
11200 if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_SLT) {
11201 Pred = CmpInst::getSwappedPredicate(Pred);
11202 std::swap(LHS, RHS);
11203 std::swap(FoundLHS, FoundRHS);
11204 }
11205
11206 // For unsigned, try to reduce it to corresponding signed comparison.
11207 if (Pred == ICmpInst::ICMP_UGT)
11208 // We can replace unsigned predicate with its signed counterpart if all
11209 // involved values are non-negative.
11210 // TODO: We could have better support for unsigned.
11211 if (isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) {
11212 // Knowing that both FoundLHS and FoundRHS are non-negative, and knowing
11213 // FoundLHS >u FoundRHS, we also know that FoundLHS >s FoundRHS. Let us
11214 // use this fact to prove that LHS and RHS are non-negative.
11215 const SCEV *MinusOne = getMinusOne(LHS->getType());
11216 if (isImpliedCondOperands(ICmpInst::ICMP_SGT, LHS, MinusOne, FoundLHS,
11217 FoundRHS) &&
11218 isImpliedCondOperands(ICmpInst::ICMP_SGT, RHS, MinusOne, FoundLHS,
11219 FoundRHS))
11220 Pred = ICmpInst::ICMP_SGT;
11221 }
11222
11223 if (Pred != ICmpInst::ICMP_SGT)
11224 return false;
11225
11226 auto GetOpFromSExt = [&](const SCEV *S) {
11227 if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S))
11228 return Ext->getOperand();
11229 // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off
11230 // the constant in some cases.
11231 return S;
11232 };
11233
11234 // Acquire values from extensions.
11235 auto *OrigLHS = LHS;
11236 auto *OrigFoundLHS = FoundLHS;
11237 LHS = GetOpFromSExt(LHS);
11238 FoundLHS = GetOpFromSExt(FoundLHS);
11239
11240 // Is the SGT predicate can be proved trivially or using the found context.
11241 auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) {
11242 return isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGT, S1, S2) ||
11243 isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS,
11244 FoundRHS, Depth + 1);
11245 };
11246
11247 if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) {
11248 // We want to avoid creation of any new non-constant SCEV. Since we are
11249 // going to compare the operands to RHS, we should be certain that we don't
11250 // need any size extensions for this. So let's decline all cases when the
11251 // sizes of types of LHS and RHS do not match.
11252 // TODO: Maybe try to get RHS from sext to catch more cases?
11253 if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType()))
11254 return false;
11255
11256 // Should not overflow.
11257 if (!LHSAddExpr->hasNoSignedWrap())
11258 return false;
11259
11260 auto *LL = LHSAddExpr->getOperand(0);
11261 auto *LR = LHSAddExpr->getOperand(1);
11262 auto *MinusOne = getMinusOne(RHS->getType());
11263
11264 // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context.
11265 auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) {
11266 return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS);
11267 };
11268 // Try to prove the following rule:
11269 // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS).
11270 // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS).
11271 if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL))
11272 return true;
11273 } else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) {
11274 Value *LL, *LR;
11275 // FIXME: Once we have SDiv implemented, we can get rid of this matching.
11276
11277 using namespace llvm::PatternMatch;
11278
11279 if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) {
11280 // Rules for division.
11281 // We are going to perform some comparisons with Denominator and its
11282 // derivative expressions. In general case, creating a SCEV for it may
11283 // lead to a complex analysis of the entire graph, and in particular it
11284 // can request trip count recalculation for the same loop. This would
11285 // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid
11286 // this, we only want to create SCEVs that are constants in this section.
11287 // So we bail if Denominator is not a constant.
11288 if (!isa<ConstantInt>(LR))
11289 return false;
11290
11291 auto *Denominator = cast<SCEVConstant>(getSCEV(LR));
11292
11293 // We want to make sure that LHS = FoundLHS / Denominator. If it is so,
11294 // then a SCEV for the numerator already exists and matches with FoundLHS.
11295 auto *Numerator = getExistingSCEV(LL);
11296 if (!Numerator || Numerator->getType() != FoundLHS->getType())
11297 return false;
11298
11299 // Make sure that the numerator matches with FoundLHS and the denominator
11300 // is positive.
11301 if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator))
11302 return false;
11303
11304 auto *DTy = Denominator->getType();
11305 auto *FRHSTy = FoundRHS->getType();
11306 if (DTy->isPointerTy() != FRHSTy->isPointerTy())
11307 // One of types is a pointer and another one is not. We cannot extend
11308 // them properly to a wider type, so let us just reject this case.
11309 // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help
11310 // to avoid this check.
11311 return false;
11312
11313 // Given that:
11314 // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0.
11315 auto *WTy = getWiderType(DTy, FRHSTy);
11316 auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy);
11317 auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy);
11318
11319 // Try to prove the following rule:
11320 // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS).
11321 // For example, given that FoundLHS > 2. It means that FoundLHS is at
11322 // least 3. If we divide it by Denominator < 4, we will have at least 1.
11323 auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2));
11324 if (isKnownNonPositive(RHS) &&
11325 IsSGTViaContext(FoundRHSExt, DenomMinusTwo))
11326 return true;
11327
11328 // Try to prove the following rule:
11329 // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS).
11330 // For example, given that FoundLHS > -3. Then FoundLHS is at least -2.
11331 // If we divide it by Denominator > 2, then:
11332 // 1. If FoundLHS is negative, then the result is 0.
11333 // 2. If FoundLHS is non-negative, then the result is non-negative.
11334 // Anyways, the result is non-negative.
11335 auto *MinusOne = getMinusOne(WTy);
11336 auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt);
11337 if (isKnownNegative(RHS) &&
11338 IsSGTViaContext(FoundRHSExt, NegDenomMinusOne))
11339 return true;
11340 }
11341 }
11342
11343 // If our expression contained SCEVUnknown Phis, and we split it down and now
11344 // need to prove something for them, try to prove the predicate for every
11345 // possible incoming values of those Phis.
11346 if (isImpliedViaMerge(Pred, OrigLHS, RHS, OrigFoundLHS, FoundRHS, Depth + 1))
11347 return true;
11348
11349 return false;
11350}
11351
11352static bool isKnownPredicateExtendIdiom(ICmpInst::Predicate Pred,
11353 const SCEV *LHS, const SCEV *RHS) {
11354 // zext x u<= sext x, sext x s<= zext x
11355 switch (Pred) {
11356 case ICmpInst::ICMP_SGE:
11357 std::swap(LHS, RHS);
11358 LLVM_FALLTHROUGH[[gnu::fallthrough]];
11359 case ICmpInst::ICMP_SLE: {
11360 // If operand >=s 0 then ZExt == SExt. If operand <s 0 then SExt <s ZExt.
11361 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(LHS);
11362 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(RHS);
11363 if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
11364 return true;
11365 break;
11366 }
11367 case ICmpInst::ICMP_UGE:
11368 std::swap(LHS, RHS);
11369 LLVM_FALLTHROUGH[[gnu::fallthrough]];
11370 case ICmpInst::ICMP_ULE: {
11371 // If operand >=s 0 then ZExt == SExt. If operand <s 0 then ZExt <u SExt.
11372 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS);
11373 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(RHS);
11374 if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
11375 return true;
11376 break;
11377 }
11378 default:
11379 break;
11380 };
11381 return false;
11382}
11383
11384bool
11385ScalarEvolution::isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
11386 const SCEV *LHS, const SCEV *RHS) {
11387 return isKnownPredicateExtendIdiom(Pred, LHS, RHS) ||
11388 isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
11389 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
11390 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
11391 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
11392}
11393
11394bool
11395ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
11396 const SCEV *LHS, const SCEV *RHS,
11397 const SCEV *FoundLHS,
11398 const SCEV *FoundRHS) {
11399 switch (Pred) {
11400 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!")__builtin_unreachable();
11401 case ICmpInst::ICMP_EQ:
11402 case ICmpInst::ICMP_NE:
11403 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
11404 return true;
11405 break;
11406 case ICmpInst::ICMP_SLT:
11407 case ICmpInst::ICMP_SLE:
11408 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
11409 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS))
11410 return true;
11411 break;
11412 case ICmpInst::ICMP_SGT:
11413 case ICmpInst::ICMP_SGE:
11414 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
11415 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS))
11416 return true;
11417 break;
11418 case ICmpInst::ICMP_ULT:
11419 case ICmpInst::ICMP_ULE:
11420 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
11421 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS))
11422 return true;
11423 break;
11424 case ICmpInst::ICMP_UGT:
11425 case ICmpInst::ICMP_UGE:
11426 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
11427 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS))
11428 return true;
11429 break;
11430 }
11431
11432 // Maybe it can be proved via operations?
11433 if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS))
11434 return true;
11435
11436 return false;
11437}
11438
11439bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
11440 const SCEV *LHS,
11441 const SCEV *RHS,
11442 const SCEV *FoundLHS,
11443 const SCEV *FoundRHS) {
11444 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
11445 // The restriction on `FoundRHS` be lifted easily -- it exists only to
11446 // reduce the compile time impact of this optimization.
11447 return false;
11448
11449 Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
11450 if (!Addend)
11451 return false;
11452
11453 const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
11454
11455 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
11456 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
11457 ConstantRange FoundLHSRange =
11458 ConstantRange::makeExactICmpRegion(Pred, ConstFoundRHS);
11459
11460 // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
11461 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));
11462
11463 // We can also compute the range of values for `LHS` that satisfy the
11464 // consequent, "`LHS` `Pred` `RHS`":
11465 const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
11466 // The antecedent implies the consequent if every value of `LHS` that
11467 // satisfies the antecedent also satisfies the consequent.
11468 return LHSRange.icmp(Pred, ConstRHS);
11469}
11470
11471bool ScalarEvolution::canIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
11472 bool IsSigned) {
11473 assert(isKnownPositive(Stride) && "Positive stride expected!")((void)0);
11474
11475 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
11476 const SCEV *One = getOne(Stride->getType());
11477
11478 if (IsSigned) {
11479 APInt MaxRHS = getSignedRangeMax(RHS);
11480 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
11481 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
11482
11483 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
11484 return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS);
11485 }
11486
11487 APInt MaxRHS = getUnsignedRangeMax(RHS);
11488 APInt MaxValue = APInt::getMaxValue(BitWidth);
11489 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
11490
11491 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
11492 return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS);
11493}
11494
11495bool ScalarEvolution::canIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
11496 bool IsSigned) {
11497
11498 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
11499 const SCEV *One = getOne(Stride->getType());
11500
11501 if (IsSigned) {
11502 APInt MinRHS = getSignedRangeMin(RHS);
11503 APInt MinValue = APInt::getSignedMinValue(BitWidth);
11504 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
11505
11506 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
11507 return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS);
11508 }
11509
11510 APInt MinRHS = getUnsignedRangeMin(RHS);
11511 APInt MinValue = APInt::getMinValue(BitWidth);
11512 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
11513
11514 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
11515 return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS);
11516}
11517
11518const SCEV *ScalarEvolution::getUDivCeilSCEV(const SCEV *N, const SCEV *D) {
11519 // umin(N, 1) + floor((N - umin(N, 1)) / D)
11520 // This is equivalent to "1 + floor((N - 1) / D)" for N != 0. The umin
11521 // expression fixes the case of N=0.
11522 const SCEV *MinNOne = getUMinExpr(N, getOne(N->getType()));
11523 const SCEV *NMinusOne = getMinusSCEV(N, MinNOne);
11524 return getAddExpr(MinNOne, getUDivExpr(NMinusOne, D));
11525}
11526
11527const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
11528 const SCEV *Stride,
11529 const SCEV *End,
11530 unsigned BitWidth,
11531 bool IsSigned) {
11532 // The logic in this function assumes we can represent a positive stride.
11533 // If we can't, the backedge-taken count must be zero.
11534 if (IsSigned && BitWidth == 1)
11535 return getZero(Stride->getType());
11536
11537 // Calculate the maximum backedge count based on the range of values
11538 // permitted by Start, End, and Stride.
11539 APInt MinStart =
11540 IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);
11541
11542 APInt MinStride =
11543 IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
11544
11545 // We assume either the stride is positive, or the backedge-taken count
11546 // is zero. So force StrideForMaxBECount to be at least one.
11547 APInt One(BitWidth, 1);
11548 APInt StrideForMaxBECount = IsSigned ? APIntOps::smax(One, MinStride)
11549 : APIntOps::umax(One, MinStride);
11550
11551 APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth)
11552 : APInt::getMaxValue(BitWidth);
11553 APInt Limit = MaxValue - (StrideForMaxBECount - 1);
11554
11555 // Although End can be a MAX expression we estimate MaxEnd considering only
11556 // the case End = RHS of the loop termination condition. This is safe because
11557 // in the other case (End - Start) is zero, leading to a zero maximum backedge
11558 // taken count.
11559 APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit)
11560 : APIntOps::umin(getUnsignedRangeMax(End), Limit);
11561
11562 // MaxBECount = ceil((max(MaxEnd, MinStart) - MinStart) / Stride)
11563 MaxEnd = IsSigned ? APIntOps::smax(MaxEnd, MinStart)
11564 : APIntOps::umax(MaxEnd, MinStart);
11565
11566 return getUDivCeilSCEV(getConstant(MaxEnd - MinStart) /* Delta */,
11567 getConstant(StrideForMaxBECount) /* Step */);
11568}
11569
11570ScalarEvolution::ExitLimit
11571ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
11572 const Loop *L, bool IsSigned,
11573 bool ControlsExit, bool AllowPredicates) {
11574 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
11575
11576 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
11577 bool PredicatedIV = false;
11578
11579 if (!IV && AllowPredicates) {
11580 // Try to make this an AddRec using runtime tests, in the first X
11581 // iterations of this loop, where X is the SCEV expression found by the
11582 // algorithm below.
11583 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
11584 PredicatedIV = true;
11585 }
11586
11587 // Avoid weird loops
11588 if (!IV || IV->getLoop() != L || !IV->isAffine())
11589 return getCouldNotCompute();
11590
11591 // A precondition of this method is that the condition being analyzed
11592 // reaches an exiting branch which dominates the latch. Given that, we can
11593 // assume that an increment which violates the nowrap specification and
11594 // produces poison must cause undefined behavior when the resulting poison
11595 // value is branched upon and thus we can conclude that the backedge is
11596 // taken no more often than would be required to produce that poison value.
11597 // Note that a well defined loop can exit on the iteration which violates
11598 // the nowrap specification if there is another exit (either explicit or
11599 // implicit/exceptional) which causes the loop to execute before the
11600 // exiting instruction we're analyzing would trigger UB.
11601 auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
11602 bool NoWrap = ControlsExit && IV->getNoWrapFlags(WrapType);
11603 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT;
11604
11605 const SCEV *Stride = IV->getStepRecurrence(*this);
11606
11607 bool PositiveStride = isKnownPositive(Stride);
11608
11609 // Avoid negative or zero stride values.
11610 if (!PositiveStride) {
11611 // We can compute the correct backedge taken count for loops with unknown
11612 // strides if we can prove that the loop is not an infinite loop with side
11613 // effects. Here's the loop structure we are trying to handle -
11614 //
11615 // i = start
11616 // do {
11617 // A[i] = i;
11618 // i += s;
11619 // } while (i < end);
11620 //
11621 // The backedge taken count for such loops is evaluated as -
11622 // (max(end, start + stride) - start - 1) /u stride
11623 //
11624 // The additional preconditions that we need to check to prove correctness
11625 // of the above formula is as follows -
11626 //
11627 // a) IV is either nuw or nsw depending upon signedness (indicated by the
11628 // NoWrap flag).
11629 // b) loop is single exit with no side effects.
