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llvm-mirror/lib/Analysis/ScalarEvolution.cpp
Bardia Mahjour 10f87c06af [NFC] [DA] Refactoring getIndexExpressionsFromGEP 
Summary:
This patch moves the getIndexExpressionsFromGEP function from polly
into ScalarEvolution so that both polly and DependenceAnalysis can
use it for the purpose of subscript delinearization when the array
sizes are not parametric.

Authored By: bmahjour

Reviewer: Meinersbur, sebpop, fhahn, dmgreen, grosser, etiotto, bollu

Reviewed By: Meinersbur

Subscribers: hiraditya, arphaman, Whitney, ppc-slack, llvm-commits

Tags: #llvm

Differential Revision: https://reviews.llvm.org/D73995
2020-02-24 17:32:30 -05:00

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//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file contains the implementation of the scalar evolution analysis
// engine, which is used primarily to analyze expressions involving induction
// variables in loops.
//
// There are several aspects to this library. First is the representation of
// scalar expressions, which are represented as subclasses of the SCEV class.
// These classes are used to represent certain types of subexpressions that we
// can handle. We only create one SCEV of a particular shape, so
// pointer-comparisons for equality are legal.
//
// One important aspect of the SCEV objects is that they are never cyclic, even
// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
// the PHI node is one of the idioms that we can represent (e.g., a polynomial
// recurrence) then we represent it directly as a recurrence node, otherwise we
// represent it as a SCEVUnknown node.
//
// In addition to being able to represent expressions of various types, we also
// have folders that are used to build the *canonical* representation for a
// particular expression. These folders are capable of using a variety of
// rewrite rules to simplify the expressions.
//
// Once the folders are defined, we can implement the more interesting
// higher-level code, such as the code that recognizes PHI nodes of various
// types, computes the execution count of a loop, etc.
//
// TODO: We should use these routines and value representations to implement
// dependence analysis!
//
//===----------------------------------------------------------------------===//
//
// There are several good references for the techniques used in this analysis.
//
// Chains of recurrences -- a method to expedite the evaluation
// of closed-form functions
// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
//
// On computational properties of chains of recurrences
// Eugene V. Zima
//
// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
// Robert A. van Engelen
//
// Efficient Symbolic Analysis for Optimizing Compilers
// Robert A. van Engelen
//
// Using the chains of recurrences algebra for data dependence testing and
// induction variable substitution
// MS Thesis, Johnie Birch
//
//===----------------------------------------------------------------------===//
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/ADT/APInt.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/DepthFirstIterator.h"
#include "llvm/ADT/EquivalenceClasses.h"
#include "llvm/ADT/FoldingSet.h"
#include "llvm/ADT/None.h"
#include "llvm/ADT/Optional.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/ScopeExit.h"
#include "llvm/ADT/Sequence.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/ADT/StringRef.h"
#include "llvm/Analysis/AssumptionCache.h"
#include "llvm/Analysis/ConstantFolding.h"
#include "llvm/Analysis/InstructionSimplify.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/TargetLibraryInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/Config/llvm-config.h"
#include "llvm/IR/Argument.h"
#include "llvm/IR/BasicBlock.h"
#include "llvm/IR/CFG.h"
#include "llvm/IR/CallSite.h"
#include "llvm/IR/Constant.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/DerivedTypes.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/GlobalAlias.h"
#include "llvm/IR/GlobalValue.h"
#include "llvm/IR/GlobalVariable.h"
#include "llvm/IR/InstIterator.h"
#include "llvm/IR/InstrTypes.h"
#include "llvm/IR/Instruction.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/Intrinsics.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Metadata.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/Type.h"
#include "llvm/IR/Use.h"
#include "llvm/IR/User.h"
#include "llvm/IR/Value.h"
#include "llvm/IR/Verifier.h"
#include "llvm/InitializePasses.h"
#include "llvm/Pass.h"
#include "llvm/Support/Casting.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/KnownBits.h"
#include "llvm/Support/SaveAndRestore.h"
#include "llvm/Support/raw_ostream.h"
#include <algorithm>
#include <cassert>
#include <climits>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <map>
#include <memory>
#include <tuple>
#include <utility>
#include <vector>
using namespace llvm;
#define DEBUG_TYPE "scalar-evolution"
STATISTIC(NumArrayLenItCounts,
"Number of trip counts computed with array length");
STATISTIC(NumTripCountsComputed,
"Number of loops with predictable loop counts");
STATISTIC(NumTripCountsNotComputed,
"Number of loops without predictable loop counts");
STATISTIC(NumBruteForceTripCountsComputed,
"Number of loops with trip counts computed by force");
static cl::opt<unsigned>
MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
cl::ZeroOrMore,
cl::desc("Maximum number of iterations SCEV will "
"symbolically execute a constant "
"derived loop"),
cl::init(100));
// FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
static cl::opt<bool> VerifySCEV(
"verify-scev", cl::Hidden,
cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
static cl::opt<bool> VerifySCEVStrict(
"verify-scev-strict", cl::Hidden,
cl::desc("Enable stricter verification with -verify-scev is passed"));
static cl::opt<bool>
VerifySCEVMap("verify-scev-maps", cl::Hidden,
cl::desc("Verify no dangling value in ScalarEvolution's "
"ExprValueMap (slow)"));
static cl::opt<bool> VerifyIR(
"scev-verify-ir", cl::Hidden,
cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
cl::init(false));
static cl::opt<unsigned> MulOpsInlineThreshold(
"scev-mulops-inline-threshold", cl::Hidden,
cl::desc("Threshold for inlining multiplication operands into a SCEV"),
cl::init(32));
static cl::opt<unsigned> AddOpsInlineThreshold(
"scev-addops-inline-threshold", cl::Hidden,
cl::desc("Threshold for inlining addition operands into a SCEV"),
cl::init(500));
static cl::opt<unsigned> MaxSCEVCompareDepth(
"scalar-evolution-max-scev-compare-depth", cl::Hidden,
cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
cl::init(32));
static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
"scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
cl::init(2));
static cl::opt<unsigned> MaxValueCompareDepth(
"scalar-evolution-max-value-compare-depth", cl::Hidden,
cl::desc("Maximum depth of recursive value complexity comparisons"),
cl::init(2));
static cl::opt<unsigned>
MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
cl::desc("Maximum depth of recursive arithmetics"),
cl::init(32));
static cl::opt<unsigned> MaxConstantEvolvingDepth(
"scalar-evolution-max-constant-evolving-depth", cl::Hidden,
cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
static cl::opt<unsigned>
MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
cl::init(8));
static cl::opt<unsigned>
MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
cl::desc("Max coefficients in AddRec during evolving"),
cl::init(8));
static cl::opt<unsigned>
HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
cl::desc("Size of the expression which is considered huge"),
cl::init(4096));
static cl::opt<bool>
ClassifyExpressions("scalar-evolution-classify-expressions",
cl::Hidden, cl::init(true),
cl::desc("When printing analysis, include information on every instruction"));
//===----------------------------------------------------------------------===//
// SCEV class definitions
//===----------------------------------------------------------------------===//
//===----------------------------------------------------------------------===//
// Implementation of the SCEV class.
//
#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
LLVM_DUMP_METHOD void SCEV::dump() const {
print(dbgs());
dbgs() << '\n';
}
#endif
void SCEV::print(raw_ostream &OS) const {
switch (static_cast<SCEVTypes>(getSCEVType())) {
case scConstant:
cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
return;
case scTruncate: {
const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
const SCEV *Op = Trunc->getOperand();
OS << "(trunc " << *Op->getType() << " " << *Op << " to "
<< *Trunc->getType() << ")";
return;
}
case scZeroExtend: {
const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
const SCEV *Op = ZExt->getOperand();
OS << "(zext " << *Op->getType() << " " << *Op << " to "
<< *ZExt->getType() << ")";
return;
}
case scSignExtend: {
const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
const SCEV *Op = SExt->getOperand();
OS << "(sext " << *Op->getType() << " " << *Op << " to "
<< *SExt->getType() << ")";
return;
}
case scAddRecExpr: {
const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
OS << "{" << *AR->getOperand(0);
for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
OS << ",+," << *AR->getOperand(i);
OS << "}<";
if (AR->hasNoUnsignedWrap())
OS << "nuw><";
if (AR->hasNoSignedWrap())
OS << "nsw><";
if (AR->hasNoSelfWrap() &&
!AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
OS << "nw><";
AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ">";
return;
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr: {
const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
const char *OpStr = nullptr;
switch (NAry->getSCEVType()) {
case scAddExpr: OpStr = " + "; break;
case scMulExpr: OpStr = " * "; break;
case scUMaxExpr: OpStr = " umax "; break;
case scSMaxExpr: OpStr = " smax "; break;
case scUMinExpr:
OpStr = " umin ";
break;
case scSMinExpr:
OpStr = " smin ";
break;
}
OS << "(";
for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
I != E; ++I) {
OS << **I;
if (std::next(I) != E)
OS << OpStr;
}
OS << ")";
switch (NAry->getSCEVType()) {
case scAddExpr:
case scMulExpr:
if (NAry->hasNoUnsignedWrap())
OS << "<nuw>";
if (NAry->hasNoSignedWrap())
OS << "<nsw>";
}
return;
}
case scUDivExpr: {
const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
return;
}
case scUnknown: {
const SCEVUnknown *U = cast<SCEVUnknown>(this);
Type *AllocTy;
if (U->isSizeOf(AllocTy)) {
OS << "sizeof(" << *AllocTy << ")";
return;
}
if (U->isAlignOf(AllocTy)) {
OS << "alignof(" << *AllocTy << ")";
return;
}
Type *CTy;
Constant *FieldNo;
if (U->isOffsetOf(CTy, FieldNo)) {
OS << "offsetof(" << *CTy << ", ";
FieldNo->printAsOperand(OS, false);
OS << ")";
return;
}
// Otherwise just print it normally.
U->getValue()->printAsOperand(OS, false);
return;
}
case scCouldNotCompute:
OS << "***COULDNOTCOMPUTE***";
return;
}
llvm_unreachable("Unknown SCEV kind!");
}
Type *SCEV::getType() const {
switch (static_cast<SCEVTypes>(getSCEVType())) {
case scConstant:
return cast<SCEVConstant>(this)->getType();
case scTruncate:
case scZeroExtend:
case scSignExtend:
return cast<SCEVCastExpr>(this)->getType();
case scAddRecExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
return cast<SCEVNAryExpr>(this)->getType();
case scAddExpr:
return cast<SCEVAddExpr>(this)->getType();
case scUDivExpr:
return cast<SCEVUDivExpr>(this)->getType();
case scUnknown:
return cast<SCEVUnknown>(this)->getType();
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
}
llvm_unreachable("Unknown SCEV kind!");
}
bool SCEV::isZero() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
return SC->getValue()->isZero();
return false;
}
bool SCEV::isOne() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
return SC->getValue()->isOne();
return false;
}
bool SCEV::isAllOnesValue() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
return SC->getValue()->isMinusOne();
return false;
}
bool SCEV::isNonConstantNegative() const {
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
if (!Mul) return false;
// If there is a constant factor, it will be first.
const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
if (!SC) return false;
// Return true if the value is negative, this matches things like (-42 * V).
return SC->getAPInt().isNegative();
}
SCEVCouldNotCompute::SCEVCouldNotCompute() :
SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {}
bool SCEVCouldNotCompute::classof(const SCEV *S) {
return S->getSCEVType() == scCouldNotCompute;
}
const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
FoldingSetNodeID ID;
ID.AddInteger(scConstant);
ID.AddPointer(V);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
UniqueSCEVs.InsertNode(S, IP);
return S;
}
const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
return getConstant(ConstantInt::get(getContext(), Val));
}
const SCEV *
ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
return getConstant(ConstantInt::get(ITy, V, isSigned));
}
SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
unsigned SCEVTy, const SCEV *op, Type *ty)
: SCEV(ID, SCEVTy, computeExpressionSize(op)), Op(op), Ty(ty) {}
SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
const SCEV *op, Type *ty)
: SCEVCastExpr(ID, scTruncate, op, ty) {
assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate non-integer value!");
}
SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
const SCEV *op, Type *ty)
: SCEVCastExpr(ID, scZeroExtend, op, ty) {
assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot zero extend non-integer value!");
}
SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
const SCEV *op, Type *ty)
: SCEVCastExpr(ID, scSignExtend, op, ty) {
assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot sign extend non-integer value!");
}
void SCEVUnknown::deleted() {
// Clear this SCEVUnknown from various maps.
SE->forgetMemoizedResults(this);
// Remove this SCEVUnknown from the uniquing map.
SE->UniqueSCEVs.RemoveNode(this);
// Release the value.
setValPtr(nullptr);
}
void SCEVUnknown::allUsesReplacedWith(Value *New) {
// Remove this SCEVUnknown from the uniquing map.
SE->UniqueSCEVs.RemoveNode(this);
// Update this SCEVUnknown to point to the new value. This is needed
// because there may still be outstanding SCEVs which still point to
// this SCEVUnknown.
setValPtr(New);
}
bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
if (VCE->getOpcode() == Instruction::PtrToInt)
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
if (CE->getOpcode() == Instruction::GetElementPtr &&
CE->getOperand(0)->isNullValue() &&
CE->getNumOperands() == 2)
if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
if (CI->isOne()) {
AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
->getElementType();
return true;
}
return false;
}
bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
if (VCE->getOpcode() == Instruction::PtrToInt)
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
if (CE->getOpcode() == Instruction::GetElementPtr &&
CE->getOperand(0)->isNullValue()) {
Type *Ty =
cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
if (StructType *STy = dyn_cast<StructType>(Ty))
if (!STy->isPacked() &&
CE->getNumOperands() == 3 &&
CE->getOperand(1)->isNullValue()) {
if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
if (CI->isOne() &&
STy->getNumElements() == 2 &&
STy->getElementType(0)->isIntegerTy(1)) {
AllocTy = STy->getElementType(1);
return true;
}
}
}
return false;
}
bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
if (VCE->getOpcode() == Instruction::PtrToInt)
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
if (CE->getOpcode() == Instruction::GetElementPtr &&
CE->getNumOperands() == 3 &&
CE->getOperand(0)->isNullValue() &&
CE->getOperand(1)->isNullValue()) {
Type *Ty =
cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
// Ignore vector types here so that ScalarEvolutionExpander doesn't
// emit getelementptrs that index into vectors.
if (Ty->isStructTy() || Ty->isArrayTy()) {
CTy = Ty;
FieldNo = CE->getOperand(2);
return true;
}
}
return false;
}
//===----------------------------------------------------------------------===//
// SCEV Utilities
//===----------------------------------------------------------------------===//
/// Compare the two values \p LV and \p RV in terms of their "complexity" where
/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
/// operands in SCEV expressions. \p EqCache is a set of pairs of values that
/// have been previously deemed to be "equally complex" by this routine. It is
/// intended to avoid exponential time complexity in cases like:
///
/// %a = f(%x, %y)
/// %b = f(%a, %a)
/// %c = f(%b, %b)
///
/// %d = f(%x, %y)
/// %e = f(%d, %d)
/// %f = f(%e, %e)
///
/// CompareValueComplexity(%f, %c)
///
/// Since we do not continue running this routine on expression trees once we
/// have seen unequal values, there is no need to track them in the cache.
static int
CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
const LoopInfo *const LI, Value *LV, Value *RV,
unsigned Depth) {
if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
return 0;
// Order pointer values after integer values. This helps SCEVExpander form
// GEPs.
bool LIsPointer = LV->getType()->isPointerTy(),
RIsPointer = RV->getType()->isPointerTy();
if (LIsPointer != RIsPointer)
return (int)LIsPointer - (int)RIsPointer;
// Compare getValueID values.
unsigned LID = LV->getValueID(), RID = RV->getValueID();
if (LID != RID)
return (int)LID - (int)RID;
// Sort arguments by their position.
if (const auto *LA = dyn_cast<Argument>(LV)) {
const auto *RA = cast<Argument>(RV);
unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
return (int)LArgNo - (int)RArgNo;
}
if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
const auto *RGV = cast<GlobalValue>(RV);
const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
auto LT = GV->getLinkage();
return !(GlobalValue::isPrivateLinkage(LT) ||
GlobalValue::isInternalLinkage(LT));
};
// Use the names to distinguish the two values, but only if the
// names are semantically important.
if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
return LGV->getName().compare(RGV->getName());
}
// For instructions, compare their loop depth, and their operand count. This
// is pretty loose.
if (const auto *LInst = dyn_cast<Instruction>(LV)) {
const auto *RInst = cast<Instruction>(RV);
// Compare loop depths.
const BasicBlock *LParent = LInst->getParent(),
*RParent = RInst->getParent();
if (LParent != RParent) {
unsigned LDepth = LI->getLoopDepth(LParent),
RDepth = LI->getLoopDepth(RParent);
if (LDepth != RDepth)
return (int)LDepth - (int)RDepth;
}
// Compare the number of operands.
unsigned LNumOps = LInst->getNumOperands(),
RNumOps = RInst->getNumOperands();
if (LNumOps != RNumOps)
return (int)LNumOps - (int)RNumOps;
for (unsigned Idx : seq(0u, LNumOps)) {
int Result =
CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
RInst->getOperand(Idx), Depth + 1);
if (Result != 0)
return Result;
}
}
EqCacheValue.unionSets(LV, RV);
return 0;
}
// Return negative, zero, or positive, if LHS is less than, equal to, or greater
// than RHS, respectively. A three-way result allows recursive comparisons to be
// more efficient.
static int CompareSCEVComplexity(
EquivalenceClasses<const SCEV *> &EqCacheSCEV,
EquivalenceClasses<const Value *> &EqCacheValue,
const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
DominatorTree &DT, unsigned Depth = 0) {
// Fast-path: SCEVs are uniqued so we can do a quick equality check.
if (LHS == RHS)
return 0;
// Primarily, sort the SCEVs by their getSCEVType().
unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
if (LType != RType)
return (int)LType - (int)RType;
if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS))
return 0;
// Aside from the getSCEVType() ordering, the particular ordering
// isn't very important except that it's beneficial to be consistent,
// so that (a + b) and (b + a) don't end up as different expressions.
switch (static_cast<SCEVTypes>(LType)) {
case scUnknown: {
const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
RU->getValue(), Depth + 1);
if (X == 0)
EqCacheSCEV.unionSets(LHS, RHS);
return X;
}
case scConstant: {
const SCEVConstant *LC = cast<SCEVConstant>(LHS);
const SCEVConstant *RC = cast<SCEVConstant>(RHS);
// Compare constant values.
const APInt &LA = LC->getAPInt();
const APInt &RA = RC->getAPInt();
unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
if (LBitWidth != RBitWidth)
return (int)LBitWidth - (int)RBitWidth;
return LA.ult(RA) ? -1 : 1;
}
case scAddRecExpr: {
const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
// There is always a dominance between two recs that are used by one SCEV,
// so we can safely sort recs by loop header dominance. We require such
// order in getAddExpr.
const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
if (LLoop != RLoop) {
const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
assert(LHead != RHead && "Two loops share the same header?");
if (DT.dominates(LHead, RHead))
return 1;
else
assert(DT.dominates(RHead, LHead) &&
"No dominance between recurrences used by one SCEV?");
return -1;
}
// Addrec complexity grows with operand count.
unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
if (LNumOps != RNumOps)
return (int)LNumOps - (int)RNumOps;
// Lexicographically compare.
for (unsigned i = 0; i != LNumOps; ++i) {
int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
LA->getOperand(i), RA->getOperand(i), DT,
Depth + 1);
if (X != 0)
return X;
}
EqCacheSCEV.unionSets(LHS, RHS);
return 0;
}
case scAddExpr:
case scMulExpr:
case scSMaxExpr:
case scUMaxExpr:
case scSMinExpr:
case scUMinExpr: {
const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
// Lexicographically compare n-ary expressions.
unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
if (LNumOps != RNumOps)
return (int)LNumOps - (int)RNumOps;
for (unsigned i = 0; i != LNumOps; ++i) {
int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
LC->getOperand(i), RC->getOperand(i), DT,
Depth + 1);
if (X != 0)
return X;
}
EqCacheSCEV.unionSets(LHS, RHS);
return 0;
}
case scUDivExpr: {
const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
// Lexicographically compare udiv expressions.
int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
RC->getLHS(), DT, Depth + 1);
if (X != 0)
return X;
X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
RC->getRHS(), DT, Depth + 1);
if (X == 0)
EqCacheSCEV.unionSets(LHS, RHS);
return X;
}
case scTruncate:
case scZeroExtend:
case scSignExtend: {
const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
// Compare cast expressions by operand.
int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
LC->getOperand(), RC->getOperand(), DT,
Depth + 1);
if (X == 0)
EqCacheSCEV.unionSets(LHS, RHS);
return X;
}
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
}
llvm_unreachable("Unknown SCEV kind!");
}
/// Given a list of SCEV objects, order them by their complexity, and group
/// objects of the same complexity together by value. When this routine is
/// finished, we know that any duplicates in the vector are consecutive and that
/// complexity is monotonically increasing.
///
/// Note that we go take special precautions to ensure that we get deterministic
/// results from this routine. In other words, we don't want the results of
/// this to depend on where the addresses of various SCEV objects happened to
/// land in memory.
static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
LoopInfo *LI, DominatorTree &DT) {
if (Ops.size() < 2) return; // Noop
EquivalenceClasses<const SCEV *> EqCacheSCEV;
EquivalenceClasses<const Value *> EqCacheValue;
if (Ops.size() == 2) {
// This is the common case, which also happens to be trivially simple.
// Special case it.
const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
if (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0)
std::swap(LHS, RHS);
return;
}
// Do the rough sort by complexity.
llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) {
return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT) <
0;
});
// Now that we are sorted by complexity, group elements of the same
// complexity. Note that this is, at worst, N^2, but the vector is likely to
// be extremely short in practice. Note that we take this approach because we
// do not want to depend on the addresses of the objects we are grouping.
for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
const SCEV *S = Ops[i];
unsigned Complexity = S->getSCEVType();
// If there are any objects of the same complexity and same value as this
// one, group them.
for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
if (Ops[j] == S) { // Found a duplicate.
// Move it to immediately after i'th element.
std::swap(Ops[i+1], Ops[j]);
++i; // no need to rescan it.
if (i == e-2) return; // Done!
}
}
}
}
// Returns the size of the SCEV S.
static inline int sizeOfSCEV(const SCEV *S) {
struct FindSCEVSize {
int Size = 0;
FindSCEVSize() = default;
bool follow(const SCEV *S) {
++Size;
// Keep looking at all operands of S.
return true;
}
bool isDone() const {
return false;
}
};
FindSCEVSize F;
SCEVTraversal<FindSCEVSize> ST(F);
ST.visitAll(S);
return F.Size;
}
/// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at
/// least HugeExprThreshold nodes).
static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) {
return any_of(Ops, [](const SCEV *S) {
return S->getExpressionSize() >= HugeExprThreshold;
});
}
namespace {
struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
public:
// Computes the Quotient and Remainder of the division of Numerator by
// Denominator.
static void divide(ScalarEvolution &SE, const SCEV *Numerator,
const SCEV *Denominator, const SCEV **Quotient,
const SCEV **Remainder) {
assert(Numerator && Denominator && "Uninitialized SCEV");
SCEVDivision D(SE, Numerator, Denominator);
// Check for the trivial case here to avoid having to check for it in the
// rest of the code.
if (Numerator == Denominator) {
*Quotient = D.One;
*Remainder = D.Zero;
return;
}
if (Numerator->isZero()) {
*Quotient = D.Zero;
*Remainder = D.Zero;
return;
}
// A simple case when N/1. The quotient is N.
if (Denominator->isOne()) {
*Quotient = Numerator;
*Remainder = D.Zero;
return;
}
// Split the Denominator when it is a product.
if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
const SCEV *Q, *R;
*Quotient = Numerator;
for (const SCEV *Op : T->operands()) {
divide(SE, *Quotient, Op, &Q, &R);
*Quotient = Q;
// Bail out when the Numerator is not divisible by one of the terms of
// the Denominator.
if (!R->isZero()) {
*Quotient = D.Zero;
*Remainder = Numerator;
return;
}
}
*Remainder = D.Zero;
return;
}
D.visit(Numerator);
*Quotient = D.Quotient;
*Remainder = D.Remainder;
}
// Except in the trivial case described above, we do not know how to divide
// Expr by Denominator for the following functions with empty implementation.
void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
void visitSMinExpr(const SCEVSMinExpr *Numerator) {}
void visitUMinExpr(const SCEVUMinExpr *Numerator) {}
void visitUnknown(const SCEVUnknown *Numerator) {}
void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
void visitConstant(const SCEVConstant *Numerator) {
if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
APInt NumeratorVal = Numerator->getAPInt();
APInt DenominatorVal = D->getAPInt();
uint32_t NumeratorBW = NumeratorVal.getBitWidth();
uint32_t DenominatorBW = DenominatorVal.getBitWidth();
if (NumeratorBW > DenominatorBW)
DenominatorVal = DenominatorVal.sext(NumeratorBW);
else if (NumeratorBW < DenominatorBW)
NumeratorVal = NumeratorVal.sext(DenominatorBW);
APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
Quotient = SE.getConstant(QuotientVal);
Remainder = SE.getConstant(RemainderVal);
return;
}
}
void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
const SCEV *StartQ, *StartR, *StepQ, *StepR;
if (!Numerator->isAffine())
return cannotDivide(Numerator);
divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
// Bail out if the types do not match.
Type *Ty = Denominator->getType();
if (Ty != StartQ->getType() || Ty != StartR->getType() ||
Ty != StepQ->getType() || Ty != StepR->getType())
return cannotDivide(Numerator);
Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
Numerator->getNoWrapFlags());
Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
Numerator->getNoWrapFlags());
}
void visitAddExpr(const SCEVAddExpr *Numerator) {
SmallVector<const SCEV *, 2> Qs, Rs;
Type *Ty = Denominator->getType();
for (const SCEV *Op : Numerator->operands()) {
const SCEV *Q, *R;
divide(SE, Op, Denominator, &Q, &R);
// Bail out if types do not match.
if (Ty != Q->getType() || Ty != R->getType())
return cannotDivide(Numerator);
Qs.push_back(Q);
Rs.push_back(R);
}
if (Qs.size() == 1) {
Quotient = Qs[0];
Remainder = Rs[0];
return;
}
Quotient = SE.getAddExpr(Qs);
Remainder = SE.getAddExpr(Rs);
}
void visitMulExpr(const SCEVMulExpr *Numerator) {
SmallVector<const SCEV *, 2> Qs;
Type *Ty = Denominator->getType();
bool FoundDenominatorTerm = false;
for (const SCEV *Op : Numerator->operands()) {
// Bail out if types do not match.
if (Ty != Op->getType())
return cannotDivide(Numerator);
if (FoundDenominatorTerm) {
Qs.push_back(Op);
continue;
}
// Check whether Denominator divides one of the product operands.
const SCEV *Q, *R;
divide(SE, Op, Denominator, &Q, &R);
if (!R->isZero()) {
Qs.push_back(Op);
continue;
}
// Bail out if types do not match.
if (Ty != Q->getType())
return cannotDivide(Numerator);
FoundDenominatorTerm = true;
Qs.push_back(Q);
}
if (FoundDenominatorTerm) {
Remainder = Zero;
if (Qs.size() == 1)
Quotient = Qs[0];
else
Quotient = SE.getMulExpr(Qs);
return;
}
if (!isa<SCEVUnknown>(Denominator))
return cannotDivide(Numerator);
// The Remainder is obtained by replacing Denominator by 0 in Numerator.
ValueToValueMap RewriteMap;
RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
cast<SCEVConstant>(Zero)->getValue();
Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
if (Remainder->isZero()) {
// The Quotient is obtained by replacing Denominator by 1 in Numerator.
RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
cast<SCEVConstant>(One)->getValue();
Quotient =
SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
return;
}
// Quotient is (Numerator - Remainder) divided by Denominator.
const SCEV *Q, *R;
const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
// This SCEV does not seem to simplify: fail the division here.
if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
return cannotDivide(Numerator);
divide(SE, Diff, Denominator, &Q, &R);
if (R != Zero)
return cannotDivide(Numerator);
Quotient = Q;
}
private:
SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
const SCEV *Denominator)
: SE(S), Denominator(Denominator) {
Zero = SE.getZero(Denominator->getType());
One = SE.getOne(Denominator->getType());
// We generally do not know how to divide Expr by Denominator. We
// initialize the division to a "cannot divide" state to simplify the rest
// of the code.
cannotDivide(Numerator);
}
// Convenience function for giving up on the division. We set the quotient to
// be equal to zero and the remainder to be equal to the numerator.
void cannotDivide(const SCEV *Numerator) {
Quotient = Zero;
Remainder = Numerator;
}
ScalarEvolution &SE;
const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
};
} // end anonymous namespace
//===----------------------------------------------------------------------===//
// Simple SCEV method implementations
//===----------------------------------------------------------------------===//
/// Compute BC(It, K). The result has width W. Assume, K > 0.
static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
ScalarEvolution &SE,
Type *ResultTy) {
// Handle the simplest case efficiently.
if (K == 1)
return SE.getTruncateOrZeroExtend(It, ResultTy);
// We are using the following formula for BC(It, K):
//
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
//
// Suppose, W is the bitwidth of the return value. We must be prepared for
// overflow. Hence, we must assure that the result of our computation is
// equal to the accurate one modulo 2^W. Unfortunately, division isn't
// safe in modular arithmetic.
//
// However, this code doesn't use exactly that formula; the formula it uses
// is something like the following, where T is the number of factors of 2 in
// K! (i.e. trailing zeros in the binary representation of K!), and ^ is
// exponentiation:
//
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
//
// This formula is trivially equivalent to the previous formula. However,
// this formula can be implemented much more efficiently. The trick is that
// K! / 2^T is odd, and exact division by an odd number *is* safe in modular
// arithmetic. To do exact division in modular arithmetic, all we have
// to do is multiply by the inverse. Therefore, this step can be done at
// width W.
//
// The next issue is how to safely do the division by 2^T. The way this
// is done is by doing the multiplication step at a width of at least W + T
// bits. This way, the bottom W+T bits of the product are accurate. Then,
// when we perform the division by 2^T (which is equivalent to a right shift
// by T), the bottom W bits are accurate. Extra bits are okay; they'll get
// truncated out after the division by 2^T.
//
// In comparison to just directly using the first formula, this technique
// is much more efficient; using the first formula requires W * K bits,
// but this formula less than W + K bits. Also, the first formula requires
// a division step, whereas this formula only requires multiplies and shifts.
//
// It doesn't matter whether the subtraction step is done in the calculation
// width or the input iteration count's width; if the subtraction overflows,
// the result must be zero anyway. We prefer here to do it in the width of
// the induction variable because it helps a lot for certain cases; CodeGen
// isn't smart enough to ignore the overflow, which leads to much less
// efficient code if the width of the subtraction is wider than the native
// register width.
//
// (It's possible to not widen at all by pulling out factors of 2 before
// the multiplication; for example, K=2 can be calculated as
// It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
// extra arithmetic, so it's not an obvious win, and it gets
// much more complicated for K > 3.)
// Protection from insane SCEVs; this bound is conservative,
// but it probably doesn't matter.
if (K > 1000)
return SE.getCouldNotCompute();
unsigned W = SE.getTypeSizeInBits(ResultTy);
// Calculate K! / 2^T and T; we divide out the factors of two before
// multiplying for calculating K! / 2^T to avoid overflow.
// Other overflow doesn't matter because we only care about the bottom
// W bits of the result.
APInt OddFactorial(W, 1);
unsigned T = 1;
for (unsigned i = 3; i <= K; ++i) {
APInt Mult(W, i);
unsigned TwoFactors = Mult.countTrailingZeros();
T += TwoFactors;
Mult.lshrInPlace(TwoFactors);
OddFactorial *= Mult;
}
// We need at least W + T bits for the multiplication step
unsigned CalculationBits = W + T;
// Calculate 2^T, at width T+W.
APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
// Calculate the multiplicative inverse of K! / 2^T;
// this multiplication factor will perform the exact division by
// K! / 2^T.
APInt Mod = APInt::getSignedMinValue(W+1);
APInt MultiplyFactor = OddFactorial.zext(W+1);
MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
MultiplyFactor = MultiplyFactor.trunc(W);
// Calculate the product, at width T+W
IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
CalculationBits);
const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
for (unsigned i = 1; i != K; ++i) {
const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
Dividend = SE.getMulExpr(Dividend,
SE.getTruncateOrZeroExtend(S, CalculationTy));
}
// Divide by 2^T
const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
// Truncate the result, and divide by K! / 2^T.
return SE.getMulExpr(SE.getConstant(MultiplyFactor),
SE.getTruncateOrZeroExtend(DivResult, ResultTy));
}
/// Return the value of this chain of recurrences at the specified iteration
/// number. We can evaluate this recurrence by multiplying each element in the
/// chain by the binomial coefficient corresponding to it. In other words, we
/// can evaluate {A,+,B,+,C,+,D} as:
///
/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
///
/// where BC(It, k) stands for binomial coefficient.
const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
ScalarEvolution &SE) const {
const SCEV *Result = getStart();
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
// The computation is correct in the face of overflow provided that the
// multiplication is performed _after_ the evaluation of the binomial
// coefficient.
const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
if (isa<SCEVCouldNotCompute>(Coeff))
return Coeff;
Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
}
return Result;
}
//===----------------------------------------------------------------------===//
// SCEV Expression folder implementations
//===----------------------------------------------------------------------===//
const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
"This is not a truncating conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
FoldingSetNodeID ID;
ID.AddInteger(scTruncate);
ID.AddPointer(Op);
ID.AddPointer(Ty);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
// Fold if the operand is constant.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getConstant(
cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
// trunc(trunc(x)) --> trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
return getTruncateExpr(ST->getOperand(), Ty, Depth + 1);
// trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1);
// trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1);
if (Depth > MaxCastDepth) {
SCEV *S =
new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
// trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
// trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
// if after transforming we have at most one truncate, not counting truncates
// that replace other casts.
if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
auto *CommOp = cast<SCEVCommutativeExpr>(Op);
SmallVector<const SCEV *, 4> Operands;
unsigned numTruncs = 0;
for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
++i) {
const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1);
if (!isa<SCEVCastExpr>(CommOp->getOperand(i)) && isa<SCEVTruncateExpr>(S))
numTruncs++;
Operands.push_back(S);
}
if (numTruncs < 2) {
if (isa<SCEVAddExpr>(Op))
return getAddExpr(Operands);
else if (isa<SCEVMulExpr>(Op))
return getMulExpr(Operands);
else
llvm_unreachable("Unexpected SCEV type for Op.");
}
// Although we checked in the beginning that ID is not in the cache, it is
// possible that during recursion and different modification ID was inserted
// into the cache. So if we find it, just return it.