11630 //
11631 //
11632 // Precondition a) implies that if the stride is negative, this is a single
11633 // trip loop. The backedge taken count formula reduces to zero in this case.
11634 //
11635 // Precondition b) implies that if rhs is invariant in L, then unknown
11636 // stride being zero means the backedge can't be taken without UB.
11637 //
11638 // The positive stride case is the same as isKnownPositive(Stride) returning
11639 // true (original behavior of the function).
11640 //
11641 // We want to make sure that the stride is truly unknown as there are edge
11642 // cases where ScalarEvolution propagates no wrap flags to the
11643 // post-increment/decrement IV even though the increment/decrement operation
11644 // itself is wrapping. The computed backedge taken count may be wrong in
11645 // such cases. This is prevented by checking that the stride is not known to
11646 // be either positive or non-positive. For example, no wrap flags are
11647 // propagated to the post-increment IV of this loop with a trip count of 2 -
11648 //
11649 // unsigned char i;
11650 // for(i=127; i<128; i+=129)
11651 // A[i] = i;
11652 //
11653 if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) ||
11654 !loopIsFiniteByAssumption(L))
11655 return getCouldNotCompute();
11656
11657 if (!isKnownNonZero(Stride)) {
11658 // If we have a step of zero, and RHS isn't invariant in L, we don't know
11659 // if it might eventually be greater than start and if so, on which
11660 // iteration. We can't even produce a useful upper bound.
11661 if (!isLoopInvariant(RHS, L))
11662 return getCouldNotCompute();
11663
11664 // We allow a potentially zero stride, but we need to divide by stride
11665 // below. Since the loop can't be infinite and this check must control
11666 // the sole exit, we can infer the exit must be taken on the first
11667 // iteration (e.g. backedge count = 0) if the stride is zero. Given that,
11668 // we know the numerator in the divides below must be zero, so we can
11669 // pick an arbitrary non-zero value for the denominator (e.g. stride)
11670 // and produce the right result.
11671 // FIXME: Handle the case where Stride is poison?
11672 auto wouldZeroStrideBeUB = [&]() {
11673 // Proof by contradiction. Suppose the stride were zero. If we can
11674 // prove that the backedge *is* taken on the first iteration, then since
11675 // we know this condition controls the sole exit, we must have an
11676 // infinite loop. We can't have a (well defined) infinite loop per
11677 // check just above.
11678 // Note: The (Start - Stride) term is used to get the start' term from
11679 // (start' + stride,+,stride). Remember that we only care about the
11680 // result of this expression when stride == 0 at runtime.
11681 auto *StartIfZero = getMinusSCEV(IV->getStart(), Stride);
11682 return isLoopEntryGuardedByCond(L, Cond, StartIfZero, RHS);
11683 };
11684 if (!wouldZeroStrideBeUB()) {
11685 Stride = getUMaxExpr(Stride, getOne(Stride->getType()));
11686 }
11687 }
11688 } else if (!Stride->isOne() && !NoWrap) {
11689 auto isUBOnWrap = [&]() {
11690 // Can we prove this loop *must* be UB if overflow of IV occurs?
11691 // Reasoning goes as follows:
11692 // * Suppose the IV did self wrap.
11693 // * If Stride evenly divides the iteration space, then once wrap
11694 // occurs, the loop must revisit the same values.
11695 // * We know that RHS is invariant, and that none of those values
11696 // caused this exit to be taken previously. Thus, this exit is
11697 // dynamically dead.
11698 // * If this is the sole exit, then a dead exit implies the loop
11699 // must be infinite if there are no abnormal exits.
11700 // * If the loop were infinite, then it must either not be mustprogress
11701 // or have side effects. Otherwise, it must be UB.
11702 // * It can't (by assumption), be UB so we have contradicted our
11703 // premise and can conclude the IV did not in fact self-wrap.
11704 // From no-self-wrap, we need to then prove no-(un)signed-wrap. This
11705 // follows trivially from the fact that every (un)signed-wrapped, but
11706 // not self-wrapped value must be LT than the last value before
11707 // (un)signed wrap. Since we know that last value didn't exit, nor
11708 // will any smaller one.
11709
11710 if (!isLoopInvariant(RHS, L))
11711 return false;
11712
11713 auto *StrideC = dyn_cast<SCEVConstant>(Stride);
11714 if (!StrideC || !StrideC->getAPInt().isPowerOf2())
11715 return false;
11716
11717 if (!ControlsExit || !loopHasNoAbnormalExits(L))
11718 return false;
11719
11720 return loopIsFiniteByAssumption(L);
11721 };
11722
11723 // Avoid proven overflow cases: this will ensure that the backedge taken
11724 // count will not generate any unsigned overflow. Relaxed no-overflow
11725 // conditions exploit NoWrapFlags, allowing to optimize in presence of
11726 // undefined behaviors like the case of C language.
11727 if (canIVOverflowOnLT(RHS, Stride, IsSigned) && !isUBOnWrap())
11728 return getCouldNotCompute();
11729 }
11730
11731 // On all paths just preceeding, we established the following invariant:
11732 // IV can be assumed not to overflow up to and including the exiting
11733 // iteration. We proved this in one of two ways:
11734 // 1) We can show overflow doesn't occur before the exiting iteration
11735 // 1a) canIVOverflowOnLT, and b) step of one
11736 // 2) We can show that if overflow occurs, the loop must execute UB
11737 // before any possible exit.
11738 // Note that we have not yet proved RHS invariant (in general).
11739
11740 const SCEV *Start = IV->getStart();
11741
11742 // Preserve pointer-typed Start/RHS to pass to isLoopEntryGuardedByCond.
11743 // Use integer-typed versions for actual computation.
11744 const SCEV *OrigStart = Start;
11745 const SCEV *OrigRHS = RHS;
11746 if (Start->getType()->isPointerTy()) {
11747 Start = getLosslessPtrToIntExpr(Start);
11748 if (isa<SCEVCouldNotCompute>(Start))
11749 return Start;
11750 }
11751 if (RHS->getType()->isPointerTy()) {
11752 RHS = getLosslessPtrToIntExpr(RHS);
11753 if (isa<SCEVCouldNotCompute>(RHS))
11754 return RHS;
11755 }
11756
11757 // When the RHS is not invariant, we do not know the end bound of the loop and
11758 // cannot calculate the ExactBECount needed by ExitLimit. However, we can
11759 // calculate the MaxBECount, given the start, stride and max value for the end
11760 // bound of the loop (RHS), and the fact that IV does not overflow (which is
11761 // checked above).
11762 if (!isLoopInvariant(RHS, L)) {
11763 const SCEV *MaxBECount = computeMaxBECountForLT(
11764 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
11765 return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
11766 false /*MaxOrZero*/, Predicates);
11767 }
11768
11769 // We use the expression (max(End,Start)-Start)/Stride to describe the
11770 // backedge count, as if the backedge is taken at least once max(End,Start)
11771 // is End and so the result is as above, and if not max(End,Start) is Start
11772 // so we get a backedge count of zero.
11773 const SCEV *BECount = nullptr;
11774 auto *StartMinusStride = getMinusSCEV(OrigStart, Stride);
11775 // Can we prove (max(RHS,Start) > Start - Stride?
11776 if (isLoopEntryGuardedByCond(L, Cond, StartMinusStride, Start) &&
11777 isLoopEntryGuardedByCond(L, Cond, StartMinusStride, RHS)) {
11778 // In this case, we can use a refined formula for computing backedge taken
11779 // count. The general formula remains:
11780 // "End-Start /uceiling Stride" where "End = max(RHS,Start)"
11781 // We want to use the alternate formula:
11782 // "((End - 1) - (Start - Stride)) /u Stride"
11783 // Let's do a quick case analysis to show these are equivalent under
11784 // our precondition that max(RHS,Start) > Start - Stride.
11785 // * For RHS <= Start, the backedge-taken count must be zero.
11786 // "((End - 1) - (Start - Stride)) /u Stride" reduces to
11787 // "((Start - 1) - (Start - Stride)) /u Stride" which simplies to
11788 // "Stride - 1 /u Stride" which is indeed zero for all non-zero values
11789 // of Stride. For 0 stride, we've use umin(1,Stride) above, reducing
11790 // this to the stride of 1 case.
11791 // * For RHS >= Start, the backedge count must be "RHS-Start /uceil Stride".
11792 // "((End - 1) - (Start - Stride)) /u Stride" reduces to
11793 // "((RHS - 1) - (Start - Stride)) /u Stride" reassociates to
11794 // "((RHS - (Start - Stride) - 1) /u Stride".
11795 // Our preconditions trivially imply no overflow in that form.
11796 const SCEV *MinusOne = getMinusOne(Stride->getType());
11797 const SCEV *Numerator =
11798 getMinusSCEV(getAddExpr(RHS, MinusOne), StartMinusStride);
11799 if (!isa<SCEVCouldNotCompute>(Numerator)) {
11800 BECount = getUDivExpr(Numerator, Stride);
11801 }
11802 }
11803
11804 const SCEV *BECountIfBackedgeTaken = nullptr;
11805 if (!BECount) {
11806 auto canProveRHSGreaterThanEqualStart = [&]() {
11807 auto CondGE = IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
11808 if (isLoopEntryGuardedByCond(L, CondGE, OrigRHS, OrigStart))
11809 return true;
11810
11811 // (RHS > Start - 1) implies RHS >= Start.
11812 // * "RHS >= Start" is trivially equivalent to "RHS > Start - 1" if
11813 // "Start - 1" doesn't overflow.
11814 // * For signed comparison, if Start - 1 does overflow, it's equal
11815 // to INT_MAX, and "RHS >s INT_MAX" is trivially false.
11816 // * For unsigned comparison, if Start - 1 does overflow, it's equal
11817 // to UINT_MAX, and "RHS >u UINT_MAX" is trivially false.
11818 //
11819 // FIXME: Should isLoopEntryGuardedByCond do this for us?
11820 auto CondGT = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
11821 auto *StartMinusOne = getAddExpr(OrigStart,
11822 getMinusOne(OrigStart->getType()));
11823 return isLoopEntryGuardedByCond(L, CondGT, OrigRHS, StartMinusOne);
11824 };
11825
11826 // If we know that RHS >= Start in the context of loop, then we know that
11827 // max(RHS, Start) = RHS at this point.
11828 const SCEV *End;
11829 if (canProveRHSGreaterThanEqualStart()) {
11830 End = RHS;
11831 } else {
11832 // If RHS < Start, the backedge will be taken zero times. So in
11833 // general, we can write the backedge-taken count as:
11834 //
11835 // RHS >= Start ? ceil(RHS - Start) / Stride : 0
11836 //
11837 // We convert it to the following to make it more convenient for SCEV:
11838 //
11839 // ceil(max(RHS, Start) - Start) / Stride
11840 End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
11841
11842 // See what would happen if we assume the backedge is taken. This is
11843 // used to compute MaxBECount.
11844 BECountIfBackedgeTaken = getUDivCeilSCEV(getMinusSCEV(RHS, Start), Stride);
11845 }
11846
11847 // At this point, we know:
11848 //
11849 // 1. If IsSigned, Start <=s End; otherwise, Start <=u End
11850 // 2. The index variable doesn't overflow.
11851 //
11852 // Therefore, we know N exists such that
11853 // (Start + Stride * N) >= End, and computing "(Start + Stride * N)"
11854 // doesn't overflow.
11855 //
11856 // Using this information, try to prove whether the addition in
11857 // "(Start - End) + (Stride - 1)" has unsigned overflow.
11858 const SCEV *One = getOne(Stride->getType());
11859 bool MayAddOverflow = [&] {
11860 if (auto *StrideC = dyn_cast<SCEVConstant>(Stride)) {
11861 if (StrideC->getAPInt().isPowerOf2()) {
11862 // Suppose Stride is a power of two, and Start/End are unsigned
11863 // integers. Let UMAX be the largest representable unsigned
11864 // integer.
11865 //
11866 // By the preconditions of this function, we know
11867 // "(Start + Stride * N) >= End", and this doesn't overflow.
11868 // As a formula:
11869 //
11870 // End <= (Start + Stride * N) <= UMAX
11871 //
11872 // Subtracting Start from all the terms:
11873 //
11874 // End - Start <= Stride * N <= UMAX - Start
11875 //
11876 // Since Start is unsigned, UMAX - Start <= UMAX. Therefore:
11877 //
11878 // End - Start <= Stride * N <= UMAX
11879 //
11880 // Stride * N is a multiple of Stride. Therefore,
11881 //
11882 // End - Start <= Stride * N <= UMAX - (UMAX mod Stride)
11883 //
11884 // Since Stride is a power of two, UMAX + 1 is divisible by Stride.
11885 // Therefore, UMAX mod Stride == Stride - 1. So we can write:
11886 //
11887 // End - Start <= Stride * N <= UMAX - Stride - 1
11888 //
11889 // Dropping the middle term:
11890 //
11891 // End - Start <= UMAX - Stride - 1
11892 //
11893 // Adding Stride - 1 to both sides:
11894 //
11895 // (End - Start) + (Stride - 1) <= UMAX
11896 //
11897 // In other words, the addition doesn't have unsigned overflow.
11898 //
11899 // A similar proof works if we treat Start/End as signed values.
11900 // Just rewrite steps before "End - Start <= Stride * N <= UMAX" to
11901 // use signed max instead of unsigned max. Note that we're trying
11902 // to prove a lack of unsigned overflow in either case.
11903 return false;
11904 }
11905 }
11906 if (Start == Stride || Start == getMinusSCEV(Stride, One)) {
11907 // If Start is equal to Stride, (End - Start) + (Stride - 1) == End - 1.
11908 // If !IsSigned, 0 <u Stride == Start <=u End; so 0 <u End - 1 <u End.
11909 // If IsSigned, 0 <s Stride == Start <=s End; so 0 <s End - 1 <s End.
11910 //
11911 // If Start is equal to Stride - 1, (End - Start) + Stride - 1 == End.
11912 return false;
11913 }
11914 return true;
11915 }();
11916
11917 const SCEV *Delta = getMinusSCEV(End, Start);
11918 if (!MayAddOverflow) {
11919 // floor((D + (S - 1)) / S)
11920 // We prefer this formulation if it's legal because it's fewer operations.
11921 BECount =
11922 getUDivExpr(getAddExpr(Delta, getMinusSCEV(Stride, One)), Stride);
11923 } else {
11924 BECount = getUDivCeilSCEV(Delta, Stride);
11925 }
11926 }
11927
11928 const SCEV *MaxBECount;
11929 bool MaxOrZero = false;
11930 if (isa<SCEVConstant>(BECount)) {
11931 MaxBECount = BECount;
11932 } else if (BECountIfBackedgeTaken &&
11933 isa<SCEVConstant>(BECountIfBackedgeTaken)) {
11934 // If we know exactly how many times the backedge will be taken if it's
11935 // taken at least once, then the backedge count will either be that or
11936 // zero.
11937 MaxBECount = BECountIfBackedgeTaken;
11938 MaxOrZero = true;
11939 } else {
11940 MaxBECount = computeMaxBECountForLT(
11941 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
11942 }
11943
11944 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
11945 !isa<SCEVCouldNotCompute>(BECount))
11946 MaxBECount = getConstant(getUnsignedRangeMax(BECount));
11947
11948 return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates);
11949}
11950
11951ScalarEvolution::ExitLimit
11952ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
11953 const Loop *L, bool IsSigned,
11954 bool ControlsExit, bool AllowPredicates) {
11955 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
11956 // We handle only IV > Invariant
11957 if (!isLoopInvariant(RHS, L))
11958 return getCouldNotCompute();
11959
11960 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
11961 if (!IV && AllowPredicates)
11962 // Try to make this an AddRec using runtime tests, in the first X
11963 // iterations of this loop, where X is the SCEV expression found by the
11964 // algorithm below.
11965 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
11966
11967 // Avoid weird loops
11968 if (!IV || IV->getLoop() != L || !IV->isAffine())
11969 return getCouldNotCompute();
11970
11971 auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
11972 bool NoWrap = ControlsExit && IV->getNoWrapFlags(WrapType);
11973 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
11974
11975 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
11976
11977 // Avoid negative or zero stride values
11978 if (!isKnownPositive(Stride))
11979 return getCouldNotCompute();
11980
11981 // Avoid proven overflow cases: this will ensure that the backedge taken count
11982 // will not generate any unsigned overflow. Relaxed no-overflow conditions
11983 // exploit NoWrapFlags, allowing to optimize in presence of undefined
11984 // behaviors like the case of C language.
11985 if (!Stride->isOne() && !NoWrap)
11986 if (canIVOverflowOnGT(RHS, Stride, IsSigned))
11987 return getCouldNotCompute();
11988
11989 const SCEV *Start = IV->getStart();
11990 const SCEV *End = RHS;
11991 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
11992 // If we know that Start >= RHS in the context of loop, then we know that
11993 // min(RHS, Start) = RHS at this point.
11994 if (isLoopEntryGuardedByCond(
11995 L, IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, Start, RHS))
11996 End = RHS;
11997 else
11998 End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
11999 }
12000
12001 if (Start->getType()->isPointerTy()) {
12002 Start = getLosslessPtrToIntExpr(Start);
12003 if (isa<SCEVCouldNotCompute>(Start))
12004 return Start;
12005 }
12006 if (End->getType()->isPointerTy()) {
12007 End = getLosslessPtrToIntExpr(End);
12008 if (isa<SCEVCouldNotCompute>(End))
12009 return End;
12010 }
12011
12012 // Compute ((Start - End) + (Stride - 1)) / Stride.
12013 // FIXME: This can overflow. Holding off on fixing this for now;
12014 // howManyGreaterThans will hopefully be gone soon.
12015 const SCEV *One = getOne(Stride->getType());
12016 const SCEV *BECount = getUDivExpr(
12017 getAddExpr(getMinusSCEV(Start, End), getMinusSCEV(Stride, One)), Stride);
12018
12019 APInt MaxStart = IsSigned ? getSignedRangeMax(Start)
12020 : getUnsignedRangeMax(Start);
12021
12022 APInt MinStride = IsSigned ? getSignedRangeMin(Stride)
12023 : getUnsignedRangeMin(Stride);
12024
12025 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
12026 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
12027 : APInt::getMinValue(BitWidth) + (MinStride - 1);
12028
12029 // Although End can be a MIN expression we estimate MinEnd considering only
12030 // the case End = RHS. This is safe because in the other case (Start - End)
12031 // is zero, leading to a zero maximum backedge taken count.
12032 APInt MinEnd =
12033 IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit)
12034 : APIntOps::umax(getUnsignedRangeMin(RHS), Limit);
12035
12036 const SCEV *MaxBECount = isa<SCEVConstant>(BECount)
12037 ? BECount
12038 : getUDivCeilSCEV(getConstant(MaxStart - MinEnd),
12039 getConstant(MinStride));
12040
12041 if (isa<SCEVCouldNotCompute>(MaxBECount))
12042 MaxBECount = BECount;
12043
12044 return ExitLimit(BECount, MaxBECount, false, Predicates);
12045}
12046
12047const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
12048 ScalarEvolution &SE) const {
12049 if (Range.isFullSet()) // Infinite loop.
12050 return SE.getCouldNotCompute();
12051
12052 // If the start is a non-zero constant, shift the range to simplify things.
12053 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
12054 if (!SC->getValue()->isZero()) {
12055 SmallVector<const SCEV *, 4> Operands(operands());
12056 Operands[0] = SE.getZero(SC->getType());
12057 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
12058 getNoWrapFlags(FlagNW));
12059 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
12060 return ShiftedAddRec->getNumIterationsInRange(
12061 Range.subtract(SC->getAPInt()), SE);
12062 // This is strange and shouldn't happen.
12063 return SE.getCouldNotCompute();
12064 }
12065
12066 // The only time we can solve this is when we have all constant indices.
12067 // Otherwise, we cannot determine the overflow conditions.
12068 if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
12069 return SE.getCouldNotCompute();
12070
12071 // Okay at this point we know that all elements of the chrec are constants and
12072 // that the start element is zero.
12073
12074 // First check to see if the range contains zero. If not, the first
12075 // iteration exits.
12076 unsigned BitWidth = SE.getTypeSizeInBits(getType());
12077 if (!Range.contains(APInt(BitWidth, 0)))
12078 return SE.getZero(getType());
12079
12080 if (isAffine()) {
12081 // If this is an affine expression then we have this situation:
12082 // Solve {0,+,A} in Range === Ax in Range
12083
12084 // We know that zero is in the range. If A is positive then we know that
12085 // the upper value of the range must be the first possible exit value.
12086 // If A is negative then the lower of the range is the last possible loop
12087 // value. Also note that we already checked for a full range.
12088 APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
12089 APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower();
12090
12091 // The exit value should be (End+A)/A.
12092 APInt ExitVal = (End + A).udiv(A);
12093 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
12094
12095 // Evaluate at the exit value. If we really did fall out of the valid
12096 // range, then we computed our trip count, otherwise wrap around or other
12097 // things must have happened.
12098 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
12099 if (Range.contains(Val->getValue()))
12100 return SE.getCouldNotCompute(); // Something strange happened
12101
12102 // Ensure that the previous value is in the range. This is a sanity check.
12103 assert(Range.contains(((void)0)
12104 EvaluateConstantChrecAtConstant(this,((void)0)
12105 ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) &&((void)0)
12106 "Linear scev computation is off in a bad way!")((void)0);
12107 return SE.getConstant(ExitValue);
12108 }
12109
12110 if (isQuadratic()) {
12111 if (auto S = SolveQuadraticAddRecRange(this, Range, SE))
12112 return SE.getConstant(S.getValue());
12113 }
12114
12115 return SE.getCouldNotCompute();
12116}
12117
12118const SCEVAddRecExpr *
12119SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const {
12120 assert(getNumOperands() > 1 && "AddRec with zero step?")((void)0);
12121 // There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)),
12122 // but in this case we cannot guarantee that the value returned will be an
12123 // AddRec because SCEV does not have a fixed point where it stops
12124 // simplification: it is legal to return ({rec1} + {rec2}). For example, it
12125 // may happen if we reach arithmetic depth limit while simplifying. So we
12126 // construct the returned value explicitly.
12127 SmallVector<const SCEV *, 3> Ops;
12128 // If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and
12129 // (this + Step) is {A+B,+,B+C,+...,+,N}.
12130 for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i)
12131 Ops.push_back(SE.getAddExpr(getOperand(i), getOperand(i + 1)));
12132 // We know that the last operand is not a constant zero (otherwise it would
12133 // have been popped out earlier). This guarantees us that if the result has
12134 // the same last operand, then it will also not be popped out, meaning that
12135 // the returned value will be an AddRec.
12136 const SCEV *Last = getOperand(getNumOperands() - 1);
12137 assert(!Last->isZero() && "Recurrency with zero step?")((void)0);
12138 Ops.push_back(Last);
12139 return cast<SCEVAddRecExpr>(SE.getAddRecExpr(Ops, getLoop(),
12140 SCEV::FlagAnyWrap));
12141}
12142
12143// Return true when S contains at least an undef value.
12144static inline bool containsUndefs(const SCEV *S) {
12145 return SCEVExprContains(S, [](const SCEV *S) {
12146 if (const auto *SU = dyn_cast<SCEVUnknown>(S))
12147 return isa<UndefValue>(SU->getValue());
12148 return false;
12149 });
12150}
12151
12152namespace {
12153
12154// Collect all steps of SCEV expressions.
12155struct SCEVCollectStrides {
12156 ScalarEvolution &SE;
12157 SmallVectorImpl<const SCEV *> &Strides;
12158
12159 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
12160 : SE(SE), Strides(S) {}
12161
12162 bool follow(const SCEV *S) {
12163 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
12164 Strides.push_back(AR->getStepRecurrence(SE));
12165 return true;
12166 }
12167
12168 bool isDone() const { return false; }
12169};
12170
12171// Collect all SCEVUnknown and SCEVMulExpr expressions.
12172struct SCEVCollectTerms {
12173 SmallVectorImpl<const SCEV *> &Terms;
12174
12175 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {}
12176
12177 bool follow(const SCEV *S) {
12178 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) ||
12179 isa<SCEVSignExtendExpr>(S)) {
12180 if (!containsUndefs(S))
12181 Terms.push_back(S);
12182
12183 // Stop recursion: once we collected a term, do not walk its operands.
12184 return false;
12185 }
12186
12187 // Keep looking.
12188 return true;
12189 }
12190
12191 bool isDone() const { return false; }
12192};
12193
12194// Check if a SCEV contains an AddRecExpr.
12195struct SCEVHasAddRec {
12196 bool &ContainsAddRec;
12197
12198 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
12199 ContainsAddRec = false;
12200 }
12201
12202 bool follow(const SCEV *S) {
12203 if (isa<SCEVAddRecExpr>(S)) {
12204 ContainsAddRec = true;
12205
12206 // Stop recursion: once we collected a term, do not walk its operands.
12207 return false;
12208 }
12209
12210 // Keep looking.
12211 return true;
12212 }
12213
12214 bool isDone() const { return false; }
12215};
12216
12217// Find factors that are multiplied with an expression that (possibly as a
12218// subexpression) contains an AddRecExpr. In the expression:
12219//
12220// 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
12221//
12222// "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
12223// that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
12224// parameters as they form a product with an induction variable.
12225//
12226// This collector expects all array size parameters to be in the same MulExpr.
12227// It might be necessary to later add support for collecting parameters that are
12228// spread over different nested MulExpr.
12229struct SCEVCollectAddRecMultiplies {
12230 SmallVectorImpl<const SCEV *> &Terms;
12231 ScalarEvolution &SE;
12232
12233 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
12234 : Terms(T), SE(SE) {}
12235
12236 bool follow(const SCEV *S) {
12237 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
12238 bool HasAddRec = false;
12239 SmallVector<const SCEV *, 0> Operands;
12240 for (auto Op : Mul->operands()) {
12241 const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op);
12242 if (Unknown && !isa<CallInst>(Unknown->getValue())) {
12243 Operands.push_back(Op);
12244 } else if (Unknown) {
12245 HasAddRec = true;
12246 } else {
12247 bool ContainsAddRec = false;
12248 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
12249 visitAll(Op, ContiansAddRec);
12250 HasAddRec |= ContainsAddRec;
12251 }
12252 }
12253 if (Operands.size() == 0)
12254 return true;
12255
12256 if (!HasAddRec)
12257 return false;
12258
12259 Terms.push_back(SE.getMulExpr(Operands));
12260 // Stop recursion: once we collected a term, do not walk its operands.
12261 return false;
12262 }
12263
12264 // Keep looking.
12265 return true;
12266 }
12267
12268 bool isDone() const { return false; }
12269};
12270
12271} // end anonymous namespace
12272
12273/// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
12274/// two places:
12275/// 1) The strides of AddRec expressions.
12276/// 2) Unknowns that are multiplied with AddRec expressions.
12277void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
12278 SmallVectorImpl<const SCEV *> &Terms) {
12279 SmallVector<const SCEV *, 4> Strides;
12280 SCEVCollectStrides StrideCollector(*this, Strides);
12281 visitAll(Expr, StrideCollector);
12282
12283 LLVM_DEBUG({do { } while (false)
12284 dbgs() << "Strides:\n";do { } while (false)
12285 for (const SCEV *S : Strides)do { } while (false)
12286 dbgs() << *S << "\n";do { } while (false)
12287 })do { } while (false);
12288
12289 for (const SCEV *S : Strides) {
12290 SCEVCollectTerms TermCollector(Terms);
12291 visitAll(S, TermCollector);
12292 }
12293
12294 LLVM_DEBUG({do { } while (false)
12295 dbgs() << "Terms:\n";do { } while (false)
12296 for (const SCEV *T : Terms)do { } while (false)
12297 dbgs() << *T << "\n";do { } while (false)
12298 })do { } while (false);
12299
12300 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
12301 visitAll(Expr, MulCollector);
12302}
12303
12304static bool findArrayDimensionsRec(ScalarEvolution &SE,
12305 SmallVectorImpl<const SCEV *> &Terms,
12306 SmallVectorImpl<const SCEV *> &Sizes) {
12307 int Last = Terms.size() - 1;
12308 const SCEV *Step = Terms[Last];
12309
12310 // End of recursion.
12311 if (Last == 0) {
12312 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
12313 SmallVector<const SCEV *, 2> Qs;
12314 for (const SCEV *Op : M->operands())
12315 if (!isa<SCEVConstant>(Op))
12316 Qs.push_back(Op);
12317
12318 Step = SE.getMulExpr(Qs);
12319 }
12320
12321 Sizes.push_back(Step);
12322 return true;
12323 }
12324
12325 for (const SCEV *&Term : Terms) {
12326 // Normalize the terms before the next call to findArrayDimensionsRec.
12327 const SCEV *Q, *R;
12328 SCEVDivision::divide(SE, Term, Step, &Q, &R);
12329
12330 // Bail out when GCD does not evenly divide one of the terms.
12331 if (!R->isZero())
12332 return false;
12333
12334 Term = Q;
12335 }
12336
12337 // Remove all SCEVConstants.
12338 erase_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); });
12339
12340 if (Terms.size() > 0)
12341 if (!findArrayDimensionsRec(SE, Terms, Sizes))
12342 return false;
12343
12344 Sizes.push_back(Step);
12345 return true;
12346}
12347
12348// Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
12349static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
12350 for (const SCEV *T : Terms)
12351 if (SCEVExprContains(T, [](const SCEV *S) { return isa<SCEVUnknown>(S); }))
12352 return true;
12353
12354 return false;
12355}
12356
12357// Return the number of product terms in S.
12358static inline int numberOfTerms(const SCEV *S) {
12359 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
12360 return Expr->getNumOperands();
12361 return 1;
12362}
12363
12364static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
12365 if (isa<SCEVConstant>(T))
12366 return nullptr;
12367
12368 if (isa<SCEVUnknown>(T))
12369 return T;
12370
12371 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
12372 SmallVector<const SCEV *, 2> Factors;
12373 for (const SCEV *Op : M->operands())
12374 if (!isa<SCEVConstant>(Op))
12375 Factors.push_back(Op);
12376
12377 return SE.getMulExpr(Factors);
12378 }
12379
12380 return T;
12381}
12382
12383/// Return the size of an element read or written by Inst.
12384const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
12385 Type *Ty;
12386 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
12387 Ty = Store->getValueOperand()->getType();
12388 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
12389 Ty = Load->getType();
12390 else
12391 return nullptr;
12392
12393 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
12394 return getSizeOfExpr(ETy, Ty);
12395}
12396
12397void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
12398 SmallVectorImpl<const SCEV *> &Sizes,
12399 const SCEV *ElementSize) {
12400 if (Terms.size() < 1 || !ElementSize)
12401 return;
12402
12403 // Early return when Terms do not contain parameters: we do not delinearize
12404 // non parametric SCEVs.
12405 if (!containsParameters(Terms))
12406 return;
12407
12408 LLVM_DEBUG({do { } while (false)
12409 dbgs() << "Terms:\n";do { } while (false)
12410 for (const SCEV *T : Terms)do { } while (false)
12411 dbgs() << *T << "\n";do { } while (false)
12412 })do { } while (false);
12413
12414 // Remove duplicates.