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
return S;
}
// If the input value is a chrec scev, truncate the chrec's operands.
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *Op : AddRec->operands())
Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1));
return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
}
// The cast wasn't folded; create an explicit cast node. We can reuse
// the existing insert position since if we get here, we won't have
// made any changes which would invalidate it.
SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
// Get the limit of a recurrence such that incrementing by Step cannot cause
// signed overflow as long as the value of the recurrence within the
// loop does not exceed this limit before incrementing.
static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
ICmpInst::Predicate *Pred,
ScalarEvolution *SE) {
unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
if (SE->isKnownPositive(Step)) {
*Pred = ICmpInst::ICMP_SLT;
return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
SE->getSignedRangeMax(Step));
}
if (SE->isKnownNegative(Step)) {
*Pred = ICmpInst::ICMP_SGT;
return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
SE->getSignedRangeMin(Step));
}
return nullptr;
}
// Get the limit of a recurrence such that incrementing by Step cannot cause
// unsigned overflow as long as the value of the recurrence within the loop does
// not exceed this limit before incrementing.
static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
ICmpInst::Predicate *Pred,
ScalarEvolution *SE) {
unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
*Pred = ICmpInst::ICMP_ULT;
return SE->getConstant(APInt::getMinValue(BitWidth) -
SE->getUnsignedRangeMax(Step));
}
namespace {
struct ExtendOpTraitsBase {
typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
unsigned);
};
// Used to make code generic over signed and unsigned overflow.
template <typename ExtendOp> struct ExtendOpTraits {
// Members present:
//
// static const SCEV::NoWrapFlags WrapType;
//
// static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
//
// static const SCEV *getOverflowLimitForStep(const SCEV *Step,
// ICmpInst::Predicate *Pred,
// ScalarEvolution *SE);
};
template <>
struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
static const GetExtendExprTy GetExtendExpr;
static const SCEV *getOverflowLimitForStep(const SCEV *Step,
ICmpInst::Predicate *Pred,
ScalarEvolution *SE) {
return getSignedOverflowLimitForStep(Step, Pred, SE);
}
};
const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
template <>
struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
static const GetExtendExprTy GetExtendExpr;
static const SCEV *getOverflowLimitForStep(const SCEV *Step,
ICmpInst::Predicate *Pred,
ScalarEvolution *SE) {
return getUnsignedOverflowLimitForStep(Step, Pred, SE);
}
};
const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
} // end anonymous namespace
// The recurrence AR has been shown to have no signed/unsigned wrap or something
// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
// easily prove NSW/NUW for its preincrement or postincrement sibling. This
// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
// expression "Step + sext/zext(PreIncAR)" is congruent with
// "sext/zext(PostIncAR)"
template <typename ExtendOpTy>
static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
ScalarEvolution *SE, unsigned Depth) {
auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
const Loop *L = AR->getLoop();
const SCEV *Start = AR->getStart();
const SCEV *Step = AR->getStepRecurrence(*SE);
// Check for a simple looking step prior to loop entry.
const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
if (!SA)
return nullptr;
// Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
// subtraction is expensive. For this purpose, perform a quick and dirty
// difference, by checking for Step in the operand list.
SmallVector<const SCEV *, 4> DiffOps;
for (const SCEV *Op : SA->operands())
if (Op != Step)
DiffOps.push_back(Op);
if (DiffOps.size() == SA->getNumOperands())
return nullptr;
// Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
// `Step`:
// 1. NSW/NUW flags on the step increment.
auto PreStartFlags =
ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
// "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
// "S+X does not sign/unsign-overflow".
//
const SCEV *BECount = SE->getBackedgeTakenCount(L);
if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
!isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
return PreStart;
// 2. Direct overflow check on the step operation's expression.
unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
const SCEV *OperandExtendedStart =
SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
(SE->*GetExtendExpr)(Step, WideTy, Depth));
if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
if (PreAR && AR->getNoWrapFlags(WrapType)) {
// If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
// or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
// `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
}
return PreStart;
}
// 3. Loop precondition.
ICmpInst::Predicate Pred;
const SCEV *OverflowLimit =
ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
if (OverflowLimit &&
SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
return PreStart;
return nullptr;
}
// Get the normalized zero or sign extended expression for this AddRec's Start.
template <typename ExtendOpTy>
static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
ScalarEvolution *SE,
unsigned Depth) {
auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
if (!PreStart)
return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
Depth),
(SE->*GetExtendExpr)(PreStart, Ty, Depth));
}
// Try to prove away overflow by looking at "nearby" add recurrences. A
// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
//
// Formally:
//
// {S,+,X} == {S-T,+,X} + T
// => Ext({S,+,X}) == Ext({S-T,+,X} + T)
//
// If ({S-T,+,X} + T) does not overflow ... (1)
//
// RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
//
// If {S-T,+,X} does not overflow ... (2)
//
// RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
// == {Ext(S-T)+Ext(T),+,Ext(X)}
//
// If (S-T)+T does not overflow ... (3)
//
// RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
// == {Ext(S),+,Ext(X)} == LHS
//
// Thus, if (1), (2) and (3) are true for some T, then
// Ext({S,+,X}) == {Ext(S),+,Ext(X)}
//
// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
// does not overflow" restricted to the 0th iteration. Therefore we only need
// to check for (1) and (2).
//
// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
// is `Delta` (defined below).
template <typename ExtendOpTy>
bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
const SCEV *Step,
const Loop *L) {
auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
// We restrict `Start` to a constant to prevent SCEV from spending too much
// time here. It is correct (but more expensive) to continue with a
// non-constant `Start` and do a general SCEV subtraction to compute
// `PreStart` below.
const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
if (!StartC)
return false;
APInt StartAI = StartC->getAPInt();
for (unsigned Delta : {-2, -1, 1, 2}) {
const SCEV *PreStart = getConstant(StartAI - Delta);
FoldingSetNodeID ID;
ID.AddInteger(scAddRecExpr);
ID.AddPointer(PreStart);
ID.AddPointer(Step);
ID.AddPointer(L);
void *IP = nullptr;
const auto *PreAR =
static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
// Give up if we don't already have the add recurrence we need because
// actually constructing an add recurrence is relatively expensive.
if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
DeltaS, &Pred, this);
if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
return true;
}
}
return false;
}
// Finds an integer D for an expression (C + x + y + ...) such that the top
// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
// the (C + x + y + ...) expression is \p WholeAddExpr.
static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
const SCEVConstant *ConstantTerm,
const SCEVAddExpr *WholeAddExpr) {
const APInt C = ConstantTerm->getAPInt();
const unsigned BitWidth = C.getBitWidth();
// Find number of trailing zeros of (x + y + ...) w/o the C first:
uint32_t TZ = BitWidth;
for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I)));
if (TZ) {
// Set D to be as many least significant bits of C as possible while still
// guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
}
return APInt(BitWidth, 0);
}
// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
const APInt &ConstantStart,
const SCEV *Step) {
const unsigned BitWidth = ConstantStart.getBitWidth();
const uint32_t TZ = SE.GetMinTrailingZeros(Step);
if (TZ)
return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
: ConstantStart;
return APInt(BitWidth, 0);
}
const SCEV *
ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
"This is not an extending conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
// Fold if the operand is constant.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getConstant(
cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
// zext(zext(x)) --> zext(x)
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
// Before doing any expensive analysis, check to see if we've already
// computed a SCEV for this Op and Ty.
FoldingSetNodeID ID;
ID.AddInteger(scZeroExtend);
ID.AddPointer(Op);
ID.AddPointer(Ty);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
if (Depth > MaxCastDepth) {
SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
// zext(trunc(x)) --> zext(x) or x or trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
// It's possible the bits taken off by the truncate were all zero bits. If
// so, we should be able to simplify this further.
const SCEV *X = ST->getOperand();
ConstantRange CR = getUnsignedRange(X);
unsigned TruncBits = getTypeSizeInBits(ST->getType());
unsigned NewBits = getTypeSizeInBits(Ty);
if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
CR.zextOrTrunc(NewBits)))
return getTruncateOrZeroExtend(X, Ty, Depth);
}
// If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can zero extend all of the
// operands (often constants). This allows analysis of something like
// this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
if (AR->isAffine()) {
const SCEV *Start = AR->getStart();
const SCEV *Step = AR->getStepRecurrence(*this);
unsigned BitWidth = getTypeSizeInBits(AR->getType());
const Loop *L = AR->getLoop();
if (!AR->hasNoUnsignedWrap()) {
auto NewFlags = proveNoWrapViaConstantRanges(AR);
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
}
// If we have special knowledge that this addrec won't overflow,
// we don't need to do any further analysis.
if (AR->hasNoUnsignedWrap())
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
// Check whether the backedge-taken count is SCEVCouldNotCompute.
// Note that this serves two purposes: It filters out loops that are
// simply not analyzable, and it covers the case where this code is
// being called from within backedge-taken count analysis, such that
// attempting to ask for the backedge-taken count would likely result
// in infinite recursion. In the later case, the analysis code will
// cope with a conservative value, and it will take care to purge
// that value once it has finished.
const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
// Manually compute the final value for AR, checking for
// overflow.
// Check whether the backedge-taken count can be losslessly casted to
// the addrec's type. The count is always unsigned.
const SCEV *CastedMaxBECount =
getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
CastedMaxBECount, MaxBECount->getType(), Depth);
if (MaxBECount == RecastedMaxBECount) {
Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
// Check whether Start+Step*MaxBECount has no unsigned overflow.
const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
SCEV::FlagAnyWrap, Depth + 1);
const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
SCEV::FlagAnyWrap,
Depth + 1),
WideTy, Depth + 1);
const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
const SCEV *WideMaxBECount =
getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
const SCEV *OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getZeroExtendExpr(Step, WideTy, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
if (ZAdd == OperandExtendedAdd) {
// Cache knowledge of AR NUW, which is propagated to this AddRec.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
// Similar to above, only this time treat the step value as signed.
// This covers loops that count down.
OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getSignExtendExpr(Step, WideTy, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
if (ZAdd == OperandExtendedAdd) {
// Cache knowledge of AR NW, which is propagated to this AddRec.
// Negative step causes unsigned wrap, but it still can't self-wrap.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
}
}
// Normally, in the cases we can prove no-overflow via a
// backedge guarding condition, we can also compute a backedge
// taken count for the loop. The exceptions are assumptions and
// guards present in the loop -- SCEV is not great at exploiting
// these to compute max backedge taken counts, but can still use
// these to prove lack of overflow. Use this fact to avoid
// doing extra work that may not pay off.
if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
!AC.assumptions().empty()) {
// If the backedge is guarded by a comparison with the pre-inc
// value the addrec is safe. Also, if the entry is guarded by
// a comparison with the start value and the backedge is
// guarded by a comparison with the post-inc value, the addrec
// is safe.
if (isKnownPositive(Step)) {
const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
getUnsignedRangeMax(Step));
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
// Cache knowledge of AR NUW, which is propagated to this
// AddRec.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
} else if (isKnownNegative(Step)) {
const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
getSignedRangeMin(Step));
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
// Cache knowledge of AR NW, which is propagated to this
// AddRec. Negative step causes unsigned wrap, but it
// still can't self-wrap.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
}
}
// zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
// if D + (C - D + Step * n) could be proven to not unsigned wrap
// where D maximizes the number of trailing zeros of (C - D + Step * n)
if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
const APInt &C = SC->getAPInt();
const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
if (D != 0) {
const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
const SCEV *SResidual =
getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
return getAddExpr(SZExtD, SZExtR,
(SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
Depth + 1);
}
}
if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
}
}
// zext(A % B) --> zext(A) % zext(B)
{
const SCEV *LHS;
const SCEV *RHS;
if (matchURem(Op, LHS, RHS))
return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
getZeroExtendExpr(RHS, Ty, Depth + 1));
}
// zext(A / B) --> zext(A) / zext(B).
if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
// zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
if (SA->hasNoUnsignedWrap()) {
// If the addition does not unsign overflow then we can, by definition,
// commute the zero extension with the addition operation.
SmallVector<const SCEV *, 4> Ops;
for (const auto *Op : SA->operands())
Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
}
// zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
// if D + (C - D + x + y + ...) could be proven to not unsigned wrap
// where D maximizes the number of trailing zeros of (C - D + x + y + ...)
//
// Often address arithmetics contain expressions like
// (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
// This transformation is useful while proving that such expressions are
// equal or differ by a small constant amount, see LoadStoreVectorizer pass.
if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
if (D != 0) {
const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
const SCEV *SResidual =
getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
return getAddExpr(SZExtD, SZExtR,
(SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
Depth + 1);
}
}
}
if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
// zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
if (SM->hasNoUnsignedWrap()) {
// If the multiply does not unsign overflow then we can, by definition,
// commute the zero extension with the multiply operation.
SmallVector<const SCEV *, 4> Ops;
for (const auto *Op : SM->operands())
Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
}
// zext(2^K * (trunc X to iN)) to iM ->
// 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
//
// Proof:
//
// zext(2^K * (trunc X to iN)) to iM
// = zext((trunc X to iN) << K) to iM
// = zext((trunc X to i{N-K}) << K)<nuw> to iM
// (because shl removes the top K bits)
// = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
// = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
//
if (SM->getNumOperands() == 2)
if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0)))
if (MulLHS->getAPInt().isPowerOf2())
if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) {
int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) -
MulLHS->getAPInt().logBase2();
Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
return getMulExpr(
getZeroExtendExpr(MulLHS, Ty),
getZeroExtendExpr(
getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty),
SCEV::FlagNUW, Depth + 1);
}
}
// The cast wasn't folded; create an explicit cast node.
// Recompute the insert position, as it may have been invalidated.
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
const SCEV *
ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
"This is not an extending conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
// Fold if the operand is constant.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getConstant(
cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
// sext(sext(x)) --> sext(x)
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
// sext(zext(x)) --> zext(x)
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
// Before doing any expensive analysis, check to see if we've already
// computed a SCEV for this Op and Ty.
FoldingSetNodeID ID;
ID.AddInteger(scSignExtend);
ID.AddPointer(Op);
ID.AddPointer(Ty);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
// Limit recursion depth.
if (Depth > MaxCastDepth) {
SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
// sext(trunc(x)) --> sext(x) or x or trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
// It's possible the bits taken off by the truncate were all sign bits. If
// so, we should be able to simplify this further.
const SCEV *X = ST->getOperand();
ConstantRange CR = getSignedRange(X);
unsigned TruncBits = getTypeSizeInBits(ST->getType());
unsigned NewBits = getTypeSizeInBits(Ty);
if (CR.truncate(TruncBits).signExtend(NewBits).contains(
CR.sextOrTrunc(NewBits)))
return getTruncateOrSignExtend(X, Ty, Depth);
}
if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
// sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
if (SA->hasNoSignedWrap()) {
// If the addition does not sign overflow then we can, by definition,
// commute the sign extension with the addition operation.
SmallVector<const SCEV *, 4> Ops;
for (const auto *Op : SA->operands())
Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
}
// sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
// if D + (C - D + x + y + ...) could be proven to not signed wrap
// where D maximizes the number of trailing zeros of (C - D + x + y + ...)
//
// For instance, this will bring two seemingly different expressions:
// 1 + sext(5 + 20 * %x + 24 * %y) and
// sext(6 + 20 * %x + 24 * %y)
// to the same form:
// 2 + sext(4 + 20 * %x + 24 * %y)
if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
if (D != 0) {
const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
const SCEV *SResidual =
getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
return getAddExpr(SSExtD, SSExtR,
(SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
Depth + 1);
}
}
}
// If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can sign extend all of the
// operands (often constants). This allows analysis of something like
// this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
if (AR->isAffine()) {
const SCEV *Start = AR->getStart();
const SCEV *Step = AR->getStepRecurrence(*this);
unsigned BitWidth = getTypeSizeInBits(AR->getType());
const Loop *L = AR->getLoop();
if (!AR->hasNoSignedWrap()) {
auto NewFlags = proveNoWrapViaConstantRanges(AR);
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
}
// If we have special knowledge that this addrec won't overflow,
// we don't need to do any further analysis.
if (AR->hasNoSignedWrap())
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
// Check whether the backedge-taken count is SCEVCouldNotCompute.
// Note that this serves two purposes: It filters out loops that are
// simply not analyzable, and it covers the case where this code is
// being called from within backedge-taken count analysis, such that
// attempting to ask for the backedge-taken count would likely result
// in infinite recursion. In the later case, the analysis code will
// cope with a conservative value, and it will take care to purge
// that value once it has finished.
const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
// Manually compute the final value for AR, checking for
// overflow.
// Check whether the backedge-taken count can be losslessly casted to
// the addrec's type. The count is always unsigned.
const SCEV *CastedMaxBECount =
getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
CastedMaxBECount, MaxBECount->getType(), Depth);
if (MaxBECount == RecastedMaxBECount) {
Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
// Check whether Start+Step*MaxBECount has no signed overflow.
const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
SCEV::FlagAnyWrap, Depth + 1);
const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
SCEV::FlagAnyWrap,
Depth + 1),
WideTy, Depth + 1);
const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
const SCEV *WideMaxBECount =
getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
const SCEV *OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getSignExtendExpr(Step, WideTy, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
if (SAdd == OperandExtendedAdd) {
// Cache knowledge of AR NSW, which is propagated to this AddRec.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
// Similar to above, only this time treat the step value as unsigned.
// This covers loops that count up with an unsigned step.
OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getZeroExtendExpr(Step, WideTy, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
if (SAdd == OperandExtendedAdd) {
// If AR wraps around then
//
// abs(Step) * MaxBECount > unsigned-max(AR->getType())
// => SAdd != OperandExtendedAdd
//
// Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
// (SAdd == OperandExtendedAdd => AR is NW)
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
}
}
// Normally, in the cases we can prove no-overflow via a
// backedge guarding condition, we can also compute a backedge
// taken count for the loop. The exceptions are assumptions and
// guards present in the loop -- SCEV is not great at exploiting
// these to compute max backedge taken counts, but can still use
// these to prove lack of overflow. Use this fact to avoid
// doing extra work that may not pay off.
if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
!AC.assumptions().empty()) {
// If the backedge is guarded by a comparison with the pre-inc
// value the addrec is safe. Also, if the entry is guarded by
// a comparison with the start value and the backedge is
// guarded by a comparison with the post-inc value, the addrec
// is safe.
ICmpInst::Predicate Pred;
const SCEV *OverflowLimit =
getSignedOverflowLimitForStep(Step, &Pred, this);
if (OverflowLimit &&
(isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
// Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
}
}
// sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
// if D + (C - D + Step * n) could be proven to not signed wrap
// where D maximizes the number of trailing zeros of (C - D + Step * n)
if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
const APInt &C = SC->getAPInt();
const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
if (D != 0) {
const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
const SCEV *SResidual =
getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
return getAddExpr(SSExtD, SSExtR,
(SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
Depth + 1);
}
}
if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
}
}
// If the input value is provably positive and we could not simplify
// away the sext build a zext instead.
if (isKnownNonNegative(Op))
return getZeroExtendExpr(Op, Ty, Depth + 1);
// The cast wasn't folded; create an explicit cast node.
// Recompute the insert position, as it may have been invalidated.
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
/// getAnyExtendExpr - Return a SCEV for the given operand extended with
/// unspecified bits out to the given type.
const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
Type *Ty) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
"This is not an extending conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
// Sign-extend negative constants.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
if (SC->getAPInt().isNegative())
return getSignExtendExpr(Op, Ty);
// Peel off a truncate cast.
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
const SCEV *NewOp = T->getOperand();
if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
return getAnyExtendExpr(NewOp, Ty);
return getTruncateOrNoop(NewOp, Ty);
}
// Next try a zext cast. If the cast is folded, use it.
const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
if (!isa<SCEVZeroExtendExpr>(ZExt))
return ZExt;
// Next try a sext cast. If the cast is folded, use it.
const SCEV *SExt = getSignExtendExpr(Op, Ty);
if (!isa<SCEVSignExtendExpr>(SExt))
return SExt;
// Force the cast to be folded into the operands of an addrec.
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
SmallVector<const SCEV *, 4> Ops;
for (const SCEV *Op : AR->operands())
Ops.push_back(getAnyExtendExpr(Op, Ty));
return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
}
// If the expression is obviously signed, use the sext cast value.
if (isa<SCEVSMaxExpr>(Op))
return SExt;
// Absent any other information, use the zext cast value.
return ZExt;
}
/// Process the given Ops list, which is a list of operands to be added under
/// the given scale, update the given map. This is a helper function for
/// getAddRecExpr. As an example of what it does, given a sequence of operands
/// that would form an add expression like this:
///
/// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
///
/// where A and B are constants, update the map with these values:
///
/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
///
/// and add 13 + A*B*29 to AccumulatedConstant.
/// This will allow getAddRecExpr to produce this:
///
/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
///
/// This form often exposes folding opportunities that are hidden in
/// the original operand list.
///
/// Return true iff it appears that any interesting folding opportunities
/// may be exposed. This helps getAddRecExpr short-circuit extra work in
/// the common case where no interesting opportunities are present, and
/// is also used as a check to avoid infinite recursion.
static bool
CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
SmallVectorImpl<const SCEV *> &NewOps,
APInt &AccumulatedConstant,
const SCEV *const *Ops, size_t NumOperands,
const APInt &Scale,
ScalarEvolution &SE) {
bool Interesting = false;
// Iterate over the add operands. They are sorted, with constants first.
unsigned i = 0;
while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
++i;
// Pull a buried constant out to the outside.
if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
Interesting = true;
AccumulatedConstant += Scale * C->getAPInt();
}
// Next comes everything else. We're especially interested in multiplies
// here, but they're in the middle, so just visit the rest with one loop.
for (; i != NumOperands; ++i) {
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
APInt NewScale =
Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
// A multiplication of a constant with another add; recurse.
const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
Interesting |=
CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
Add->op_begin(), Add->getNumOperands(),
NewScale, SE);
} else {
// A multiplication of a constant with some other value. Update
// the map.
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
const SCEV *Key = SE.getMulExpr(MulOps);
auto Pair = M.insert({Key, NewScale});
if (Pair.second) {
NewOps.push_back(Pair.first->first);
} else {
Pair.first->second += NewScale;
// The map already had an entry for this value, which may indicate
// a folding opportunity.
Interesting = true;
}
}
} else {
// An ordinary operand. Update the map.
std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
M.insert({Ops[i], Scale});
if (Pair.second) {
NewOps.push_back(Pair.first->first);
} else {
Pair.first->second += Scale;
// The map already had an entry for this value, which may indicate
// a folding opportunity.
Interesting = true;
}
}
}
return Interesting;
}
// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
// `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
// can't-overflow flags for the operation if possible.
static SCEV::NoWrapFlags
StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
const ArrayRef<const SCEV *> Ops,
SCEV::NoWrapFlags Flags) {
using namespace std::placeholders;
using OBO = OverflowingBinaryOperator;
bool CanAnalyze =
Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
(void)CanAnalyze;
assert(CanAnalyze && "don't call from other places!");
int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
SCEV::NoWrapFlags SignOrUnsignWrap =
ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
// If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
auto IsKnownNonNegative = [&](const SCEV *S) {
return SE->isKnownNonNegative(S);
};
if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
Flags =
ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
if (SignOrUnsignWrap != SignOrUnsignMask &&
(Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
isa<SCEVConstant>(Ops[0])) {
auto Opcode = [&] {
switch (Type) {
case scAddExpr:
return Instruction::Add;
case scMulExpr:
return Instruction::Mul;
default:
llvm_unreachable("Unexpected SCEV op.");
}
}();
const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
// (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
Opcode, C, OBO::NoSignedWrap);
if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
}
// (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
Opcode, C, OBO::NoUnsignedWrap);
if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
}
}
return Flags;
}
bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
}
/// Get a canonical add expression, or something simpler if possible.
const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
SCEV::NoWrapFlags Flags,
unsigned Depth) {
assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
"only nuw or nsw allowed");
assert(!Ops.empty() && "Cannot get empty add!");
if (Ops.size() == 1) return Ops[0];
#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVAddExpr operand types don't match!");
#endif
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI, DT);
Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
++Idx;
assert(Idx < Ops.size());
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
if (Ops.size() == 2) return Ops[0];
Ops.erase(Ops.begin()+1); // Erase the folded element
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant zero being added, strip it off.
if (LHSC->getValue()->isZero()) {
Ops.erase(Ops.begin());
--Idx;
}
if (Ops.size() == 1) return Ops[0];
}
// Limit recursion calls depth.
if (Depth > MaxArithDepth || hasHugeExpression(Ops))
return getOrCreateAddExpr(Ops, Flags);
// Okay, check to see if the same value occurs in the operand list more than
// once. If so, merge them together into an multiply expression. Since we
// sorted the list, these values are required to be adjacent.
Type *Ty = Ops[0]->getType();
bool FoundMatch = false;
for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
// Scan ahead to count how many equal operands there are.
unsigned Count = 2;
while (i+Count != e && Ops[i+Count] == Ops[i])
++Count;
// Merge the values into a multiply.
const SCEV *Scale = getConstant(Ty, Count);
const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
if (Ops.size() == Count)
return Mul;
Ops[i] = Mul;
Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
--i; e -= Count - 1;
FoundMatch = true;
}
if (FoundMatch)
return getAddExpr(Ops, Flags, Depth + 1);
// Check for truncates. If all the operands are truncated from the same
// type, see if factoring out the truncate would permit the result to be
// folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
// if the contents of the resulting outer trunc fold to something simple.
auto FindTruncSrcType = [&]() -> Type * {
// We're ultimately looking to fold an addrec of truncs and muls of only
// constants and truncs, so if we find any other types of SCEV
// as operands of the addrec then we bail and return nullptr here.
// Otherwise, we return the type of the operand of a trunc that we find.
if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
return T->getOperand()->getType();
if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
return T->getOperand()->getType();
}
return nullptr;
};
if (auto *SrcType = FindTruncSrcType()) {
SmallVector<const SCEV *, 8> LargeOps;
bool Ok = true;
// Check all the operands to see if they can be represented in the
// source type of the truncate.
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
if (T->getOperand()->getType() != SrcType) {
Ok = false;
break;
}
LargeOps.push_back(T->getOperand());
} else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
LargeOps.push_back(getAnyExtendExpr(C, SrcType));
} else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
SmallVector<const SCEV *, 8> LargeMulOps;
for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
if (const SCEVTruncateExpr *T =
dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
if (T->getOperand()->getType() != SrcType) {
Ok = false;
break;
}
LargeMulOps.push_back(T->getOperand());
} else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
} else {
Ok = false;
break;
}
}
if (Ok)
LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
} else {
Ok = false;
break;
}
}
if (Ok) {
// Evaluate the expression in the larger type.
const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
// If it folds to something simple, use it. Otherwise, don't.
if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
return getTruncateExpr(Fold, Ty);
}
}
// Skip past any other cast SCEVs.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
++Idx;
// If there are add operands they would be next.
if (Idx < Ops.size()) {
bool DeletedAdd = false;
while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
if (Ops.size() > AddOpsInlineThreshold ||
Add->getNumOperands() > AddOpsInlineThreshold)
break;
// If we have an add, expand the add operands onto the end of the operands
// list.
Ops.erase(Ops.begin()+Idx);
Ops.append(Add->op_begin(), Add->op_end());
DeletedAdd = true;
}
// If we deleted at least one add, we added operands to the end of the list,
// and they are not necessarily sorted. Recurse to resort and resimplify
// any operands we just acquired.
if (DeletedAdd)
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
++Idx;
// Check to see if there are any folding opportunities present with
// operands multiplied by constant values.
if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
uint64_t BitWidth = getTypeSizeInBits(Ty);
DenseMap<const SCEV *, APInt> M;
SmallVector<const SCEV *, 8> NewOps;
APInt AccumulatedConstant(BitWidth, 0);
if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
Ops.data(), Ops.size(),
APInt(BitWidth, 1), *this)) {
struct APIntCompare {
bool operator()(const APInt &LHS, const APInt &RHS) const {
return LHS.ult(RHS);
}
};
// Some interesting folding opportunity is present, so its worthwhile to
// re-generate the operands list. Group the operands by constant scale,
// to avoid multiplying by the same constant scale multiple times.
std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
for (const SCEV *NewOp : NewOps)
MulOpLists[M.find(NewOp)->second].push_back(NewOp);
// Re-generate the operands list.
Ops.clear();
if (AccumulatedConstant != 0)
Ops.push_back(getConstant(AccumulatedConstant));
for (auto &MulOp : MulOpLists)
if (MulOp.first != 0)
Ops.push_back(getMulExpr(
getConstant(MulOp.first),
getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1));
if (Ops.empty())
return getZero(Ty);
if (Ops.size() == 1)
return Ops[0];
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
}
// If we are adding something to a multiply expression, make sure the
// something is not already an operand of the multiply. If so, merge it into
// the multiply.
for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
if (isa<SCEVConstant>(MulOpSCEV))
continue;
for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
if (MulOpSCEV == Ops[AddOp]) {
// Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
if (Mul->getNumOperands() != 2) {
// If the multiply has more than two operands, we must get the
// Y*Z term.
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
Mul->op_begin()+MulOp);
MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
}
SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
SCEV::FlagAnyWrap, Depth + 1);
if (Ops.size() == 2) return OuterMul;
if (AddOp < Idx) {
Ops.erase(Ops.begin()+AddOp);
Ops.erase(Ops.begin()+Idx-1);
} else {
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+AddOp-1);
}
Ops.push_back(OuterMul);
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// Check this multiply against other multiplies being added together.
for (unsigned OtherMulIdx = Idx+1;
OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
++OtherMulIdx) {
const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
// If MulOp occurs in OtherMul, we can fold the two multiplies
// together.
for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
OMulOp != e; ++OMulOp)
if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
// Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
if (Mul->getNumOperands() != 2) {
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
Mul->op_begin()+MulOp);
MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
}
const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
if (OtherMul->getNumOperands() != 2) {
SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
OtherMul->op_begin()+OMulOp);
MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
}
SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
const SCEV *InnerMulSum =
getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
SCEV::FlagAnyWrap, Depth + 1);
if (Ops.size() == 2) return OuterMul;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherMulIdx-1);
Ops.push_back(OuterMul);
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
}
}
}
// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant. If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
++Idx;
// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
// Scan all of the other operands to this add and add them to the vector if
// they are loop invariant w.r.t. the recurrence.
SmallVector<const SCEV *, 8> LIOps;
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
const Loop *AddRecLoop = AddRec->getLoop();
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
LIOps.push_back(Ops[i]);
Ops.erase(Ops.begin()+i);
--i; --e;
}
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
// NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
LIOps.push_back(AddRec->getStart());
SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
AddRec->op_end());
// This follows from the fact that the no-wrap flags on the outer add
// expression are applicable on the 0th iteration, when the add recurrence
// will be equal to its start value.
AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
// Build the new addrec. Propagate the NUW and NSW flags if both the
// outer add and the inner addrec are guaranteed to have no overflow.
// Always propagate NW.
Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
// Otherwise, add the folded AddRec by the non-invariant parts.
for (unsigned i = 0;; ++i)
if (Ops[i] == AddRec) {
Ops[i] = NewRec;
break;
}
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// Okay, if there weren't any loop invariants to be folded, check to see if
// there are multiple AddRec's with the same loop induction variable being
// added together. If so, we can fold them.
for (unsigned OtherIdx = Idx+1;
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
++OtherIdx) {
// We expect the AddRecExpr's to be sorted in reverse dominance order,
// so that the 1st found AddRecExpr is dominated by all others.
assert(DT.dominates(
cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
AddRec->getLoop()->getHeader()) &&
"AddRecExprs are not sorted in reverse dominance order?");
if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
// Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
AddRec->op_end());
for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
++OtherIdx) {
const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
if (OtherAddRec->getLoop() == AddRecLoop) {
for (unsigned i = 0, e = OtherAddRec->getNumOperands();
i != e; ++i) {
if (i >= AddRecOps.size()) {
AddRecOps.append(OtherAddRec->op_begin()+i,
OtherAddRec->op_end());
break;
}
SmallVector<const SCEV *, 2> TwoOps = {
AddRecOps[i], OtherAddRec->getOperand(i)};
AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
}
Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
}
}
// Step size has changed, so we cannot guarantee no self-wraparound.
Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
}
// Otherwise couldn't fold anything into this recurrence. Move onto the
// next one.