12415 array_pod_sort(Terms.begin(), Terms.end());
12416 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
12417
12418 // Put larger terms first.
12419 llvm::sort(Terms, [](const SCEV *LHS, const SCEV *RHS) {
12420 return numberOfTerms(LHS) > numberOfTerms(RHS);
12421 });
12422
12423 // Try to divide all terms by the element size. If term is not divisible by
12424 // element size, proceed with the original term.
12425 for (const SCEV *&Term : Terms) {
12426 const SCEV *Q, *R;
12427 SCEVDivision::divide(*this, Term, ElementSize, &Q, &R);
12428 if (!Q->isZero())
12429 Term = Q;
12430 }
12431
12432 SmallVector<const SCEV *, 4> NewTerms;
12433
12434 // Remove constant factors.
12435 for (const SCEV *T : Terms)
12436 if (const SCEV *NewT = removeConstantFactors(*this, T))
12437 NewTerms.push_back(NewT);
12438
12439 LLVM_DEBUG({do { } while (false)
12440 dbgs() << "Terms after sorting:\n";do { } while (false)
12441 for (const SCEV *T : NewTerms)do { } while (false)
12442 dbgs() << *T << "\n";do { } while (false)
12443 })do { } while (false);
12444
12445 if (NewTerms.empty() || !findArrayDimensionsRec(*this, NewTerms, Sizes)) {
12446 Sizes.clear();
12447 return;
12448 }
12449
12450 // The last element to be pushed into Sizes is the size of an element.
12451 Sizes.push_back(ElementSize);
12452
12453 LLVM_DEBUG({do { } while (false)
12454 dbgs() << "Sizes:\n";do { } while (false)
12455 for (const SCEV *S : Sizes)do { } while (false)
12456 dbgs() << *S << "\n";do { } while (false)
12457 })do { } while (false);
12458}
12459
12460void ScalarEvolution::computeAccessFunctions(
12461 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
12462 SmallVectorImpl<const SCEV *> &Sizes) {
12463 // Early exit in case this SCEV is not an affine multivariate function.
12464 if (Sizes.empty())
12465 return;
12466
12467 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
12468 if (!AR->isAffine())
12469 return;
12470
12471 const SCEV *Res = Expr;
12472 int Last = Sizes.size() - 1;
12473 for (int i = Last; i >= 0; i--) {
12474 const SCEV *Q, *R;
12475 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
12476
12477 LLVM_DEBUG({do { } while (false)
12478 dbgs() << "Res: " << *Res << "\n";do { } while (false)
12479 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";do { } while (false)
12480 dbgs() << "Res divided by Sizes[i]:\n";do { } while (false)
12481 dbgs() << "Quotient: " << *Q << "\n";do { } while (false)
12482 dbgs() << "Remainder: " << *R << "\n";do { } while (false)
12483 })do { } while (false);
12484
12485 Res = Q;
12486
12487 // Do not record the last subscript corresponding to the size of elements in
12488 // the array.
12489 if (i == Last) {
12490
12491 // Bail out if the remainder is too complex.
12492 if (isa<SCEVAddRecExpr>(R)) {
12493 Subscripts.clear();
12494 Sizes.clear();
12495 return;
12496 }
12497
12498 continue;
12499 }
12500
12501 // Record the access function for the current subscript.
12502 Subscripts.push_back(R);
12503 }
12504
12505 // Also push in last position the remainder of the last division: it will be
12506 // the access function of the innermost dimension.
12507 Subscripts.push_back(Res);
12508
12509 std::reverse(Subscripts.begin(), Subscripts.end());
12510
12511 LLVM_DEBUG({do { } while (false)
12512 dbgs() << "Subscripts:\n";do { } while (false)
12513 for (const SCEV *S : Subscripts)do { } while (false)
12514 dbgs() << *S << "\n";do { } while (false)
12515 })do { } while (false);
12516}
12517
12518/// Splits the SCEV into two vectors of SCEVs representing the subscripts and
12519/// sizes of an array access. Returns the remainder of the delinearization that
12520/// is the offset start of the array. The SCEV->delinearize algorithm computes
12521/// the multiples of SCEV coefficients: that is a pattern matching of sub
12522/// expressions in the stride and base of a SCEV corresponding to the
12523/// computation of a GCD (greatest common divisor) of base and stride. When
12524/// SCEV->delinearize fails, it returns the SCEV unchanged.
12525///
12526/// For example: when analyzing the memory access A[i][j][k] in this loop nest
12527///
12528/// void foo(long n, long m, long o, double A[n][m][o]) {
12529///
12530/// for (long i = 0; i < n; i++)
12531/// for (long j = 0; j < m; j++)
12532/// for (long k = 0; k < o; k++)
12533/// A[i][j][k] = 1.0;
12534/// }
12535///
12536/// the delinearization input is the following AddRec SCEV:
12537///
12538/// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
12539///
12540/// From this SCEV, we are able to say that the base offset of the access is %A
12541/// because it appears as an offset that does not divide any of the strides in
12542/// the loops:
12543///
12544/// CHECK: Base offset: %A
12545///
12546/// and then SCEV->delinearize determines the size of some of the dimensions of
12547/// the array as these are the multiples by which the strides are happening:
12548///
12549/// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
12550///
12551/// Note that the outermost dimension remains of UnknownSize because there are
12552/// no strides that would help identifying the size of the last dimension: when
12553/// the array has been statically allocated, one could compute the size of that
12554/// dimension by dividing the overall size of the array by the size of the known
12555/// dimensions: %m * %o * 8.
12556///
12557/// Finally delinearize provides the access functions for the array reference
12558/// that does correspond to A[i][j][k] of the above C testcase:
12559///
12560/// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
12561///
12562/// The testcases are checking the output of a function pass:
12563/// DelinearizationPass that walks through all loads and stores of a function
12564/// asking for the SCEV of the memory access with respect to all enclosing
12565/// loops, calling SCEV->delinearize on that and printing the results.
12566void ScalarEvolution::delinearize(const SCEV *Expr,
12567 SmallVectorImpl<const SCEV *> &Subscripts,
12568 SmallVectorImpl<const SCEV *> &Sizes,
12569 const SCEV *ElementSize) {
12570 // First step: collect parametric terms.
12571 SmallVector<const SCEV *, 4> Terms;
12572 collectParametricTerms(Expr, Terms);
12573
12574 if (Terms.empty())
12575 return;
12576
12577 // Second step: find subscript sizes.
12578 findArrayDimensions(Terms, Sizes, ElementSize);
12579
12580 if (Sizes.empty())
12581 return;
12582
12583 // Third step: compute the access functions for each subscript.
12584 computeAccessFunctions(Expr, Subscripts, Sizes);
12585
12586 if (Subscripts.empty())
12587 return;
12588
12589 LLVM_DEBUG({do { } while (false)
12590 dbgs() << "succeeded to delinearize " << *Expr << "\n";do { } while (false)
12591 dbgs() << "ArrayDecl[UnknownSize]";do { } while (false)
12592 for (const SCEV *S : Sizes)do { } while (false)
12593 dbgs() << "[" << *S << "]";do { } while (false)
12594
12595 dbgs() << "\nArrayRef";do { } while (false)
12596 for (const SCEV *S : Subscripts)do { } while (false)
12597 dbgs() << "[" << *S << "]";do { } while (false)
12598 dbgs() << "\n";do { } while (false)
12599 })do { } while (false);
12600}
12601
12602bool ScalarEvolution::getIndexExpressionsFromGEP(
12603 const GetElementPtrInst *GEP, SmallVectorImpl<const SCEV *> &Subscripts,
12604 SmallVectorImpl<int> &Sizes) {
12605 assert(Subscripts.empty() && Sizes.empty() &&((void)0)
12606 "Expected output lists to be empty on entry to this function.")((void)0);
12607 assert(GEP && "getIndexExpressionsFromGEP called with a null GEP")((void)0);
12608 Type *Ty = nullptr;
12609 bool DroppedFirstDim = false;
12610 for (unsigned i = 1; i < GEP->getNumOperands(); i++) {
12611 const SCEV *Expr = getSCEV(GEP->getOperand(i));
12612 if (i == 1) {
12613 Ty = GEP->getSourceElementType();
12614 if (auto *Const = dyn_cast<SCEVConstant>(Expr))
12615 if (Const->getValue()->isZero()) {
12616 DroppedFirstDim = true;
12617 continue;
12618 }
12619 Subscripts.push_back(Expr);
12620 continue;
12621 }
12622
12623 auto *ArrayTy = dyn_cast<ArrayType>(Ty);
12624 if (!ArrayTy) {
12625 Subscripts.clear();
12626 Sizes.clear();
12627 return false;
12628 }
12629
12630 Subscripts.push_back(Expr);
12631 if (!(DroppedFirstDim && i == 2))
12632 Sizes.push_back(ArrayTy->getNumElements());
12633
12634 Ty = ArrayTy->getElementType();
12635 }
12636 return !Subscripts.empty();
12637}
12638
12639//===----------------------------------------------------------------------===//
12640// SCEVCallbackVH Class Implementation
12641//===----------------------------------------------------------------------===//
12642
12643void ScalarEvolution::SCEVCallbackVH::deleted() {
12644 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!")((void)0);
12645 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
12646 SE->ConstantEvolutionLoopExitValue.erase(PN);
12647 SE->eraseValueFromMap(getValPtr());
12648 // this now dangles!
12649}
12650
12651void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
12652 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!")((void)0);
12653
12654 // Forget all the expressions associated with users of the old value,
12655 // so that future queries will recompute the expressions using the new
12656 // value.
12657 Value *Old = getValPtr();
12658 SmallVector<User *, 16> Worklist(Old->users());
12659 SmallPtrSet<User *, 8> Visited;
12660 while (!Worklist.empty()) {
12661 User *U = Worklist.pop_back_val();
12662 // Deleting the Old value will cause this to dangle. Postpone
12663 // that until everything else is done.
12664 if (U == Old)
12665 continue;
12666 if (!Visited.insert(U).second)
12667 continue;
12668 if (PHINode *PN = dyn_cast<PHINode>(U))
12669 SE->ConstantEvolutionLoopExitValue.erase(PN);
12670 SE->eraseValueFromMap(U);
12671 llvm::append_range(Worklist, U->users());
12672 }
12673 // Delete the Old value.
12674 if (PHINode *PN = dyn_cast<PHINode>(Old))
12675 SE->ConstantEvolutionLoopExitValue.erase(PN);
12676 SE->eraseValueFromMap(Old);
12677 // this now dangles!
12678}
12679
12680ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
12681 : CallbackVH(V), SE(se) {}
12682
12683//===----------------------------------------------------------------------===//
12684// ScalarEvolution Class Implementation
12685//===----------------------------------------------------------------------===//
12686
12687ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
12688 AssumptionCache &AC, DominatorTree &DT,
12689 LoopInfo &LI)
12690 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
12691 CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64),
12692 LoopDispositions(64), BlockDispositions(64) {
12693 // To use guards for proving predicates, we need to scan every instruction in
12694 // relevant basic blocks, and not just terminators. Doing this is a waste of
12695 // time if the IR does not actually contain any calls to
12696 // @llvm.experimental.guard, so do a quick check and remember this beforehand.
12697 //
12698 // This pessimizes the case where a pass that preserves ScalarEvolution wants
12699 // to _add_ guards to the module when there weren't any before, and wants
12700 // ScalarEvolution to optimize based on those guards. For now we prefer to be
12701 // efficient in lieu of being smart in that rather obscure case.
12702
12703 auto *GuardDecl = F.getParent()->getFunction(
12704 Intrinsic::getName(Intrinsic::experimental_guard));
12705 HasGuards = GuardDecl && !GuardDecl->use_empty();
12706}
12707
12708ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
12709 : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
12710 LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
12711 ValueExprMap(std::move(Arg.ValueExprMap)),
12712 PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
12713 PendingPhiRanges(std::move(Arg.PendingPhiRanges)),
12714 PendingMerges(std::move(Arg.PendingMerges)),
12715 MinTrailingZerosCache(std::move(Arg.MinTrailingZerosCache)),
12716 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
12717 PredicatedBackedgeTakenCounts(
12718 std::move(Arg.PredicatedBackedgeTakenCounts)),
12719 ConstantEvolutionLoopExitValue(
12720 std::move(Arg.ConstantEvolutionLoopExitValue)),
12721 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
12722 LoopDispositions(std::move(Arg.LoopDispositions)),
12723 LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
12724 BlockDispositions(std::move(Arg.BlockDispositions)),
12725 UnsignedRanges(std::move(Arg.UnsignedRanges)),
12726 SignedRanges(std::move(Arg.SignedRanges)),
12727 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
12728 UniquePreds(std::move(Arg.UniquePreds)),
12729 SCEVAllocator(std::move(Arg.SCEVAllocator)),
12730 LoopUsers(std::move(Arg.LoopUsers)),
12731 PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
12732 FirstUnknown(Arg.FirstUnknown) {
12733 Arg.FirstUnknown = nullptr;
12734}
12735
12736ScalarEvolution::~ScalarEvolution() {
12737 // Iterate through all the SCEVUnknown instances and call their
12738 // destructors, so that they release their references to their values.
12739 for (SCEVUnknown *U = FirstUnknown; U;) {
12740 SCEVUnknown *Tmp = U;
12741 U = U->Next;
12742 Tmp->~SCEVUnknown();
12743 }
12744 FirstUnknown = nullptr;
12745
12746 ExprValueMap.clear();
12747 ValueExprMap.clear();
12748 HasRecMap.clear();
12749 BackedgeTakenCounts.clear();
12750 PredicatedBackedgeTakenCounts.clear();
12751
12752 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage")((void)0);
12753 assert(PendingPhiRanges.empty() && "getRangeRef garbage")((void)0);
12754 assert(PendingMerges.empty() && "isImpliedViaMerge garbage")((void)0);
12755 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!")((void)0);
12756 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!")((void)0);
12757}
12758
12759bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
12760 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
12761}
12762
12763static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
12764 const Loop *L) {
12765 // Print all inner loops first
12766 for (Loop *I : *L)
12767 PrintLoopInfo(OS, SE, I);
12768
12769 OS << "Loop ";
12770 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
12771 OS << ": ";
12772
12773 SmallVector<BasicBlock *, 8> ExitingBlocks;
12774 L->getExitingBlocks(ExitingBlocks);
12775 if (ExitingBlocks.size() != 1)
12776 OS << "<multiple exits> ";
12777
12778 if (SE->hasLoopInvariantBackedgeTakenCount(L))
12779 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L) << "\n";
12780 else
12781 OS << "Unpredictable backedge-taken count.\n";
12782
12783 if (ExitingBlocks.size() > 1)
12784 for (BasicBlock *ExitingBlock : ExitingBlocks) {
12785 OS << " exit count for " << ExitingBlock->getName() << ": "
12786 << *SE->getExitCount(L, ExitingBlock) << "\n";
12787 }
12788
12789 OS << "Loop ";
12790 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
12791 OS << ": ";
12792
12793 if (!isa<SCEVCouldNotCompute>(SE->getConstantMaxBackedgeTakenCount(L))) {
12794 OS << "max backedge-taken count is " << *SE->getConstantMaxBackedgeTakenCount(L);
12795 if (SE->isBackedgeTakenCountMaxOrZero(L))
12796 OS << ", actual taken count either this or zero.";
12797 } else {
12798 OS << "Unpredictable max backedge-taken count. ";
12799 }
12800
12801 OS << "\n"
12802 "Loop ";
12803 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
12804 OS << ": ";
12805
12806 SCEVUnionPredicate Pred;
12807 auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
12808 if (!isa<SCEVCouldNotCompute>(PBT)) {
12809 OS << "Predicated backedge-taken count is " << *PBT << "\n";
12810 OS << " Predicates:\n";
12811 Pred.print(OS, 4);
12812 } else {
12813 OS << "Unpredictable predicated backedge-taken count. ";
12814 }
12815 OS << "\n";
12816
12817 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
12818 OS << "Loop ";
12819 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
12820 OS << ": ";
12821 OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n";
12822 }
12823}
12824
12825static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
12826 switch (LD) {
12827 case ScalarEvolution::LoopVariant:
12828 return "Variant";
12829 case ScalarEvolution::LoopInvariant:
12830 return "Invariant";
12831 case ScalarEvolution::LoopComputable:
12832 return "Computable";
12833 }
12834 llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!")__builtin_unreachable();
12835}
12836
12837void ScalarEvolution::print(raw_ostream &OS) const {
12838 // ScalarEvolution's implementation of the print method is to print
12839 // out SCEV values of all instructions that are interesting. Doing
12840 // this potentially causes it to create new SCEV objects though,
12841 // which technically conflicts with the const qualifier. This isn't
12842 // observable from outside the class though, so casting away the
12843 // const isn't dangerous.
12844 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
12845
12846 if (ClassifyExpressions) {
12847 OS << "Classifying expressions for: ";
12848 F.printAsOperand(OS, /*PrintType=*/false);
12849 OS << "\n";
12850 for (Instruction &I : instructions(F))
12851 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
12852 OS << I << '\n';
12853 OS << " --> ";
12854 const SCEV *SV = SE.getSCEV(&I);
12855 SV->print(OS);
12856 if (!isa<SCEVCouldNotCompute>(SV)) {
12857 OS << " U: ";
12858 SE.getUnsignedRange(SV).print(OS);
12859 OS << " S: ";
12860 SE.getSignedRange(SV).print(OS);
12861 }
12862
12863 const Loop *L = LI.getLoopFor(I.getParent());
12864
12865 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
12866 if (AtUse != SV) {
12867 OS << " --> ";
12868 AtUse->print(OS);
12869 if (!isa<SCEVCouldNotCompute>(AtUse)) {
12870 OS << " U: ";
12871 SE.getUnsignedRange(AtUse).print(OS);
12872 OS << " S: ";
12873 SE.getSignedRange(AtUse).print(OS);
12874 }
12875 }
12876
12877 if (L) {
12878 OS << "\t\t" "Exits: ";
12879 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
12880 if (!SE.isLoopInvariant(ExitValue, L)) {
12881 OS << "<<Unknown>>";
12882 } else {
12883 OS << *ExitValue;
12884 }
12885
12886 bool First = true;
12887 for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
12888 if (First) {
12889 OS << "\t\t" "LoopDispositions: { ";
12890 First = false;
12891 } else {
12892 OS << ", ";
12893 }
12894
12895 Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
12896 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
12897 }
12898
12899 for (auto *InnerL : depth_first(L)) {
12900 if (InnerL == L)
12901 continue;
12902 if (First) {
12903 OS << "\t\t" "LoopDispositions: { ";
12904 First = false;
12905 } else {
12906 OS << ", ";
12907 }
12908
12909 InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
12910 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
12911 }
12912
12913 OS << " }";
12914 }
12915
12916 OS << "\n";
12917 }
12918 }
12919
12920 OS << "Determining loop execution counts for: ";
12921 F.printAsOperand(OS, /*PrintType=*/false);
12922 OS << "\n";
12923 for (Loop *I : LI)
12924 PrintLoopInfo(OS, &SE, I);
12925}
12926
12927ScalarEvolution::LoopDisposition
12928ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
12929 auto &Values = LoopDispositions[S];
12930 for (auto &V : Values) {
12931 if (V.getPointer() == L)
12932 return V.getInt();
12933 }
12934 Values.emplace_back(L, LoopVariant);
12935 LoopDisposition D = computeLoopDisposition(S, L);
12936 auto &Values2 = LoopDispositions[S];
12937 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
12938 if (V.getPointer() == L) {
12939 V.setInt(D);
12940 break;
12941 }
12942 }
12943 return D;
12944}
12945
12946ScalarEvolution::LoopDisposition
12947ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
12948 switch (S->getSCEVType()) {
12949 case scConstant:
12950 return LoopInvariant;
12951 case scPtrToInt:
12952 case scTruncate:
12953 case scZeroExtend:
12954 case scSignExtend:
12955 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
12956 case scAddRecExpr: {
12957 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
12958
12959 // If L is the addrec's loop, it's computable.
12960 if (AR->getLoop() == L)
12961 return LoopComputable;
12962
12963 // Add recurrences are never invariant in the function-body (null loop).
12964 if (!L)
12965 return LoopVariant;
12966
12967 // Everything that is not defined at loop entry is variant.
12968 if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader()))
12969 return LoopVariant;
12970 assert(!L->contains(AR->getLoop()) && "Containing loop's header does not"((void)0)
12971 " dominate the contained loop's header?")((void)0);
12972
12973 // This recurrence is invariant w.r.t. L if AR's loop contains L.
12974 if (AR->getLoop()->contains(L))
12975 return LoopInvariant;
12976
12977 // This recurrence is variant w.r.t. L if any of its operands
12978 // are variant.
12979 for (auto *Op : AR->operands())
12980 if (!isLoopInvariant(Op, L))
12981 return LoopVariant;
12982
12983 // Otherwise it's loop-invariant.
12984 return LoopInvariant;
12985 }
12986 case scAddExpr:
12987 case scMulExpr:
12988 case scUMaxExpr:
12989 case scSMaxExpr:
12990 case scUMinExpr:
12991 case scSMinExpr: {
12992 bool HasVarying = false;
12993 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
12994 LoopDisposition D = getLoopDisposition(Op, L);
12995 if (D == LoopVariant)
12996 return LoopVariant;
12997 if (D == LoopComputable)
12998 HasVarying = true;
12999 }
13000 return HasVarying ? LoopComputable : LoopInvariant;
13001 }
13002 case scUDivExpr: {
13003 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
13004 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
13005 if (LD == LoopVariant)
13006 return LoopVariant;
13007 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
13008 if (RD == LoopVariant)
13009 return LoopVariant;
13010 return (LD == LoopInvariant && RD == LoopInvariant) ?
13011 LoopInvariant : LoopComputable;
13012 }
13013 case scUnknown:
13014 // All non-instruction values are loop invariant. All instructions are loop
13015 // invariant if they are not contained in the specified loop.
13016 // Instructions are never considered invariant in the function body
13017 // (null loop) because they are defined within the "loop".
13018 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
13019 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
13020 return LoopInvariant;
13021 case scCouldNotCompute:
13022 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")__builtin_unreachable();
13023 }
13024 llvm_unreachable("Unknown SCEV kind!")__builtin_unreachable();
13025}
13026
13027bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
13028 return getLoopDisposition(S, L) == LoopInvariant;
13029}
13030
13031bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
13032 return getLoopDisposition(S, L) == LoopComputable;
13033}
13034
13035ScalarEvolution::BlockDisposition
13036ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
13037 auto &Values = BlockDispositions[S];
13038 for (auto &V : Values) {
13039 if (V.getPointer() == BB)
13040 return V.getInt();
13041 }
13042 Values.emplace_back(BB, DoesNotDominateBlock);
13043 BlockDisposition D = computeBlockDisposition(S, BB);
13044 auto &Values2 = BlockDispositions[S];
13045 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
13046 if (V.getPointer() == BB) {
13047 V.setInt(D);
13048 break;
13049 }
13050 }
13051 return D;
13052}
13053
13054ScalarEvolution::BlockDisposition
13055ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
13056 switch (S->getSCEVType()) {
13057 case scConstant:
13058 return ProperlyDominatesBlock;
13059 case scPtrToInt:
13060 case scTruncate:
13061 case scZeroExtend:
13062 case scSignExtend:
13063 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
13064 case scAddRecExpr: {
13065 // This uses a "dominates" query instead of "properly dominates" query
13066 // to test for proper dominance too, because the instruction which
13067 // produces the addrec's value is a PHI, and a PHI effectively properly
13068 // dominates its entire containing block.
13069 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
13070 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
13071 return DoesNotDominateBlock;
13072
13073 // Fall through into SCEVNAryExpr handling.
13074 LLVM_FALLTHROUGH[[gnu::fallthrough]];
13075 }
13076 case scAddExpr:
13077 case scMulExpr:
13078 case scUMaxExpr:
13079 case scSMaxExpr:
13080 case scUMinExpr:
13081 case scSMinExpr: {
13082 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
13083 bool Proper = true;
13084 for (const SCEV *NAryOp : NAry->operands()) {
13085 BlockDisposition D = getBlockDisposition(NAryOp, BB);
13086 if (D == DoesNotDominateBlock)
13087 return DoesNotDominateBlock;
13088 if (D == DominatesBlock)
13089 Proper = false;
13090 }
13091 return Proper ? ProperlyDominatesBlock : DominatesBlock;
13092 }
13093 case scUDivExpr: {
13094 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
13095 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
13096 BlockDisposition LD = getBlockDisposition(LHS, BB);
13097 if (LD == DoesNotDominateBlock)
13098 return DoesNotDominateBlock;
13099 BlockDisposition RD = getBlockDisposition(RHS, BB);
13100 if (RD == DoesNotDominateBlock)
13101 return DoesNotDominateBlock;
13102 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
13103 ProperlyDominatesBlock : DominatesBlock;
13104 }
13105 case scUnknown:
13106 if (Instruction *I =
13107 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
13108 if (I->getParent() == BB)
13109 return DominatesBlock;
13110 if (DT.properlyDominates(I->getParent(), BB))
13111 return ProperlyDominatesBlock;
13112 return DoesNotDominateBlock;
13113 }
13114 return ProperlyDominatesBlock;
13115 case scCouldNotCompute:
13116 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")__builtin_unreachable();
13117 }
13118 llvm_unreachable("Unknown SCEV kind!")__builtin_unreachable();
13119}
13120
13121bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
13122 return getBlockDisposition(S, BB) >= DominatesBlock;
13123}
13124
13125bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
13126 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
13127}
13128
13129bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
13130 return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
13131}
13132
13133void
13134ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
13135 ValuesAtScopes.erase(S);
13136 LoopDispositions.erase(S);
13137 BlockDispositions.erase(S);
13138 UnsignedRanges.erase(S);
13139 SignedRanges.erase(S);
13140 ExprValueMap.erase(S);
13141 HasRecMap.erase(S);
13142 MinTrailingZerosCache.erase(S);
13143
13144 for (auto I = PredicatedSCEVRewrites.begin();
13145 I != PredicatedSCEVRewrites.end();) {
13146 std::pair<const SCEV *, const Loop *> Entry = I->first;
13147 if (Entry.first == S)
13148 PredicatedSCEVRewrites.erase(I++);
13149 else
13150 ++I;
13151 }
13152
13153 auto RemoveSCEVFromBackedgeMap =
13154 [S](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
13155 for (auto I = Map.begin(), E = Map.end(); I != E;) {
13156 BackedgeTakenInfo &BEInfo = I->second;
13157 if (BEInfo.hasOperand(S))
13158 Map.erase(I++);
13159 else
13160 ++I;
13161 }
13162 };
13163
13164 RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
13165 RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
13166}
13167
13168void
13169ScalarEvolution::getUsedLoops(const SCEV *S,
13170 SmallPtrSetImpl<const Loop *> &LoopsUsed) {
13171 struct FindUsedLoops {
13172 FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed)
13173 : LoopsUsed(LoopsUsed) {}
13174 SmallPtrSetImpl<const Loop *> &LoopsUsed;
13175 bool follow(const SCEV *S) {
13176 if (auto *AR = dyn_cast<SCEVAddRecExpr>(S))
13177 LoopsUsed.insert(AR->getLoop());
13178 return true;
13179 }
13180
13181 bool isDone() const { return false; }
13182 };
13183
13184 FindUsedLoops F(LoopsUsed);
13185 SCEVTraversal<FindUsedLoops>(F).visitAll(S);
13186}
13187
13188void ScalarEvolution::addToLoopUseLists(const SCEV *S) {
13189 SmallPtrSet<const Loop *, 8> LoopsUsed;
13190 getUsedLoops(S, LoopsUsed);
13191 for (auto *L : LoopsUsed)
13192 LoopUsers[L].push_back(S);
13193}
13194
13195void ScalarEvolution::verify() const {
13196 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
13197 ScalarEvolution SE2(F, TLI, AC, DT, LI);
13198
13199 SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end());
13200
13201 // Map's SCEV expressions from one ScalarEvolution "universe" to another.
13202 struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> {
13203 SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {}
13204
13205 const SCEV *visitConstant(const SCEVConstant *Constant) {
13206 return SE.getConstant(Constant->getAPInt());
13207 }
13208
13209 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
13210 return SE.getUnknown(Expr->getValue());
13211 }
13212
13213 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
13214 return SE.getCouldNotCompute();
13215 }
13216 };
13217
13218 SCEVMapper SCM(SE2);
13219
13220 while (!LoopStack.empty()) {
13221 auto *L = LoopStack.pop_back_val();
13222 llvm::append_range(LoopStack, *L);
13223
13224 auto *CurBECount = SCM.visit(
13225 const_cast<ScalarEvolution *>(this)->getBackedgeTakenCount(L));
13226 auto *NewBECount = SE2.getBackedgeTakenCount(L);
13227
13228 if (CurBECount == SE2.getCouldNotCompute() ||
13229 NewBECount == SE2.getCouldNotCompute()) {
13230 // NB! This situation is legal, but is very suspicious -- whatever pass
13231 // change the loop to make a trip count go from could not compute to
13232 // computable or vice-versa *should have* invalidated SCEV. However, we
13233 // choose not to assert here (for now) since we don't want false
13234 // positives.
13235 continue;
13236 }
13237
13238 if (containsUndefs(CurBECount) || containsUndefs(NewBECount)) {
13239 // SCEV treats "undef" as an unknown but consistent value (i.e. it does
13240 // not propagate undef aggressively). This means we can (and do) fail
13241 // verification in cases where a transform makes the trip count of a loop
13242 // go from "undef" to "undef+1" (say). The transform is fine, since in
13243 // both cases the loop iterates "undef" times, but SCEV thinks we
13244 // increased the trip count of the loop by 1 incorrectly.
13245 continue;
13246 }
13247
13248 if (SE.getTypeSizeInBits(CurBECount->getType()) >
13249 SE.getTypeSizeInBits(NewBECount->getType()))
13250 NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType());
13251 else if (SE.getTypeSizeInBits(CurBECount->getType()) <
13252 SE.getTypeSizeInBits(NewBECount->getType()))
13253 CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType());
13254
13255 const SCEV *Delta = SE2.getMinusSCEV(CurBECount, NewBECount);
13256
13257 // Unless VerifySCEVStrict is set, we only compare constant deltas.
13258 if ((VerifySCEVStrict || isa<SCEVConstant>(Delta)) && !Delta->isZero()) {
13259 dbgs() << "Trip Count for " << *L << " Changed!\n";
13260 dbgs() << "Old: " << *CurBECount << "\n";
13261 dbgs() << "New: " << *NewBECount << "\n";
13262 dbgs() << "Delta: " << *Delta << "\n";
13263 std::abort();
13264 }
13265 }
13266
13267 // Collect all valid loops currently in LoopInfo.
13268 SmallPtrSet<Loop *, 32> ValidLoops;
13269 SmallVector<Loop *, 32> Worklist(LI.begin(), LI.end());
13270 while (!Worklist.empty()) {
13271 Loop *L = Worklist.pop_back_val();
13272 if (ValidLoops.contains(L))
13273 continue;
13274 ValidLoops.insert(L);
13275 Worklist.append(L->begin(), L->end());
13276 }
13277 // Check for SCEV expressions referencing invalid/deleted loops.