}
// Okay, it looks like we really DO need an add expr. Check to see if we
// already have one, otherwise create a new one.
return getOrCreateAddExpr(Ops, Flags);
}
const SCEV *
ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scAddExpr);
for (const SCEV *Op : Ops)
ID.AddPointer(Op);
void *IP = nullptr;
SCEVAddExpr *S =
static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
if (!S) {
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
S = new (SCEVAllocator)
SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
}
S->setNoWrapFlags(Flags);
return S;
}
const SCEV *
ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
const Loop *L, SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scAddRecExpr);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
ID.AddPointer(Ops[i]);
ID.AddPointer(L);
void *IP = nullptr;
SCEVAddRecExpr *S =
static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
if (!S) {
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
S = new (SCEVAllocator)
SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
}
S->setNoWrapFlags(Flags);
return S;
}
const SCEV *
ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scMulExpr);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
ID.AddPointer(Ops[i]);
void *IP = nullptr;
SCEVMulExpr *S =
static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
if (!S) {
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
O, Ops.size());
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
}
S->setNoWrapFlags(Flags);
return S;
}
static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
uint64_t k = i*j;
if (j > 1 && k / j != i) Overflow = true;
return k;
}
/// Compute the result of "n choose k", the binomial coefficient. If an
/// intermediate computation overflows, Overflow will be set and the return will
/// be garbage. Overflow is not cleared on absence of overflow.
static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
// We use the multiplicative formula:
// n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
// At each iteration, we take the n-th term of the numeral and divide by the
// (k-n)th term of the denominator. This division will always produce an
// integral result, and helps reduce the chance of overflow in the
// intermediate computations. However, we can still overflow even when the
// final result would fit.
if (n == 0 || n == k) return 1;
if (k > n) return 0;
if (k > n/2)
k = n-k;
uint64_t r = 1;
for (uint64_t i = 1; i <= k; ++i) {
r = umul_ov(r, n-(i-1), Overflow);
r /= i;
}
return r;
}
/// Determine if any of the operands in this SCEV are a constant or if
/// any of the add or multiply expressions in this SCEV contain a constant.
static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
struct FindConstantInAddMulChain {
bool FoundConstant = false;
bool follow(const SCEV *S) {
FoundConstant |= isa<SCEVConstant>(S);
return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
}
bool isDone() const {
return FoundConstant;
}
};
FindConstantInAddMulChain F;
SCEVTraversal<FindConstantInAddMulChain> ST(F);
ST.visitAll(StartExpr);
return F.FoundConstant;
}
/// Get a canonical multiply expression, or something simpler if possible.
const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
SCEV::NoWrapFlags Flags,
unsigned Depth) {
assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
"only nuw or nsw allowed");
assert(!Ops.empty() && "Cannot get empty mul!");
if (Ops.size() == 1) return Ops[0];
#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVMulExpr operand types don't match!");
#endif
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI, DT);
Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
// Limit recursion calls depth.
if (Depth > MaxArithDepth || hasHugeExpression(Ops))
return getOrCreateMulExpr(Ops, Flags);
// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
if (Ops.size() == 2)
// C1*(C2+V) -> C1*C2 + C1*V
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
// If any of Add's ops are Adds or Muls with a constant, apply this
// transformation as well.
//
// TODO: There are some cases where this transformation is not
// profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
// this transformation should be narrowed down.
if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add))
return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
SCEV::FlagAnyWrap, Depth + 1),
getMulExpr(LHSC, Add->getOperand(1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
++Idx;
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
ConstantInt *Fold =
ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant one being multiplied, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
Ops.erase(Ops.begin());
--Idx;
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
// If we have a multiply of zero, it will always be zero.
return Ops[0];
} else if (Ops[0]->isAllOnesValue()) {
// If we have a mul by -1 of an add, try distributing the -1 among the
// add operands.
if (Ops.size() == 2) {
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
SmallVector<const SCEV *, 4> NewOps;
bool AnyFolded = false;
for (const SCEV *AddOp : Add->operands()) {
const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
Depth + 1);
if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
NewOps.push_back(Mul);
}
if (AnyFolded)
return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
} else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
// Negation preserves a recurrence's no self-wrap property.
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *AddRecOp : AddRec->operands())
Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
Depth + 1));
return getAddRecExpr(Operands, AddRec->getLoop(),
AddRec->getNoWrapFlags(SCEV::FlagNW));
}
}
}
if (Ops.size() == 1)
return Ops[0];
}
// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
++Idx;
// If there are mul operands inline them all into this expression.
if (Idx < Ops.size()) {
bool DeletedMul = false;
while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
if (Ops.size() > MulOpsInlineThreshold)
break;
// If we have an mul, expand the mul operands onto the end of the
// operands list.
Ops.erase(Ops.begin()+Idx);
Ops.append(Mul->op_begin(), Mul->op_end());
DeletedMul = true;
}
// If we deleted at least one mul, we added operands to the end of the
// list, and they are not necessarily sorted. Recurse to resort and
// resimplify any operands we just acquired.
if (DeletedMul)
return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant. If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
++Idx;
// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
// Scan all of the other operands to this mul and add them to the vector
// if they are loop invariant w.r.t. the recurrence.
SmallVector<const SCEV *, 8> LIOps;
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
const Loop *AddRecLoop = AddRec->getLoop();
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
LIOps.push_back(Ops[i]);
Ops.erase(Ops.begin()+i);
--i; --e;
}
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
// NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
SmallVector<const SCEV *, 4> NewOps;
NewOps.reserve(AddRec->getNumOperands());
const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
SCEV::FlagAnyWrap, Depth + 1));
// Build the new addrec. Propagate the NUW and NSW flags if both the
// outer mul and the inner addrec are guaranteed to have no overflow.
//
// No self-wrap cannot be guaranteed after changing the step size, but
// will be inferred if either NUW or NSW is true.
Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
// Otherwise, multiply the folded AddRec by the non-invariant parts.
for (unsigned i = 0;; ++i)
if (Ops[i] == AddRec) {
Ops[i] = NewRec;
break;
}
return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// Okay, if there weren't any loop invariants to be folded, check to see
// if there are multiple AddRec's with the same loop induction variable
// being multiplied together. If so, we can fold them.
// {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
// = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
// choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
// ]]],+,...up to x=2n}.
// Note that the arguments to choose() are always integers with values
// known at compile time, never SCEV objects.
//
// The implementation avoids pointless extra computations when the two
// addrec's are of different length (mathematically, it's equivalent to
// an infinite stream of zeros on the right).
bool OpsModified = false;
for (unsigned OtherIdx = Idx+1;
OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
++OtherIdx) {
const SCEVAddRecExpr *OtherAddRec =
dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
continue;
// Limit max number of arguments to avoid creation of unreasonably big
// SCEVAddRecs with very complex operands.
if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
MaxAddRecSize || hasHugeExpression({AddRec, OtherAddRec}))
continue;
bool Overflow = false;
Type *Ty = AddRec->getType();
bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
SmallVector<const SCEV*, 7> AddRecOps;
for (int x = 0, xe = AddRec->getNumOperands() +
OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
SmallVector <const SCEV *, 7> SumOps;
for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
z < ze && !Overflow; ++z) {
uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
uint64_t Coeff;
if (LargerThan64Bits)
Coeff = umul_ov(Coeff1, Coeff2, Overflow);
else
Coeff = Coeff1*Coeff2;
const SCEV *CoeffTerm = getConstant(Ty, Coeff);
const SCEV *Term1 = AddRec->getOperand(y-z);
const SCEV *Term2 = OtherAddRec->getOperand(z);
SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
SCEV::FlagAnyWrap, Depth + 1));
}
}
if (SumOps.empty())
SumOps.push_back(getZero(Ty));
AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
}
if (!Overflow) {
const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRecLoop,
SCEV::FlagAnyWrap);
if (Ops.size() == 2) return NewAddRec;
Ops[Idx] = NewAddRec;
Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
OpsModified = true;
AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
if (!AddRec)
break;
}
}
if (OpsModified)
return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
// Otherwise couldn't fold anything into this recurrence. Move onto the
// next one.
}
// Okay, it looks like we really DO need an mul expr. Check to see if we
// already have one, otherwise create a new one.
return getOrCreateMulExpr(Ops, Flags);
}
/// Represents an unsigned remainder expression based on unsigned division.
const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
const SCEV *RHS) {
assert(getEffectiveSCEVType(LHS->getType()) ==
getEffectiveSCEVType(RHS->getType()) &&
"SCEVURemExpr operand types don't match!");
// Short-circuit easy cases
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
// If constant is one, the result is trivial
if (RHSC->getValue()->isOne())
return getZero(LHS->getType()); // X urem 1 --> 0
// If constant is a power of two, fold into a zext(trunc(LHS)).
if (RHSC->getAPInt().isPowerOf2()) {
Type *FullTy = LHS->getType();
Type *TruncTy =
IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
}
}
// Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
const SCEV *UDiv = getUDivExpr(LHS, RHS);
const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
}
/// Get a canonical unsigned division expression, or something simpler if
/// possible.
const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
const SCEV *RHS) {
assert(getEffectiveSCEVType(LHS->getType()) ==
getEffectiveSCEVType(RHS->getType()) &&
"SCEVUDivExpr operand types don't match!");
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
if (RHSC->getValue()->isOne())
return LHS; // X udiv 1 --> x
// If the denominator is zero, the result of the udiv is undefined. Don't
// try to analyze it, because the resolution chosen here may differ from
// the resolution chosen in other parts of the compiler.
if (!RHSC->getValue()->isZero()) {
// Determine if the division can be folded into the operands of
// its operands.
// TODO: Generalize this to non-constants by using known-bits information.
Type *Ty = LHS->getType();
unsigned LZ = RHSC->getAPInt().countLeadingZeros();
unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
// For non-power-of-two values, effectively round the value up to the
// nearest power of two.
if (!RHSC->getAPInt().isPowerOf2())
++MaxShiftAmt;
IntegerType *ExtTy =
IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
if (const SCEVConstant *Step =
dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
// {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
const APInt &StepInt = Step->getAPInt();
const APInt &DivInt = RHSC->getAPInt();
if (!StepInt.urem(DivInt) &&
getZeroExtendExpr(AR, ExtTy) ==
getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
getZeroExtendExpr(Step, ExtTy),
AR->getLoop(), SCEV::FlagAnyWrap)) {
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *Op : AR->operands())
Operands.push_back(getUDivExpr(Op, RHS));
return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
}
/// Get a canonical UDivExpr for a recurrence.
/// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
// We can currently only fold X%N if X is constant.
const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
if (StartC && !DivInt.urem(StepInt) &&
getZeroExtendExpr(AR, ExtTy) ==
getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
getZeroExtendExpr(Step, ExtTy),
AR->getLoop(), SCEV::FlagAnyWrap)) {
const APInt &StartInt = StartC->getAPInt();
const APInt &StartRem = StartInt.urem(StepInt);
if (StartRem != 0)
LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
AR->getLoop(), SCEV::FlagNW);
}
}
// (A*B)/C --> A*(B/C) if safe and B/C can be folded.
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *Op : M->operands())
Operands.push_back(getZeroExtendExpr(Op, ExtTy));
if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
// Find an operand that's safely divisible.
for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
const SCEV *Op = M->getOperand(i);
const SCEV *Div = getUDivExpr(Op, RHSC);
if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
M->op_end());
Operands[i] = Div;
return getMulExpr(Operands);
}
}
}
// (A/B)/C --> A/(B*C) if safe and B*C can be folded.
if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
if (auto *DivisorConstant =
dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
bool Overflow = false;
APInt NewRHS =
DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
if (Overflow) {
return getConstant(RHSC->getType(), 0, false);
}
return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
}
}
// (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *Op : A->operands())
Operands.push_back(getZeroExtendExpr(Op, ExtTy));
if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
Operands.clear();
for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
if (isa<SCEVUDivExpr>(Op) ||
getMulExpr(Op, RHS) != A->getOperand(i))
break;
Operands.push_back(Op);
}
if (Operands.size() == A->getNumOperands())
return getAddExpr(Operands);
}
}
// Fold if both operands are constant.
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
Constant *LHSCV = LHSC->getValue();
Constant *RHSCV = RHSC->getValue();
return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
RHSCV)));
}
}
}
FoldingSetNodeID ID;
ID.AddInteger(scUDivExpr);
ID.AddPointer(LHS);
ID.AddPointer(RHS);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
LHS, RHS);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
APInt A = C1->getAPInt().abs();
APInt B = C2->getAPInt().abs();
uint32_t ABW = A.getBitWidth();
uint32_t BBW = B.getBitWidth();
if (ABW > BBW)
B = B.zext(ABW);
else if (ABW < BBW)
A = A.zext(BBW);
return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
}
/// Get a canonical unsigned division expression, or something simpler if
/// possible. There is no representation for an exact udiv in SCEV IR, but we
/// can attempt to remove factors from the LHS and RHS. We can't do this when
/// it's not exact because the udiv may be clearing bits.
const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
const SCEV *RHS) {
// TODO: we could try to find factors in all sorts of things, but for now we
// just deal with u/exact (multiply, constant). See SCEVDivision towards the
// end of this file for inspiration.
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
if (!Mul || !Mul->hasNoUnsignedWrap())
return getUDivExpr(LHS, RHS);
if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
// If the mulexpr multiplies by a constant, then that constant must be the
// first element of the mulexpr.
if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
if (LHSCst == RHSCst) {
SmallVector<const SCEV *, 2> Operands;
Operands.append(Mul->op_begin() + 1, Mul->op_end());
return getMulExpr(Operands);
}
// We can't just assume that LHSCst divides RHSCst cleanly, it could be
// that there's a factor provided by one of the other terms. We need to
// check.
APInt Factor = gcd(LHSCst, RHSCst);
if (!Factor.isIntN(1)) {
LHSCst =
cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
RHSCst =
cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
SmallVector<const SCEV *, 2> Operands;
Operands.push_back(LHSCst);
Operands.append(Mul->op_begin() + 1, Mul->op_end());
LHS = getMulExpr(Operands);
RHS = RHSCst;
Mul = dyn_cast<SCEVMulExpr>(LHS);
if (!Mul)
return getUDivExactExpr(LHS, RHS);
}
}
}
for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
if (Mul->getOperand(i) == RHS) {
SmallVector<const SCEV *, 2> Operands;
Operands.append(Mul->op_begin(), Mul->op_begin() + i);
Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
return getMulExpr(Operands);
}
}
return getUDivExpr(LHS, RHS);
}
/// Get an add recurrence expression for the specified loop. Simplify the
/// expression as much as possible.
const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
const Loop *L,
SCEV::NoWrapFlags Flags) {
SmallVector<const SCEV *, 4> Operands;
Operands.push_back(Start);
if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
if (StepChrec->getLoop() == L) {
Operands.append(StepChrec->op_begin(), StepChrec->op_end());
return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
}
Operands.push_back(Step);
return getAddRecExpr(Operands, L, Flags);
}
/// Get an add recurrence expression for the specified loop. Simplify the
/// expression as much as possible.
const SCEV *
ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
const Loop *L, SCEV::NoWrapFlags Flags) {
if (Operands.size() == 1) return Operands[0];
#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
"SCEVAddRecExpr operand types don't match!");
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
assert(isLoopInvariant(Operands[i], L) &&
"SCEVAddRecExpr operand is not loop-invariant!");
#endif
if (Operands.back()->isZero()) {
Operands.pop_back();
return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
}
// It's tempting to want to call getConstantMaxBackedgeTakenCount count here and
// use that information to infer NUW and NSW flags. However, computing a
// BE count requires calling getAddRecExpr, so we may not yet have a
// meaningful BE count at this point (and if we don't, we'd be stuck
// with a SCEVCouldNotCompute as the cached BE count).
Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
// Canonicalize nested AddRecs in by nesting them in order of loop depth.
if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
const Loop *NestedLoop = NestedAR->getLoop();
if (L->contains(NestedLoop)
? (L->getLoopDepth() < NestedLoop->getLoopDepth())
: (!NestedLoop->contains(L) &&
DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
NestedAR->op_end());
Operands[0] = NestedAR->getStart();
// AddRecs require their operands be loop-invariant with respect to their
// loops. Don't perform this transformation if it would break this
// requirement.
bool AllInvariant = all_of(
Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
if (AllInvariant) {
// Create a recurrence for the outer loop with the same step size.
//
// The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
// inner recurrence has the same property.
SCEV::NoWrapFlags OuterFlags =
maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
return isLoopInvariant(Op, NestedLoop);
});
if (AllInvariant) {
// Ok, both add recurrences are valid after the transformation.
//
// The inner recurrence keeps its NW flag but only keeps NUW/NSW if
// the outer recurrence has the same property.
SCEV::NoWrapFlags InnerFlags =
maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
}
}
// Reset Operands to its original state.
Operands[0] = NestedAR;
}
}
// Okay, it looks like we really DO need an addrec expr. Check to see if we
// already have one, otherwise create a new one.
return getOrCreateAddRecExpr(Operands, L, Flags);
}
const SCEV *
ScalarEvolution::getGEPExpr(GEPOperator *GEP,
const SmallVectorImpl<const SCEV *> &IndexExprs) {
const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
// getSCEV(Base)->getType() has the same address space as Base->getType()
// because SCEV::getType() preserves the address space.
Type *IntIdxTy = getEffectiveSCEVType(BaseExpr->getType());
// FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
// instruction to its SCEV, because the Instruction may be guarded by control
// flow and the no-overflow bits may not be valid for the expression in any
// context. This can be fixed similarly to how these flags are handled for
// adds.
SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
: SCEV::FlagAnyWrap;
const SCEV *TotalOffset = getZero(IntIdxTy);
// The array size is unimportant. The first thing we do on CurTy is getting
// its element type.
Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
for (const SCEV *IndexExpr : IndexExprs) {
// Compute the (potentially symbolic) offset in bytes for this index.
if (StructType *STy = dyn_cast<StructType>(CurTy)) {
// For a struct, add the member offset.
ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
unsigned FieldNo = Index->getZExtValue();
const SCEV *FieldOffset = getOffsetOfExpr(IntIdxTy, STy, FieldNo);
// Add the field offset to the running total offset.
TotalOffset = getAddExpr(TotalOffset, FieldOffset);
// Update CurTy to the type of the field at Index.
CurTy = STy->getTypeAtIndex(Index);
} else {
// Update CurTy to its element type.
CurTy = cast<SequentialType>(CurTy)->getElementType();
// For an array, add the element offset, explicitly scaled.
const SCEV *ElementSize = getSizeOfExpr(IntIdxTy, CurTy);
// Getelementptr indices are signed.
IndexExpr = getTruncateOrSignExtend(IndexExpr, IntIdxTy);
// Multiply the index by the element size to compute the element offset.
const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
// Add the element offset to the running total offset.
TotalOffset = getAddExpr(TotalOffset, LocalOffset);
}
}
// Add the total offset from all the GEP indices to the base.
return getAddExpr(BaseExpr, TotalOffset, Wrap);
}
std::tuple<const SCEV *, FoldingSetNodeID, void *>
ScalarEvolution::findExistingSCEVInCache(int SCEVType,
ArrayRef<const SCEV *> Ops) {
FoldingSetNodeID ID;
void *IP = nullptr;
ID.AddInteger(SCEVType);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
ID.AddPointer(Ops[i]);
return std::tuple<const SCEV *, FoldingSetNodeID, void *>(
UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP);
}
const SCEV *ScalarEvolution::getMinMaxExpr(unsigned Kind,
SmallVectorImpl<const SCEV *> &Ops) {
assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!");
if (Ops.size() == 1) return Ops[0];
#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"Operand types don't match!");
#endif
bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI, DT);
// Check if we have created the same expression before.
if (const SCEV *S = std::get<0>(findExistingSCEVInCache(Kind, Ops))) {
return S;
}
// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
++Idx;
assert(Idx < Ops.size());
auto FoldOp = [&](const APInt &LHS, const APInt &RHS) {
if (Kind == scSMaxExpr)
return APIntOps::smax(LHS, RHS);
else if (Kind == scSMinExpr)
return APIntOps::smin(LHS, RHS);
else if (Kind == scUMaxExpr)
return APIntOps::umax(LHS, RHS);
else if (Kind == scUMinExpr)
return APIntOps::umin(LHS, RHS);
llvm_unreachable("Unknown SCEV min/max opcode");
};
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
ConstantInt *Fold = ConstantInt::get(
getContext(), FoldOp(LHSC->getAPInt(), RHSC->getAPInt()));
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
bool IsMinV = LHSC->getValue()->isMinValue(IsSigned);
bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned);
if (IsMax ? IsMinV : IsMaxV) {
// If we are left with a constant minimum(/maximum)-int, strip it off.
Ops.erase(Ops.begin());
--Idx;
} else if (IsMax ? IsMaxV : IsMinV) {
// If we have a max(/min) with a constant maximum(/minimum)-int,
// it will always be the extremum.
return LHSC;
}
if (Ops.size() == 1) return Ops[0];
}
// Find the first operation of the same kind
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
++Idx;
// Check to see if one of the operands is of the same kind. If so, expand its
// operands onto our operand list, and recurse to simplify.
if (Idx < Ops.size()) {
bool DeletedAny = false;
while (Ops[Idx]->getSCEVType() == Kind) {
const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]);
Ops.erase(Ops.begin()+Idx);
Ops.append(SMME->op_begin(), SMME->op_end());
DeletedAny = true;
}
if (DeletedAny)
return getMinMaxExpr(Kind, Ops);
}
// Okay, check to see if the same value occurs in the operand list twice. If
// so, delete one. Since we sorted the list, these values are required to
// be adjacent.
llvm::CmpInst::Predicate GEPred =
IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
llvm::CmpInst::Predicate LEPred =
IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
if (Ops[i] == Ops[i + 1] ||
isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) {
// X op Y op Y --> X op Y
// X op Y --> X, if we know X, Y are ordered appropriately
Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
--i;
--e;
} else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i],
Ops[i + 1])) {
// X op Y --> Y, if we know X, Y are ordered appropriately
Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
--i;
--e;
}
}
if (Ops.size() == 1) return Ops[0];
assert(!Ops.empty() && "Reduced smax down to nothing!");
// Okay, it looks like we really DO need an expr. Check to see if we
// already have one, otherwise create a new one.
const SCEV *ExistingSCEV;
FoldingSetNodeID ID;
void *IP;
std::tie(ExistingSCEV, ID, IP) = findExistingSCEVInCache(Kind, Ops);
if (ExistingSCEV)
return ExistingSCEV;
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
SCEV *S = new (SCEVAllocator) SCEVMinMaxExpr(
ID.Intern(SCEVAllocator), static_cast<SCEVTypes>(Kind), O, Ops.size());
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
return getSMaxExpr(Ops);
}
const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scSMaxExpr, Ops);
}
const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
return getUMaxExpr(Ops);
}
const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scUMaxExpr, Ops);
}
const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getSMinExpr(Ops);
}
const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scSMinExpr, Ops);
}
const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getUMinExpr(Ops);
}
const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scUMinExpr, Ops);
}
const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
// We can bypass creating a target-independent
// constant expression and then folding it back into a ConstantInt.
// This is just a compile-time optimization.
return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
}
const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
StructType *STy,
unsigned FieldNo) {
// We can bypass creating a target-independent
// constant expression and then folding it back into a ConstantInt.
// This is just a compile-time optimization.
return getConstant(
IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
}
const SCEV *ScalarEvolution::getUnknown(Value *V) {
// Don't attempt to do anything other than create a SCEVUnknown object
// here. createSCEV only calls getUnknown after checking for all other
// interesting possibilities, and any other code that calls getUnknown
// is doing so in order to hide a value from SCEV canonicalization.
FoldingSetNodeID ID;
ID.AddInteger(scUnknown);
ID.AddPointer(V);
void *IP = nullptr;
if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
assert(cast<SCEVUnknown>(S)->getValue() == V &&
"Stale SCEVUnknown in uniquing map!");
return S;
}
SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
FirstUnknown);
FirstUnknown = cast<SCEVUnknown>(S);
UniqueSCEVs.InsertNode(S, IP);
return S;
}
//===----------------------------------------------------------------------===//
// Basic SCEV Analysis and PHI Idiom Recognition Code
//
/// Test if values of the given type are analyzable within the SCEV
/// framework. This primarily includes integer types, and it can optionally
/// include pointer types if the ScalarEvolution class has access to
/// target-specific information.
bool ScalarEvolution::isSCEVable(Type *Ty) const {
// Integers and pointers are always SCEVable.
return Ty->isIntOrPtrTy();
}
/// Return the size in bits of the specified type, for which isSCEVable must
/// return true.
uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!");
if (Ty->isPointerTy())
return getDataLayout().getIndexTypeSizeInBits(Ty);
return getDataLayout().getTypeSizeInBits(Ty);
}
/// Return a type with the same bitwidth as the given type and which represents
/// how SCEV will treat the given type, for which isSCEVable must return
/// true. For pointer types, this is the pointer index sized integer type.
Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!");
if (Ty->isIntegerTy())
return Ty;
// The only other support type is pointer.
assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
return getDataLayout().getIndexType(Ty);
}
Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
}
const SCEV *ScalarEvolution::getCouldNotCompute() {
return CouldNotCompute.get();
}
bool ScalarEvolution::checkValidity(const SCEV *S) const {
bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
auto *SU = dyn_cast<SCEVUnknown>(S);
return SU && SU->getValue() == nullptr;
});
return !ContainsNulls;
}
bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
HasRecMapType::iterator I = HasRecMap.find(S);
if (I != HasRecMap.end())
return I->second;
bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
HasRecMap.insert({S, FoundAddRec});
return FoundAddRec;
}
/// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
/// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
/// offset I, then return {S', I}, else return {\p S, nullptr}.
static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
const auto *Add = dyn_cast<SCEVAddExpr>(S);
if (!Add)
return {S, nullptr};
if (Add->getNumOperands() != 2)
return {S, nullptr};
auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
if (!ConstOp)
return {S, nullptr};
return {Add->getOperand(1), ConstOp->getValue()};
}
/// Return the ValueOffsetPair set for \p S. \p S can be represented
/// by the value and offset from any ValueOffsetPair in the set.
SetVector<ScalarEvolution::ValueOffsetPair> *
ScalarEvolution::getSCEVValues(const SCEV *S) {
ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
if (SI == ExprValueMap.end())
return nullptr;
#ifndef NDEBUG
if (VerifySCEVMap) {
// Check there is no dangling Value in the set returned.
for (const auto &VE : SI->second)
assert(ValueExprMap.count(VE.first));
}
#endif
return &SI->second;
}
/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
/// cannot be used separately. eraseValueFromMap should be used to remove
/// V from ValueExprMap and ExprValueMap at the same time.
void ScalarEvolution::eraseValueFromMap(Value *V) {
ValueExprMapType::iterator I = ValueExprMap.find_as(V);
if (I != ValueExprMap.end()) {
const SCEV *S = I->second;
// Remove {V, 0} from the set of ExprValueMap[S]
if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
SV->remove({V, nullptr});
// Remove {V, Offset} from the set of ExprValueMap[Stripped]
const SCEV *Stripped;
ConstantInt *Offset;
std::tie(Stripped, Offset) = splitAddExpr(S);
if (Offset != nullptr) {
if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
SV->remove({V, Offset});
}
ValueExprMap.erase(V);
}
}
/// Check whether value has nuw/nsw/exact set but SCEV does not.
/// TODO: In reality it is better to check the poison recursively
/// but this is better than nothing.
static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) {
if (auto *I = dyn_cast<Instruction>(V)) {
if (isa<OverflowingBinaryOperator>(I)) {
if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) {
if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap())
return true;
if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap())
return true;
}
} else if (isa<PossiblyExactOperator>(I) && I->isExact())
return true;
}
return false;
}
/// Return an existing SCEV if it exists, otherwise analyze the expression and
/// create a new one.
const SCEV *ScalarEvolution::getSCEV(Value *V) {
assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
const SCEV *S = getExistingSCEV(V);
if (S == nullptr) {
S = createSCEV(V);
// During PHI resolution, it is possible to create two SCEVs for the same
// V, so it is needed to double check whether V->S is inserted into
// ValueExprMap before insert S->{V, 0} into ExprValueMap.
std::pair<ValueExprMapType::iterator, bool> Pair =
ValueExprMap.insert({SCEVCallbackVH(V, this), S});
if (Pair.second && !SCEVLostPoisonFlags(S, V)) {
ExprValueMap[S].insert({V, nullptr});
// If S == Stripped + Offset, add Stripped -> {V, Offset} into
// ExprValueMap.
const SCEV *Stripped = S;
ConstantInt *Offset = nullptr;
std::tie(Stripped, Offset) = splitAddExpr(S);
// If stripped is SCEVUnknown, don't bother to save
// Stripped -> {V, offset}. It doesn't simplify and sometimes even
// increase the complexity of the expansion code.
// If V is GetElementPtrInst, don't save Stripped -> {V, offset}
// because it may generate add/sub instead of GEP in SCEV expansion.
if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
!isa<GetElementPtrInst>(V))
ExprValueMap[Stripped].insert({V, Offset});
}
}
return S;
}
const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
ValueExprMapType::iterator I = ValueExprMap.find_as(V);
if (I != ValueExprMap.end()) {
const SCEV *S = I->second;
if (checkValidity(S))
return S;
eraseValueFromMap(V);
forgetMemoizedResults(S);
}
return nullptr;
}
/// Return a SCEV corresponding to -V = -1*V
const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
SCEV::NoWrapFlags Flags) {
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
return getConstant(
cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
Type *Ty = V->getType();
Ty = getEffectiveSCEVType(Ty);
return getMulExpr(
V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
}
/// If Expr computes ~A, return A else return nullptr
static const SCEV *MatchNotExpr(const SCEV *Expr) {
const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
if (!Add || Add->getNumOperands() != 2 ||
!Add->getOperand(0)->isAllOnesValue())
return nullptr;
const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
if (!AddRHS || AddRHS->getNumOperands() != 2 ||
!AddRHS->getOperand(0)->isAllOnesValue())
return nullptr;
return AddRHS->getOperand(1);
}
/// Return a SCEV corresponding to ~V = -1-V
const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
return getConstant(
cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
// Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) {
auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
SmallVector<const SCEV *, 2> MatchedOperands;
for (const SCEV *Operand : MME->operands()) {
const SCEV *Matched = MatchNotExpr(Operand);
if (!Matched)
return (const SCEV *)nullptr;
MatchedOperands.push_back(Matched);
}
return getMinMaxExpr(
SCEVMinMaxExpr::negate(static_cast<SCEVTypes>(MME->getSCEVType())),
MatchedOperands);
};
if (const SCEV *Replaced = MatchMinMaxNegation(MME))
return Replaced;
}
Type *Ty = V->getType();
Ty = getEffectiveSCEVType(Ty);
const SCEV *AllOnes =
getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
return getMinusSCEV(AllOnes, V);
}
const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
SCEV::NoWrapFlags Flags,
unsigned Depth) {
// Fast path: X - X --> 0.
if (LHS == RHS)
return getZero(LHS->getType());
// We represent LHS - RHS as LHS + (-1)*RHS. This transformation
// makes it so that we cannot make much use of NUW.
auto AddFlags = SCEV::FlagAnyWrap;
const bool RHSIsNotMinSigned =
!getSignedRangeMin(RHS).isMinSignedValue();
if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
// Let M be the minimum representable signed value. Then (-1)*RHS
// signed-wraps if and only if RHS is M. That can happen even for
// a NSW subtraction because e.g. (-1)*M signed-wraps even though
// -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
// (-1)*RHS, we need to prove that RHS != M.
//
// If LHS is non-negative and we know that LHS - RHS does not
// signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
// either by proving that RHS > M or that LHS >= 0.
if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
AddFlags = SCEV::FlagNSW;
}
}
// FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
// RHS is NSW and LHS >= 0.
//
// The difficulty here is that the NSW flag may have been proven
// relative to a loop that is to be found in a recurrence in LHS and
// not in RHS. Applying NSW to (-1)*M may then let the NSW have a
// larger scope than intended.
auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
}
const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
unsigned Depth) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or zero extend with non-integer arguments!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
return getTruncateExpr(V, Ty, Depth);
return getZeroExtendExpr(V, Ty, Depth);
}
const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
unsigned Depth) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or zero extend with non-integer arguments!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
return getTruncateExpr(V, Ty, Depth);
return getSignExtendExpr(V, Ty, Depth);
}
const SCEV *
ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or zero extend with non-integer arguments!");
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrZeroExtend cannot truncate!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
return getZeroExtendExpr(V, Ty);
}
const SCEV *
ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or sign extend with non-integer arguments!");
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrSignExtend cannot truncate!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
return getSignExtendExpr(V, Ty);
}
const SCEV *
ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or any extend with non-integer arguments!");
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrAnyExtend cannot truncate!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
return getAnyExtendExpr(V, Ty);
}
const SCEV *
ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or noop with non-integer arguments!");
assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
"getTruncateOrNoop cannot extend!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
return getTruncateExpr(V, Ty);
}
const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
const SCEV *RHS) {
const SCEV *PromotedLHS = LHS;
const SCEV *PromotedRHS = RHS;
if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
else
PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
return getUMaxExpr(PromotedLHS, PromotedRHS);
}
const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getUMinFromMismatchedTypes(Ops);
}
const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(
SmallVectorImpl<const SCEV *> &Ops) {
assert(!Ops.empty() && "At least one operand must be!");
// Trivial case.
if (Ops.size() == 1)
return Ops[0];
// Find the max type first.
Type *MaxType = nullptr;
for (auto *S : Ops)
if (MaxType)
MaxType = getWiderType(MaxType, S->getType());
else
MaxType = S->getType();
// Extend all ops to max type.