13278 for (auto &KV : ValueExprMap) {
13279 auto *AR = dyn_cast<SCEVAddRecExpr>(KV.second);
13280 if (!AR)
13281 continue;
13282 assert(ValidLoops.contains(AR->getLoop()) &&((void)0)
13283 "AddRec references invalid loop")((void)0);
13284 }
13285}
13286
13287bool ScalarEvolution::invalidate(
13288 Function &F, const PreservedAnalyses &PA,
13289 FunctionAnalysisManager::Invalidator &Inv) {
13290 // Invalidate the ScalarEvolution object whenever it isn't preserved or one
13291 // of its dependencies is invalidated.
13292 auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
13293 return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
13294 Inv.invalidate<AssumptionAnalysis>(F, PA) ||
13295 Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
13296 Inv.invalidate<LoopAnalysis>(F, PA);
13297}
13298
13299AnalysisKey ScalarEvolutionAnalysis::Key;
13300
13301ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
13302 FunctionAnalysisManager &AM) {
13303 return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
13304 AM.getResult<AssumptionAnalysis>(F),
13305 AM.getResult<DominatorTreeAnalysis>(F),
13306 AM.getResult<LoopAnalysis>(F));
13307}
13308
13309PreservedAnalyses
13310ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) {
13311 AM.getResult<ScalarEvolutionAnalysis>(F).verify();
13312 return PreservedAnalyses::all();
13313}
13314
13315PreservedAnalyses
13316ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
13317 // For compatibility with opt's -analyze feature under legacy pass manager
13318 // which was not ported to NPM. This keeps tests using
13319 // update_analyze_test_checks.py working.
13320 OS << "Printing analysis 'Scalar Evolution Analysis' for function '"
13321 << F.getName() << "':\n";
13322 AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
13323 return PreservedAnalyses::all();
13324}
13325
13326INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",static void *initializeScalarEvolutionWrapperPassPassOnce(PassRegistry
&Registry) {
13327 "Scalar Evolution Analysis", false, true)static void *initializeScalarEvolutionWrapperPassPassOnce(PassRegistry
&Registry) {
13328INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)initializeAssumptionCacheTrackerPass(Registry);
13329INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)initializeLoopInfoWrapperPassPass(Registry);
13330INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)initializeDominatorTreeWrapperPassPass(Registry);
13331INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)initializeTargetLibraryInfoWrapperPassPass(Registry);
13332INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",PassInfo *PI = new PassInfo( "Scalar Evolution Analysis", "scalar-evolution"
, &ScalarEvolutionWrapperPass::ID, PassInfo::NormalCtor_t
(callDefaultCtor<ScalarEvolutionWrapperPass>), false, true
); Registry.registerPass(*PI, true); return PI; } static llvm
::once_flag InitializeScalarEvolutionWrapperPassPassFlag; void
llvm::initializeScalarEvolutionWrapperPassPass(PassRegistry &
Registry) { llvm::call_once(InitializeScalarEvolutionWrapperPassPassFlag
, initializeScalarEvolutionWrapperPassPassOnce, std::ref(Registry
)); }
13333 "Scalar Evolution Analysis", false, true)PassInfo *PI = new PassInfo( "Scalar Evolution Analysis", "scalar-evolution"
, &ScalarEvolutionWrapperPass::ID, PassInfo::NormalCtor_t
(callDefaultCtor<ScalarEvolutionWrapperPass>), false, true
); Registry.registerPass(*PI, true); return PI; } static llvm
::once_flag InitializeScalarEvolutionWrapperPassPassFlag; void
llvm::initializeScalarEvolutionWrapperPassPass(PassRegistry &
Registry) { llvm::call_once(InitializeScalarEvolutionWrapperPassPassFlag
, initializeScalarEvolutionWrapperPassPassOnce, std::ref(Registry
)); }
13334
13335char ScalarEvolutionWrapperPass::ID = 0;
13336
13337ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
13338 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
13339}
13340
13341bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
13342 SE.reset(new ScalarEvolution(
13343 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F),
13344 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
13345 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
13346 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
13347 return false;
13348}
13349
13350void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
13351
13352void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
13353 SE->print(OS);
13354}
13355
13356void ScalarEvolutionWrapperPass::verifyAnalysis() const {
13357 if (!VerifySCEV)
13358 return;
13359
13360 SE->verify();
13361}
13362
13363void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
13364 AU.setPreservesAll();
13365 AU.addRequiredTransitive<AssumptionCacheTracker>();
13366 AU.addRequiredTransitive<LoopInfoWrapperPass>();
13367 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
13368 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
13369}
13370
13371const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS,
13372 const SCEV *RHS) {
13373 FoldingSetNodeID ID;
13374 assert(LHS->getType() == RHS->getType() &&((void)0)
13375 "Type mismatch between LHS and RHS")((void)0);
13376 // Unique this node based on the arguments
13377 ID.AddInteger(SCEVPredicate::P_Equal);
13378 ID.AddPointer(LHS);
13379 ID.AddPointer(RHS);
13380 void *IP = nullptr;
13381 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
13382 return S;
13383 SCEVEqualPredicate *Eq = new (SCEVAllocator)
13384 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
13385 UniquePreds.InsertNode(Eq, IP);
13386 return Eq;
13387}
13388
13389const SCEVPredicate *ScalarEvolution::getWrapPredicate(
13390 const SCEVAddRecExpr *AR,
13391 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
13392 FoldingSetNodeID ID;
13393 // Unique this node based on the arguments
13394 ID.AddInteger(SCEVPredicate::P_Wrap);
13395 ID.AddPointer(AR);
13396 ID.AddInteger(AddedFlags);
13397 void *IP = nullptr;
13398 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
13399 return S;
13400 auto *OF = new (SCEVAllocator)
13401 SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
13402 UniquePreds.InsertNode(OF, IP);
13403 return OF;
13404}
13405
13406namespace {
13407
13408class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
13409public:
13410
13411 /// Rewrites \p S in the context of a loop L and the SCEV predication
13412 /// infrastructure.
13413 ///
13414 /// If \p Pred is non-null, the SCEV expression is rewritten to respect the
13415 /// equivalences present in \p Pred.
13416 ///
13417 /// If \p NewPreds is non-null, rewrite is free to add further predicates to
13418 /// \p NewPreds such that the result will be an AddRecExpr.
13419 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
13420 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
13421 SCEVUnionPredicate *Pred) {
13422 SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
13423 return Rewriter.visit(S);
13424 }
13425
13426 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
13427 if (Pred) {
13428 auto ExprPreds = Pred->getPredicatesForExpr(Expr);
13429 for (auto *Pred : ExprPreds)
13430 if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
13431 if (IPred->getLHS() == Expr)
13432 return IPred->getRHS();
13433 }
13434 return convertToAddRecWithPreds(Expr);
13435 }
13436
13437 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
13438 const SCEV *Operand = visit(Expr->getOperand());
13439 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
13440 if (AR && AR->getLoop() == L && AR->isAffine()) {
13441 // This couldn't be folded because the operand didn't have the nuw
13442 // flag. Add the nusw flag as an assumption that we could make.
13443 const SCEV *Step = AR->getStepRecurrence(SE);
13444 Type *Ty = Expr->getType();
13445 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
13446 return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
13447 SE.getSignExtendExpr(Step, Ty), L,
13448 AR->getNoWrapFlags());
13449 }
13450 return SE.getZeroExtendExpr(Operand, Expr->getType());
13451 }
13452
13453 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
13454 const SCEV *Operand = visit(Expr->getOperand());
13455 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
13456 if (AR && AR->getLoop() == L && AR->isAffine()) {
13457 // This couldn't be folded because the operand didn't have the nsw
13458 // flag. Add the nssw flag as an assumption that we could make.
13459 const SCEV *Step = AR->getStepRecurrence(SE);
13460 Type *Ty = Expr->getType();
13461 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
13462 return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
13463 SE.getSignExtendExpr(Step, Ty), L,
13464 AR->getNoWrapFlags());
13465 }
13466 return SE.getSignExtendExpr(Operand, Expr->getType());
13467 }
13468
13469private:
13470 explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
13471 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
13472 SCEVUnionPredicate *Pred)
13473 : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
13474
13475 bool addOverflowAssumption(const SCEVPredicate *P) {
13476 if (!NewPreds) {
13477 // Check if we've already made this assumption.
13478 return Pred && Pred->implies(P);
13479 }
13480 NewPreds->insert(P);
13481 return true;
13482 }
13483
13484 bool addOverflowAssumption(const SCEVAddRecExpr *AR,
13485 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
13486 auto *A = SE.getWrapPredicate(AR, AddedFlags);
13487 return addOverflowAssumption(A);
13488 }
13489
13490 // If \p Expr represents a PHINode, we try to see if it can be represented
13491 // as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible
13492 // to add this predicate as a runtime overflow check, we return the AddRec.
13493 // If \p Expr does not meet these conditions (is not a PHI node, or we
13494 // couldn't create an AddRec for it, or couldn't add the predicate), we just
13495 // return \p Expr.
13496 const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) {
13497 if (!isa<PHINode>(Expr->getValue()))
13498 return Expr;
13499 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
13500 PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr);
13501 if (!PredicatedRewrite)
13502 return Expr;
13503 for (auto *P : PredicatedRewrite->second){
13504 // Wrap predicates from outer loops are not supported.
13505 if (auto *WP = dyn_cast<const SCEVWrapPredicate>(P)) {
13506 auto *AR = cast<const SCEVAddRecExpr>(WP->getExpr());
13507 if (L != AR->getLoop())
13508 return Expr;
13509 }
13510 if (!addOverflowAssumption(P))
13511 return Expr;
13512 }
13513 return PredicatedRewrite->first;
13514 }
13515
13516 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds;
13517 SCEVUnionPredicate *Pred;
13518 const Loop *L;
13519};
13520
13521} // end anonymous namespace
13522
13523const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
13524 SCEVUnionPredicate &Preds) {
13525 return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
13526}
13527
13528const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
13529 const SCEV *S, const Loop *L,
13530 SmallPtrSetImpl<const SCEVPredicate *> &Preds) {
13531 SmallPtrSet<const SCEVPredicate *, 4> TransformPreds;
13532 S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
13533 auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
13534
13535 if (!AddRec)
13536 return nullptr;
13537
13538 // Since the transformation was successful, we can now transfer the SCEV
13539 // predicates.
13540 for (auto *P : TransformPreds)
13541 Preds.insert(P);
13542
13543 return AddRec;
13544}
13545
13546/// SCEV predicates
13547SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
13548 SCEVPredicateKind Kind)
13549 : FastID(ID), Kind(Kind) {}
13550
13551SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
13552 const SCEV *LHS, const SCEV *RHS)
13553 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {
13554 assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match")((void)0);
13555 assert(LHS != RHS && "LHS and RHS are the same SCEV")((void)0);
13556}
13557
13558bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
13559 const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
13560
13561 if (!Op)
13562 return false;
13563
13564 return Op->LHS == LHS && Op->RHS == RHS;
13565}
13566
13567bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
13568
13569const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
13570
13571void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
13572 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
13573}
13574
13575SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
13576 const SCEVAddRecExpr *AR,
13577 IncrementWrapFlags Flags)
13578 : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
13579
13580const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
13581
13582bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
13583 const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
13584
13585 return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
13586}
13587
13588bool SCEVWrapPredicate::isAlwaysTrue() const {
13589 SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
13590 IncrementWrapFlags IFlags = Flags;
13591
13592 if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
13593 IFlags = clearFlags(IFlags, IncrementNSSW);
13594
13595 return IFlags == IncrementAnyWrap;
13596}
13597
13598void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
13599 OS.indent(Depth) << *getExpr() << " Added Flags: ";
13600 if (SCEVWrapPredicate::IncrementNUSW & getFlags())
13601 OS << "<nusw>";
13602 if (SCEVWrapPredicate::IncrementNSSW & getFlags())
13603 OS << "<nssw>";
13604 OS << "\n";
13605}
13606
13607SCEVWrapPredicate::IncrementWrapFlags
13608SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
13609 ScalarEvolution &SE) {
13610 IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
13611 SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
13612
13613 // We can safely transfer the NSW flag as NSSW.
13614 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
13615 ImpliedFlags = IncrementNSSW;
13616
13617 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
13618 // If the increment is positive, the SCEV NUW flag will also imply the
13619 // WrapPredicate NUSW flag.
13620 if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
13621 if (Step->getValue()->getValue().isNonNegative())
13622 ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
13623 }
13624
13625 return ImpliedFlags;
13626}
13627
13628/// Union predicates don't get cached so create a dummy set ID for it.
13629SCEVUnionPredicate::SCEVUnionPredicate()
13630 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
13631
13632bool SCEVUnionPredicate::isAlwaysTrue() const {
13633 return all_of(Preds,
13634 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
13635}
13636
13637ArrayRef<const SCEVPredicate *>
13638SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
13639 auto I = SCEVToPreds.find(Expr);
13640 if (I == SCEVToPreds.end())
13641 return ArrayRef<const SCEVPredicate *>();
13642 return I->second;
13643}
13644
13645bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
13646 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
13647 return all_of(Set->Preds,
13648 [this](const SCEVPredicate *I) { return this->implies(I); });
13649
13650 auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
13651 if (ScevPredsIt == SCEVToPreds.end())
13652 return false;
13653 auto &SCEVPreds = ScevPredsIt->second;
13654
13655 return any_of(SCEVPreds,
13656 [N](const SCEVPredicate *I) { return I->implies(N); });
13657}
13658
13659const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
13660
13661void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
13662 for (auto Pred : Preds)
13663 Pred->print(OS, Depth);
13664}
13665
13666void SCEVUnionPredicate::add(const SCEVPredicate *N) {
13667 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
13668 for (auto Pred : Set->Preds)
13669 add(Pred);
13670 return;
13671 }
13672
13673 if (implies(N))
13674 return;
13675
13676 const SCEV *Key = N->getExpr();
13677 assert(Key && "Only SCEVUnionPredicate doesn't have an "((void)0)
13678 " associated expression!")((void)0);
13679
13680 SCEVToPreds[Key].push_back(N);
13681 Preds.push_back(N);
13682}
13683
13684PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
13685 Loop &L)
13686 : SE(SE), L(L) {}
13687
13688const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
13689 const SCEV *Expr = SE.getSCEV(V);
13690 RewriteEntry &Entry = RewriteMap[Expr];
13691
13692 // If we already have an entry and the version matches, return it.
13693 if (Entry.second && Generation == Entry.first)
13694 return Entry.second;
13695
13696 // We found an entry but it's stale. Rewrite the stale entry
13697 // according to the current predicate.
13698 if (Entry.second)
13699 Expr = Entry.second;
13700
13701 const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
13702 Entry = {Generation, NewSCEV};
13703
13704 return NewSCEV;
13705}
13706
13707const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
13708 if (!BackedgeCount) {
13709 SCEVUnionPredicate BackedgePred;
13710 BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
13711 addPredicate(BackedgePred);
13712 }
13713 return BackedgeCount;
13714}
13715
13716void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
13717 if (Preds.implies(&Pred))
13718 return;
13719 Preds.add(&Pred);
13720 updateGeneration();
13721}
13722
13723const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
13724 return Preds;
13725}
13726
13727void PredicatedScalarEvolution::updateGeneration() {
13728 // If the generation number wrapped recompute everything.
13729 if (++Generation == 0) {
13730 for (auto &II : RewriteMap) {
13731 const SCEV *Rewritten = II.second.second;
13732 II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
13733 }
13734 }
13735}
13736
13737void PredicatedScalarEvolution::setNoOverflow(
13738 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
13739 const SCEV *Expr = getSCEV(V);
13740 const auto *AR = cast<SCEVAddRecExpr>(Expr);
13741
13742 auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
13743
13744 // Clear the statically implied flags.