SmallVector<const SCEV *, 2> PromotedOps;
for (auto *S : Ops)
PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
// Generate umin.
return getUMinExpr(PromotedOps);
}
const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
// A pointer operand may evaluate to a nonpointer expression, such as null.
if (!V->getType()->isPointerTy())
return V;
if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
return getPointerBase(Cast->getOperand());
} else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
const SCEV *PtrOp = nullptr;
for (const SCEV *NAryOp : NAry->operands()) {
if (NAryOp->getType()->isPointerTy()) {
// Cannot find the base of an expression with multiple pointer operands.
if (PtrOp)
return V;
PtrOp = NAryOp;
}
}
if (!PtrOp)
return V;
return getPointerBase(PtrOp);
}
return V;
}
/// Push users of the given Instruction onto the given Worklist.
static void
PushDefUseChildren(Instruction *I,
SmallVectorImpl<Instruction *> &Worklist) {
// Push the def-use children onto the Worklist stack.
for (User *U : I->users())
Worklist.push_back(cast<Instruction>(U));
}
void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
SmallVector<Instruction *, 16> Worklist;
PushDefUseChildren(PN, Worklist);
SmallPtrSet<Instruction *, 8> Visited;
Visited.insert(PN);
while (!Worklist.empty()) {
Instruction *I = Worklist.pop_back_val();
if (!Visited.insert(I).second)
continue;
auto It = ValueExprMap.find_as(static_cast<Value *>(I));
if (It != ValueExprMap.end()) {
const SCEV *Old = It->second;
// Short-circuit the def-use traversal if the symbolic name
// ceases to appear in expressions.
if (Old != SymName && !hasOperand(Old, SymName))
continue;
// SCEVUnknown for a PHI either means that it has an unrecognized
// structure, it's a PHI that's in the progress of being computed
// by createNodeForPHI, or it's a single-value PHI. In the first case,
// additional loop trip count information isn't going to change anything.
// In the second case, createNodeForPHI will perform the necessary
// updates on its own when it gets to that point. In the third, we do
// want to forget the SCEVUnknown.
if (!isa<PHINode>(I) ||
!isa<SCEVUnknown>(Old) ||
(I != PN && Old == SymName)) {
eraseValueFromMap(It->first);
forgetMemoizedResults(Old);
}
}
PushDefUseChildren(I, Worklist);
}
}
namespace {
/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
/// expression in case its Loop is L. If it is not L then
/// if IgnoreOtherLoops is true then use AddRec itself
/// otherwise rewrite cannot be done.
/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
public:
static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
bool IgnoreOtherLoops = true) {
SCEVInitRewriter Rewriter(L, SE);
const SCEV *Result = Rewriter.visit(S);
if (Rewriter.hasSeenLoopVariantSCEVUnknown())
return SE.getCouldNotCompute();
return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
? SE.getCouldNotCompute()
: Result;
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
if (!SE.isLoopInvariant(Expr, L))
SeenLoopVariantSCEVUnknown = true;
return Expr;
}
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
// Only re-write AddRecExprs for this loop.
if (Expr->getLoop() == L)
return Expr->getStart();
SeenOtherLoops = true;
return Expr;
}
bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
bool hasSeenOtherLoops() { return SeenOtherLoops; }
private:
explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L) {}
const Loop *L;
bool SeenLoopVariantSCEVUnknown = false;
bool SeenOtherLoops = false;
};
/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
/// increment expression in case its Loop is L. If it is not L then
/// use AddRec itself.
/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
public:
static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
SCEVPostIncRewriter Rewriter(L, SE);
const SCEV *Result = Rewriter.visit(S);
return Rewriter.hasSeenLoopVariantSCEVUnknown()
? SE.getCouldNotCompute()
: Result;
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
if (!SE.isLoopInvariant(Expr, L))
SeenLoopVariantSCEVUnknown = true;
return Expr;
}
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
// Only re-write AddRecExprs for this loop.
if (Expr->getLoop() == L)
return Expr->getPostIncExpr(SE);
SeenOtherLoops = true;
return Expr;
}
bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
bool hasSeenOtherLoops() { return SeenOtherLoops; }
private:
explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L) {}
const Loop *L;
bool SeenLoopVariantSCEVUnknown = false;
bool SeenOtherLoops = false;
};
/// This class evaluates the compare condition by matching it against the
/// condition of loop latch. If there is a match we assume a true value
/// for the condition while building SCEV nodes.
class SCEVBackedgeConditionFolder
: public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
public:
static const SCEV *rewrite(const SCEV *S, const Loop *L,
ScalarEvolution &SE) {
bool IsPosBECond = false;
Value *BECond = nullptr;
if (BasicBlock *Latch = L->getLoopLatch()) {
BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
if (BI && BI->isConditional()) {
assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&
"Both outgoing branches should not target same header!");
BECond = BI->getCondition();
IsPosBECond = BI->getSuccessor(0) == L->getHeader();
} else {
return S;
}
}
SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
return Rewriter.visit(S);
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
const SCEV *Result = Expr;
bool InvariantF = SE.isLoopInvariant(Expr, L);
if (!InvariantF) {
Instruction *I = cast<Instruction>(Expr->getValue());
switch (I->getOpcode()) {
case Instruction::Select: {
SelectInst *SI = cast<SelectInst>(I);
Optional<const SCEV *> Res =
compareWithBackedgeCondition(SI->getCondition());
if (Res.hasValue()) {
bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
}
break;
}
default: {
Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
if (Res.hasValue())
Result = Res.getValue();
break;
}
}
}
return Result;
}
private:
explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
bool IsPosBECond, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
IsPositiveBECond(IsPosBECond) {}
Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
const Loop *L;
/// Loop back condition.
Value *BackedgeCond = nullptr;
/// Set to true if loop back is on positive branch condition.
bool IsPositiveBECond;
};
Optional<const SCEV *>
SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
// If value matches the backedge condition for loop latch,
// then return a constant evolution node based on loopback
// branch taken.
if (BackedgeCond == IC)
return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
: SE.getZero(Type::getInt1Ty(SE.getContext()));
return None;
}
class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
public:
static const SCEV *rewrite(const SCEV *S, const Loop *L,
ScalarEvolution &SE) {
SCEVShiftRewriter Rewriter(L, SE);
const SCEV *Result = Rewriter.visit(S);
return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
// Only allow AddRecExprs for this loop.
if (!SE.isLoopInvariant(Expr, L))
Valid = false;
return Expr;
}
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
if (Expr->getLoop() == L && Expr->isAffine())
return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
Valid = false;
return Expr;
}
bool isValid() { return Valid; }
private:
explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L) {}
const Loop *L;
bool Valid = true;
};
} // end anonymous namespace
SCEV::NoWrapFlags
ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
if (!AR->isAffine())
return SCEV::FlagAnyWrap;
using OBO = OverflowingBinaryOperator;
SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
if (!AR->hasNoSignedWrap()) {
ConstantRange AddRecRange = getSignedRange(AR);
ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
Instruction::Add, IncRange, OBO::NoSignedWrap);
if (NSWRegion.contains(AddRecRange))
Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
}
if (!AR->hasNoUnsignedWrap()) {
ConstantRange AddRecRange = getUnsignedRange(AR);
ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
Instruction::Add, IncRange, OBO::NoUnsignedWrap);
if (NUWRegion.contains(AddRecRange))
Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
}
return Result;
}
namespace {
/// Represents an abstract binary operation. This may exist as a
/// normal instruction or constant expression, or may have been
/// derived from an expression tree.
struct BinaryOp {
unsigned Opcode;
Value *LHS;
Value *RHS;
bool IsNSW = false;
bool IsNUW = false;
/// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
/// constant expression.
Operator *Op = nullptr;
explicit BinaryOp(Operator *Op)
: Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
Op(Op) {
if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
IsNSW = OBO->hasNoSignedWrap();
IsNUW = OBO->hasNoUnsignedWrap();
}
}
explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
bool IsNUW = false)
: Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
};
} // end anonymous namespace
/// Try to map \p V into a BinaryOp, and return \c None on failure.
static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
auto *Op = dyn_cast<Operator>(V);
if (!Op)
return None;
// Implementation detail: all the cleverness here should happen without
// creating new SCEV expressions -- our caller knowns tricks to avoid creating
// SCEV expressions when possible, and we should not break that.
switch (Op->getOpcode()) {
case Instruction::Add:
case Instruction::Sub:
case Instruction::Mul:
case Instruction::UDiv:
case Instruction::URem:
case Instruction::And:
case Instruction::Or:
case Instruction::AShr:
case Instruction::Shl:
return BinaryOp(Op);
case Instruction::Xor:
if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
// If the RHS of the xor is a signmask, then this is just an add.
// Instcombine turns add of signmask into xor as a strength reduction step.
if (RHSC->getValue().isSignMask())
return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
return BinaryOp(Op);
case Instruction::LShr:
// Turn logical shift right of a constant into a unsigned divide.
if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
// If the shift count is not less than the bitwidth, the result of
// the shift is undefined. Don't try to analyze it, because the
// resolution chosen here may differ from the resolution chosen in
// other parts of the compiler.
if (SA->getValue().ult(BitWidth)) {
Constant *X =
ConstantInt::get(SA->getContext(),
APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
}
}
return BinaryOp(Op);
case Instruction::ExtractValue: {
auto *EVI = cast<ExtractValueInst>(Op);
if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
break;
auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand());
if (!WO)
break;
Instruction::BinaryOps BinOp = WO->getBinaryOp();
bool Signed = WO->isSigned();
// TODO: Should add nuw/nsw flags for mul as well.
if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());
// Now that we know that all uses of the arithmetic-result component of
// CI are guarded by the overflow check, we can go ahead and pretend
// that the arithmetic is non-overflowing.
return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
/* IsNSW = */ Signed, /* IsNUW = */ !Signed);
}
default:
break;
}
// Recognise intrinsic loop.decrement.reg, and as this has exactly the same
// semantics as a Sub, return a binary sub expression.
if (auto *II = dyn_cast<IntrinsicInst>(V))
if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg)
return BinaryOp(Instruction::Sub, II->getOperand(0), II->getOperand(1));
return None;
}
/// Helper function to createAddRecFromPHIWithCasts. We have a phi
/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
/// follows one of the following patterns:
/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
/// If the SCEV expression of \p Op conforms with one of the expected patterns
/// we return the type of the truncation operation, and indicate whether the
/// truncated type should be treated as signed/unsigned by setting
/// \p Signed to true/false, respectively.
static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
bool &Signed, ScalarEvolution &SE) {
// The case where Op == SymbolicPHI (that is, with no type conversions on
// the way) is handled by the regular add recurrence creating logic and
// would have already been triggered in createAddRecForPHI. Reaching it here
// means that createAddRecFromPHI had failed for this PHI before (e.g.,
// because one of the other operands of the SCEVAddExpr updating this PHI is
// not invariant).
//
// Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
// this case predicates that allow us to prove that Op == SymbolicPHI will
// be added.
if (Op == SymbolicPHI)
return nullptr;
unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
if (SourceBits != NewBits)
return nullptr;
const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
if (!SExt && !ZExt)
return nullptr;
const SCEVTruncateExpr *Trunc =
SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
: dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
if (!Trunc)
return nullptr;
const SCEV *X = Trunc->getOperand();
if (X != SymbolicPHI)
return nullptr;
Signed = SExt != nullptr;
return Trunc->getType();
}
static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
if (!PN->getType()->isIntegerTy())
return nullptr;
const Loop *L = LI.getLoopFor(PN->getParent());
if (!L || L->getHeader() != PN->getParent())
return nullptr;
return L;
}
// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
// computation that updates the phi follows the following pattern:
// (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
// which correspond to a phi->trunc->sext/zext->add->phi update chain.
// If so, try to see if it can be rewritten as an AddRecExpr under some
// Predicates. If successful, return them as a pair. Also cache the results
// of the analysis.
//
// Example usage scenario:
// Say the Rewriter is called for the following SCEV:
// 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
// where:
// %X = phi i64 (%Start, %BEValue)
// It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
// and call this function with %SymbolicPHI = %X.
//
// The analysis will find that the value coming around the backedge has
// the following SCEV:
// BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
// Upon concluding that this matches the desired pattern, the function
// will return the pair {NewAddRec, SmallPredsVec} where:
// NewAddRec = {%Start,+,%Step}
// SmallPredsVec = {P1, P2, P3} as follows:
// P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
// P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
// P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
// The returned pair means that SymbolicPHI can be rewritten into NewAddRec
// under the predicates {P1,P2,P3}.
// This predicated rewrite will be cached in PredicatedSCEVRewrites:
// PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
//
// TODO's:
//
// 1) Extend the Induction descriptor to also support inductions that involve
// casts: When needed (namely, when we are called in the context of the
// vectorizer induction analysis), a Set of cast instructions will be
// populated by this method, and provided back to isInductionPHI. This is
// needed to allow the vectorizer to properly record them to be ignored by
// the cost model and to avoid vectorizing them (otherwise these casts,
// which are redundant under the runtime overflow checks, will be
// vectorized, which can be costly).
//
// 2) Support additional induction/PHISCEV patterns: We also want to support
// inductions where the sext-trunc / zext-trunc operations (partly) occur
// after the induction update operation (the induction increment):
//
// (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
// which correspond to a phi->add->trunc->sext/zext->phi update chain.
//
// (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
// which correspond to a phi->trunc->add->sext/zext->phi update chain.
//
// 3) Outline common code with createAddRecFromPHI to avoid duplication.
Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
SmallVector<const SCEVPredicate *, 3> Predicates;
// *** Part1: Analyze if we have a phi-with-cast pattern for which we can
// return an AddRec expression under some predicate.
auto *PN = cast<PHINode>(SymbolicPHI->getValue());
const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
assert(L && "Expecting an integer loop header phi");
// The loop may have multiple entrances or multiple exits; we can analyze
// this phi as an addrec if it has a unique entry value and a unique
// backedge value.
Value *BEValueV = nullptr, *StartValueV = nullptr;
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
Value *V = PN->getIncomingValue(i);
if (L->contains(PN->getIncomingBlock(i))) {
if (!BEValueV) {
BEValueV = V;
} else if (BEValueV != V) {
BEValueV = nullptr;
break;
}
} else if (!StartValueV) {
StartValueV = V;
} else if (StartValueV != V) {
StartValueV = nullptr;
break;
}
}
if (!BEValueV || !StartValueV)
return None;
const SCEV *BEValue = getSCEV(BEValueV);
// If the value coming around the backedge is an add with the symbolic
// value we just inserted, possibly with casts that we can ignore under
// an appropriate runtime guard, then we found a simple induction variable!
const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
if (!Add)
return None;
// If there is a single occurrence of the symbolic value, possibly
// casted, replace it with a recurrence.
unsigned FoundIndex = Add->getNumOperands();
Type *TruncTy = nullptr;
bool Signed;
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if ((TruncTy =
isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
if (FoundIndex == e) {
FoundIndex = i;
break;
}
if (FoundIndex == Add->getNumOperands())
return None;
// Create an add with everything but the specified operand.
SmallVector<const SCEV *, 8> Ops;
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (i != FoundIndex)
Ops.push_back(Add->getOperand(i));
const SCEV *Accum = getAddExpr(Ops);
// The runtime checks will not be valid if the step amount is
// varying inside the loop.
if (!isLoopInvariant(Accum, L))
return None;
// *** Part2: Create the predicates
// Analysis was successful: we have a phi-with-cast pattern for which we
// can return an AddRec expression under the following predicates:
//
// P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
// fits within the truncated type (does not overflow) for i = 0 to n-1.
// P2: An Equal predicate that guarantees that
// Start = (Ext ix (Trunc iy (Start) to ix) to iy)
// P3: An Equal predicate that guarantees that
// Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
//
// As we next prove, the above predicates guarantee that:
// Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
//
//
// More formally, we want to prove that:
// Expr(i+1) = Start + (i+1) * Accum
// = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
//
// Given that:
// 1) Expr(0) = Start
// 2) Expr(1) = Start + Accum
// = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
// 3) Induction hypothesis (step i):
// Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
//
// Proof:
// Expr(i+1) =
// = Start + (i+1)*Accum
// = (Start + i*Accum) + Accum
// = Expr(i) + Accum
// = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
// :: from step i
//
// = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
//
// = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
// + (Ext ix (Trunc iy (Accum) to ix) to iy)
// + Accum :: from P3
//
// = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
// + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
//
// = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
// = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
//
// By induction, the same applies to all iterations 1<=i<n:
//
// Create a truncated addrec for which we will add a no overflow check (P1).
const SCEV *StartVal = getSCEV(StartValueV);
const SCEV *PHISCEV =
getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
// PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
// ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
// will be constant.
//
// If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
// add P1.
if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
Signed ? SCEVWrapPredicate::IncrementNSSW
: SCEVWrapPredicate::IncrementNUSW;
const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
Predicates.push_back(AddRecPred);
}
// Create the Equal Predicates P2,P3:
// It is possible that the predicates P2 and/or P3 are computable at
// compile time due to StartVal and/or Accum being constants.
// If either one is, then we can check that now and escape if either P2
// or P3 is false.
// Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
// for each of StartVal and Accum
auto getExtendedExpr = [&](const SCEV *Expr,
bool CreateSignExtend) -> const SCEV * {
assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
const SCEV *ExtendedExpr =
CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
: getZeroExtendExpr(TruncatedExpr, Expr->getType());
return ExtendedExpr;
};
// Given:
// ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
// = getExtendedExpr(Expr)
// Determine whether the predicate P: Expr == ExtendedExpr
// is known to be false at compile time
auto PredIsKnownFalse = [&](const SCEV *Expr,
const SCEV *ExtendedExpr) -> bool {
return Expr != ExtendedExpr &&
isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
};
const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
if (PredIsKnownFalse(StartVal, StartExtended)) {
LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";);
return None;
}
// The Step is always Signed (because the overflow checks are either
// NSSW or NUSW)
const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
if (PredIsKnownFalse(Accum, AccumExtended)) {
LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";);
return None;
}
auto AppendPredicate = [&](const SCEV *Expr,
const SCEV *ExtendedExpr) -> void {
if (Expr != ExtendedExpr &&
!isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred);
Predicates.push_back(Pred);
}
};
AppendPredicate(StartVal, StartExtended);
AppendPredicate(Accum, AccumExtended);
// *** Part3: Predicates are ready. Now go ahead and create the new addrec in
// which the casts had been folded away. The caller can rewrite SymbolicPHI
// into NewAR if it will also add the runtime overflow checks specified in
// Predicates.
auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
std::make_pair(NewAR, Predicates);
// Remember the result of the analysis for this SCEV at this locayyytion.
PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
return PredRewrite;
}
Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
auto *PN = cast<PHINode>(SymbolicPHI->getValue());
const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
if (!L)
return None;
// Check to see if we already analyzed this PHI.
auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
if (I != PredicatedSCEVRewrites.end()) {
std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
I->second;
// Analysis was done before and failed to create an AddRec:
if (Rewrite.first == SymbolicPHI)
return None;
// Analysis was done before and succeeded to create an AddRec under
// a predicate:
assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
assert(!(Rewrite.second).empty() && "Expected to find Predicates");
return Rewrite;
}
Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
// Record in the cache that the analysis failed
if (!Rewrite) {
SmallVector<const SCEVPredicate *, 3> Predicates;
PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
return None;
}
return Rewrite;
}
// FIXME: This utility is currently required because the Rewriter currently
// does not rewrite this expression:
// {0, +, (sext ix (trunc iy to ix) to iy)}
// into {0, +, %step},
// even when the following Equal predicate exists:
// "%step == (sext ix (trunc iy to ix) to iy)".
bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
if (AR1 == AR2)
return true;
auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
!Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
return false;
return true;
};
if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
!areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
return false;
return true;
}
/// A helper function for createAddRecFromPHI to handle simple cases.
///
/// This function tries to find an AddRec expression for the simplest (yet most
/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
/// If it fails, createAddRecFromPHI will use a more general, but slow,
/// technique for finding the AddRec expression.
const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
Value *BEValueV,
Value *StartValueV) {
const Loop *L = LI.getLoopFor(PN->getParent());
assert(L && L->getHeader() == PN->getParent());
assert(BEValueV && StartValueV);
auto BO = MatchBinaryOp(BEValueV, DT);
if (!BO)
return nullptr;
if (BO->Opcode != Instruction::Add)
return nullptr;
const SCEV *Accum = nullptr;
if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
Accum = getSCEV(BO->RHS);
else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
Accum = getSCEV(BO->LHS);
if (!Accum)
return nullptr;
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (BO->IsNUW)
Flags = setFlags(Flags, SCEV::FlagNUW);
if (BO->IsNSW)
Flags = setFlags(Flags, SCEV::FlagNSW);
const SCEV *StartVal = getSCEV(StartValueV);
const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
// We can add Flags to the post-inc expression only if we
// know that it is *undefined behavior* for BEValueV to
// overflow.
if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
(void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
return PHISCEV;
}
const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
const Loop *L = LI.getLoopFor(PN->getParent());
if (!L || L->getHeader() != PN->getParent())
return nullptr;
// The loop may have multiple entrances or multiple exits; we can analyze
// this phi as an addrec if it has a unique entry value and a unique
// backedge value.
Value *BEValueV = nullptr, *StartValueV = nullptr;
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
Value *V = PN->getIncomingValue(i);
if (L->contains(PN->getIncomingBlock(i))) {
if (!BEValueV) {
BEValueV = V;
} else if (BEValueV != V) {
BEValueV = nullptr;
break;
}
} else if (!StartValueV) {
StartValueV = V;
} else if (StartValueV != V) {
StartValueV = nullptr;
break;
}
}
if (!BEValueV || !StartValueV)
return nullptr;
assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
"PHI node already processed?");
// First, try to find AddRec expression without creating a fictituos symbolic
// value for PN.
if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
return S;
// Handle PHI node value symbolically.
const SCEV *SymbolicName = getUnknown(PN);
ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
// Using this symbolic name for the PHI, analyze the value coming around
// the back-edge.
const SCEV *BEValue = getSCEV(BEValueV);
// NOTE: If BEValue is loop invariant, we know that the PHI node just
// has a special value for the first iteration of the loop.
// If the value coming around the backedge is an add with the symbolic
// value we just inserted, then we found a simple induction variable!
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
// If there is a single occurrence of the symbolic value, replace it
// with a recurrence.
unsigned FoundIndex = Add->getNumOperands();
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (Add->getOperand(i) == SymbolicName)
if (FoundIndex == e) {
FoundIndex = i;
break;
}
if (FoundIndex != Add->getNumOperands()) {
// Create an add with everything but the specified operand.
SmallVector<const SCEV *, 8> Ops;
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (i != FoundIndex)
Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
L, *this));
const SCEV *Accum = getAddExpr(Ops);
// This is not a valid addrec if the step amount is varying each
// loop iteration, but is not itself an addrec in this loop.
if (isLoopInvariant(Accum, L) ||
(isa<SCEVAddRecExpr>(Accum) &&
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (auto BO = MatchBinaryOp(BEValueV, DT)) {
if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
if (BO->IsNUW)
Flags = setFlags(Flags, SCEV::FlagNUW);
if (BO->IsNSW)
Flags = setFlags(Flags, SCEV::FlagNSW);
}
} else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
// If the increment is an inbounds GEP, then we know the address
// space cannot be wrapped around. We cannot make any guarantee
// about signed or unsigned overflow because pointers are
// unsigned but we may have a negative index from the base
// pointer. We can guarantee that no unsigned wrap occurs if the
// indices form a positive value.
if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
Flags = setFlags(Flags, SCEV::FlagNW);
const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
Flags = setFlags(Flags, SCEV::FlagNUW);
}
// We cannot transfer nuw and nsw flags from subtraction
// operations -- sub nuw X, Y is not the same as add nuw X, -Y
// for instance.
}
const SCEV *StartVal = getSCEV(StartValueV);
const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
// Okay, for the entire analysis of this edge we assumed the PHI
// to be symbolic. We now need to go back and purge all of the
// entries for the scalars that use the symbolic expression.
forgetSymbolicName(PN, SymbolicName);
ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
// We can add Flags to the post-inc expression only if we
// know that it is *undefined behavior* for BEValueV to
// overflow.
if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
(void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
return PHISCEV;
}
}
} else {
// Otherwise, this could be a loop like this:
// i = 0; for (j = 1; ..; ++j) { .... i = j; }
// In this case, j = {1,+,1} and BEValue is j.
// Because the other in-value of i (0) fits the evolution of BEValue
// i really is an addrec evolution.
//
// We can generalize this saying that i is the shifted value of BEValue
// by one iteration:
// PHI(f(0), f({1,+,1})) --> f({0,+,1})
const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
if (Shifted != getCouldNotCompute() &&
Start != getCouldNotCompute()) {
const SCEV *StartVal = getSCEV(StartValueV);
if (Start == StartVal) {
// Okay, for the entire analysis of this edge we assumed the PHI
// to be symbolic. We now need to go back and purge all of the
// entries for the scalars that use the symbolic expression.
forgetSymbolicName(PN, SymbolicName);
ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
return Shifted;
}
}
}
// Remove the temporary PHI node SCEV that has been inserted while intending
// to create an AddRecExpr for this PHI node. We can not keep this temporary
// as it will prevent later (possibly simpler) SCEV expressions to be added
// to the ValueExprMap.
eraseValueFromMap(PN);
return nullptr;
}
// Checks if the SCEV S is available at BB. S is considered available at BB
// if S can be materialized at BB without introducing a fault.
static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
BasicBlock *BB) {
struct CheckAvailable {
bool TraversalDone = false;
bool Available = true;
const Loop *L = nullptr; // The loop BB is in (can be nullptr)
BasicBlock *BB = nullptr;
DominatorTree &DT;
CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
: L(L), BB(BB), DT(DT) {}
bool setUnavailable() {
TraversalDone = true;
Available = false;
return false;
}
bool follow(const SCEV *S) {
switch (S->getSCEVType()) {
case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
// These expressions are available if their operand(s) is/are.
return true;
case scAddRecExpr: {
// We allow add recurrences that are on the loop BB is in, or some
// outer loop. This guarantees availability because the value of the
// add recurrence at BB is simply the "current" value of the induction
// variable. We can relax this in the future; for instance an add
// recurrence on a sibling dominating loop is also available at BB.
const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
if (L && (ARLoop == L || ARLoop->contains(L)))
return true;
return setUnavailable();
}
case scUnknown: {
// For SCEVUnknown, we check for simple dominance.
const auto *SU = cast<SCEVUnknown>(S);
Value *V = SU->getValue();
if (isa<Argument>(V))
return false;
if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
return false;
return setUnavailable();
}
case scUDivExpr:
case scCouldNotCompute:
// We do not try to smart about these at all.
return setUnavailable();
}
llvm_unreachable("switch should be fully covered!");
}
bool isDone() { return TraversalDone; }
};
CheckAvailable CA(L, BB, DT);
SCEVTraversal<CheckAvailable> ST(CA);
ST.visitAll(S);
return CA.Available;
}
// Try to match a control flow sequence that branches out at BI and merges back
// at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
// match.
static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
Value *&C, Value *&LHS, Value *&RHS) {
C = BI->getCondition();
BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
if (!LeftEdge.isSingleEdge())
return false;
assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
Use &LeftUse = Merge->getOperandUse(0);
Use &RightUse = Merge->getOperandUse(1);
if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
LHS = LeftUse;
RHS = RightUse;
return true;
}
if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
LHS = RightUse;
RHS = LeftUse;
return true;
}
return false;
}
const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
auto IsReachable =
[&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
const Loop *L = LI.getLoopFor(PN->getParent());
// We don't want to break LCSSA, even in a SCEV expression tree.
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
return nullptr;
// Try to match
//
// br %cond, label %left, label %right
// left:
// br label %merge
// right:
// br label %merge
// merge:
// V = phi [ %x, %left ], [ %y, %right ]
//
// as "select %cond, %x, %y"
BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
assert(IDom && "At least the entry block should dominate PN");
auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
if (BI && BI->isConditional() &&
BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
}
return nullptr;
}
const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
if (const SCEV *S = createAddRecFromPHI(PN))
return S;
if (const SCEV *S = createNodeFromSelectLikePHI(PN))
return S;
// If the PHI has a single incoming value, follow that value, unless the
// PHI's incoming blocks are in a different loop, in which case doing so
// risks breaking LCSSA form. Instcombine would normally zap these, but
// it doesn't have DominatorTree information, so it may miss cases.
if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
if (LI.replacementPreservesLCSSAForm(PN, V))
return getSCEV(V);
// If it's not a loop phi, we can't handle it yet.
return getUnknown(PN);
}
const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
Value *Cond,
Value *TrueVal,
Value *FalseVal) {
// Handle "constant" branch or select. This can occur for instance when a
// loop pass transforms an inner loop and moves on to process the outer loop.
if (auto *CI = dyn_cast<ConstantInt>(Cond))
return getSCEV(CI->isOne() ? TrueVal : FalseVal);
// Try to match some simple smax or umax patterns.
auto *ICI = dyn_cast<ICmpInst>(Cond);
if (!ICI)
return getUnknown(I);
Value *LHS = ICI->getOperand(0);
Value *RHS = ICI->getOperand(1);
switch (ICI->getPredicate()) {
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
// a >s b ? a+x : b+x -> smax(a, b)+x
// a >s b ? b+x : a+x -> smin(a, b)+x
if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
const SCEV *LA = getSCEV(TrueVal);
const SCEV *RA = getSCEV(FalseVal);
const SCEV *LDiff = getMinusSCEV(LA, LS);
const SCEV *RDiff = getMinusSCEV(RA, RS);
if (LDiff == RDiff)
return getAddExpr(getSMaxExpr(LS, RS), LDiff);
LDiff = getMinusSCEV(LA, RS);
RDiff = getMinusSCEV(RA, LS);
if (LDiff == RDiff)
return getAddExpr(getSMinExpr(LS, RS), LDiff);
}
break;
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
// a >u b ? a+x : b+x -> umax(a, b)+x
// a >u b ? b+x : a+x -> umin(a, b)+x
if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
const SCEV *LA = getSCEV(TrueVal);
const SCEV *RA = getSCEV(FalseVal);
const SCEV *LDiff = getMinusSCEV(LA, LS);
const SCEV *RDiff = getMinusSCEV(RA, RS);
if (LDiff == RDiff)
return getAddExpr(getUMaxExpr(LS, RS), LDiff);
LDiff = getMinusSCEV(LA, RS);
RDiff = getMinusSCEV(RA, LS);
if (LDiff == RDiff)
return getAddExpr(getUMinExpr(LS, RS), LDiff);
}
break;
case ICmpInst::ICMP_NE:
// n != 0 ? n+x : 1+x -> umax(n, 1)+x
if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
const SCEV *One = getOne(I->getType());
const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
const SCEV *LA = getSCEV(TrueVal);
const SCEV *RA = getSCEV(FalseVal);
const SCEV *LDiff = getMinusSCEV(LA, LS);
const SCEV *RDiff = getMinusSCEV(RA, One);
if (LDiff == RDiff)
return getAddExpr(getUMaxExpr(One, LS), LDiff);
}
break;
case ICmpInst::ICMP_EQ:
// n == 0 ? 1+x : n+x -> umax(n, 1)+x
if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
const SCEV *One = getOne(I->getType());
const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
const SCEV *LA = getSCEV(TrueVal);
const SCEV *RA = getSCEV(FalseVal);
const SCEV *LDiff = getMinusSCEV(LA, One);
const SCEV *RDiff = getMinusSCEV(RA, LS);
if (LDiff == RDiff)
return getAddExpr(getUMaxExpr(One, LS), LDiff);
}
break;
default:
break;
}
return getUnknown(I);
}
/// Expand GEP instructions into add and multiply operations. This allows them
/// to be analyzed by regular SCEV code.
const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
// Don't attempt to analyze GEPs over unsized objects.
if (!GEP->getSourceElementType()->isSized())
return getUnknown(GEP);
SmallVector<const SCEV *, 4> IndexExprs;
for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
IndexExprs.push_back(getSCEV(*Index));
return getGEPExpr(GEP, IndexExprs);
}
uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
return C->getAPInt().countTrailingZeros();
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
return std::min(GetMinTrailingZeros(T->getOperand()),
(uint32_t)getTypeSizeInBits(T->getType()));
if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
return OpRes == getTypeSizeInBits(E->getOperand()->getType())
? getTypeSizeInBits(E->getType())
: OpRes;
}
if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
return OpRes == getTypeSizeInBits(E->getOperand()->getType())
? getTypeSizeInBits(E->getType())
: OpRes;
}
if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
return MinOpRes;
}
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
// The result is the sum of all operands results.
uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
uint32_t BitWidth = getTypeSizeInBits(M->getType());
for (unsigned i = 1, e = M->getNumOperands();
SumOpRes != BitWidth && i != e; ++i)
SumOpRes =
std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
return SumOpRes;
}
if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
return MinOpRes;
}
if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
return MinOpRes;
}
if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
return MinOpRes;
}
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
// For a SCEVUnknown, ask ValueTracking.
KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
return Known.countMinTrailingZeros();
}
// SCEVUDivExpr
return 0;
}
uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
auto I = MinTrailingZerosCache.find(S);
if (I != MinTrailingZerosCache.end())
return I->second;
uint32_t Result = GetMinTrailingZerosImpl(S);
auto InsertPair = MinTrailingZerosCache.insert({S, Result});
assert(InsertPair.second && "Should insert a new key");
return InsertPair.first->second;
}
/// Helper method to assign a range to V from metadata present in the IR.
static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
if (Instruction *I = dyn_cast<Instruction>(V))
if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
return getConstantRangeFromMetadata(*MD);
return None;
}
/// Determine the range for a particular SCEV. If SignHint is
/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
/// with a "cleaner" unsigned (resp. signed) representation.
const ConstantRange &
ScalarEvolution::getRangeRef(const SCEV *S,
ScalarEvolution::RangeSignHint SignHint) {
DenseMap<const SCEV *, ConstantRange> &Cache =
SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
: SignedRanges;
ConstantRange::PreferredRangeType RangeType =
SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED
? ConstantRange::Unsigned : ConstantRange::Signed;
// See if we've computed this range already.
DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
if (I != Cache.end())
return I->second;
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
return setRange(C, SignHint, ConstantRange(C->getAPInt()));
unsigned BitWidth = getTypeSizeInBits(S->getType());
ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
using OBO = OverflowingBinaryOperator;
// If the value has known zeros, the maximum value will have those known zeros
// as well.
uint32_t TZ = GetMinTrailingZeros(S);
if (TZ != 0) {
if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
ConservativeResult =
ConstantRange(APInt::getMinValue(BitWidth),
APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
else
ConservativeResult = ConstantRange(
APInt::getSignedMinValue(BitWidth),
APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
}
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
unsigned WrapType = OBO::AnyWrap;
if (Add->hasNoSignedWrap())
WrapType |= OBO::NoSignedWrap;
if (Add->hasNoUnsignedWrap())
WrapType |= OBO::NoUnsignedWrap;
for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
X = X.addWithNoWrap(getRangeRef(Add->getOperand(i), SignHint),
WrapType, RangeType);
return setRange(Add, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
return setRange(Mul, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
return setRange(SMax, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
return setRange(UMax, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVSMinExpr *SMin = dyn_cast<SCEVSMinExpr>(S)) {
ConstantRange X = getRangeRef(SMin->getOperand(0), SignHint);
for (unsigned i = 1, e = SMin->getNumOperands(); i != e; ++i)
X = X.smin(getRangeRef(SMin->getOperand(i), SignHint));
return setRange(SMin, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVUMinExpr *UMin = dyn_cast<SCEVUMinExpr>(S)) {
ConstantRange X = getRangeRef(UMin->getOperand(0), SignHint);
for (unsigned i = 1, e = UMin->getNumOperands(); i != e; ++i)
X = X.umin(getRangeRef(UMin->getOperand(i), SignHint));
return setRange(UMin, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
return setRange(UDiv, SignHint,
ConservativeResult.intersectWith(X.udiv(Y), RangeType));
}
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
return setRange(ZExt, SignHint,
ConservativeResult.intersectWith(X.zeroExtend(BitWidth),
RangeType));
}
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
return setRange(SExt, SignHint,
ConservativeResult.intersectWith(X.signExtend(BitWidth),
RangeType));
}
if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
return setRange(Trunc, SignHint,
ConservativeResult.intersectWith(X.truncate(BitWidth),
RangeType));
}
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
// If there's no unsigned wrap, the value will never be less than its
// initial value.
if (AddRec->hasNoUnsignedWrap()) {
APInt UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart());
if (!UnsignedMinValue.isNullValue())
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType);
}
// If there's no signed wrap, and all the operands except initial value have
// the same sign or zero, the value won't ever be:
// 1: smaller than initial value if operands are non negative,
// 2: bigger than initial value if operands are non positive.
// For both cases, value can not cross signed min/max boundary.
if (AddRec->hasNoSignedWrap()) {
bool AllNonNeg = true;
bool AllNonPos = true;
for (unsigned i = 1, e = AddRec->getNumOperands(); i != e; ++i) {
if (!isKnownNonNegative(AddRec->getOperand(i)))
AllNonNeg = false;
if (!isKnownNonPositive(AddRec->getOperand(i)))
AllNonPos = false;
}
if (AllNonNeg)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange::getNonEmpty(getSignedRangeMin(AddRec->getStart()),
APInt::getSignedMinValue(BitWidth)),
RangeType);
else if (AllNonPos)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange::getNonEmpty(
APInt::getSignedMinValue(BitWidth),
getSignedRangeMax(AddRec->getStart()) + 1),
RangeType);
}
// TODO: non-affine addrec
if (AddRec->isAffine()) {
const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(AddRec->getLoop());
if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
auto RangeFromAffine = getRangeForAffineAR(
AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
BitWidth);
if (!RangeFromAffine.isFullSet())
ConservativeResult =
ConservativeResult.intersectWith(RangeFromAffine, RangeType);
auto RangeFromFactoring = getRangeViaFactoring(
AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
BitWidth);
if (!RangeFromFactoring.isFullSet())
ConservativeResult =
ConservativeResult.intersectWith(RangeFromFactoring, RangeType);
}
}
return setRange(AddRec, SignHint, std::move(ConservativeResult));
}
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
// Check if the IR explicitly contains !range metadata.
Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
if (MDRange.hasValue())
ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue(),
RangeType);
// Split here to avoid paying the compile-time cost of calling both
// computeKnownBits and ComputeNumSignBits. This restriction can be lifted
// if needed.
const DataLayout &DL = getDataLayout();
if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
// For a SCEVUnknown, ask ValueTracking.
KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
if (Known.getBitWidth() != BitWidth)
Known = Known.zextOrTrunc(BitWidth);
// If Known does not result in full-set, intersect with it.
if (Known.getMinValue() != Known.getMaxValue() + 1)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1),
RangeType);
} else {
assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
"generalize as needed!");
unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
// If the pointer size is larger than the index size type, this can cause
// NS to be larger than BitWidth. So compensate for this.
if (U->getType()->isPointerTy()) {
unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType());
int ptrIdxDiff = ptrSize - BitWidth;
if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff)
NS -= ptrIdxDiff;
}
if (NS > 1)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1),
RangeType);
}
// A range of Phi is a subset of union of all ranges of its input.
if (const PHINode *Phi = dyn_cast<PHINode>(U->getValue())) {
// Make sure that we do not run over cycled Phis.
if (PendingPhiRanges.insert(Phi).second) {
ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
for (auto &Op : Phi->operands()) {
auto OpRange = getRangeRef(getSCEV(Op), SignHint);
RangeFromOps = RangeFromOps.unionWith(OpRange);
// No point to continue if we already have a full set.
if (RangeFromOps.isFullSet())
break;
}
ConservativeResult =
ConservativeResult.intersectWith(RangeFromOps, RangeType);
bool Erased = PendingPhiRanges.erase(Phi);
assert(Erased && "Failed to erase Phi properly?");
(void) Erased;
}
}
return setRange(U, SignHint, std::move(ConservativeResult));
}
return setRange(S, SignHint, std::move(ConservativeResult));
}
// Given a StartRange, Step and MaxBECount for an expression compute a range of
// values that the expression can take. Initially, the expression has a value
// from StartRange and then is changed by Step up to MaxBECount times. Signed
// argument defines if we treat Step as signed or unsigned.
static ConstantRange getRangeForAffineARHelper(APInt Step,
const ConstantRange &StartRange,
const APInt &MaxBECount,
unsigned BitWidth, bool Signed) {
// If either Step or MaxBECount is 0, then the expression won't change, and we
// just need to return the initial range.
if (Step == 0 || MaxBECount == 0)
return StartRange;
// If we don't know anything about the initial value (i.e. StartRange is
// FullRange), then we don't know anything about the final range either.
// Return FullRange.
if (StartRange.isFullSet())
return ConstantRange::getFull(BitWidth);
// If Step is signed and negative, then we use its absolute value, but we also
// note that we're moving in the opposite direction.
bool Descending = Signed && Step.isNegative();
if (Signed)
// This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
// abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
// This equations hold true due to the well-defined wrap-around behavior of
// APInt.
Step = Step.abs();
// Check if Offset is more than full span of BitWidth. If it is, the
// expression is guaranteed to overflow.
if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
return ConstantRange::getFull(BitWidth);
// Offset is by how much the expression can change. Checks above guarantee no
// overflow here.
APInt Offset = Step * MaxBECount;
// Minimum value of the final range will match the minimal value of StartRange
// if the expression is increasing and will be decreased by Offset otherwise.
// Maximum value of the final range will match the maximal value of StartRange
// if the expression is decreasing and will be increased by Offset otherwise.
APInt StartLower = StartRange.getLower();
APInt StartUpper = StartRange.getUpper() - 1;
APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
: (StartUpper + std::move(Offset));
// It's possible that the new minimum/maximum value will fall into the initial
// range (due to wrap around). This means that the expression can take any
// value in this bitwidth, and we have to return full range.
if (StartRange.contains(MovedBoundary))
return ConstantRange::getFull(BitWidth);
APInt NewLower =
Descending ? std::move(MovedBoundary) : std::move(StartLower);
APInt NewUpper =
Descending ? std::move(StartUpper) : std::move(MovedBoundary);
NewUpper += 1;
// No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
return ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper));
}
ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
const SCEV *Step,
const SCEV *MaxBECount,
unsigned BitWidth) {
assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
"Precondition!");
MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount);
// First, consider step signed.
ConstantRange StartSRange = getSignedRange(Start);
ConstantRange StepSRange = getSignedRange(Step);
// If Step can be both positive and negative, we need to find ranges for the
// maximum absolute step values in both directions and union them.
ConstantRange SR =
getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange,
MaxBECountValue, BitWidth, /* Signed = */ true);
SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(),
StartSRange, MaxBECountValue,
BitWidth, /* Signed = */ true));
// Next, consider step unsigned.
ConstantRange UR = getRangeForAffineARHelper(
getUnsignedRangeMax(Step), getUnsignedRange(Start),
MaxBECountValue, BitWidth, /* Signed = */ false);
// Finally, intersect signed and unsigned ranges.
return SR.intersectWith(UR, ConstantRange::Smallest);
}
ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
const SCEV *Step,
const SCEV *MaxBECount,
unsigned BitWidth) {
// RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
// == RangeOf({A,+,P}) union RangeOf({B,+,Q})
struct SelectPattern {
Value *Condition = nullptr;
APInt TrueValue;
APInt FalseValue;
explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
const SCEV *S) {
Optional<unsigned> CastOp;
APInt Offset(BitWidth, 0);
assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
"Should be!");
// Peel off a constant offset:
if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
// In the future we could consider being smarter here and handle
// {Start+Step,+,Step} too.
if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
return;
Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
S = SA->getOperand(1);
}
// Peel off a cast operation
if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
CastOp = SCast->getSCEVType();
S = SCast->getOperand();
}
using namespace llvm::PatternMatch;
auto *SU = dyn_cast<SCEVUnknown>(S);
const APInt *TrueVal, *FalseVal;
if (!SU ||
!match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
m_APInt(FalseVal)))) {
Condition = nullptr;
return;
}
TrueValue = *TrueVal;
FalseValue = *FalseVal;
// Re-apply the cast we peeled off earlier
if (CastOp.hasValue())
switch (*CastOp) {
default:
llvm_unreachable("Unknown SCEV cast type!");
case scTruncate:
TrueValue = TrueValue.trunc(BitWidth);
FalseValue = FalseValue.trunc(BitWidth);
break;
case scZeroExtend:
TrueValue = TrueValue.zext(BitWidth);
FalseValue = FalseValue.zext(BitWidth);
break;
case scSignExtend:
TrueValue = TrueValue.sext(BitWidth);
FalseValue = FalseValue.sext(BitWidth);
break;
}
// Re-apply the constant offset we peeled off earlier
TrueValue += Offset;
FalseValue += Offset;
}
bool isRecognized() { return Condition != nullptr; }
};
SelectPattern StartPattern(*this, BitWidth, Start);
if (!StartPattern.isRecognized())
return ConstantRange::getFull(BitWidth);
SelectPattern StepPattern(*this, BitWidth, Step);
if (!StepPattern.isRecognized())
return ConstantRange::getFull(BitWidth);
if (StartPattern.Condition != StepPattern.Condition) {
// We don't handle this case today; but we could, by considering four
// possibilities below instead of two. I'm not sure if there are cases where
// that will help over what getRange already does, though.
return ConstantRange::getFull(BitWidth);
}
// NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
// construct arbitrary general SCEV expressions here. This function is called
// from deep in the call stack, and calling getSCEV (on a sext instruction,
// say) can end up caching a suboptimal value.
// FIXME: without the explicit `this` receiver below, MSVC errors out with
// C2352 and C2512 (otherwise it isn't needed).
const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
ConstantRange TrueRange =
this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
ConstantRange FalseRange =
this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
return TrueRange.unionWith(FalseRange);
}
SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
const BinaryOperator *BinOp = cast<BinaryOperator>(V);
// Return early if there are no flags to propagate to the SCEV.
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (BinOp->hasNoUnsignedWrap())
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
if (BinOp->hasNoSignedWrap())
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
if (Flags == SCEV::FlagAnyWrap)
return SCEV::FlagAnyWrap;
return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
}
bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
// Here we check that I is in the header of the innermost loop containing I,
// since we only deal with instructions in the loop header. The actual loop we
// need to check later will come from an add recurrence, but getting that
// requires computing the SCEV of the operands, which can be expensive. This
// check we can do cheaply to rule out some cases early.
Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
if (InnermostContainingLoop == nullptr ||
InnermostContainingLoop->getHeader() != I->getParent())
return false;
// Only proceed if we can prove that I does not yield poison.
if (!programUndefinedIfFullPoison(I))
return false;
// At this point we know that if I is executed, then it does not wrap
// according to at least one of NSW or NUW. If I is not executed, then we do
// not know if the calculation that I represents would wrap. Multiple
// instructions can map to the same SCEV. If we apply NSW or NUW from I to
// the SCEV, we must guarantee no wrapping for that SCEV also when it is
// derived from other instructions that map to the same SCEV. We cannot make
// that guarantee for cases where I is not executed. So we need to find the
// loop that I is considered in relation to and prove that I is executed for
// every iteration of that loop. That implies that the value that I
// calculates does not wrap anywhere in the loop, so then we can apply the
// flags to the SCEV.
//
// We check isLoopInvariant to disambiguate in case we are adding recurrences
// from different loops, so that we know which loop to prove that I is
// executed in.
for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
// I could be an extractvalue from a call to an overflow intrinsic.
// TODO: We can do better here in some cases.
if (!isSCEVable(I->getOperand(OpIndex)->getType()))
return false;
const SCEV *Op = getSCEV(I->getOperand(OpIndex));
if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
bool AllOtherOpsLoopInvariant = true;
for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
++OtherOpIndex) {
if (OtherOpIndex != OpIndex) {
const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
AllOtherOpsLoopInvariant = false;
break;
}
}
}
if (AllOtherOpsLoopInvariant &&
isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
return true;
}
}
return false;
}
bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
// If we know that \c I can never be poison period, then that's enough.
if (isSCEVExprNeverPoison(I))
return true;
// For an add recurrence specifically, we assume that infinite loops without
// side effects are undefined behavior, and then reason as follows:
//
// If the add recurrence is poison in any iteration, it is poison on all
// future iterations (since incrementing poison yields poison). If the result
// of the add recurrence is fed into the loop latch condition and the loop
// does not contain any throws or exiting blocks other than the latch, we now
// have the ability to "choose" whether the backedge is taken or not (by
// choosing a sufficiently evil value for the poison feeding into the branch)
// for every iteration including and after the one in which \p I first became
// poison. There are two possibilities (let's call the iteration in which \p
// I first became poison as K):
//
// 1. In the set of iterations including and after K, the loop body executes
// no side effects. In this case executing the backege an infinte number
// of times will yield undefined behavior.
//
// 2. In the set of iterations including and after K, the loop body executes
// at least one side effect. In this case, that specific instance of side
// effect is control dependent on poison, which also yields undefined
// behavior.
auto *ExitingBB = L->getExitingBlock();
auto *LatchBB = L->getLoopLatch();
if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
return false;
SmallPtrSet<const Instruction *, 16> Pushed;
SmallVector<const Instruction *, 8> PoisonStack;
// We start by assuming \c I, the post-inc add recurrence, is poison. Only
// things that are known to be fully poison under that assumption go on the
// PoisonStack.
Pushed.insert(I);
PoisonStack.push_back(I);
bool LatchControlDependentOnPoison = false;
while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
const Instruction *Poison = PoisonStack.pop_back_val();
for (auto *PoisonUser : Poison->users()) {
if (propagatesFullPoison(cast<Instruction>(PoisonUser))) {
if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
PoisonStack.push_back(cast<Instruction>(PoisonUser));
} else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
assert(BI->isConditional() && "Only possibility!");
if (BI->getParent() == LatchBB) {
LatchControlDependentOnPoison = true;
break;
}
}
}
}
return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
}
ScalarEvolution::LoopProperties
ScalarEvolution::getLoopProperties(const Loop *L) {
using LoopProperties = ScalarEvolution::LoopProperties;
auto Itr = LoopPropertiesCache.find(L);
if (Itr == LoopPropertiesCache.end()) {
auto HasSideEffects = [](Instruction *I) {
if (auto *SI = dyn_cast<StoreInst>(I))
return !SI->isSimple();
return I->mayHaveSideEffects();
};
LoopProperties LP = {/* HasNoAbnormalExits */ true,
/*HasNoSideEffects*/ true};
for (auto *BB : L->getBlocks())
for (auto &I : *BB) {
if (!isGuaranteedToTransferExecutionToSuccessor(&I))
LP.HasNoAbnormalExits = false;
if (HasSideEffects(&I))
LP.HasNoSideEffects = false;
if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
break; // We're already as pessimistic as we can get.
}
auto InsertPair = LoopPropertiesCache.insert({L, LP});
assert(InsertPair.second && "We just checked!");
Itr = InsertPair.first;
}
return Itr->second;
}
const SCEV *ScalarEvolution::createSCEV(Value *V) {
if (!isSCEVable(V->getType()))
return getUnknown(V);
if (Instruction *I = dyn_cast<Instruction>(V)) {
// Don't attempt to analyze instructions in blocks that aren't
// reachable. Such instructions don't matter, and they aren't required
// to obey basic rules for definitions dominating uses which this
// analysis depends on.
if (!DT.isReachableFromEntry(I->getParent()))
return getUnknown(UndefValue::get(V->getType()));
} else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
return getConstant(CI);
else if (isa<ConstantPointerNull>(V))
return getZero(V->getType());
else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
else if (!isa<ConstantExpr>(V))
return getUnknown(V);
Operator *U = cast<Operator>(V);
if (auto BO = MatchBinaryOp(U, DT)) {
switch (BO->Opcode) {
case Instruction::Add: {
// The simple thing to do would be to just call getSCEV on both operands
// and call getAddExpr with the result. However if we're looking at a
// bunch of things all added together, this can be quite inefficient,
// because it leads to N-1 getAddExpr calls for N ultimate operands.
// Instead, gather up all the operands and make a single getAddExpr call.
// LLVM IR canonical form means we need only traverse the left operands.
SmallVector<const SCEV *, 4> AddOps;
do {
if (BO->Op) {
if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
AddOps.push_back(OpSCEV);
break;
}
// If a NUW or NSW flag can be applied to the SCEV for this
// addition, then compute the SCEV for this addition by itself
// with a separate call to getAddExpr. We need to do that
// instead of pushing the operands of the addition onto AddOps,
// since the flags are only known to apply to this particular
// addition - they may not apply to other additions that can be
// formed with operands from AddOps.
const SCEV *RHS = getSCEV(BO->RHS);
SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
if (Flags != SCEV::FlagAnyWrap) {
const SCEV *LHS = getSCEV(BO->LHS);
if (BO->Opcode == Instruction::Sub)
AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
else
AddOps.push_back(getAddExpr(LHS, RHS, Flags));
break;
}
}
if (BO->Opcode == Instruction::Sub)
AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
else
AddOps.push_back(getSCEV(BO->RHS));
auto NewBO = MatchBinaryOp(BO->LHS, DT);
if (!NewBO || (NewBO->Opcode != Instruction::Add &&
NewBO->Opcode != Instruction::Sub)) {
AddOps.push_back(getSCEV(BO->LHS));
break;
}
BO = NewBO;
} while (true);
return getAddExpr(AddOps);
}
case Instruction::Mul: {
SmallVector<const SCEV *, 4> MulOps;
do {
if (BO->Op) {
if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
MulOps.push_back(OpSCEV);
break;
}
SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
if (Flags != SCEV::FlagAnyWrap) {
MulOps.push_back(
getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
break;
}
}
MulOps.push_back(getSCEV(BO->RHS));
auto NewBO = MatchBinaryOp(BO->LHS, DT);
if (!NewBO || NewBO->Opcode != Instruction::Mul) {
MulOps.push_back(getSCEV(BO->LHS));
break;
}
BO = NewBO;
} while (true);
return getMulExpr(MulOps);
}
case Instruction::UDiv:
return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
case Instruction::URem:
return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
case Instruction::Sub: {
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (BO->Op)
Flags = getNoWrapFlagsFromUB(BO->Op);
return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
}
case Instruction::And:
// For an expression like x&255 that merely masks off the high bits,
// use zext(trunc(x)) as the SCEV expression.
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
if (CI->isZero())
return getSCEV(BO->RHS);
if (CI->isMinusOne())
return getSCEV(BO->LHS);
const APInt &A = CI->getValue();
// Instcombine's ShrinkDemandedConstant may strip bits out of
// constants, obscuring what would otherwise be a low-bits mask.
// Use computeKnownBits to compute what ShrinkDemandedConstant
// knew about to reconstruct a low-bits mask value.
unsigned LZ = A.countLeadingZeros();
unsigned TZ = A.countTrailingZeros();
unsigned BitWidth = A.getBitWidth();
KnownBits Known(BitWidth);
computeKnownBits(BO->LHS, Known, getDataLayout(),
0, &AC, nullptr, &DT);
APInt EffectiveMask =
APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ));
const SCEV *LHS = getSCEV(BO->LHS);
const SCEV *ShiftedLHS = nullptr;
if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) {
if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) {
// For an expression like (x * 8) & 8, simplify the multiply.
unsigned MulZeros = OpC->getAPInt().countTrailingZeros();
unsigned GCD = std::min(MulZeros, TZ);
APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD);
SmallVector<const SCEV*, 4> MulOps;
MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD)));
MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end());
auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags());
ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt));
}
}
if (!ShiftedLHS)
ShiftedLHS = getUDivExpr(LHS, MulCount);
return getMulExpr(
getZeroExtendExpr(
getTruncateExpr(ShiftedLHS,
IntegerType::get(getContext(), BitWidth - LZ - TZ)),
BO->LHS->getType()),
MulCount);
}
}
break;
case Instruction::Or:
// If the RHS of the Or is a constant, we may have something like:
// X*4+1 which got turned into X*4|1. Handle this as an Add so loop
// optimizations will transparently handle this case.
//
// In order for this transformation to be safe, the LHS must be of the
// form X*(2^n) and the Or constant must be less than 2^n.
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
const SCEV *LHS = getSCEV(BO->LHS);
const APInt &CIVal = CI->getValue();
if (GetMinTrailingZeros(LHS) >=
(CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
// Build a plain add SCEV.
const SCEV *S = getAddExpr(LHS, getSCEV(CI));
// If the LHS of the add was an addrec and it has no-wrap flags,
// transfer the no-wrap flags, since an or won't introduce a wrap.
if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
OldAR->getNoWrapFlags());
}
return S;
}
}
break;
case Instruction::Xor:
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
// If the RHS of xor is -1, then this is a not operation.
if (CI->isMinusOne())
return getNotSCEV(getSCEV(BO->LHS));
// Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
// This is a variant of the check for xor with -1, and it handles
// the case where instcombine has trimmed non-demanded bits out
// of an xor with -1.
if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
if (LBO->getOpcode() == Instruction::And &&
LCI->getValue() == CI->getValue())
if (const SCEVZeroExtendExpr *Z =
dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
Type *UTy = BO->LHS->getType();
const SCEV *Z0 = Z->getOperand();
Type *Z0Ty = Z0->getType();
unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
// If C is a low-bits mask, the zero extend is serving to
// mask off the high bits. Complement the operand and
// re-apply the zext.
if (CI->getValue().isMask(Z0TySize))
return getZeroExtendExpr(getNotSCEV(Z0), UTy);
// If C is a single bit, it may be in the sign-bit position
// before the zero-extend. In this case, represent the xor
// using an add, which is equivalent, and re-apply the zext.
APInt Trunc = CI->getValue().trunc(Z0TySize);
if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
Trunc.isSignMask())
return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
UTy);
}
}
break;
case Instruction::Shl:
// Turn shift left of a constant amount into a multiply.
if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
// If the shift count is not less than the bitwidth, the result of
// the shift is undefined. Don't try to analyze it, because the
// resolution chosen here may differ from the resolution chosen in
// other parts of the compiler.
if (SA->getValue().uge(BitWidth))
break;
// It is currently not resolved how to interpret NSW for left
// shift by BitWidth - 1, so we avoid applying flags in that
// case. Remove this check (or this comment) once the situation
// is resolved. See
// http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
// and http://reviews.llvm.org/D8890 .
auto Flags = SCEV::FlagAnyWrap;
if (BO->Op && SA->getValue().ult(BitWidth - 1))
Flags = getNoWrapFlagsFromUB(BO->Op);
Constant *X = ConstantInt::get(
getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
}
break;
case Instruction::AShr: {
// AShr X, C, where C is a constant.
ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS);
if (!CI)
break;
Type *OuterTy = BO->LHS->getType();
uint64_t BitWidth = getTypeSizeInBits(OuterTy);
// If the shift count is not less than the bitwidth, the result of
// the shift is undefined. Don't try to analyze it, because the
// resolution chosen here may differ from the resolution chosen in
// other parts of the compiler.
if (CI->getValue().uge(BitWidth))
break;
if (CI->isZero())
return getSCEV(BO->LHS); // shift by zero --> noop
uint64_t AShrAmt = CI->getZExtValue();
Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt);
Operator *L = dyn_cast<Operator>(BO->LHS);
if (L && L->getOpcode() == Instruction::Shl) {
// X = Shl A, n
// Y = AShr X, m
// Both n and m are constant.
const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0));
if (L->getOperand(1) == BO->RHS)
// For a two-shift sext-inreg, i.e. n = m,
// use sext(trunc(x)) as the SCEV expression.
return getSignExtendExpr(
getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy);
ConstantInt *ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1));
if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) {
uint64_t ShlAmt = ShlAmtCI->getZExtValue();
if (ShlAmt > AShrAmt) {
// When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
// expression. We already checked that ShlAmt < BitWidth, so
// the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
// ShlAmt - AShrAmt < Amt.
APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt,
ShlAmt - AShrAmt);
return getSignExtendExpr(
getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy),
getConstant(Mul)), OuterTy);
}
}
}
break;
}
}
}
switch (U->getOpcode()) {
case Instruction::Trunc:
return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
case Instruction::ZExt:
return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
case Instruction::SExt:
if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) {
// The NSW flag of a subtract does not always survive the conversion to
// A + (-1)*B. By pushing sign extension onto its operands we are much
// more likely to preserve NSW and allow later AddRec optimisations.
//
// NOTE: This is effectively duplicating this logic from getSignExtend:
// sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
// but by that point the NSW information has potentially been lost.
if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
Type *Ty = U->getType();
auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
return getMinusSCEV(V1, V2, SCEV::FlagNSW);
}
}
return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
case Instruction::BitCast:
// BitCasts are no-op casts so we just eliminate the cast.
if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
return getSCEV(U->getOperand(0));
break;
// It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
// lead to pointer expressions which cannot safely be expanded to GEPs,
// because ScalarEvolution doesn't respect the GEP aliasing rules when
// simplifying integer expressions.
case Instruction::GetElementPtr:
return createNodeForGEP(cast<GEPOperator>(U));
case Instruction::PHI:
return createNodeForPHI(cast<PHINode>(U));
case Instruction::Select:
// U can also be a select constant expr, which let fall through. Since
// createNodeForSelect only works for a condition that is an `ICmpInst`, and
// constant expressions cannot have instructions as operands, we'd have
// returned getUnknown for a select constant expressions anyway.
if (isa<Instruction>(U))
return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
U->getOperand(1), U->getOperand(2));
break;
case Instruction::Call:
case Instruction::Invoke:
if (Value *RV = CallSite(U).getReturnedArgOperand())
return getSCEV(RV);
break;
}
return getUnknown(V);
}
//===----------------------------------------------------------------------===//
// Iteration Count Computation Code
//
static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
if (!ExitCount)
return 0;
ConstantInt *ExitConst = ExitCount->getValue();
// Guard against huge trip counts.
if (ExitConst->getValue().getActiveBits() > 32)
return 0;
// In case of integer overflow, this returns 0, which is correct.
return ((unsigned)ExitConst->getZExtValue()) + 1;
}
unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
if (BasicBlock *ExitingBB = L->getExitingBlock())
return getSmallConstantTripCount(L, ExitingBB);
// No trip count information for multiple exits.
return 0;
}
unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L,
BasicBlock *ExitingBlock) {
assert(ExitingBlock && "Must pass a non-null exiting block!");
assert(L->isLoopExiting(ExitingBlock) &&
"Exiting block must actually branch out of the loop!");
const SCEVConstant *ExitCount =
dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
return getConstantTripCount(ExitCount);
}
unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) {
const auto *MaxExitCount =
dyn_cast<SCEVConstant>(getConstantMaxBackedgeTakenCount(L));
return getConstantTripCount(MaxExitCount);
}
unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
if (BasicBlock *ExitingBB = L->getExitingBlock())
return getSmallConstantTripMultiple(L, ExitingBB);
// No trip multiple information for multiple exits.
return 0;
}
/// Returns the largest constant divisor of the trip count of this loop as a
/// normal unsigned value, if possible. This means that the actual trip count is
/// always a multiple of the returned value (don't forget the trip count could
/// very well be zero as well!).
///
/// Returns 1 if the trip count is unknown or not guaranteed to be the
/// multiple of a constant (which is also the case if the trip count is simply
/// constant, use getSmallConstantTripCount for that case), Will also return 1
/// if the trip count is very large (>= 2^32).
///
/// As explained in the comments for getSmallConstantTripCount, this assumes
/// that control exits the loop via ExitingBlock.
unsigned
ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
BasicBlock *ExitingBlock) {
assert(ExitingBlock && "Must pass a non-null exiting block!");
assert(L->isLoopExiting(ExitingBlock) &&
"Exiting block must actually branch out of the loop!");
const SCEV *ExitCount = getExitCount(L, ExitingBlock);
if (ExitCount == getCouldNotCompute())
return 1;
// Get the trip count from the BE count by adding 1.
const SCEV *TCExpr = getAddExpr(ExitCount, getOne(ExitCount->getType()));
const SCEVConstant *TC = dyn_cast<SCEVConstant>(TCExpr);
if (!TC)
// Attempt to factor more general cases. Returns the greatest power of
// two divisor. If overflow happens, the trip count expression is still
// divisible by the greatest power of 2 divisor returned.
return 1U << std::min((uint32_t)31, GetMinTrailingZeros(TCExpr));
ConstantInt *Result = TC->getValue();
// Guard against huge trip counts (this requires checking
// for zero to handle the case where the trip count == -1 and the
// addition wraps).
if (!Result || Result->getValue().getActiveBits() > 32 ||
Result->getValue().getActiveBits() == 0)
return 1;
return (unsigned)Result->getZExtValue();
}
const SCEV *ScalarEvolution::getExitCount(const Loop *L,
BasicBlock *ExitingBlock,
ExitCountKind Kind) {
switch (Kind) {
case Exact:
return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
case ConstantMaximum:
return getBackedgeTakenInfo(L).getMax(ExitingBlock, this);
};
llvm_unreachable("Invalid ExitCountKind!");
}
const SCEV *
ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
SCEVUnionPredicate &Preds) {
return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds);
}
const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L,
ExitCountKind Kind) {
switch (Kind) {
case Exact:
return getBackedgeTakenInfo(L).getExact(L, this);
case ConstantMaximum:
return getBackedgeTakenInfo(L).getMax(this);
};
llvm_unreachable("Invalid ExitCountKind!");
}
bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
return getBackedgeTakenInfo(L).isMaxOrZero(this);
}
/// Push PHI nodes in the header of the given loop onto the given Worklist.
static void
PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
BasicBlock *Header = L->getHeader();
// Push all Loop-header PHIs onto the Worklist stack.
for (PHINode &PN : Header->phis())
Worklist.push_back(&PN);
}
const ScalarEvolution::BackedgeTakenInfo &
ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
auto &BTI = getBackedgeTakenInfo(L);
if (BTI.hasFullInfo())
return BTI;
auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
if (!Pair.second)
return Pair.first->second;
BackedgeTakenInfo Result =
computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
}
const ScalarEvolution::BackedgeTakenInfo &
ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
// Initially insert an invalid entry for this loop. If the insertion
// succeeds, proceed to actually compute a backedge-taken count and
// update the value. The temporary CouldNotCompute value tells SCEV
// code elsewhere that it shouldn't attempt to request a new
// backedge-taken count, which could result in infinite recursion.
std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
if (!Pair.second)
return Pair.first->second;
// computeBackedgeTakenCount may allocate memory for its result. Inserting it
// into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
// must be cleared in this scope.
BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
// In product build, there are no usage of statistic.
(void)NumTripCountsComputed;
(void)NumTripCountsNotComputed;
#if LLVM_ENABLE_STATS || !defined(NDEBUG)
const SCEV *BEExact = Result.getExact(L, this);
if (BEExact != getCouldNotCompute()) {
assert(isLoopInvariant(BEExact, L) &&
isLoopInvariant(Result.getMax(this), L) &&
"Computed backedge-taken count isn't loop invariant for loop!");
++NumTripCountsComputed;
}
else if (Result.getMax(this) == getCouldNotCompute() &&
isa<PHINode>(L->getHeader()->begin())) {
// Only count loops that have phi nodes as not being computable.
++NumTripCountsNotComputed;
}
#endif // LLVM_ENABLE_STATS || !defined(NDEBUG)
// Now that we know more about the trip count for this loop, forget any
// existing SCEV values for PHI nodes in this loop since they are only
// conservative estimates made without the benefit of trip count
// information. This is similar to the code in forgetLoop, except that
// it handles SCEVUnknown PHI nodes specially.
if (Result.hasAnyInfo()) {
SmallVector<Instruction *, 16> Worklist;
PushLoopPHIs(L, Worklist);
SmallPtrSet<Instruction *, 8> Discovered;
while (!Worklist.empty()) {
Instruction *I = Worklist.pop_back_val();
ValueExprMapType::iterator It =
ValueExprMap.find_as(static_cast<Value *>(I));
if (It != ValueExprMap.end()) {
const SCEV *Old = It->second;
// SCEVUnknown for a PHI either means that it has an unrecognized
// structure, or it's a PHI that's in the progress of being computed
// by createNodeForPHI. In the former case, additional loop trip
// count information isn't going to change anything. In the later
// case, createNodeForPHI will perform the necessary updates on its
// own when it gets to that point.
if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
eraseValueFromMap(It->first);
forgetMemoizedResults(Old);
}
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
// Since we don't need to invalidate anything for correctness and we're
// only invalidating to make SCEV's results more precise, we get to stop
// early to avoid invalidating too much. This is especially important in
// cases like:
//
// %v = f(pn0, pn1) // pn0 and pn1 used through some other phi node
// loop0:
// %pn0 = phi
// ...