13745 Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
13746 addPredicate(*SE.getWrapPredicate(AR, Flags));
13747
13748 auto II = FlagsMap.insert({V, Flags});
13749 if (!II.second)
13750 II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
13751}
13752
13753bool PredicatedScalarEvolution::hasNoOverflow(
13754 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
13755 const SCEV *Expr = getSCEV(V);
13756 const auto *AR = cast<SCEVAddRecExpr>(Expr);
13757
13758 Flags = SCEVWrapPredicate::clearFlags(
13759 Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
13760
13761 auto II = FlagsMap.find(V);
13762
13763 if (II != FlagsMap.end())
13764 Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
13765
13766 return Flags == SCEVWrapPredicate::IncrementAnyWrap;
13767}
13768
13769const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
13770 const SCEV *Expr = this->getSCEV(V);
13771 SmallPtrSet<const SCEVPredicate *, 4> NewPreds;
13772 auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);
13773
13774 if (!New)
13775 return nullptr;
13776
13777 for (auto *P : NewPreds)
13778 Preds.add(P);
13779
13780 updateGeneration();
13781 RewriteMap[SE.getSCEV(V)] = {Generation, New};
13782 return New;
13783}
13784
13785PredicatedScalarEvolution::PredicatedScalarEvolution(
13786 const PredicatedScalarEvolution &Init)
13787 : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
13788 Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
13789 for (auto I : Init.FlagsMap)
13790 FlagsMap.insert(I);
13791}
13792
13793void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
13794 // For each block.
13795 for (auto *BB : L.getBlocks())
13796 for (auto &I : *BB) {
13797 if (!SE.isSCEVable(I.getType()))
13798 continue;
13799
13800 auto *Expr = SE.getSCEV(&I);
13801 auto II = RewriteMap.find(Expr);
13802
13803 if (II == RewriteMap.end())
13804 continue;
13805
13806 // Don't print things that are not interesting.
13807 if (II->second.second == Expr)
13808 continue;
13809
13810 OS.indent(Depth) << "[PSE]" << I << ":\n";
13811 OS.indent(Depth + 2) << *Expr << "\n";
13812 OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
13813 }
13814}
13815
13816// Match the mathematical pattern A - (A / B) * B, where A and B can be
13817// arbitrary expressions. Also match zext (trunc A to iB) to iY, which is used
13818// for URem with constant power-of-2 second operands.
13819// It's not always easy, as A and B can be folded (imagine A is X / 2, and B is
13820// 4, A / B becomes X / 8).
13821bool ScalarEvolution::matchURem(const SCEV *Expr, const SCEV *&LHS,
13822 const SCEV *&RHS) {
13823 // Try to match 'zext (trunc A to iB) to iY', which is used
13824 // for URem with constant power-of-2 second operands. Make sure the size of
13825 // the operand A matches the size of the whole expressions.
13826 if (const auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(Expr))
13827 if (const auto *Trunc = dyn_cast<SCEVTruncateExpr>(ZExt->getOperand(0))) {
13828 LHS = Trunc->getOperand();
13829 // Bail out if the type of the LHS is larger than the type of the
13830 // expression for now.
13831 if (getTypeSizeInBits(LHS->getType()) >
13832 getTypeSizeInBits(Expr->getType()))
13833 return false;
13834 if (LHS->getType() != Expr->getType())
13835 LHS = getZeroExtendExpr(LHS, Expr->getType());
13836 RHS = getConstant(APInt(getTypeSizeInBits(Expr->getType()), 1)
13837 << getTypeSizeInBits(Trunc->getType()));
13838 return true;
13839 }
13840 const auto *Add = dyn_cast<SCEVAddExpr>(Expr);
13841 if (Add == nullptr || Add->getNumOperands() != 2)
13842 return false;
13843
13844 const SCEV *A = Add->getOperand(1);
13845 const auto *Mul = dyn_cast<SCEVMulExpr>(Add->getOperand(0));
13846
13847 if (Mul == nullptr)
13848 return false;
13849
13850 const auto MatchURemWithDivisor = [&](const SCEV *B) {
13851 // (SomeExpr + (-(SomeExpr / B) * B)).
13852 if (Expr == getURemExpr(A, B)) {
13853 LHS = A;
13854 RHS = B;
13855 return true;
13856 }
13857 return false;
13858 };
13859
13860 // (SomeExpr + (-1 * (SomeExpr / B) * B)).
13861 if (Mul->getNumOperands() == 3 && isa<SCEVConstant>(Mul->getOperand(0)))
13862 return MatchURemWithDivisor(Mul->getOperand(1)) ||
13863 MatchURemWithDivisor(Mul->getOperand(2));
13864
13865 // (SomeExpr + ((-SomeExpr / B) * B)) or (SomeExpr + ((SomeExpr / B) * -B)).
13866 if (Mul->getNumOperands() == 2)
13867 return MatchURemWithDivisor(Mul->getOperand(1)) ||
13868 MatchURemWithDivisor(Mul->getOperand(0)) ||
13869 MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(1))) ||
13870 MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(0)));
13871 return false;
13872}
13873
13874const SCEV *
13875ScalarEvolution::computeSymbolicMaxBackedgeTakenCount(const Loop *L) {
13876 SmallVector<BasicBlock*, 16> ExitingBlocks;
13877 L->getExitingBlocks(ExitingBlocks);
13878
13879 // Form an expression for the maximum exit count possible for this loop. We
13880 // merge the max and exact information to approximate a version of
13881 // getConstantMaxBackedgeTakenCount which isn't restricted to just constants.
13882 SmallVector<const SCEV*, 4> ExitCounts;
13883 for (BasicBlock *ExitingBB : ExitingBlocks) {
13884 const SCEV *ExitCount = getExitCount(L, ExitingBB);
13885 if (isa<SCEVCouldNotCompute>(ExitCount))
13886 ExitCount = getExitCount(L, ExitingBB,
13887 ScalarEvolution::ConstantMaximum);
13888 if (!isa<SCEVCouldNotCompute>(ExitCount)) {
13889 assert(DT.dominates(ExitingBB, L->getLoopLatch()) &&((void)0)
13890 "We should only have known counts for exiting blocks that "((void)0)
13891 "dominate latch!")((void)0);
13892 ExitCounts.push_back(ExitCount);
13893 }
13894 }
13895 if (ExitCounts.empty())
13896 return getCouldNotCompute();
13897 return getUMinFromMismatchedTypes(ExitCounts);
13898}
13899
13900/// This rewriter is similar to SCEVParameterRewriter (it replaces SCEVUnknown
13901/// components following the Map (Value -> SCEV)), but skips AddRecExpr because
13902/// we cannot guarantee that the replacement is loop invariant in the loop of
13903/// the AddRec.
13904class SCEVLoopGuardRewriter : public SCEVRewriteVisitor<SCEVLoopGuardRewriter> {
13905 ValueToSCEVMapTy &Map;
13906
13907public:
13908 SCEVLoopGuardRewriter(ScalarEvolution &SE, ValueToSCEVMapTy &M)
13909 : SCEVRewriteVisitor(SE), Map(M) {}
13910
13911 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; }
13912
13913 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
13914 auto I = Map.find(Expr->getValue());
13915 if (I == Map.end())
13916 return Expr;
13917 return I->second;
13918 }
13919};
13920
13921const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr, const Loop *L) {
13922 auto CollectCondition = [&](ICmpInst::Predicate Predicate, const SCEV *LHS,
13923 const SCEV *RHS, ValueToSCEVMapTy &RewriteMap) {
13924 // If we have LHS == 0, check if LHS is computing a property of some unknown
13925 // SCEV %v which we can rewrite %v to express explicitly.
13926 const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS);
13927 if (Predicate == CmpInst::ICMP_EQ && RHSC &&
13928 RHSC->getValue()->isNullValue()) {
13929 // If LHS is A % B, i.e. A % B == 0, rewrite A to (A /u B) * B to
13930 // explicitly express that.
13931 const SCEV *URemLHS = nullptr;
13932 const SCEV *URemRHS = nullptr;
13933 if (matchURem(LHS, URemLHS, URemRHS)) {
13934 if (const SCEVUnknown *LHSUnknown = dyn_cast<SCEVUnknown>(URemLHS)) {
13935 Value *V = LHSUnknown->getValue();
13936 auto Multiple =
13937 getMulExpr(getUDivExpr(URemLHS, URemRHS), URemRHS,
13938 (SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNSW));
13939 RewriteMap[V] = Multiple;
13940 return;
13941 }
13942 }
13943 }
13944
13945 if (!isa<SCEVUnknown>(LHS) && isa<SCEVUnknown>(RHS)) {
13946 std::swap(LHS, RHS);
13947 Predicate = CmpInst::getSwappedPredicate(Predicate);
13948 }
13949
13950 // Check for a condition of the form (-C1 + X < C2). InstCombine will
13951 // create this form when combining two checks of the form (X u< C2 + C1) and
13952 // (X >=u C1).
13953 auto MatchRangeCheckIdiom = [this, Predicate, LHS, RHS, &RewriteMap]() {
13954 auto *AddExpr = dyn_cast<SCEVAddExpr>(LHS);
13955 if (!AddExpr || AddExpr->getNumOperands() != 2)
13956 return false;
13957
13958 auto *C1 = dyn_cast<SCEVConstant>(AddExpr->getOperand(0));
13959 auto *LHSUnknown = dyn_cast<SCEVUnknown>(AddExpr->getOperand(1));
13960 auto *C2 = dyn_cast<SCEVConstant>(RHS);
13961 if (!C1 || !C2 || !LHSUnknown)
13962 return false;
13963
13964 auto ExactRegion =
13965 ConstantRange::makeExactICmpRegion(Predicate, C2->getAPInt())
13966 .sub(C1->getAPInt());
13967
13968 // Bail out, unless we have a non-wrapping, monotonic range.
13969 if (ExactRegion.isWrappedSet() || ExactRegion.isFullSet())
13970 return false;
13971 auto I = RewriteMap.find(LHSUnknown->getValue());
13972 const SCEV *RewrittenLHS = I != RewriteMap.end() ? I->second : LHSUnknown;
13973 RewriteMap[LHSUnknown->getValue()] = getUMaxExpr(
13974 getConstant(ExactRegion.getUnsignedMin()),
13975 getUMinExpr(RewrittenLHS, getConstant(ExactRegion.getUnsignedMax())));
13976 return true;
13977 };
13978 if (MatchRangeCheckIdiom())
13979 return;
13980
13981 // For now, limit to conditions that provide information about unknown
13982 // expressions. RHS also cannot contain add recurrences.
13983 auto *LHSUnknown = dyn_cast<SCEVUnknown>(LHS);
13984 if (!LHSUnknown || containsAddRecurrence(RHS))
13985 return;
13986
13987 // Check whether LHS has already been rewritten. In that case we want to
13988 // chain further rewrites onto the already rewritten value.
13989 auto I = RewriteMap.find(LHSUnknown->getValue());
13990 const SCEV *RewrittenLHS = I != RewriteMap.end() ? I->second : LHS;
13991 const SCEV *RewrittenRHS = nullptr;
13992 switch (Predicate) {
13993 case CmpInst::ICMP_ULT:
13994 RewrittenRHS =
13995 getUMinExpr(RewrittenLHS, getMinusSCEV(RHS, getOne(RHS->getType())));
13996 break;
13997 case CmpInst::ICMP_SLT:
13998 RewrittenRHS =
13999 getSMinExpr(RewrittenLHS, getMinusSCEV(RHS, getOne(RHS->getType())));
14000 break;
14001 case CmpInst::ICMP_ULE:
14002 RewrittenRHS = getUMinExpr(RewrittenLHS, RHS);
14003 break;
14004 case CmpInst::ICMP_SLE:
14005 RewrittenRHS = getSMinExpr(RewrittenLHS, RHS);
14006 break;
14007 case CmpInst::ICMP_UGT:
14008 RewrittenRHS =
14009 getUMaxExpr(RewrittenLHS, getAddExpr(RHS, getOne(RHS->getType())));
14010 break;
14011 case CmpInst::ICMP_SGT:
14012 RewrittenRHS =
14013 getSMaxExpr(RewrittenLHS, getAddExpr(RHS, getOne(RHS->getType())));
14014 break;
14015 case CmpInst::ICMP_UGE:
14016 RewrittenRHS = getUMaxExpr(RewrittenLHS, RHS);
14017 break;
14018 case CmpInst::ICMP_SGE:
14019 RewrittenRHS = getSMaxExpr(RewrittenLHS, RHS);
14020 break;
14021 case CmpInst::ICMP_EQ:
14022 if (isa<SCEVConstant>(RHS))
14023 RewrittenRHS = RHS;
14024 break;
14025 case CmpInst::ICMP_NE:
14026 if (isa<SCEVConstant>(RHS) &&
14027 cast<SCEVConstant>(RHS)->getValue()->isNullValue())
14028 RewrittenRHS = getUMaxExpr(RewrittenLHS, getOne(RHS->getType()));
14029 break;
14030 default:
14031 break;
14032 }
14033
14034 if (RewrittenRHS)
14035 RewriteMap[LHSUnknown->getValue()] = RewrittenRHS;
14036 };
14037 // Starting at the loop predecessor, climb up the predecessor chain, as long
14038 // as there are predecessors that can be found that have unique successors
14039 // leading to the original header.
14040 // TODO: share this logic with isLoopEntryGuardedByCond.
14041 ValueToSCEVMapTy RewriteMap;
14042 for (std::pair<const BasicBlock *, const BasicBlock *> Pair(
14043 L->getLoopPredecessor(), L->getHeader());
14044 Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
14045
14046 const BranchInst *LoopEntryPredicate =
14047 dyn_cast<BranchInst>(Pair.first->getTerminator());
14048 if (!LoopEntryPredicate || LoopEntryPredicate->isUnconditional())
14049 continue;
14050
14051 bool EnterIfTrue = LoopEntryPredicate->getSuccessor(0) == Pair.second;
14052 SmallVector<Value *, 8> Worklist;
14053 SmallPtrSet<Value *, 8> Visited;
14054 Worklist.push_back(LoopEntryPredicate->getCondition());
14055 while (!Worklist.empty()) {
14056 Value *Cond = Worklist.pop_back_val();
14057 if (!Visited.insert(Cond).second)
14058 continue;
14059
14060 if (auto *Cmp = dyn_cast<ICmpInst>(Cond)) {
14061 auto Predicate =
14062 EnterIfTrue ? Cmp->getPredicate() : Cmp->getInversePredicate();
14063 CollectCondition(Predicate, getSCEV(Cmp->getOperand(0)),
14064 getSCEV(Cmp->getOperand(1)), RewriteMap);
14065 continue;
14066 }
14067
14068 Value *L, *R;
14069 if (EnterIfTrue ? match(Cond, m_LogicalAnd(m_Value(L), m_Value(R)))
14070 : match(Cond, m_LogicalOr(m_Value(L), m_Value(R)))) {
14071 Worklist.push_back(L);
14072 Worklist.push_back(R);
14073 }
14074 }
14075 }
14076
14077 // Also collect information from assumptions dominating the loop.