// loop1:
// %pn1 = phi
// ...
//
// where both loop0 and loop1's backedge taken count uses the SCEV
// expression for %v. If we don't have the early stop below then in cases
// like the above, getBackedgeTakenInfo(loop1) will clear out the trip
// count for loop0 and getBackedgeTakenInfo(loop0) will clear out the trip
// count for loop1, effectively nullifying SCEV's trip count cache.
for (auto *U : I->users())
if (auto *I = dyn_cast<Instruction>(U)) {
auto *LoopForUser = LI.getLoopFor(I->getParent());
if (LoopForUser && L->contains(LoopForUser) &&
Discovered.insert(I).second)
Worklist.push_back(I);
}
}
}
// Re-lookup the insert position, since the call to
// computeBackedgeTakenCount above could result in a
// recusive call to getBackedgeTakenInfo (on a different
// loop), which would invalidate the iterator computed
// earlier.
return BackedgeTakenCounts.find(L)->second = std::move(Result);
}
void ScalarEvolution::forgetAllLoops() {
// This method is intended to forget all info about loops. It should
// invalidate caches as if the following happened:
// - The trip counts of all loops have changed arbitrarily
// - Every llvm::Value has been updated in place to produce a different
// result.
BackedgeTakenCounts.clear();
PredicatedBackedgeTakenCounts.clear();
LoopPropertiesCache.clear();
ConstantEvolutionLoopExitValue.clear();
ValueExprMap.clear();
ValuesAtScopes.clear();
LoopDispositions.clear();
BlockDispositions.clear();
UnsignedRanges.clear();
SignedRanges.clear();
ExprValueMap.clear();
HasRecMap.clear();
MinTrailingZerosCache.clear();
PredicatedSCEVRewrites.clear();
}
void ScalarEvolution::forgetLoop(const Loop *L) {
// Drop any stored trip count value.
auto RemoveLoopFromBackedgeMap =
[](DenseMap<const Loop *, BackedgeTakenInfo> &Map, const Loop *L) {
auto BTCPos = Map.find(L);
if (BTCPos != Map.end()) {
BTCPos->second.clear();
Map.erase(BTCPos);
}
};
SmallVector<const Loop *, 16> LoopWorklist(1, L);
SmallVector<Instruction *, 32> Worklist;
SmallPtrSet<Instruction *, 16> Visited;
// Iterate over all the loops and sub-loops to drop SCEV information.
while (!LoopWorklist.empty()) {
auto *CurrL = LoopWorklist.pop_back_val();
RemoveLoopFromBackedgeMap(BackedgeTakenCounts, CurrL);
RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts, CurrL);
// Drop information about predicated SCEV rewrites for this loop.
for (auto I = PredicatedSCEVRewrites.begin();
I != PredicatedSCEVRewrites.end();) {
std::pair<const SCEV *, const Loop *> Entry = I->first;
if (Entry.second == CurrL)
PredicatedSCEVRewrites.erase(I++);
else
++I;
}
auto LoopUsersItr = LoopUsers.find(CurrL);
if (LoopUsersItr != LoopUsers.end()) {
for (auto *S : LoopUsersItr->second)
forgetMemoizedResults(S);
LoopUsers.erase(LoopUsersItr);
}
// Drop information about expressions based on loop-header PHIs.
PushLoopPHIs(CurrL, Worklist);
while (!Worklist.empty()) {
Instruction *I = Worklist.pop_back_val();
if (!Visited.insert(I).second)
continue;
ValueExprMapType::iterator It =
ValueExprMap.find_as(static_cast<Value *>(I));
if (It != ValueExprMap.end()) {
eraseValueFromMap(It->first);
forgetMemoizedResults(It->second);
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
PushDefUseChildren(I, Worklist);
}
LoopPropertiesCache.erase(CurrL);
// Forget all contained loops too, to avoid dangling entries in the
// ValuesAtScopes map.
LoopWorklist.append(CurrL->begin(), CurrL->end());
}
}
void ScalarEvolution::forgetTopmostLoop(const Loop *L) {
while (Loop *Parent = L->getParentLoop())
L = Parent;
forgetLoop(L);
}
void ScalarEvolution::forgetValue(Value *V) {
Instruction *I = dyn_cast<Instruction>(V);
if (!I) return;
// Drop information about expressions based on loop-header PHIs.
SmallVector<Instruction *, 16> Worklist;
Worklist.push_back(I);
SmallPtrSet<Instruction *, 8> Visited;
while (!Worklist.empty()) {
I = Worklist.pop_back_val();
if (!Visited.insert(I).second)
continue;
ValueExprMapType::iterator It =
ValueExprMap.find_as(static_cast<Value *>(I));
if (It != ValueExprMap.end()) {
eraseValueFromMap(It->first);
forgetMemoizedResults(It->second);
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
PushDefUseChildren(I, Worklist);
}
}
/// Get the exact loop backedge taken count considering all loop exits. A
/// computable result can only be returned for loops with all exiting blocks
/// dominating the latch. howFarToZero assumes that the limit of each loop test
/// is never skipped. This is a valid assumption as long as the loop exits via
/// that test. For precise results, it is the caller's responsibility to specify
/// the relevant loop exiting block using getExact(ExitingBlock, SE).
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getExact(const Loop *L, ScalarEvolution *SE,
SCEVUnionPredicate *Preds) const {
// If any exits were not computable, the loop is not computable.
if (!isComplete() || ExitNotTaken.empty())
return SE->getCouldNotCompute();
const BasicBlock *Latch = L->getLoopLatch();
// All exiting blocks we have collected must dominate the only backedge.
if (!Latch)
return SE->getCouldNotCompute();
// All exiting blocks we have gathered dominate loop's latch, so exact trip
// count is simply a minimum out of all these calculated exit counts.
SmallVector<const SCEV *, 2> Ops;
for (auto &ENT : ExitNotTaken) {
const SCEV *BECount = ENT.ExactNotTaken;
assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!");
assert(SE->DT.dominates(ENT.ExitingBlock, Latch) &&
"We should only have known counts for exiting blocks that dominate "
"latch!");
Ops.push_back(BECount);
if (Preds && !ENT.hasAlwaysTruePredicate())
Preds->add(ENT.Predicate.get());
assert((Preds || ENT.hasAlwaysTruePredicate()) &&
"Predicate should be always true!");
}
return SE->getUMinFromMismatchedTypes(Ops);
}
/// Get the exact not taken count for this loop exit.
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
ScalarEvolution *SE) const {
for (auto &ENT : ExitNotTaken)
if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
return ENT.ExactNotTaken;
return SE->getCouldNotCompute();
}
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getMax(BasicBlock *ExitingBlock,
ScalarEvolution *SE) const {
for (auto &ENT : ExitNotTaken)
if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
return ENT.MaxNotTaken;
return SE->getCouldNotCompute();
}
/// getMax - Get the max backedge taken count for the loop.
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
return !ENT.hasAlwaysTruePredicate();
};
if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax())
return SE->getCouldNotCompute();
assert((isa<SCEVCouldNotCompute>(getMax()) || isa<SCEVConstant>(getMax())) &&
"No point in having a non-constant max backedge taken count!");
return getMax();
}
bool ScalarEvolution::BackedgeTakenInfo::isMaxOrZero(ScalarEvolution *SE) const {
auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
return !ENT.hasAlwaysTruePredicate();
};
return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
}
bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
ScalarEvolution *SE) const {
if (getMax() && getMax() != SE->getCouldNotCompute() &&
SE->hasOperand(getMax(), S))
return true;
for (auto &ENT : ExitNotTaken)
if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
SE->hasOperand(ENT.ExactNotTaken, S))
return true;
return false;
}
ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
: ExactNotTaken(E), MaxNotTaken(E) {
assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
isa<SCEVConstant>(MaxNotTaken)) &&
"No point in having a non-constant max backedge taken count!");
}
ScalarEvolution::ExitLimit::ExitLimit(
const SCEV *E, const SCEV *M, bool MaxOrZero,
ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList)
: ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) {
assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
!isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
"Exact is not allowed to be less precise than Max");
assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
isa<SCEVConstant>(MaxNotTaken)) &&
"No point in having a non-constant max backedge taken count!");
for (auto *PredSet : PredSetList)
for (auto *P : *PredSet)
addPredicate(P);
}
ScalarEvolution::ExitLimit::ExitLimit(
const SCEV *E, const SCEV *M, bool MaxOrZero,
const SmallPtrSetImpl<const SCEVPredicate *> &PredSet)
: ExitLimit(E, M, MaxOrZero, {&PredSet}) {
assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
isa<SCEVConstant>(MaxNotTaken)) &&
"No point in having a non-constant max backedge taken count!");
}
ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M,
bool MaxOrZero)
: ExitLimit(E, M, MaxOrZero, None) {
assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
isa<SCEVConstant>(MaxNotTaken)) &&
"No point in having a non-constant max backedge taken count!");
}
/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
/// computable exit into a persistent ExitNotTakenInfo array.
ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo>
ExitCounts,
bool Complete, const SCEV *MaxCount, bool MaxOrZero)
: MaxAndComplete(MaxCount, Complete), MaxOrZero(MaxOrZero) {
using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
ExitNotTaken.reserve(ExitCounts.size());
std::transform(
ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken),
[&](const EdgeExitInfo &EEI) {
BasicBlock *ExitBB = EEI.first;
const ExitLimit &EL = EEI.second;
if (EL.Predicates.empty())
return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
nullptr);
std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate);
for (auto *Pred : EL.Predicates)
Predicate->add(Pred);
return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
std::move(Predicate));
});
assert((isa<SCEVCouldNotCompute>(MaxCount) || isa<SCEVConstant>(MaxCount)) &&
"No point in having a non-constant max backedge taken count!");
}
/// Invalidate this result and free the ExitNotTakenInfo array.
void ScalarEvolution::BackedgeTakenInfo::clear() {
ExitNotTaken.clear();
}
/// Compute the number of times the backedge of the specified loop will execute.
ScalarEvolution::BackedgeTakenInfo
ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
bool AllowPredicates) {
SmallVector<BasicBlock *, 8> ExitingBlocks;
L->getExitingBlocks(ExitingBlocks);
using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
SmallVector<EdgeExitInfo, 4> ExitCounts;
bool CouldComputeBECount = true;
BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
const SCEV *MustExitMaxBECount = nullptr;
const SCEV *MayExitMaxBECount = nullptr;
bool MustExitMaxOrZero = false;
// Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
// and compute maxBECount.
// Do a union of all the predicates here.
for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
BasicBlock *ExitBB = ExitingBlocks[i];
// We canonicalize untaken exits to br (constant), ignore them so that
// proving an exit untaken doesn't negatively impact our ability to reason
// about the loop as whole.
if (auto *BI = dyn_cast<BranchInst>(ExitBB->getTerminator()))
if (auto *CI = dyn_cast<ConstantInt>(BI->getCondition())) {
bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
if ((ExitIfTrue && CI->isZero()) || (!ExitIfTrue && CI->isOne()))
continue;
}
ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
assert((AllowPredicates || EL.Predicates.empty()) &&
"Predicated exit limit when predicates are not allowed!");
// 1. For each exit that can be computed, add an entry to ExitCounts.
// CouldComputeBECount is true only if all exits can be computed.
if (EL.ExactNotTaken == getCouldNotCompute())
// We couldn't compute an exact value for this exit, so
// we won't be able to compute an exact value for the loop.
CouldComputeBECount = false;
else
ExitCounts.emplace_back(ExitBB, EL);
// 2. Derive the loop's MaxBECount from each exit's max number of
// non-exiting iterations. Partition the loop exits into two kinds:
// LoopMustExits and LoopMayExits.
//
// If the exit dominates the loop latch, it is a LoopMustExit otherwise it
// is a LoopMayExit. If any computable LoopMustExit is found, then
// MaxBECount is the minimum EL.MaxNotTaken of computable
// LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
// EL.MaxNotTaken, where CouldNotCompute is considered greater than any
// computable EL.MaxNotTaken.
if (EL.MaxNotTaken != getCouldNotCompute() && Latch &&
DT.dominates(ExitBB, Latch)) {
if (!MustExitMaxBECount) {
MustExitMaxBECount = EL.MaxNotTaken;
MustExitMaxOrZero = EL.MaxOrZero;
} else {
MustExitMaxBECount =
getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken);
}
} else if (MayExitMaxBECount != getCouldNotCompute()) {
if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute())
MayExitMaxBECount = EL.MaxNotTaken;
else {
MayExitMaxBECount =
getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken);
}
}
}
const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
(MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
// The loop backedge will be taken the maximum or zero times if there's
// a single exit that must be taken the maximum or zero times.
bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
MaxBECount, MaxOrZero);
}
ScalarEvolution::ExitLimit
ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
bool AllowPredicates) {
assert(L->contains(ExitingBlock) && "Exit count for non-loop block?");
// If our exiting block does not dominate the latch, then its connection with
// loop's exit limit may be far from trivial.
const BasicBlock *Latch = L->getLoopLatch();
if (!Latch || !DT.dominates(ExitingBlock, Latch))
return getCouldNotCompute();
bool IsOnlyExit = (L->getExitingBlock() != nullptr);
Instruction *Term = ExitingBlock->getTerminator();
if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
assert(BI->isConditional() && "If unconditional, it can't be in loop!");
bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) &&
"It should have one successor in loop and one exit block!");
// Proceed to the next level to examine the exit condition expression.
return computeExitLimitFromCond(
L, BI->getCondition(), ExitIfTrue,
/*ControlsExit=*/IsOnlyExit, AllowPredicates);
}
if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) {
// For switch, make sure that there is a single exit from the loop.
BasicBlock *Exit = nullptr;
for (auto *SBB : successors(ExitingBlock))
if (!L->contains(SBB)) {
if (Exit) // Multiple exit successors.
return getCouldNotCompute();
Exit = SBB;
}
assert(Exit && "Exiting block must have at least one exit");
return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
/*ControlsExit=*/IsOnlyExit);
}
return getCouldNotCompute();
}
ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
const Loop *L, Value *ExitCond, bool ExitIfTrue,
bool ControlsExit, bool AllowPredicates) {
ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates);
return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue,
ControlsExit, AllowPredicates);
}
Optional<ScalarEvolution::ExitLimit>
ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
bool ExitIfTrue, bool ControlsExit,
bool AllowPredicates) {
(void)this->L;
(void)this->ExitIfTrue;
(void)this->AllowPredicates;
assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
this->AllowPredicates == AllowPredicates &&
"Variance in assumed invariant key components!");
auto Itr = TripCountMap.find({ExitCond, ControlsExit});
if (Itr == TripCountMap.end())
return None;
return Itr->second;
}
void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
bool ExitIfTrue,
bool ControlsExit,
bool AllowPredicates,
const ExitLimit &EL) {
assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
this->AllowPredicates == AllowPredicates &&
"Variance in assumed invariant key components!");
auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL});
assert(InsertResult.second && "Expected successful insertion!");
(void)InsertResult;
(void)ExitIfTrue;
}
ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
bool ControlsExit, bool AllowPredicates) {
if (auto MaybeEL =
Cache.find(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates))
return *MaybeEL;
ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, ExitIfTrue,
ControlsExit, AllowPredicates);
Cache.insert(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates, EL);
return EL;
}
ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
bool ControlsExit, bool AllowPredicates) {
// Check if the controlling expression for this loop is an And or Or.
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
if (BO->getOpcode() == Instruction::And) {
// Recurse on the operands of the and.
bool EitherMayExit = !ExitIfTrue;
ExitLimit EL0 = computeExitLimitFromCondCached(
Cache, L, BO->getOperand(0), ExitIfTrue,
ControlsExit && !EitherMayExit, AllowPredicates);
ExitLimit EL1 = computeExitLimitFromCondCached(
Cache, L, BO->getOperand(1), ExitIfTrue,
ControlsExit && !EitherMayExit, AllowPredicates);
// Be robust against unsimplified IR for the form "and i1 X, true"
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(1)))
return CI->isOne() ? EL0 : EL1;
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(0)))
return CI->isOne() ? EL1 : EL0;
const SCEV *BECount = getCouldNotCompute();
const SCEV *MaxBECount = getCouldNotCompute();
if (EitherMayExit) {
// Both conditions must be true for the loop to continue executing.
// Choose the less conservative count.
if (EL0.ExactNotTaken == getCouldNotCompute() ||
EL1.ExactNotTaken == getCouldNotCompute())
BECount = getCouldNotCompute();
else
BECount =
getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
if (EL0.MaxNotTaken == getCouldNotCompute())
MaxBECount = EL1.MaxNotTaken;
else if (EL1.MaxNotTaken == getCouldNotCompute())
MaxBECount = EL0.MaxNotTaken;
else
MaxBECount =
getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
} else {
// Both conditions must be true at the same time for the loop to exit.
// For now, be conservative.
if (EL0.MaxNotTaken == EL1.MaxNotTaken)
MaxBECount = EL0.MaxNotTaken;
if (EL0.ExactNotTaken == EL1.ExactNotTaken)
BECount = EL0.ExactNotTaken;
}
// There are cases (e.g. PR26207) where computeExitLimitFromCond is able
// to be more aggressive when computing BECount than when computing
// MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
// EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
// to not.
if (isa<SCEVCouldNotCompute>(MaxBECount) &&
!isa<SCEVCouldNotCompute>(BECount))
MaxBECount = getConstant(getUnsignedRangeMax(BECount));
return ExitLimit(BECount, MaxBECount, false,
{&EL0.Predicates, &EL1.Predicates});
}
if (BO->getOpcode() == Instruction::Or) {
// Recurse on the operands of the or.
bool EitherMayExit = ExitIfTrue;
ExitLimit EL0 = computeExitLimitFromCondCached(
Cache, L, BO->getOperand(0), ExitIfTrue,
ControlsExit && !EitherMayExit, AllowPredicates);
ExitLimit EL1 = computeExitLimitFromCondCached(
Cache, L, BO->getOperand(1), ExitIfTrue,
ControlsExit && !EitherMayExit, AllowPredicates);
// Be robust against unsimplified IR for the form "or i1 X, true"
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(1)))
return CI->isZero() ? EL0 : EL1;
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(0)))
return CI->isZero() ? EL1 : EL0;
const SCEV *BECount = getCouldNotCompute();
const SCEV *MaxBECount = getCouldNotCompute();
if (EitherMayExit) {
// Both conditions must be false for the loop to continue executing.
// Choose the less conservative count.
if (EL0.ExactNotTaken == getCouldNotCompute() ||
EL1.ExactNotTaken == getCouldNotCompute())
BECount = getCouldNotCompute();
else
BECount =
getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
if (EL0.MaxNotTaken == getCouldNotCompute())
MaxBECount = EL1.MaxNotTaken;
else if (EL1.MaxNotTaken == getCouldNotCompute())
MaxBECount = EL0.MaxNotTaken;
else
MaxBECount =
getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
} else {
// Both conditions must be false at the same time for the loop to exit.
// For now, be conservative.
if (EL0.MaxNotTaken == EL1.MaxNotTaken)
MaxBECount = EL0.MaxNotTaken;
if (EL0.ExactNotTaken == EL1.ExactNotTaken)
BECount = EL0.ExactNotTaken;
}
// There are cases (e.g. PR26207) where computeExitLimitFromCond is able
// to be more aggressive when computing BECount than when computing
// MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
// EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
// to not.
if (isa<SCEVCouldNotCompute>(MaxBECount) &&
!isa<SCEVCouldNotCompute>(BECount))
MaxBECount = getConstant(getUnsignedRangeMax(BECount));
return ExitLimit(BECount, MaxBECount, false,
{&EL0.Predicates, &EL1.Predicates});
}
}
// With an icmp, it may be feasible to compute an exact backedge-taken count.
// Proceed to the next level to examine the icmp.
if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
ExitLimit EL =
computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit);
if (EL.hasFullInfo() || !AllowPredicates)
return EL;
// Try again, but use SCEV predicates this time.
return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit,
/*AllowPredicates=*/true);
}
// Check for a constant condition. These are normally stripped out by
// SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
// preserve the CFG and is temporarily leaving constant conditions
// in place.
if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
if (ExitIfTrue == !CI->getZExtValue())
// The backedge is always taken.
return getCouldNotCompute();
else
// The backedge is never taken.
return getZero(CI->getType());
}
// If it's not an integer or pointer comparison then compute it the hard way.
return computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
}
ScalarEvolution::ExitLimit
ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
ICmpInst *ExitCond,
bool ExitIfTrue,
bool ControlsExit,
bool AllowPredicates) {
// If the condition was exit on true, convert the condition to exit on false
ICmpInst::Predicate Pred;
if (!ExitIfTrue)
Pred = ExitCond->getPredicate();
else
Pred = ExitCond->getInversePredicate();
const ICmpInst::Predicate OriginalPred = Pred;
// Handle common loops like: for (X = "string"; *X; ++X)
if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
ExitLimit ItCnt =
computeLoadConstantCompareExitLimit(LI, RHS, L, Pred);
if (ItCnt.hasAnyInfo())
return ItCnt;
}
const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
// Try to evaluate any dependencies out of the loop.
LHS = getSCEVAtScope(LHS, L);
RHS = getSCEVAtScope(RHS, L);
// At this point, we would like to compute how many iterations of the
// loop the predicate will return true for these inputs.
if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
// If there is a loop-invariant, force it into the RHS.
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
}
// Simplify the operands before analyzing them.
(void)SimplifyICmpOperands(Pred, LHS, RHS);
// If we have a comparison of a chrec against a constant, try to use value
// ranges to answer this query.
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
if (AddRec->getLoop() == L) {
// Form the constant range.
ConstantRange CompRange =
ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt());
const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
}
switch (Pred) {
case ICmpInst::ICMP_NE: { // while (X != Y)
// Convert to: while (X-Y != 0)
ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
AllowPredicates);
if (EL.hasAnyInfo()) return EL;
break;
}
case ICmpInst::ICMP_EQ: { // while (X == Y)
// Convert to: while (X-Y == 0)
ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
if (EL.hasAnyInfo()) return EL;
break;
}
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_ULT: { // while (X < Y)
bool IsSigned = Pred == ICmpInst::ICMP_SLT;
ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
AllowPredicates);
if (EL.hasAnyInfo()) return EL;
break;
}
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_UGT: { // while (X > Y)
bool IsSigned = Pred == ICmpInst::ICMP_SGT;
ExitLimit EL =
howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
AllowPredicates);
if (EL.hasAnyInfo()) return EL;
break;
}
default:
break;
}
auto *ExhaustiveCount =
computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
return ExhaustiveCount;
return computeShiftCompareExitLimit(ExitCond->getOperand(0),
ExitCond->getOperand(1), L, OriginalPred);
}
ScalarEvolution::ExitLimit
ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
SwitchInst *Switch,
BasicBlock *ExitingBlock,
bool ControlsExit) {
assert(!L->contains(ExitingBlock) && "Not an exiting block!");
// Give up if the exit is the default dest of a switch.
if (Switch->getDefaultDest() == ExitingBlock)
return getCouldNotCompute();
assert(L->contains(Switch->getDefaultDest()) &&
"Default case must not exit the loop!");
const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
// while (X != Y) --> while (X-Y != 0)
ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
if (EL.hasAnyInfo())
return EL;
return getCouldNotCompute();
}
static ConstantInt *
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
ScalarEvolution &SE) {
const SCEV *InVal = SE.getConstant(C);
const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
assert(isa<SCEVConstant>(Val) &&
"Evaluation of SCEV at constant didn't fold correctly?");
return cast<SCEVConstant>(Val)->getValue();
}
/// Given an exit condition of 'icmp op load X, cst', try to see if we can
/// compute the backedge execution count.
ScalarEvolution::ExitLimit
ScalarEvolution::computeLoadConstantCompareExitLimit(
LoadInst *LI,
Constant *RHS,
const Loop *L,
ICmpInst::Predicate predicate) {
if (LI->isVolatile()) return getCouldNotCompute();
// Check to see if the loaded pointer is a getelementptr of a global.
// TODO: Use SCEV instead of manually grubbing with GEPs.
GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
if (!GEP) return getCouldNotCompute();
// Make sure that it is really a constant global we are gepping, with an
// initializer, and make sure the first IDX is really 0.
GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
!cast<Constant>(GEP->getOperand(1))->isNullValue())
return getCouldNotCompute();
// Okay, we allow one non-constant index into the GEP instruction.
Value *VarIdx = nullptr;
std::vector<Constant*> Indexes;
unsigned VarIdxNum = 0;
for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
Indexes.push_back(CI);
} else if (!isa<ConstantInt>(GEP->getOperand(i))) {
if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
VarIdx = GEP->getOperand(i);
VarIdxNum = i-2;
Indexes.push_back(nullptr);
}
// Loop-invariant loads may be a byproduct of loop optimization. Skip them.
if (!VarIdx)
return getCouldNotCompute();
// Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
// Check to see if X is a loop variant variable value now.
const SCEV *Idx = getSCEV(VarIdx);
Idx = getSCEVAtScope(Idx, L);
// We can only recognize very limited forms of loop index expressions, in
// particular, only affine AddRec's like {C1,+,C2}.
const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
!isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
!isa<SCEVConstant>(IdxExpr->getOperand(1)))
return getCouldNotCompute();
unsigned MaxSteps = MaxBruteForceIterations;
for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
ConstantInt *ItCst = ConstantInt::get(
cast<IntegerType>(IdxExpr->getType()), IterationNum);
ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
// Form the GEP offset.
Indexes[VarIdxNum] = Val;
Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
Indexes);
if (!Result) break; // Cannot compute!
// Evaluate the condition for this iteration.
Result = ConstantExpr::getICmp(predicate, Result, RHS);
if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
++NumArrayLenItCounts;
return getConstant(ItCst); // Found terminating iteration!
}
}
return getCouldNotCompute();
}
ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
if (!RHS)
return getCouldNotCompute();
const BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
return getCouldNotCompute();
const BasicBlock *Predecessor = L->getLoopPredecessor();
if (!Predecessor)
return getCouldNotCompute();
// Return true if V is of the form "LHS `shift_op` <positive constant>".
// Return LHS in OutLHS and shift_opt in OutOpCode.
auto MatchPositiveShift =
[](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
using namespace PatternMatch;
ConstantInt *ShiftAmt;
if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
OutOpCode = Instruction::LShr;
else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
OutOpCode = Instruction::AShr;
else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
OutOpCode = Instruction::Shl;
else
return false;
return ShiftAmt->getValue().isStrictlyPositive();
};
// Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
//
// loop:
// %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
// %iv.shifted = lshr i32 %iv, <positive constant>
//
// Return true on a successful match. Return the corresponding PHI node (%iv
// above) in PNOut and the opcode of the shift operation in OpCodeOut.
auto MatchShiftRecurrence =
[&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
Optional<Instruction::BinaryOps> PostShiftOpCode;
{
Instruction::BinaryOps OpC;
Value *V;
// If we encounter a shift instruction, "peel off" the shift operation,
// and remember that we did so. Later when we inspect %iv's backedge
// value, we will make sure that the backedge value uses the same
// operation.
//
// Note: the peeled shift operation does not have to be the same
// instruction as the one feeding into the PHI's backedge value. We only
// really care about it being the same *kind* of shift instruction --
// that's all that is required for our later inferences to hold.
if (MatchPositiveShift(LHS, V, OpC)) {
PostShiftOpCode = OpC;
LHS = V;
}
}
PNOut = dyn_cast<PHINode>(LHS);
if (!PNOut || PNOut->getParent() != L->getHeader())
return false;
Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
Value *OpLHS;
return
// The backedge value for the PHI node must be a shift by a positive
// amount
MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
// of the PHI node itself
OpLHS == PNOut &&
// and the kind of shift should be match the kind of shift we peeled
// off, if any.
(!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
};
PHINode *PN;
Instruction::BinaryOps OpCode;
if (!MatchShiftRecurrence(LHS, PN, OpCode))
return getCouldNotCompute();
const DataLayout &DL = getDataLayout();
// The key rationale for this optimization is that for some kinds of shift
// recurrences, the value of the recurrence "stabilizes" to either 0 or -1
// within a finite number of iterations. If the condition guarding the
// backedge (in the sense that the backedge is taken if the condition is true)
// is false for the value the shift recurrence stabilizes to, then we know
// that the backedge is taken only a finite number of times.
ConstantInt *StableValue = nullptr;
switch (OpCode) {
default:
llvm_unreachable("Impossible case!");
case Instruction::AShr: {
// {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
// bitwidth(K) iterations.
Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
KnownBits Known = computeKnownBits(FirstValue, DL, 0, nullptr,
Predecessor->getTerminator(), &DT);
auto *Ty = cast<IntegerType>(RHS->getType());
if (Known.isNonNegative())
StableValue = ConstantInt::get(Ty, 0);
else if (Known.isNegative())
StableValue = ConstantInt::get(Ty, -1, true);
else
return getCouldNotCompute();
break;
}
case Instruction::LShr:
case Instruction::Shl:
// Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
// stabilize to 0 in at most bitwidth(K) iterations.
StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
break;
}
auto *Result =
ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
assert(Result->getType()->isIntegerTy(1) &&
"Otherwise cannot be an operand to a branch instruction");
if (Result->isZeroValue()) {
unsigned BitWidth = getTypeSizeInBits(RHS->getType());
const SCEV *UpperBound =
getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
return ExitLimit(getCouldNotCompute(), UpperBound, false);
}
return getCouldNotCompute();
}
/// Return true if we can constant fold an instruction of the specified type,
/// assuming that all operands were constants.
static bool CanConstantFold(const Instruction *I) {
if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
isa<LoadInst>(I) || isa<ExtractValueInst>(I))
return true;
if (const CallInst *CI = dyn_cast<CallInst>(I))
if (const Function *F = CI->getCalledFunction())
return canConstantFoldCallTo(CI, F);
return false;
}
/// Determine whether this instruction can constant evolve within this loop
/// assuming its operands can all constant evolve.
static bool canConstantEvolve(Instruction *I, const Loop *L) {
// An instruction outside of the loop can't be derived from a loop PHI.
if (!L->contains(I)) return false;
if (isa<PHINode>(I)) {
// We don't currently keep track of the control flow needed to evaluate
// PHIs, so we cannot handle PHIs inside of loops.
return L->getHeader() == I->getParent();
}
// If we won't be able to constant fold this expression even if the operands
// are constants, bail early.
return CanConstantFold(I);
}
/// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
/// recursing through each instruction operand until reaching a loop header phi.
static PHINode *
getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
DenseMap<Instruction *, PHINode *> &PHIMap,
unsigned Depth) {
if (Depth > MaxConstantEvolvingDepth)
return nullptr;
// Otherwise, we can evaluate this instruction if all of its operands are
// constant or derived from a PHI node themselves.
PHINode *PHI = nullptr;
for (Value *Op : UseInst->operands()) {
if (isa<Constant>(Op)) continue;
Instruction *OpInst = dyn_cast<Instruction>(Op);
if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
PHINode *P = dyn_cast<PHINode>(OpInst);
if (!P)
// If this operand is already visited, reuse the prior result.
// We may have P != PHI if this is the deepest point at which the
// inconsistent paths meet.
P = PHIMap.lookup(OpInst);
if (!P) {
// Recurse and memoize the results, whether a phi is found or not.
// This recursive call invalidates pointers into PHIMap.
P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1);
PHIMap[OpInst] = P;
}
if (!P)
return nullptr; // Not evolving from PHI
if (PHI && PHI != P)
return nullptr; // Evolving from multiple different PHIs.
PHI = P;
}
// This is a expression evolving from a constant PHI!
return PHI;
}
/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
/// in the loop that V is derived from. We allow arbitrary operations along the
/// way, but the operands of an operation must either be constants or a value
/// derived from a constant PHI. If this expression does not fit with these
/// constraints, return null.
static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
Instruction *I = dyn_cast<Instruction>(V);
if (!I || !canConstantEvolve(I, L)) return nullptr;
if (PHINode *PN = dyn_cast<PHINode>(I))
return PN;
// Record non-constant instructions contained by the loop.
DenseMap<Instruction *, PHINode *> PHIMap;
return getConstantEvolvingPHIOperands(I, L, PHIMap, 0);
}
/// EvaluateExpression - Given an expression that passes the
/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
/// in the loop has the value PHIVal. If we can't fold this expression for some
/// reason, return null.
static Constant *EvaluateExpression(Value *V, const Loop *L,
DenseMap<Instruction *, Constant *> &Vals,
const DataLayout &DL,
const TargetLibraryInfo *TLI) {
// Convenient constant check, but redundant for recursive calls.
if (Constant *C = dyn_cast<Constant>(V)) return C;
Instruction *I = dyn_cast<Instruction>(V);
if (!I) return nullptr;
if (Constant *C = Vals.lookup(I)) return C;
// An instruction inside the loop depends on a value outside the loop that we
// weren't given a mapping for, or a value such as a call inside the loop.
if (!canConstantEvolve(I, L)) return nullptr;
// An unmapped PHI can be due to a branch or another loop inside this loop,
// or due to this not being the initial iteration through a loop where we
// couldn't compute the evolution of this particular PHI last time.
if (isa<PHINode>(I)) return nullptr;
std::vector<Constant*> Operands(I->getNumOperands());
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
if (!Operand) {
Operands[i] = dyn_cast<Constant>(I->getOperand(i));
if (!Operands[i]) return nullptr;
continue;
}
Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
Vals[Operand] = C;
if (!C) return nullptr;
Operands[i] = C;
}
if (CmpInst *CI = dyn_cast<CmpInst>(I))
return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
Operands[1], DL, TLI);
if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
if (!LI->isVolatile())
return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
}
return ConstantFoldInstOperands(I, Operands, DL, TLI);
}
// If every incoming value to PN except the one for BB is a specific Constant,
// return that, else return nullptr.
static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
Constant *IncomingVal = nullptr;
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
if (PN->getIncomingBlock(i) == BB)
continue;
auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
if (!CurrentVal)
return nullptr;
if (IncomingVal != CurrentVal) {
if (IncomingVal)
return nullptr;
IncomingVal = CurrentVal;
}
}
return IncomingVal;
}
/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
/// in the header of its containing loop, we know the loop executes a
/// constant number of times, and the PHI node is just a recurrence
/// involving constants, fold it.
Constant *
ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
const APInt &BEs,
const Loop *L) {
auto I = ConstantEvolutionLoopExitValue.find(PN);
if (I != ConstantEvolutionLoopExitValue.end())
return I->second;
if (BEs.ugt(MaxBruteForceIterations))
return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
DenseMap<Instruction *, Constant *> CurrentIterVals;
BasicBlock *Header = L->getHeader();
assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
return nullptr;
for (PHINode &PHI : Header->phis()) {
if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
CurrentIterVals[&PHI] = StartCST;
}
if (!CurrentIterVals.count(PN))
return RetVal = nullptr;
Value *BEValue = PN->getIncomingValueForBlock(Latch);
// Execute the loop symbolically to determine the exit value.
assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&
"BEs is <= MaxBruteForceIterations which is an 'unsigned'!");
unsigned NumIterations = BEs.getZExtValue(); // must be in range
unsigned IterationNum = 0;
const DataLayout &DL = getDataLayout();
for (; ; ++IterationNum) {
if (IterationNum == NumIterations)
return RetVal = CurrentIterVals[PN]; // Got exit value!
// Compute the value of the PHIs for the next iteration.
// EvaluateExpression adds non-phi values to the CurrentIterVals map.
DenseMap<Instruction *, Constant *> NextIterVals;
Constant *NextPHI =
EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
if (!NextPHI)
return nullptr; // Couldn't evaluate!
NextIterVals[PN] = NextPHI;
bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
// Also evaluate the other PHI nodes. However, we don't get to stop if we
// cease to be able to evaluate one of them or if they stop evolving,
// because that doesn't necessarily prevent us from computing PN.
SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
for (const auto &I : CurrentIterVals) {
PHINode *PHI = dyn_cast<PHINode>(I.first);
if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
PHIsToCompute.emplace_back(PHI, I.second);
}
// We use two distinct loops because EvaluateExpression may invalidate any
// iterators into CurrentIterVals.
for (const auto &I : PHIsToCompute) {
PHINode *PHI = I.first;
Constant *&NextPHI = NextIterVals[PHI];
if (!NextPHI) { // Not already computed.
Value *BEValue = PHI->getIncomingValueForBlock(Latch);
NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
}
if (NextPHI != I.second)
StoppedEvolving = false;
}
// If all entries in CurrentIterVals == NextIterVals then we can stop
// iterating, the loop can't continue to change.
if (StoppedEvolving)
return RetVal = CurrentIterVals[PN];
CurrentIterVals.swap(NextIterVals);
}
}
const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
Value *Cond,
bool ExitWhen) {
PHINode *PN = getConstantEvolvingPHI(Cond, L);
if (!PN) return getCouldNotCompute();
// If the loop is canonicalized, the PHI will have exactly two entries.
// That's the only form we support here.
if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
DenseMap<Instruction *, Constant *> CurrentIterVals;
BasicBlock *Header = L->getHeader();
assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
BasicBlock *Latch = L->getLoopLatch();
assert(Latch && "Should follow from NumIncomingValues == 2!");
for (PHINode &PHI : Header->phis()) {
if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
CurrentIterVals[&PHI] = StartCST;
}
if (!CurrentIterVals.count(PN))
return getCouldNotCompute();
// Okay, we find a PHI node that defines the trip count of this loop. Execute
// the loop symbolically to determine when the condition gets a value of
// "ExitWhen".
unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
const DataLayout &DL = getDataLayout();
for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
auto *CondVal = dyn_cast_or_null<ConstantInt>(
EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
// Couldn't symbolically evaluate.
if (!CondVal) return getCouldNotCompute();
if (CondVal->getValue() == uint64_t(ExitWhen)) {
++NumBruteForceTripCountsComputed;
return getConstant(Type::getInt32Ty(getContext()), IterationNum);
}
// Update all the PHI nodes for the next iteration.
DenseMap<Instruction *, Constant *> NextIterVals;
// Create a list of which PHIs we need to compute. We want to do this before
// calling EvaluateExpression on them because that may invalidate iterators
// into CurrentIterVals.
SmallVector<PHINode *, 8> PHIsToCompute;
for (const auto &I : CurrentIterVals) {
PHINode *PHI = dyn_cast<PHINode>(I.first);
if (!PHI || PHI->getParent() != Header) continue;
PHIsToCompute.push_back(PHI);
}
for (PHINode *PHI : PHIsToCompute) {
Constant *&NextPHI = NextIterVals[PHI];
if (NextPHI) continue; // Already computed!
Value *BEValue = PHI->getIncomingValueForBlock(Latch);
NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
}
CurrentIterVals.swap(NextIterVals);
}
// Too many iterations were needed to evaluate.
return getCouldNotCompute();
}
const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
ValuesAtScopes[V];
// Check to see if we've folded this expression at this loop before.
for (auto &LS : Values)
if (LS.first == L)
return LS.second ? LS.second : V;
Values.emplace_back(L, nullptr);
// Otherwise compute it.
const SCEV *C = computeSCEVAtScope(V, L);
for (auto &LS : reverse(ValuesAtScopes[V]))
if (LS.first == L) {
LS.second = C;
break;
}
return C;
}
/// This builds up a Constant using the ConstantExpr interface. That way, we
/// will return Constants for objects which aren't represented by a
/// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
/// Returns NULL if the SCEV isn't representable as a Constant.
static Constant *BuildConstantFromSCEV(const SCEV *V) {
switch (static_cast<SCEVTypes>(V->getSCEVType())) {
case scCouldNotCompute:
case scAddRecExpr:
break;
case scConstant:
return cast<SCEVConstant>(V)->getValue();
case scUnknown:
return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
case scSignExtend: {
const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
return ConstantExpr::getSExt(CastOp, SS->getType());
break;
}
case scZeroExtend: {
const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
return ConstantExpr::getZExt(CastOp, SZ->getType());
break;
}
case scTruncate: {
const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
return ConstantExpr::getTrunc(CastOp, ST->getType());
break;
}
case scAddExpr: {
const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
unsigned AS = PTy->getAddressSpace();
Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
C = ConstantExpr::getBitCast(C, DestPtrTy);
}
for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
if (!C2) return nullptr;
// First pointer!
if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
unsigned AS = C2->getType()->getPointerAddressSpace();
std::swap(C, C2);
Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
// The offsets have been converted to bytes. We can add bytes to an
// i8* by GEP with the byte count in the first index.
C = ConstantExpr::getBitCast(C, DestPtrTy);
}
// Don't bother trying to sum two pointers. We probably can't
// statically compute a load that results from it anyway.
if (C2->getType()->isPointerTy())
return nullptr;
if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
if (PTy->getElementType()->isStructTy())
C2 = ConstantExpr::getIntegerCast(
C2, Type::getInt32Ty(C->getContext()), true);
C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
} else
C = ConstantExpr::getAdd(C, C2);
}
return C;
}
break;
}
case scMulExpr: {
const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
// Don't bother with pointers at all.
if (C->getType()->isPointerTy()) return nullptr;
for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
if (!C2 || C2->getType()->isPointerTy()) return nullptr;
C = ConstantExpr::getMul(C, C2);
}
return C;
}
break;
}
case scUDivExpr: {
const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
if (LHS->getType() == RHS->getType())
return ConstantExpr::getUDiv(LHS, RHS);
break;
}
case scSMaxExpr:
case scUMaxExpr:
case scSMinExpr:
case scUMinExpr:
break; // TODO: smax, umax, smin, umax.
}
return nullptr;
}
const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
if (isa<SCEVConstant>(V)) return V;
// If this instruction is evolved from a constant-evolving PHI, compute the
// exit value from the loop without using SCEVs.
if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
if (PHINode *PN = dyn_cast<PHINode>(I)) {
const Loop *LI = this->LI[I->getParent()];
// Looking for loop exit value.
if (LI && LI->getParentLoop() == L &&
PN->getParent() == LI->getHeader()) {
// Okay, there is no closed form solution for the PHI node. Check
// to see if the loop that contains it has a known backedge-taken
// count. If so, we may be able to force computation of the exit
// value.
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
// This trivial case can show up in some degenerate cases where
// the incoming IR has not yet been fully simplified.
if (BackedgeTakenCount->isZero()) {
Value *InitValue = nullptr;
bool MultipleInitValues = false;
for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
if (!LI->contains(PN->getIncomingBlock(i))) {
if (!InitValue)
InitValue = PN->getIncomingValue(i);
else if (InitValue != PN->getIncomingValue(i)) {
MultipleInitValues = true;
break;
}
}
}
if (!MultipleInitValues && InitValue)
return getSCEV(InitValue);
}
// Do we have a loop invariant value flowing around the backedge
// for a loop which must execute the backedge?
if (!isa<SCEVCouldNotCompute>(BackedgeTakenCount) &&
isKnownPositive(BackedgeTakenCount) &&
PN->getNumIncomingValues() == 2) {
unsigned InLoopPred = LI->contains(PN->getIncomingBlock(0)) ? 0 : 1;
const SCEV *OnBackedge = getSCEV(PN->getIncomingValue(InLoopPred));
if (IsAvailableOnEntry(LI, DT, OnBackedge, PN->getParent()))
return OnBackedge;
}
if (auto *BTCC = dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
// Okay, we know how many times the containing loop executes. If
// this is a constant evolving PHI node, get the final value at
// the specified iteration number.
Constant *RV =
getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
if (RV) return getSCEV(RV);
}
}
// If there is a single-input Phi, evaluate it at our scope. If we can
// prove that this replacement does not break LCSSA form, use new value.
if (PN->getNumOperands() == 1) {
const SCEV *Input = getSCEV(PN->getOperand(0));
const SCEV *InputAtScope = getSCEVAtScope(Input, L);
// TODO: We can generalize it using LI.replacementPreservesLCSSAForm,
// for the simplest case just support constants.
if (isa<SCEVConstant>(InputAtScope)) return InputAtScope;
}
}
// Okay, this is an expression that we cannot symbolically evaluate
// into a SCEV. Check to see if it's possible to symbolically evaluate
// the arguments into constants, and if so, try to constant propagate the
// result. This is particularly useful for computing loop exit values.
if (CanConstantFold(I)) {
SmallVector<Constant *, 4> Operands;
bool MadeImprovement = false;
for (Value *Op : I->operands()) {
if (Constant *C = dyn_cast<Constant>(Op)) {
Operands.push_back(C);
continue;
}
// If any of the operands is non-constant and if they are
// non-integer and non-pointer, don't even try to analyze them
// with scev techniques.
if (!isSCEVable(Op->getType()))
return V;
const SCEV *OrigV = getSCEV(Op);
const SCEV *OpV = getSCEVAtScope(OrigV, L);
MadeImprovement |= OrigV != OpV;
Constant *C = BuildConstantFromSCEV(OpV);
if (!C) return V;
if (C->getType() != Op->getType())
C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
Op->getType(),
false),
C, Op->getType());
Operands.push_back(C);
}
// Check to see if getSCEVAtScope actually made an improvement.
if (MadeImprovement) {
Constant *C = nullptr;
const DataLayout &DL = getDataLayout();
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
Operands[1], DL, &TLI);
else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
if (!LI->isVolatile())
C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
} else
C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
if (!C) return V;
return getSCEV(C);
}
}
}
// This is some other type of SCEVUnknown, just return it.
return V;
}
if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
// Avoid performing the look-up in the common case where the specified
// expression has no loop-variant portions.
for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
if (OpAtScope != Comm->getOperand(i)) {
// Okay, at least one of these operands is loop variant but might be
// foldable. Build a new instance of the folded commutative expression.
SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
Comm->op_begin()+i);
NewOps.push_back(OpAtScope);
for (++i; i != e; ++i) {
OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
NewOps.push_back(OpAtScope);
}
if (isa<SCEVAddExpr>(Comm))
return getAddExpr(NewOps, Comm->getNoWrapFlags());
if (isa<SCEVMulExpr>(Comm))
return getMulExpr(NewOps, Comm->getNoWrapFlags());
if (isa<SCEVMinMaxExpr>(Comm))
return getMinMaxExpr(Comm->getSCEVType(), NewOps);
llvm_unreachable("Unknown commutative SCEV type!");
}
}
// If we got here, all operands are loop invariant.
return Comm;
}
if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
if (LHS == Div->getLHS() && RHS == Div->getRHS())
return Div; // must be loop invariant
return getUDivExpr(LHS, RHS);
}
// If this is a loop recurrence for a loop that does not contain L, then we
// are dealing with the final value computed by the loop.
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
// First, attempt to evaluate each operand.
// Avoid performing the look-up in the common case where the specified
// expression has no loop-variant portions.
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
if (OpAtScope == AddRec->getOperand(i))
continue;
// Okay, at least one of these operands is loop variant but might be
// foldable. Build a new instance of the folded commutative expression.
SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
AddRec->op_begin()+i);
NewOps.push_back(OpAtScope);
for (++i; i != e; ++i)
NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
const SCEV *FoldedRec =
getAddRecExpr(NewOps, AddRec->getLoop(),
AddRec->getNoWrapFlags(SCEV::FlagNW));
AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
// The addrec may be folded to a nonrecurrence, for example, if the
// induction variable is multiplied by zero after constant folding. Go
// ahead and return the folded value.
if (!AddRec)
return FoldedRec;
break;
}
// If the scope is outside the addrec's loop, evaluate it by using the
// loop exit value of the addrec.
if (!AddRec->getLoop()->contains(L)) {
// To evaluate this recurrence, we need to know how many times the AddRec
// loop iterates. Compute this now.
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
// Then, evaluate the AddRec.
return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
}
return AddRec;
}
if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
if (Op == Cast->getOperand())
return Cast; // must be loop invariant
return getZeroExtendExpr(Op, Cast->getType());
}
if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
if (Op == Cast->getOperand())
return Cast; // must be loop invariant
return getSignExtendExpr(Op, Cast->getType());
}
if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
if (Op == Cast->getOperand())
return Cast; // must be loop invariant
return getTruncateExpr(Op, Cast->getType());
}
llvm_unreachable("Unknown SCEV type!");
}
const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
return getSCEVAtScope(getSCEV(V), L);
}
const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const {
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S))
return stripInjectiveFunctions(ZExt->getOperand());
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S))
return stripInjectiveFunctions(SExt->getOperand());
return S;
}
/// Finds the minimum unsigned root of the following equation:
///
/// A * X = B (mod N)
///
/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
/// A and B isn't important.
///
/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
ScalarEvolution &SE) {
uint32_t BW = A.getBitWidth();
assert(BW == SE.getTypeSizeInBits(B->getType()));
assert(A != 0 && "A must be non-zero.");
// 1. D = gcd(A, N)
//
// The gcd of A and N may have only one prime factor: 2. The number of
// trailing zeros in A is its multiplicity
uint32_t Mult2 = A.countTrailingZeros();
// D = 2^Mult2
// 2. Check if B is divisible by D.
//
// B is divisible by D if and only if the multiplicity of prime factor 2 for B
// is not less than multiplicity of this prime factor for D.
if (SE.GetMinTrailingZeros(B) < Mult2)
return SE.getCouldNotCompute();
// 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
// modulo (N / D).
//
// If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
// (N / D) in general. The inverse itself always fits into BW bits, though,
// so we immediately truncate it.
APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
APInt Mod(BW + 1, 0);
Mod.setBit(BW - Mult2); // Mod = N / D
APInt I = AD.multiplicativeInverse(Mod).trunc(BW);
// 4. Compute the minimum unsigned root of the equation:
// I * (B / D) mod (N / D)
// To simplify the computation, we factor out the divide by D:
// (I * B mod N) / D
const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
}
/// For a given quadratic addrec, generate coefficients of the corresponding
/// quadratic equation, multiplied by a common value to ensure that they are
/// integers.
/// The returned value is a tuple { A, B, C, M, BitWidth }, where
/// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C
/// were multiplied by, and BitWidth is the bit width of the original addrec
/// coefficients.
/// This function returns None if the addrec coefficients are not compile-
/// time constants.
static Optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>>
GetQuadraticEquation(const SCEVAddRecExpr *AddRec) {
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: "
<< *AddRec << '\n');
// We currently can only solve this if the coefficients are constants.
if (!LC || !MC || !NC) {
LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n");
return None;
}
APInt L = LC->getAPInt();
APInt M = MC->getAPInt();
APInt N = NC->getAPInt();
assert(!N.isNullValue() && "This is not a quadratic addrec");
unsigned BitWidth = LC->getAPInt().getBitWidth();
unsigned NewWidth = BitWidth + 1;
LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: "
<< BitWidth << '\n');
// The sign-extension (as opposed to a zero-extension) here matches the
// extension used in SolveQuadraticEquationWrap (with the same motivation).
N = N.sext(NewWidth);
M = M.sext(NewWidth);
L = L.sext(NewWidth);
// The increments are M, M+N, M+2N, ..., so the accumulated values are
// L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is,
// L+M, L+2M+N, L+3M+3N, ...
// After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N.
//
// The equation Acc = 0 is then
// L + nM + n(n-1)/2 N = 0, or 2L + 2M n + n(n-1) N = 0.
// In a quadratic form it becomes:
// N n^2 + (2M-N) n + 2L = 0.
APInt A = N;
APInt B = 2 * M - A;
APInt C = 2 * L;
APInt T = APInt(NewWidth, 2);
LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << B
<< "x + " << C << ", coeff bw: " << NewWidth
<< ", multiplied by " << T << '\n');
return std::make_tuple(A, B, C, T, BitWidth);
}
/// Helper function to compare optional APInts:
/// (a) if X and Y both exist, return min(X, Y),
/// (b) if neither X nor Y exist, return None,
/// (c) if exactly one of X and Y exists, return that value.
static Optional<APInt> MinOptional(Optional<APInt> X, Optional<APInt> Y) {
if (X.hasValue() && Y.hasValue()) {
unsigned W = std::max(X->getBitWidth(), Y->getBitWidth());
APInt XW = X->sextOrSelf(W);
APInt YW = Y->sextOrSelf(W);
return XW.slt(YW) ? *X : *Y;
}
if (!X.hasValue() && !Y.hasValue())
return None;
return X.hasValue() ? *X : *Y;
}
/// Helper function to truncate an optional APInt to a given BitWidth.
/// When solving addrec-related equations, it is preferable to return a value
/// that has the same bit width as the original addrec's coefficients. If the
/// solution fits in the original bit width, truncate it (except for i1).
/// Returning a value of a different bit width may inhibit some optimizations.
///
/// In general, a solution to a quadratic equation generated from an addrec
/// may require BW+1 bits, where BW is the bit width of the addrec's
/// coefficients. The reason is that the coefficients of the quadratic
/// equation are BW+1 bits wide (to avoid truncation when converting from
/// the addrec to the equation).
static Optional<APInt> TruncIfPossible(Optional<APInt> X, unsigned BitWidth) {
if (!X.hasValue())
return None;
unsigned W = X->getBitWidth();
if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth))
return X->trunc(BitWidth);
return X;
}
/// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n
/// iterations. The values L, M, N are assumed to be signed, and they
/// should all have the same bit widths.
/// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW,
/// where BW is the bit width of the addrec's coefficients.
/// If the calculated value is a BW-bit integer (for BW > 1), it will be
/// returned as such, otherwise the bit width of the returned value may
/// be greater than BW.
///
/// This function returns None if
/// (a) the addrec coefficients are not constant, or
/// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases
/// like x^2 = 5, no integer solutions exist, in other cases an integer
/// solution may exist, but SolveQuadraticEquationWrap may fail to find it.
static Optional<APInt>
SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
APInt A, B, C, M;
unsigned BitWidth;
auto T = GetQuadraticEquation(AddRec);
if (!T.hasValue())
return None;
std::tie(A, B, C, M, BitWidth) = *T;
LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n");
Optional<APInt> X = APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth+1);
if (!X.hasValue())
return None;
ConstantInt *CX = ConstantInt::get(SE.getContext(), *X);
ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE);
if (!V->isZero())
return None;
return TruncIfPossible(X, BitWidth);
}
/// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n
/// iterations. The values M, N are assumed to be signed, and they
/// should all have the same bit widths.
/// Find the least n such that c(n) does not belong to the given range,
/// while c(n-1) does.
///
/// This function returns None if
/// (a) the addrec coefficients are not constant, or
/// (b) SolveQuadraticEquationWrap was unable to find a solution for the
/// bounds of the range.
static Optional<APInt>
SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec,
const ConstantRange &Range, ScalarEvolution &SE) {
assert(AddRec->getOperand(0)->isZero() &&
"Starting value of addrec should be 0");
LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range "
<< Range << ", addrec " << *AddRec << '\n');
// This case is handled in getNumIterationsInRange. Here we can assume that
// we start in the range.
assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) &&
"Addrec's initial value should be in range");
APInt A, B, C, M;
unsigned BitWidth;
auto T = GetQuadraticEquation(AddRec);
if (!T.hasValue())
return None;
// Be careful about the return value: there can be two reasons for not
// returning an actual number. First, if no solutions to the equations
// were found, and second, if the solutions don't leave the given range.
// The first case means that the actual solution is "unknown", the second
// means that it's known, but not valid. If the solution is unknown, we
// cannot make any conclusions.
// Return a pair: the optional solution and a flag indicating if the
// solution was found.
auto SolveForBoundary = [&](APInt Bound) -> std::pair<Optional<APInt>,bool> {
// Solve for signed overflow and unsigned overflow, pick the lower
// solution.
LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary "
<< Bound << " (before multiplying by " << M << ")\n");
Bound *= M; // The quadratic equation multiplier.
Optional<APInt> SO = None;
if (BitWidth > 1) {
LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
"signed overflow\n");
SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth);
}
LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
"unsigned overflow\n");
Optional<APInt> UO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound,
BitWidth+1);
auto LeavesRange = [&] (const APInt &X) {
ConstantInt *C0 = ConstantInt::get(SE.getContext(), X);
ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE);
if (Range.contains(V0->getValue()))
return false;
// X should be at least 1, so X-1 is non-negative.
ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1);
ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE);
if (Range.contains(V1->getValue()))
return true;
return false;
};
// If SolveQuadraticEquationWrap returns None, it means that there can
// be a solution, but the function failed to find it. We cannot treat it
// as "no solution".
if (!SO.hasValue() || !UO.hasValue())
return { None, false };
// Check the smaller value first to see if it leaves the range.
// At this point, both SO and UO must have values.
Optional<APInt> Min = MinOptional(SO, UO);
if (LeavesRange(*Min))
return { Min, true };
Optional<APInt> Max = Min == SO ? UO : SO;
if (LeavesRange(*Max))
return { Max, true };
// Solutions were found, but were eliminated, hence the "true".
return { None, true };
};
std::tie(A, B, C, M, BitWidth) = *T;
// Lower bound is inclusive, subtract 1 to represent the exiting value.
APInt Lower = Range.getLower().sextOrSelf(A.getBitWidth()) - 1;
APInt Upper = Range.getUpper().sextOrSelf(A.getBitWidth());
auto SL = SolveForBoundary(Lower);
auto SU = SolveForBoundary(Upper);
// If any of the solutions was unknown, no meaninigful conclusions can
// be made.
if (!SL.second || !SU.second)
return None;
// Claim: The correct solution is not some value between Min and Max.
//
// Justification: Assuming that Min and Max are different values, one of
// them is when the first signed overflow happens, the other is when the
// first unsigned overflow happens. Crossing the range boundary is only
// possible via an overflow (treating 0 as a special case of it, modeling
// an overflow as crossing k*2^W for some k).
//
// The interesting case here is when Min was eliminated as an invalid
// solution, but Max was not. The argument is that if there was another
// overflow between Min and Max, it would also have been eliminated if
// it was considered.
//
// For a given boundary, it is possible to have two overflows of the same
// type (signed/unsigned) without having the other type in between: this
// can happen when the vertex of the parabola is between the iterations
// corresponding to the overflows. This is only possible when the two
// overflows cross k*2^W for the same k. In such case, if the second one
// left the range (and was the first one to do so), the first overflow
// would have to enter the range, which would mean that either we had left
// the range before or that we started outside of it. Both of these cases
// are contradictions.
//
// Claim: In the case where SolveForBoundary returns None, the correct
// solution is not some value between the Max for this boundary and the
// Min of the other boundary.
//
// Justification: Assume that we had such Max_A and Min_B corresponding
// to range boundaries A and B and such that Max_A < Min_B. If there was
// a solution between Max_A and Min_B, it would have to be caused by an
// overflow corresponding to either A or B. It cannot correspond to B,
// since Min_B is the first occurrence of such an overflow. If it
// corresponded to A, it would have to be either a signed or an unsigned
// overflow that is larger than both eliminated overflows for A. But
// between the eliminated overflows and this overflow, the values would
// cover the entire value space, thus crossing the other boundary, which
// is a contradiction.
return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth);
}
ScalarEvolution::ExitLimit
ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
bool AllowPredicates) {
// This is only used for loops with a "x != y" exit test. The exit condition
// is now expressed as a single expression, V = x-y. So the exit test is
// effectively V != 0. We know and take advantage of the fact that this
// expression only being used in a comparison by zero context.
SmallPtrSet<const SCEVPredicate *, 4> Predicates;
// If the value is a constant
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
// If the value is already zero, the branch will execute zero times.
if (C->getValue()->isZero()) return C;
return getCouldNotCompute(); // Otherwise it will loop infinitely.
}
const SCEVAddRecExpr *AddRec =
dyn_cast<SCEVAddRecExpr>(stripInjectiveFunctions(V));
if (!AddRec && AllowPredicates)
// Try to make this an AddRec using runtime tests, in the first X
// iterations of this loop, where X is the SCEV expression found by the
// algorithm below.
AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
if (!AddRec || AddRec->getLoop() != L)
return getCouldNotCompute();
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
// the quadratic equation to solve it.
if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
// We can only use this value if the chrec ends up with an exact zero
// value at this index. When solving for "X*X != 5", for example, we
// should not accept a root of 2.
if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) {
const auto *R = cast<SCEVConstant>(getConstant(S.getValue()));
return ExitLimit(R, R, false, Predicates);
}
return getCouldNotCompute();
}
// Otherwise we can only handle this if it is affine.
if (!AddRec->isAffine())
return getCouldNotCompute();
// If this is an affine expression, the execution count of this branch is
// the minimum unsigned root of the following equation:
//
// Start + Step*N = 0 (mod 2^BW)
//
// equivalent to:
//
// Step*N = -Start (mod 2^BW)
//
// where BW is the common bit width of Start and Step.
// Get the initial value for the loop.
const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
// For now we handle only constant steps.
//
// TODO: Handle a nonconstant Step given AddRec<NUW>. If the
// AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
// to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
// We have not yet seen any such cases.
const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
if (!StepC || StepC->getValue()->isZero())
return getCouldNotCompute();
// For positive steps (counting up until unsigned overflow):
// N = -Start/Step (as unsigned)
// For negative steps (counting down to zero):
// N = Start/-Step
// First compute the unsigned distance from zero in the direction of Step.
bool CountDown = StepC->getAPInt().isNegative();
const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
// Handle unitary steps, which cannot wraparound.
// 1*N = -Start; -1*N = Start (mod 2^BW), so:
// N = Distance (as unsigned)
if (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne()) {
APInt MaxBECount = getUnsignedRangeMax(Distance);
// When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
// we end up with a loop whose backedge-taken count is n - 1. Detect this
// case, and see if we can improve the bound.
//
// Explicitly handling this here is necessary because getUnsignedRange
// isn't context-sensitive; it doesn't know that we only care about the
// range inside the loop.
const SCEV *Zero = getZero(Distance->getType());
const SCEV *One = getOne(Distance->getType());
const SCEV *DistancePlusOne = getAddExpr(Distance, One);
if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
// If Distance + 1 doesn't overflow, we can compute the maximum distance
// as "unsigned_max(Distance + 1) - 1".
ConstantRange CR = getUnsignedRange(DistancePlusOne);
MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
}
return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
}
// If the condition controls loop exit (the loop exits only if the expression
// is true) and the addition is no-wrap we can use unsigned divide to
// compute the backedge count. In this case, the step may not divide the
// distance, but we don't care because if the condition is "missed" the loop
// will have undefined behavior due to wrapping.
if (ControlsExit && AddRec->hasNoSelfWrap() &&
loopHasNoAbnormalExits(AddRec->getLoop())) {
const SCEV *Exact =
getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
const SCEV *Max =
Exact == getCouldNotCompute()
? Exact
: getConstant(getUnsignedRangeMax(Exact));
return ExitLimit(Exact, Max, false, Predicates);
}
// Solve the general equation.
const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(),
getNegativeSCEV(Start), *this);
const SCEV *M = E == getCouldNotCompute()
? E
: getConstant(getUnsignedRangeMax(E));
return ExitLimit(E, M, false, Predicates);
}
ScalarEvolution::ExitLimit
ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
// Loops that look like: while (X == 0) are very strange indeed. We don't
// handle them yet except for the trivial case. This could be expanded in the
// future as needed.
// If the value is a constant, check to see if it is known to be non-zero
// already. If so, the backedge will execute zero times.
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
if (!C->getValue()->isZero())
return getZero(C->getType());
return getCouldNotCompute(); // Otherwise it will loop infinitely.
}
// We could implement others, but I really doubt anyone writes loops like
// this, and if they did, they would already be constant folded.
return getCouldNotCompute();
}
std::pair<BasicBlock *, BasicBlock *>
ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
// If the block has a unique predecessor, then there is no path from the
// predecessor to the block that does not go through the direct edge
// from the predecessor to the block.
if (BasicBlock *Pred = BB->getSinglePredecessor())
return {Pred, BB};
// A loop's header is defined to be a block that dominates the loop.
// If the header has a unique predecessor outside the loop, it must be
// a block that has exactly one successor that can reach the loop.
if (Loop *L = LI.getLoopFor(BB))
return {L->getLoopPredecessor(), L->getHeader()};
return {nullptr, nullptr};
}
/// SCEV structural equivalence is usually sufficient for testing whether two
/// expressions are equal, however for the purposes of looking for a condition
/// guarding a loop, it can be useful to be a little more general, since a
/// front-end may have replicated the controlling expression.
static bool HasSameValue(const SCEV *A, const SCEV *B) {
// Quick check to see if they are the same SCEV.
if (A == B) return true;
auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
// Not all instructions that are "identical" compute the same value. For
// instance, two distinct alloca instructions allocating the same type are
// identical and do not read memory; but compute distinct values.
return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
};
// Otherwise, if they're both SCEVUnknown, it's possible that they hold
// two different instructions with the same value. Check for this case.
if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
if (ComputesEqualValues(AI, BI))
return true;
// Otherwise assume they may have a different value.
return false;
}
bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
const SCEV *&LHS, const SCEV *&RHS,
unsigned Depth) {
bool Changed = false;
// Simplifies ICMP to trivial true or false by turning it into '0 == 0' or
// '0 != 0'.
auto TrivialCase = [&](bool TriviallyTrue) {
LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE;
return true;
};
// If we hit the max recursion limit bail out.
if (Depth >= 3)
return false;
// Canonicalize a constant to the right side.
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
// Check for both operands constant.
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
if (ConstantExpr::getICmp(Pred,
LHSC->getValue(),
RHSC->getValue())->isNullValue())
return TrivialCase(false);
else
return TrivialCase(true);
}
// Otherwise swap the operands to put the constant on the right.
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
Changed = true;
}
// If we're comparing an addrec with a value which is loop-invariant in the
// addrec's loop, put the addrec on the left. Also make a dominance check,
// as both operands could be addrecs loop-invariant in each other's loop.
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
const Loop *L = AR->getLoop();
if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
Changed = true;
}
}
// If there's a constant operand, canonicalize comparisons with boundary
// cases, and canonicalize *-or-equal comparisons to regular comparisons.
if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
const APInt &RA = RC->getAPInt();
bool SimplifiedByConstantRange = false;
if (!ICmpInst::isEquality(Pred)) {
ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
if (ExactCR.isFullSet())
return TrivialCase(true);
else if (ExactCR.isEmptySet())
return TrivialCase(false);
APInt NewRHS;
CmpInst::Predicate NewPred;
if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
ICmpInst::isEquality(NewPred)) {
// We were able to convert an inequality to an equality.