14078 for (auto &AssumeVH : AC.assumptions()) {
14079 if (!AssumeVH)
14080 continue;
14081 auto *AssumeI = cast<CallInst>(AssumeVH);
14082 auto *Cmp = dyn_cast<ICmpInst>(AssumeI->getOperand(0));
14083 if (!Cmp || !DT.dominates(AssumeI, L->getHeader()))
14084 continue;
14085 CollectCondition(Cmp->getPredicate(), getSCEV(Cmp->getOperand(0)),
14086 getSCEV(Cmp->getOperand(1)), RewriteMap);
14087 }
14088
14089 if (RewriteMap.empty())
14090 return Expr;
14091 SCEVLoopGuardRewriter Rewriter(*this, RewriteMap);
14092 return Rewriter.visit(Expr);
14093}

/usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ADT/Optional.h

1//===- Optional.h - Simple variant for passing optional values --*- C++ -*-===//
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 provides Optional, a template class modeled in the spirit of
10// OCaml's 'opt' variant. The idea is to strongly type whether or not
11// a value can be optional.
12//
13//===----------------------------------------------------------------------===//
14
15#ifndef LLVM_ADT_OPTIONAL_H
16#define LLVM_ADT_OPTIONAL_H
17
18#include "llvm/ADT/Hashing.h"
19#include "llvm/ADT/None.h"
20#include "llvm/ADT/STLForwardCompat.h"
21#include "llvm/Support/Compiler.h"
22#include "llvm/Support/type_traits.h"
23#include <cassert>
24#include <memory>
25#include <new>
26#include <utility>
27
28namespace llvm {
29
30class raw_ostream;
31
32namespace optional_detail {
33
34/// Storage for any type.
35//
36// The specialization condition intentionally uses
37// llvm::is_trivially_copy_constructible instead of
38// std::is_trivially_copy_constructible. GCC versions prior to 7.4 may
39// instantiate the copy constructor of `T` when
40// std::is_trivially_copy_constructible is instantiated. This causes
41// compilation to fail if we query the trivially copy constructible property of
42// a class which is not copy constructible.
43//
44// The current implementation of OptionalStorage insists that in order to use
45// the trivial specialization, the value_type must be trivially copy
46// constructible and trivially copy assignable due to =default implementations
47// of the copy/move constructor/assignment. It does not follow that this is
48// necessarily the case std::is_trivially_copyable is true (hence the expanded
49// specialization condition).
50//
51// The move constructible / assignable conditions emulate the remaining behavior
52// of std::is_trivially_copyable.
53template <typename T, bool = (llvm::is_trivially_copy_constructible<T>::value &&
54 std::is_trivially_copy_assignable<T>::value &&
55 (std::is_trivially_move_constructible<T>::value ||
56 !std::is_move_constructible<T>::value) &&
57 (std::is_trivially_move_assignable<T>::value ||
58 !std::is_move_assignable<T>::value))>
59class OptionalStorage {
60 union {
61 char empty;
62 T value;
63 };
64 bool hasVal;
65
66public:
67 ~OptionalStorage() { reset(); }
68
69 constexpr OptionalStorage() noexcept : empty(), hasVal(false) {}
70
71 constexpr OptionalStorage(OptionalStorage const &other) : OptionalStorage() {
72 if (other.hasValue()) {
73 emplace(other.value);
74 }
75 }
76 constexpr OptionalStorage(OptionalStorage &&other) : OptionalStorage() {
77 if (other.hasValue()) {
78 emplace(std::move(other.value));
79 }
80 }
81
82 template <class... Args>
83 constexpr explicit OptionalStorage(in_place_t, Args &&... args)
84 : value(std::forward<Args>(args)...), hasVal(true) {}
85
86 void reset() noexcept {
87 if (hasVal) {
88 value.~T();
89 hasVal = false;
90 }
91 }
92
93 constexpr bool hasValue() const noexcept { return hasVal; }
94
95 T &getValue() LLVM_LVALUE_FUNCTION& noexcept {
96 assert(hasVal)((void)0);
97 return value;
98 }
99 constexpr T const &getValue() const LLVM_LVALUE_FUNCTION& noexcept {
100 assert(hasVal)((void)0);
101 return value;
102 }
103#if LLVM_HAS_RVALUE_REFERENCE_THIS1
104 T &&getValue() && noexcept {
105 assert(hasVal)((void)0);
106 return std::move(value);
107 }
108#endif
109
110 template <class... Args> void emplace(Args &&... args) {
111 reset();
112 ::new ((void *)std::addressof(value)) T(std::forward<Args>(args)...);
113 hasVal = true;
114 }
115
116 OptionalStorage &operator=(T const &y) {
117 if (hasValue()) {
118 value = y;
119 } else {
120 ::new ((void *)std::addressof(value)) T(y);
121 hasVal = true;
122 }
123 return *this;
124 }
125 OptionalStorage &operator=(T &&y) {
126 if (hasValue()) {
127 value = std::move(y);
128 } else {
129 ::new ((void *)std::addressof(value)) T(std::move(y));
130 hasVal = true;
131 }
132 return *this;
133 }
134
135 OptionalStorage &operator=(OptionalStorage const &other) {
136 if (other.hasValue()) {
137 if (hasValue()) {
138 value = other.value;
139 } else {
140 ::new ((void *)std::addressof(value)) T(other.value);
141 hasVal = true;
142 }
143 } else {
144 reset();
145 }
146 return *this;
147 }
148
149 OptionalStorage &operator=(OptionalStorage &&other) {
150 if (other.hasValue()) {
151 if (hasValue()) {
152 value = std::move(other.value);
153 } else {
154 ::new ((void *)std::addressof(value)) T(std::move(other.value));
155 hasVal = true;
156 }
157 } else {
158 reset();
159 }
160 return *this;
161 }
162};
163
164template <typename T> class OptionalStorage<T, true> {
165 union {
166 char empty;
167 T value;
168 };
169 bool hasVal = false;
170
171public:
172 ~OptionalStorage() = default;
173
174 constexpr OptionalStorage() noexcept : empty{} {}
175
176 constexpr OptionalStorage(OptionalStorage const &other) = default;
177 constexpr OptionalStorage(OptionalStorage &&other) = default;
178
179 OptionalStorage &operator=(OptionalStorage const &other) = default;
180 OptionalStorage &operator=(OptionalStorage &&other) = default;
181
182 template <class... Args>
183 constexpr explicit OptionalStorage(in_place_t, Args &&... args)
184 : value(std::forward<Args>(args)...), hasVal(true) {}
185
186 void reset() noexcept {
187 if (hasVal) {
188 value.~T();
189 hasVal = false;
190 }
191 }
192
193 constexpr bool hasValue() const noexcept { return hasVal; }
4
Returning zero, which participates in a condition later
194
195 T &getValue() LLVM_LVALUE_FUNCTION& noexcept {
196 assert(hasVal)((void)0);
197 return value;
198 }
199 constexpr T const &getValue() const LLVM_LVALUE_FUNCTION& noexcept {
200 assert(hasVal)((void)0);
201 return value;
202 }
203#if LLVM_HAS_RVALUE_REFERENCE_THIS1
204 T &&getValue() && noexcept {
205 assert(hasVal)((void)0);
206 return std::move(value);
207 }
208#endif
209
210 template <class... Args> void emplace(Args &&... args) {
211 reset();
212 ::new ((void *)std::addressof(value)) T(std::forward<Args>(args)...);
213 hasVal = true;
214 }
215
216 OptionalStorage &operator=(T const &y) {
217 if (hasValue()) {
218 value = y;
219 } else {
220 ::new ((void *)std::addressof(value)) T(y);
221 hasVal = true;
222 }
223 return *this;
224 }
225 OptionalStorage &operator=(T &&y) {
226 if (hasValue()) {
227 value = std::move(y);
228 } else {
229 ::new ((void *)std::addressof(value)) T(std::move(y));
230 hasVal = true;
231 }
232 return *this;
233 }
234};
235
236} // namespace optional_detail
237
238template <typename T> class Optional {
239 optional_detail::OptionalStorage<T> Storage;
240
241public:
242 using value_type = T;
243
244 constexpr Optional() {}
245 constexpr Optional(NoneType) {}
246
247 constexpr Optional(const T &y) : Storage(in_place, y) {}
248 constexpr Optional(const Optional &O) = default;
249
250 constexpr Optional(T &&y) : Storage(in_place, std::move(y)) {}
251 constexpr Optional(Optional &&O) = default;
252
253 template <typename... ArgTypes>
254 constexpr Optional(in_place_t, ArgTypes &&...Args)
255 : Storage(in_place, std::forward<ArgTypes>(Args)...) {}
256
257 Optional &operator=(T &&y) {
258 Storage = std::move(y);
259 return *this;
260 }
261 Optional &operator=(Optional &&O) = default;
262
263 /// Create a new object by constructing it in place with the given arguments.
264 template <typename... ArgTypes> void emplace(ArgTypes &&... Args) {
265 Storage.emplace(std::forward<ArgTypes>(Args)...);
266 }
267
268 static constexpr Optional create(const T *y) {
269 return y ? Optional(*y) : Optional();
270 }
271
272 Optional &operator=(const T &y) {
273 Storage = y;
274 return *this;
275 }
276 Optional &operator=(const Optional &O) = default;
277
278 void reset() { Storage.reset(); }
279
280 constexpr const T *getPointer() const { return &Storage.getValue(); }
281 T *getPointer() { return &Storage.getValue(); }
282 constexpr const T &getValue() const LLVM_LVALUE_FUNCTION& {
283 return Storage.getValue();
284 }
285 T &getValue() LLVM_LVALUE_FUNCTION& { return Storage.getValue(); }
286
287 constexpr explicit operator bool() const { return hasValue(); }
2
Calling 'Optional::hasValue'
7
Returning from 'Optional::hasValue'
8
Returning zero, which participates in a condition later
288 constexpr bool hasValue() const { return Storage.hasValue(); }
3
Calling 'OptionalStorage::hasValue'
5
Returning from 'OptionalStorage::hasValue'
6
Returning zero, which participates in a condition later
289 constexpr const T *operator->() const { return getPointer(); }
290 T *operator->() { return getPointer(); }
291 constexpr const T &operator*() const LLVM_LVALUE_FUNCTION& {
292 return getValue();
293 }
294 T &operator*() LLVM_LVALUE_FUNCTION& { return getValue(); }
295
296 template <typename U>
297 constexpr T getValueOr(U &&value) const LLVM_LVALUE_FUNCTION& {
298 return hasValue() ? getValue() : std::forward<U>(value);
299 }
300
301 /// Apply a function to the value if present; otherwise return None.
302 template <class Function>
303 auto map(const Function &F) const LLVM_LVALUE_FUNCTION&
304 -> Optional<decltype(F(getValue()))> {
305 if (*this) return F(getValue());
306 return None;
307 }
308
309#if LLVM_HAS_RVALUE_REFERENCE_THIS1
310 T &&getValue() && { return std::move(Storage.getValue()); }
311 T &&operator*() && { return std::move(Storage.getValue()); }
312
313 template <typename U>
314 T getValueOr(U &&value) && {
315 return hasValue() ? std::move(getValue()) : std::forward<U>(value);
316 }
317
318 /// Apply a function to the value if present; otherwise return None.
319 template <class Function>
320 auto map(const Function &F) &&
321 -> Optional<decltype(F(std::move(*this).getValue()))> {
322 if (*this) return F(std::move(*this).getValue());
323 return None;
324 }
325#endif
326};
327
328template <class T> llvm::hash_code hash_value(const Optional<T> &O) {
329 return O ? hash_combine(true, *O) : hash_value(false);
330}
331
332template <typename T, typename U>
333constexpr bool operator==(const Optional<T> &X, const Optional<U> &Y) {
334 if (X && Y)
335 return *X == *Y;
336 return X.hasValue() == Y.hasValue();
337}
338
339template <typename T, typename U>
340constexpr bool operator!=(const Optional<T> &X, const Optional<U> &Y) {
341 return !(X == Y);
342}
343
344template <typename T, typename U>
345constexpr bool operator<(const Optional<T> &X, const Optional<U> &Y) {
346 if (X && Y)
347 return *X < *Y;
348 return X.hasValue() < Y.hasValue();
349}
350
351template <typename T, typename U>
352constexpr bool operator<=(const Optional<T> &X, const Optional<U> &Y) {
353 return !(Y < X);
354}
355
356template <typename T, typename U>
357constexpr bool operator>(const Optional<T> &X, const Optional<U> &Y) {
358 return Y < X;
359}
360
361template <typename T, typename U>
362constexpr bool operator>=(const Optional<T> &X, const Optional<U> &Y) {
363 return !(X < Y);
364}
365
366template <typename T>
367constexpr bool operator==(const Optional<T> &X, NoneType) {
368 return !X;
369}
370
371template <typename T>
372constexpr bool operator==(NoneType, const Optional<T> &X) {
373 return X == None;
374}
375
376template <typename T>
377constexpr bool operator!=(const Optional<T> &X, NoneType) {
378 return !(X == None);
379}
380
381template <typename T>
382constexpr bool operator!=(NoneType, const Optional<T> &X) {
383 return X != None;
384}
385
386template <typename T> constexpr bool operator<(const Optional<T> &, NoneType) {
387 return false;
388}
389
390template <typename T> constexpr bool operator<(NoneType, const Optional<T> &X) {
391 return X.hasValue();
392}
393
394template <typename T>
395constexpr bool operator<=(const Optional<T> &X, NoneType) {
396 return !(None < X);
397}
398
399template <typename T>
400constexpr bool operator<=(NoneType, const Optional<T> &X) {
401 return !(X < None);
402}
403
404template <typename T> constexpr bool operator>(const Optional<T> &X, NoneType) {
405 return None < X;
406}
407
408template <typename T> constexpr bool operator>(NoneType, const Optional<T> &X) {
409 return X < None;
410}
411
412template <typename T>
413constexpr bool operator>=(const Optional<T> &X, NoneType) {
414 return None <= X;
415}
416
417template <typename T>
418constexpr bool operator>=(NoneType, const Optional<T> &X) {
419 return X <= None;
420}
421
422template <typename T>
423constexpr bool operator==(const Optional<T> &X, const T &Y) {
424 return X && *X == Y;
425}
426
427template <typename T>
428constexpr bool operator==(const T &X, const Optional<T> &Y) {
429 return Y && X == *Y;
430}
431
432template <typename T>
433constexpr bool operator!=(const Optional<T> &X, const T &Y) {
434 return !(X == Y);
435}
436
437template <typename T>
438constexpr bool operator!=(const T &X, const Optional<T> &Y) {
439 return !(X == Y);
440}
441
442template <typename T>
443constexpr bool operator<(const Optional<T> &X, const T &Y) {
444 return !X || *X < Y;
445}
446
447template <typename T>
448constexpr bool operator<(const T &X, const Optional<T> &Y) {
449 return Y && X < *Y;
450}
451
452template <typename T>
453constexpr bool operator<=(const Optional<T> &X, const T &Y) {
454 return !(Y < X);
455}
456
457template <typename T>
458constexpr bool operator<=(const T &X, const Optional<T> &Y) {
459 return !(Y < X);
460}
461
462template <typename T>
463constexpr bool operator>(const Optional<T> &X, const T &Y) {
464 return Y < X;
465}
466
467template <typename T>
468constexpr bool operator>(const T &X, const Optional<T> &Y) {
469 return Y < X;
470}
471
472template <typename T>
473constexpr bool operator>=(const Optional<T> &X, const T &Y) {
474 return !(X < Y);
475}
476
477template <typename T>
478constexpr bool operator>=(const T &X, const Optional<T> &Y) {
479 return !(X < Y);
480}
481
482raw_ostream &operator<<(raw_ostream &OS, NoneType);
483
484template <typename T, typename = decltype(std::declval<raw_ostream &>()
485 << std::declval<const T &>())>
486raw_ostream &operator<<(raw_ostream &OS, const Optional<T> &O) {
487 if (O)
488 OS << *O;
489 else
490 OS << None;
491 return OS;
492}
493
494} // end namespace llvm
495
496#endif // LLVM_ADT_OPTIONAL_H