Pred = NewPred;
RHS = getConstant(NewRHS);
Changed = SimplifiedByConstantRange = true;
}
}
if (!SimplifiedByConstantRange) {
switch (Pred) {
default:
break;
case ICmpInst::ICMP_EQ:
case ICmpInst::ICMP_NE:
// Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
if (!RA)
if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
if (const SCEVMulExpr *ME =
dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
ME->getOperand(0)->isAllOnesValue()) {
RHS = AE->getOperand(1);
LHS = ME->getOperand(1);
Changed = true;
}
break;
// The "Should have been caught earlier!" messages refer to the fact
// that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
// should have fired on the corresponding cases, and canonicalized the
// check to trivial case.
case ICmpInst::ICMP_UGE:
assert(!RA.isMinValue() && "Should have been caught earlier!");
Pred = ICmpInst::ICMP_UGT;
RHS = getConstant(RA - 1);
Changed = true;
break;
case ICmpInst::ICMP_ULE:
assert(!RA.isMaxValue() && "Should have been caught earlier!");
Pred = ICmpInst::ICMP_ULT;
RHS = getConstant(RA + 1);
Changed = true;
break;
case ICmpInst::ICMP_SGE:
assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
Pred = ICmpInst::ICMP_SGT;
RHS = getConstant(RA - 1);
Changed = true;
break;
case ICmpInst::ICMP_SLE:
assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
Pred = ICmpInst::ICMP_SLT;
RHS = getConstant(RA + 1);
Changed = true;
break;
}
}
}
// Check for obvious equality.
if (HasSameValue(LHS, RHS)) {
if (ICmpInst::isTrueWhenEqual(Pred))
return TrivialCase(true);
if (ICmpInst::isFalseWhenEqual(Pred))
return TrivialCase(false);
}
// If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
// adding or subtracting 1 from one of the operands.
switch (Pred) {
case ICmpInst::ICMP_SLE:
if (!getSignedRangeMax(RHS).isMaxSignedValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SLT;
Changed = true;
} else if (!getSignedRangeMin(LHS).isMinSignedValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SLT;
Changed = true;
}
break;
case ICmpInst::ICMP_SGE:
if (!getSignedRangeMin(RHS).isMinSignedValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SGT;
Changed = true;
} else if (!getSignedRangeMax(LHS).isMaxSignedValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SGT;
Changed = true;
}
break;
case ICmpInst::ICMP_ULE:
if (!getUnsignedRangeMax(RHS).isMaxValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
SCEV::FlagNUW);
Pred = ICmpInst::ICMP_ULT;
Changed = true;
} else if (!getUnsignedRangeMin(LHS).isMinValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
Pred = ICmpInst::ICMP_ULT;
Changed = true;
}
break;
case ICmpInst::ICMP_UGE:
if (!getUnsignedRangeMin(RHS).isMinValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
Pred = ICmpInst::ICMP_UGT;
Changed = true;
} else if (!getUnsignedRangeMax(LHS).isMaxValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
SCEV::FlagNUW);
Pred = ICmpInst::ICMP_UGT;
Changed = true;
}
break;
default:
break;
}
// TODO: More simplifications are possible here.
// Recursively simplify until we either hit a recursion limit or nothing
// changes.
if (Changed)
return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
return Changed;
}
bool ScalarEvolution::isKnownNegative(const SCEV *S) {
return getSignedRangeMax(S).isNegative();
}
bool ScalarEvolution::isKnownPositive(const SCEV *S) {
return getSignedRangeMin(S).isStrictlyPositive();
}
bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
return !getSignedRangeMin(S).isNegative();
}
bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
return !getSignedRangeMax(S).isStrictlyPositive();
}
bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
return isKnownNegative(S) || isKnownPositive(S);
}
std::pair<const SCEV *, const SCEV *>
ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) {
// Compute SCEV on entry of loop L.
const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this);
if (Start == getCouldNotCompute())
return { Start, Start };
// Compute post increment SCEV for loop L.
const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this);
assert(PostInc != getCouldNotCompute() && "Unexpected could not compute");
return { Start, PostInc };
}
bool ScalarEvolution::isKnownViaInduction(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// First collect all loops.
SmallPtrSet<const Loop *, 8> LoopsUsed;
getUsedLoops(LHS, LoopsUsed);
getUsedLoops(RHS, LoopsUsed);
if (LoopsUsed.empty())
return false;
// Domination relationship must be a linear order on collected loops.
#ifndef NDEBUG
for (auto *L1 : LoopsUsed)
for (auto *L2 : LoopsUsed)
assert((DT.dominates(L1->getHeader(), L2->getHeader()) ||
DT.dominates(L2->getHeader(), L1->getHeader())) &&
"Domination relationship is not a linear order");
#endif
const Loop *MDL =
*std::max_element(LoopsUsed.begin(), LoopsUsed.end(),
[&](const Loop *L1, const Loop *L2) {
return DT.properlyDominates(L1->getHeader(), L2->getHeader());
});
// Get init and post increment value for LHS.
auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS);
// if LHS contains unknown non-invariant SCEV then bail out.
if (SplitLHS.first == getCouldNotCompute())
return false;
assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC");
// Get init and post increment value for RHS.
auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS);
// if RHS contains unknown non-invariant SCEV then bail out.
if (SplitRHS.first == getCouldNotCompute())
return false;
assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC");
// It is possible that init SCEV contains an invariant load but it does
// not dominate MDL and is not available at MDL loop entry, so we should
// check it here.
if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) ||
!isAvailableAtLoopEntry(SplitRHS.first, MDL))
return false;
// It seems backedge guard check is faster than entry one so in some cases
// it can speed up whole estimation by short circuit
return isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second,
SplitRHS.second) &&
isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first);
}
bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// Canonicalize the inputs first.
(void)SimplifyICmpOperands(Pred, LHS, RHS);
if (isKnownViaInduction(Pred, LHS, RHS))
return true;
if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
return true;
// Otherwise see what can be done with some simple reasoning.
return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS);
}
bool ScalarEvolution::isKnownOnEveryIteration(ICmpInst::Predicate Pred,
const SCEVAddRecExpr *LHS,
const SCEV *RHS) {
const Loop *L = LHS->getLoop();
return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) &&
isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS);
}
bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
ICmpInst::Predicate Pred,
bool &Increasing) {
bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
#ifndef NDEBUG
// Verify an invariant: inverting the predicate should turn a monotonically
// increasing change to a monotonically decreasing one, and vice versa.
bool IncreasingSwapped;
bool ResultSwapped = isMonotonicPredicateImpl(
LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
assert(Result == ResultSwapped && "should be able to analyze both!");
if (ResultSwapped)
assert(Increasing == !IncreasingSwapped &&
"monotonicity should flip as we flip the predicate");
#endif
return Result;
}
bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
ICmpInst::Predicate Pred,
bool &Increasing) {
// A zero step value for LHS means the induction variable is essentially a
// loop invariant value. We don't really depend on the predicate actually
// flipping from false to true (for increasing predicates, and the other way
// around for decreasing predicates), all we care about is that *if* the
// predicate changes then it only changes from false to true.
//
// A zero step value in itself is not very useful, but there may be places
// where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
// as general as possible.
switch (Pred) {
default:
return false; // Conservative answer
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
if (!LHS->hasNoUnsignedWrap())
return false;
Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
return true;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE: {
if (!LHS->hasNoSignedWrap())
return false;
const SCEV *Step = LHS->getStepRecurrence(*this);
if (isKnownNonNegative(Step)) {
Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
return true;
}
if (isKnownNonPositive(Step)) {
Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
return true;
}
return false;
}
}
llvm_unreachable("switch has default clause!");
}
bool ScalarEvolution::isLoopInvariantPredicate(
ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
const SCEV *&InvariantRHS) {
// If there is a loop-invariant, force it into the RHS, otherwise bail out.
if (!isLoopInvariant(RHS, L)) {
if (!isLoopInvariant(LHS, L))
return false;
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
}
const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
if (!ArLHS || ArLHS->getLoop() != L)
return false;
bool Increasing;
if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
return false;
// If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
// true as the loop iterates, and the backedge is control dependent on
// "ArLHS `Pred` RHS" == true then we can reason as follows:
//
// * if the predicate was false in the first iteration then the predicate
// is never evaluated again, since the loop exits without taking the
// backedge.
// * if the predicate was true in the first iteration then it will
// continue to be true for all future iterations since it is
// monotonically increasing.
//
// For both the above possibilities, we can replace the loop varying
// predicate with its value on the first iteration of the loop (which is
// loop invariant).
//
// A similar reasoning applies for a monotonically decreasing predicate, by
// replacing true with false and false with true in the above two bullets.
auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
return false;
InvariantPred = Pred;
InvariantLHS = ArLHS->getStart();
InvariantRHS = RHS;
return true;
}
bool ScalarEvolution::isKnownPredicateViaConstantRanges(
ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
if (HasSameValue(LHS, RHS))
return ICmpInst::isTrueWhenEqual(Pred);
// This code is split out from isKnownPredicate because it is called from
// within isLoopEntryGuardedByCond.
auto CheckRanges =
[&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
.contains(RangeLHS);
};
// The check at the top of the function catches the case where the values are
// known to be equal.
if (Pred == CmpInst::ICMP_EQ)
return false;
if (Pred == CmpInst::ICMP_NE)
return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
isKnownNonZero(getMinusSCEV(LHS, RHS));
if (CmpInst::isSigned(Pred))
return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
}
bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
const SCEV *LHS,
const SCEV *RHS) {
// Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
// Return Y via OutY.
auto MatchBinaryAddToConst =
[this](const SCEV *Result, const SCEV *X, APInt &OutY,
SCEV::NoWrapFlags ExpectedFlags) {
const SCEV *NonConstOp, *ConstOp;
SCEV::NoWrapFlags FlagsPresent;
if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
!isa<SCEVConstant>(ConstOp) || NonConstOp != X)
return false;
OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
};
APInt C;
switch (Pred) {
default:
break;
case ICmpInst::ICMP_SGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SLE:
// X s<= (X + C)<nsw> if C >= 0
if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
return true;
// (X + C)<nsw> s<= X if C <= 0
if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
!C.isStrictlyPositive())
return true;
break;
case ICmpInst::ICMP_SGT:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SLT:
// X s< (X + C)<nsw> if C > 0
if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
C.isStrictlyPositive())
return true;
// (X + C)<nsw> s< X if C < 0
if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
return true;
break;
}
return false;
}
bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
const SCEV *LHS,
const SCEV *RHS) {
if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
return false;
// Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
// the stack can result in exponential time complexity.
SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
// If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
//
// To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
// isKnownPredicate. isKnownPredicate is more powerful, but also more
// expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
// interesting cases seen in practice. We can consider "upgrading" L >= 0 to
// use isKnownPredicate later if needed.
return isKnownNonNegative(RHS) &&
isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
}
bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// No need to even try if we know the module has no guards.
if (!HasGuards)
return false;
return any_of(*BB, [&](Instruction &I) {
using namespace llvm::PatternMatch;
Value *Condition;
return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
m_Value(Condition))) &&
isImpliedCond(Pred, LHS, RHS, Condition, false);
});
}
/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
/// protected by a conditional between LHS and RHS. This is used to
/// to eliminate casts.
bool
ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// Interpret a null as meaning no loop, where there is obviously no guard
// (interprocedural conditions notwithstanding).
if (!L) return true;
if (VerifyIR)
assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&
"This cannot be done on broken IR!");
if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
return true;
BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
return false;
BranchInst *LoopContinuePredicate =
dyn_cast<BranchInst>(Latch->getTerminator());
if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
isImpliedCond(Pred, LHS, RHS,
LoopContinuePredicate->getCondition(),
LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
return true;
// We don't want more than one activation of the following loops on the stack
// -- that can lead to O(n!) time complexity.
if (WalkingBEDominatingConds)
return false;
SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
// See if we can exploit a trip count to prove the predicate.
const auto &BETakenInfo = getBackedgeTakenInfo(L);
const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
if (LatchBECount != getCouldNotCompute()) {
// We know that Latch branches back to the loop header exactly
// LatchBECount times. This means the backdege condition at Latch is
// equivalent to "{0,+,1} u< LatchBECount".
Type *Ty = LatchBECount->getType();
auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
const SCEV *LoopCounter =
getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
LatchBECount))
return true;
}
// Check conditions due to any @llvm.assume intrinsics.
for (auto &AssumeVH : AC.assumptions()) {
if (!AssumeVH)
continue;
auto *CI = cast<CallInst>(AssumeVH);
if (!DT.dominates(CI, Latch->getTerminator()))
continue;
if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
return true;
}
// If the loop is not reachable from the entry block, we risk running into an
// infinite loop as we walk up into the dom tree. These loops do not matter
// anyway, so we just return a conservative answer when we see them.
if (!DT.isReachableFromEntry(L->getHeader()))
return false;
if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
return true;
for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
DTN != HeaderDTN; DTN = DTN->getIDom()) {
assert(DTN && "should reach the loop header before reaching the root!");
BasicBlock *BB = DTN->getBlock();
if (isImpliedViaGuard(BB, Pred, LHS, RHS))
return true;
BasicBlock *PBB = BB->getSinglePredecessor();
if (!PBB)
continue;
BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
if (!ContinuePredicate || !ContinuePredicate->isConditional())
continue;
Value *Condition = ContinuePredicate->getCondition();
// If we have an edge `E` within the loop body that dominates the only
// latch, the condition guarding `E` also guards the backedge. This
// reasoning works only for loops with a single latch.
BasicBlockEdge DominatingEdge(PBB, BB);
if (DominatingEdge.isSingleEdge()) {
// We're constructively (and conservatively) enumerating edges within the
// loop body that dominate the latch. The dominator tree better agree
// with us on this:
assert(DT.dominates(DominatingEdge, Latch) && "should be!");
if (isImpliedCond(Pred, LHS, RHS, Condition,
BB != ContinuePredicate->getSuccessor(0)))
return true;
}
}
return false;
}
bool
ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// Interpret a null as meaning no loop, where there is obviously no guard
// (interprocedural conditions notwithstanding).
if (!L) return false;
if (VerifyIR)
assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&
"This cannot be done on broken IR!");
// Both LHS and RHS must be available at loop entry.
assert(isAvailableAtLoopEntry(LHS, L) &&
"LHS is not available at Loop Entry");
assert(isAvailableAtLoopEntry(RHS, L) &&
"RHS is not available at Loop Entry");
if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
return true;
// If we cannot prove strict comparison (e.g. a > b), maybe we can prove
// the facts (a >= b && a != b) separately. A typical situation is when the
// non-strict comparison is known from ranges and non-equality is known from
// dominating predicates. If we are proving strict comparison, we always try
// to prove non-equality and non-strict comparison separately.
auto NonStrictPredicate = ICmpInst::getNonStrictPredicate(Pred);
const bool ProvingStrictComparison = (Pred != NonStrictPredicate);
bool ProvedNonStrictComparison = false;
bool ProvedNonEquality = false;
if (ProvingStrictComparison) {
ProvedNonStrictComparison =
isKnownViaNonRecursiveReasoning(NonStrictPredicate, LHS, RHS);
ProvedNonEquality =
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_NE, LHS, RHS);
if (ProvedNonStrictComparison && ProvedNonEquality)
return true;
}
// Try to prove (Pred, LHS, RHS) using isImpliedViaGuard.
auto ProveViaGuard = [&](BasicBlock *Block) {
if (isImpliedViaGuard(Block, Pred, LHS, RHS))
return true;
if (ProvingStrictComparison) {
if (!ProvedNonStrictComparison)
ProvedNonStrictComparison =
isImpliedViaGuard(Block, NonStrictPredicate, LHS, RHS);
if (!ProvedNonEquality)
ProvedNonEquality =
isImpliedViaGuard(Block, ICmpInst::ICMP_NE, LHS, RHS);
if (ProvedNonStrictComparison && ProvedNonEquality)
return true;
}
return false;
};
// Try to prove (Pred, LHS, RHS) using isImpliedCond.
auto ProveViaCond = [&](Value *Condition, bool Inverse) {
if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse))
return true;
if (ProvingStrictComparison) {
if (!ProvedNonStrictComparison)
ProvedNonStrictComparison =
isImpliedCond(NonStrictPredicate, LHS, RHS, Condition, Inverse);
if (!ProvedNonEquality)
ProvedNonEquality =
isImpliedCond(ICmpInst::ICMP_NE, LHS, RHS, Condition, Inverse);
if (ProvedNonStrictComparison && ProvedNonEquality)
return true;
}
return false;
};
// Starting at the loop predecessor, climb up the predecessor chain, as long
// as there are predecessors that can be found that have unique successors
// leading to the original header.
for (std::pair<BasicBlock *, BasicBlock *>
Pair(L->getLoopPredecessor(), L->getHeader());
Pair.first;
Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
if (ProveViaGuard(Pair.first))
return true;
BranchInst *LoopEntryPredicate =
dyn_cast<BranchInst>(Pair.first->getTerminator());
if (!LoopEntryPredicate ||
LoopEntryPredicate->isUnconditional())
continue;
if (ProveViaCond(LoopEntryPredicate->getCondition(),
LoopEntryPredicate->getSuccessor(0) != Pair.second))
return true;
}
// Check conditions due to any @llvm.assume intrinsics.
for (auto &AssumeVH : AC.assumptions()) {
if (!AssumeVH)
continue;
auto *CI = cast<CallInst>(AssumeVH);
if (!DT.dominates(CI, L->getHeader()))
continue;
if (ProveViaCond(CI->getArgOperand(0), false))
return true;
}
return false;
}
bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
Value *FoundCondValue,
bool Inverse) {
if (!PendingLoopPredicates.insert(FoundCondValue).second)
return false;
auto ClearOnExit =
make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); });
// Recursively handle And and Or conditions.
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
if (BO->getOpcode() == Instruction::And) {
if (!Inverse)
return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
} else if (BO->getOpcode() == Instruction::Or) {
if (Inverse)
return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
}
}
ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
if (!ICI) return false;
// Now that we found a conditional branch that dominates the loop or controls
// the loop latch. Check to see if it is the comparison we are looking for.
ICmpInst::Predicate FoundPred;
if (Inverse)
FoundPred = ICI->getInversePredicate();
else
FoundPred = ICI->getPredicate();
const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
}
bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
const SCEV *RHS,
ICmpInst::Predicate FoundPred,
const SCEV *FoundLHS,
const SCEV *FoundRHS) {
// Balance the types.
if (getTypeSizeInBits(LHS->getType()) <
getTypeSizeInBits(FoundLHS->getType())) {
if (CmpInst::isSigned(Pred)) {
LHS = getSignExtendExpr(LHS, FoundLHS->getType());
RHS = getSignExtendExpr(RHS, FoundLHS->getType());
} else {
LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
}
} else if (getTypeSizeInBits(LHS->getType()) >
getTypeSizeInBits(FoundLHS->getType())) {
if (CmpInst::isSigned(FoundPred)) {
FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
} else {
FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
}
}
// Canonicalize the query to match the way instcombine will have
// canonicalized the comparison.
if (SimplifyICmpOperands(Pred, LHS, RHS))
if (LHS == RHS)
return CmpInst::isTrueWhenEqual(Pred);
if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
if (FoundLHS == FoundRHS)
return CmpInst::isFalseWhenEqual(FoundPred);
// Check to see if we can make the LHS or RHS match.
if (LHS == FoundRHS || RHS == FoundLHS) {
if (isa<SCEVConstant>(RHS)) {
std::swap(FoundLHS, FoundRHS);
FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
} else {
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
}
}
// Check whether the found predicate is the same as the desired predicate.
if (FoundPred == Pred)
return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
// Check whether swapping the found predicate makes it the same as the
// desired predicate.
if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
if (isa<SCEVConstant>(RHS))
return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
else
return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
RHS, LHS, FoundLHS, FoundRHS);
}
// Unsigned comparison is the same as signed comparison when both the operands
// are non-negative.
if (CmpInst::isUnsigned(FoundPred) &&
CmpInst::getSignedPredicate(FoundPred) == Pred &&
isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
// Check if we can make progress by sharpening ranges.
if (FoundPred == ICmpInst::ICMP_NE &&
(isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
const SCEVConstant *C = nullptr;
const SCEV *V = nullptr;
if (isa<SCEVConstant>(FoundLHS)) {
C = cast<SCEVConstant>(FoundLHS);
V = FoundRHS;
} else {
C = cast<SCEVConstant>(FoundRHS);
V = FoundLHS;
}
// The guarding predicate tells us that C != V. If the known range
// of V is [C, t), we can sharpen the range to [C + 1, t). The
// range we consider has to correspond to same signedness as the
// predicate we're interested in folding.
APInt Min = ICmpInst::isSigned(Pred) ?
getSignedRangeMin(V) : getUnsignedRangeMin(V);
if (Min == C->getAPInt()) {
// Given (V >= Min && V != Min) we conclude V >= (Min + 1).
// This is true even if (Min + 1) wraps around -- in case of
// wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
APInt SharperMin = Min + 1;
switch (Pred) {
case ICmpInst::ICMP_SGE:
case ICmpInst::ICMP_UGE:
// We know V `Pred` SharperMin. If this implies LHS `Pred`
// RHS, we're done.
if (isImpliedCondOperands(Pred, LHS, RHS, V,
getConstant(SharperMin)))
return true;
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_UGT:
// We know from the range information that (V `Pred` Min ||
// V == Min). We know from the guarding condition that !(V
// == Min). This gives us
//
// V `Pred` Min || V == Min && !(V == Min)
// => V `Pred` Min
//
// If V `Pred` Min implies LHS `Pred` RHS, we're done.
if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
return true;
LLVM_FALLTHROUGH;
default:
// No change
break;
}
}
}
// Check whether the actual condition is beyond sufficient.
if (FoundPred == ICmpInst::ICMP_EQ)
if (ICmpInst::isTrueWhenEqual(Pred))
if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
return true;
if (Pred == ICmpInst::ICMP_NE)
if (!ICmpInst::isTrueWhenEqual(FoundPred))
if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
return true;
// Otherwise assume the worst.
return false;
}
bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
const SCEV *&L, const SCEV *&R,
SCEV::NoWrapFlags &Flags) {
const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
if (!AE || AE->getNumOperands() != 2)
return false;
L = AE->getOperand(0);
R = AE->getOperand(1);
Flags = AE->getNoWrapFlags();
return true;
}
Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More,
const SCEV *Less) {
// We avoid subtracting expressions here because this function is usually
// fairly deep in the call stack (i.e. is called many times).
// X - X = 0.
if (More == Less)
return APInt(getTypeSizeInBits(More->getType()), 0);
if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
const auto *LAR = cast<SCEVAddRecExpr>(Less);
const auto *MAR = cast<SCEVAddRecExpr>(More);
if (LAR->getLoop() != MAR->getLoop())
return None;
// We look at affine expressions only; not for correctness but to keep
// getStepRecurrence cheap.
if (!LAR->isAffine() || !MAR->isAffine())
return None;
if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
return None;
Less = LAR->getStart();
More = MAR->getStart();
// fall through
}
if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
const auto &M = cast<SCEVConstant>(More)->getAPInt();
const auto &L = cast<SCEVConstant>(Less)->getAPInt();
return M - L;
}
SCEV::NoWrapFlags Flags;
const SCEV *LLess = nullptr, *RLess = nullptr;
const SCEV *LMore = nullptr, *RMore = nullptr;
const SCEVConstant *C1 = nullptr, *C2 = nullptr;
// Compare (X + C1) vs X.
if (splitBinaryAdd(Less, LLess, RLess, Flags))
if ((C1 = dyn_cast<SCEVConstant>(LLess)))
if (RLess == More)
return -(C1->getAPInt());
// Compare X vs (X + C2).
if (splitBinaryAdd(More, LMore, RMore, Flags))
if ((C2 = dyn_cast<SCEVConstant>(LMore)))
if (RMore == Less)
return C2->getAPInt();
// Compare (X + C1) vs (X + C2).
if (C1 && C2 && RLess == RMore)
return C2->getAPInt() - C1->getAPInt();
return None;
}
bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS, const SCEV *FoundRHS) {
if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
return false;
const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
if (!AddRecLHS)
return false;
const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
if (!AddRecFoundLHS)
return false;
// We'd like to let SCEV reason about control dependencies, so we constrain
// both the inequalities to be about add recurrences on the same loop. This
// way we can use isLoopEntryGuardedByCond later.
const Loop *L = AddRecFoundLHS->getLoop();
if (L != AddRecLHS->getLoop())
return false;
// FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
//
// FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
// ... (2)
//
// Informal proof for (2), assuming (1) [*]:
//
// We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
//
// Then
//
// FoundLHS s< FoundRHS s< INT_MIN - C
// <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
// <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
// <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
// (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
// <=> FoundLHS + C s< FoundRHS + C
//
// [*]: (1) can be proved by ruling out overflow.
//
// [**]: This can be proved by analyzing all the four possibilities:
// (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
// (A s>= 0, B s>= 0).
//
// Note:
// Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
// will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
// = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
// s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
// neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
// C)".
Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
if (!LDiff || !RDiff || *LDiff != *RDiff)
return false;
if (LDiff->isMinValue())
return true;
APInt FoundRHSLimit;
if (Pred == CmpInst::ICMP_ULT) {
FoundRHSLimit = -(*RDiff);
} else {
assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
}
// Try to prove (1) or (2), as needed.
return isAvailableAtLoopEntry(FoundRHS, L) &&
isLoopEntryGuardedByCond(L, Pred, FoundRHS,
getConstant(FoundRHSLimit));
}
bool ScalarEvolution::isImpliedViaMerge(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS, unsigned Depth) {
const PHINode *LPhi = nullptr, *RPhi = nullptr;
auto ClearOnExit = make_scope_exit([&]() {
if (LPhi) {
bool Erased = PendingMerges.erase(LPhi);
assert(Erased && "Failed to erase LPhi!");
(void)Erased;
}
if (RPhi) {
bool Erased = PendingMerges.erase(RPhi);
assert(Erased && "Failed to erase RPhi!");
(void)Erased;
}
});
// Find respective Phis and check that they are not being pending.
if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS))
if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) {
if (!PendingMerges.insert(Phi).second)
return false;
LPhi = Phi;
}
if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS))
if (auto *Phi = dyn_cast<PHINode>(RU->getValue())) {
// If we detect a loop of Phi nodes being processed by this method, for
// example:
//
// %a = phi i32 [ %some1, %preheader ], [ %b, %latch ]
// %b = phi i32 [ %some2, %preheader ], [ %a, %latch ]
//
// we don't want to deal with a case that complex, so return conservative
// answer false.
if (!PendingMerges.insert(Phi).second)
return false;
RPhi = Phi;
}
// If none of LHS, RHS is a Phi, nothing to do here.
if (!LPhi && !RPhi)
return false;
// If there is a SCEVUnknown Phi we are interested in, make it left.
if (!LPhi) {
std::swap(LHS, RHS);
std::swap(FoundLHS, FoundRHS);
std::swap(LPhi, RPhi);
Pred = ICmpInst::getSwappedPredicate(Pred);
}
assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!");
const BasicBlock *LBB = LPhi->getParent();
const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) {
return isKnownViaNonRecursiveReasoning(Pred, S1, S2) ||
isImpliedCondOperandsViaRanges(Pred, S1, S2, FoundLHS, FoundRHS) ||
isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth);
};
if (RPhi && RPhi->getParent() == LBB) {
// Case one: RHS is also a SCEVUnknown Phi from the same basic block.
// If we compare two Phis from the same block, and for each entry block
// the predicate is true for incoming values from this block, then the
// predicate is also true for the Phis.
for (const BasicBlock *IncBB : predecessors(LBB)) {
const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB));
if (!ProvedEasily(L, R))
return false;
}
} else if (RAR && RAR->getLoop()->getHeader() == LBB) {
// Case two: RHS is also a Phi from the same basic block, and it is an
// AddRec. It means that there is a loop which has both AddRec and Unknown
// PHIs, for it we can compare incoming values of AddRec from above the loop
// and latch with their respective incoming values of LPhi.
// TODO: Generalize to handle loops with many inputs in a header.
if (LPhi->getNumIncomingValues() != 2) return false;
auto *RLoop = RAR->getLoop();
auto *Predecessor = RLoop->getLoopPredecessor();
assert(Predecessor && "Loop with AddRec with no predecessor?");
const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor));
if (!ProvedEasily(L1, RAR->getStart()))
return false;
auto *Latch = RLoop->getLoopLatch();
assert(Latch && "Loop with AddRec with no latch?");
const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch));
if (!ProvedEasily(L2, RAR->getPostIncExpr(*this)))
return false;
} else {
// In all other cases go over inputs of LHS and compare each of them to RHS,
// the predicate is true for (LHS, RHS) if it is true for all such pairs.
// At this point RHS is either a non-Phi, or it is a Phi from some block
// different from LBB.
for (const BasicBlock *IncBB : predecessors(LBB)) {
// Check that RHS is available in this block.
if (!dominates(RHS, IncBB))
return false;
const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
if (!ProvedEasily(L, RHS))
return false;
}
}
return true;
}
bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS) {
if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
return true;
if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
return true;
return isImpliedCondOperandsHelper(Pred, LHS, RHS,
FoundLHS, FoundRHS) ||
// ~x < ~y --> x > y
isImpliedCondOperandsHelper(Pred, LHS, RHS,
getNotSCEV(FoundRHS),
getNotSCEV(FoundLHS));
}
/// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values?
template <typename MinMaxExprType>
static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr,
const SCEV *Candidate) {
const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr);
if (!MinMaxExpr)
return false;
return find(MinMaxExpr->operands(), Candidate) != MinMaxExpr->op_end();
}
static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// If both sides are affine addrecs for the same loop, with equal
// steps, and we know the recurrences don't wrap, then we only
// need to check the predicate on the starting values.
if (!ICmpInst::isRelational(Pred))
return false;
const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
if (!LAR)
return false;
const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
if (!RAR)
return false;
if (LAR->getLoop() != RAR->getLoop())
return false;
if (!LAR->isAffine() || !RAR->isAffine())
return false;
if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
return false;
SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
SCEV::FlagNSW : SCEV::FlagNUW;
if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
return false;
return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
}
/// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
/// expression?
static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
switch (Pred) {
default:
return false;
case ICmpInst::ICMP_SGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SLE:
return
// min(A, ...) <= A
IsMinMaxConsistingOf<SCEVSMinExpr>(LHS, RHS) ||
// A <= max(A, ...)
IsMinMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
case ICmpInst::ICMP_UGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_ULE:
return
// min(A, ...) <= A
IsMinMaxConsistingOf<SCEVUMinExpr>(LHS, RHS) ||
// A <= max(A, ...)
IsMinMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
}
llvm_unreachable("covered switch fell through?!");
}
bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS,
unsigned Depth) {
assert(getTypeSizeInBits(LHS->getType()) ==
getTypeSizeInBits(RHS->getType()) &&
"LHS and RHS have different sizes?");
assert(getTypeSizeInBits(FoundLHS->getType()) ==
getTypeSizeInBits(FoundRHS->getType()) &&
"FoundLHS and FoundRHS have different sizes?");
// We want to avoid hurting the compile time with analysis of too big trees.
if (Depth > MaxSCEVOperationsImplicationDepth)
return false;
// We only want to work with ICMP_SGT comparison so far.
// TODO: Extend to ICMP_UGT?
if (Pred == ICmpInst::ICMP_SLT) {
Pred = ICmpInst::ICMP_SGT;
std::swap(LHS, RHS);
std::swap(FoundLHS, FoundRHS);
}
if (Pred != ICmpInst::ICMP_SGT)
return false;
auto GetOpFromSExt = [&](const SCEV *S) {
if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S))
return Ext->getOperand();
// TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off
// the constant in some cases.
return S;
};
// Acquire values from extensions.
auto *OrigLHS = LHS;
auto *OrigFoundLHS = FoundLHS;
LHS = GetOpFromSExt(LHS);
FoundLHS = GetOpFromSExt(FoundLHS);
// Is the SGT predicate can be proved trivially or using the found context.
auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) {
return isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGT, S1, S2) ||
isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS,
FoundRHS, Depth + 1);
};
if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) {
// We want to avoid creation of any new non-constant SCEV. Since we are
// going to compare the operands to RHS, we should be certain that we don't
// need any size extensions for this. So let's decline all cases when the
// sizes of types of LHS and RHS do not match.
// TODO: Maybe try to get RHS from sext to catch more cases?
if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType()))
return false;
// Should not overflow.
if (!LHSAddExpr->hasNoSignedWrap())
return false;
auto *LL = LHSAddExpr->getOperand(0);
auto *LR = LHSAddExpr->getOperand(1);
auto *MinusOne = getNegativeSCEV(getOne(RHS->getType()));
// Checks that S1 >= 0 && S2 > RHS, trivially or using the found context.
auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) {
return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS);
};
// Try to prove the following rule:
// (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS).
// (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS).
if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL))
return true;
} else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) {
Value *LL, *LR;
// FIXME: Once we have SDiv implemented, we can get rid of this matching.
using namespace llvm::PatternMatch;
if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) {
// Rules for division.
// We are going to perform some comparisons with Denominator and its
// derivative expressions. In general case, creating a SCEV for it may
// lead to a complex analysis of the entire graph, and in particular it
// can request trip count recalculation for the same loop. This would
// cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid
// this, we only want to create SCEVs that are constants in this section.
// So we bail if Denominator is not a constant.
if (!isa<ConstantInt>(LR))
return false;
auto *Denominator = cast<SCEVConstant>(getSCEV(LR));
// We want to make sure that LHS = FoundLHS / Denominator. If it is so,
// then a SCEV for the numerator already exists and matches with FoundLHS.
auto *Numerator = getExistingSCEV(LL);
if (!Numerator || Numerator->getType() != FoundLHS->getType())
return false;
// Make sure that the numerator matches with FoundLHS and the denominator
// is positive.
if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator))
return false;
auto *DTy = Denominator->getType();
auto *FRHSTy = FoundRHS->getType();
if (DTy->isPointerTy() != FRHSTy->isPointerTy())
// One of types is a pointer and another one is not. We cannot extend
// them properly to a wider type, so let us just reject this case.
// TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help
// to avoid this check.
return false;
// Given that:
// FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0.
auto *WTy = getWiderType(DTy, FRHSTy);
auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy);
auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy);
// Try to prove the following rule:
// (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS).
// For example, given that FoundLHS > 2. It means that FoundLHS is at
// least 3. If we divide it by Denominator < 4, we will have at least 1.
auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2));
if (isKnownNonPositive(RHS) &&
IsSGTViaContext(FoundRHSExt, DenomMinusTwo))
return true;
// Try to prove the following rule:
// (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS).
// For example, given that FoundLHS > -3. Then FoundLHS is at least -2.
// If we divide it by Denominator > 2, then:
// 1. If FoundLHS is negative, then the result is 0.
// 2. If FoundLHS is non-negative, then the result is non-negative.
// Anyways, the result is non-negative.
auto *MinusOne = getNegativeSCEV(getOne(WTy));
auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt);
if (isKnownNegative(RHS) &&
IsSGTViaContext(FoundRHSExt, NegDenomMinusOne))
return true;
}
}
// If our expression contained SCEVUnknown Phis, and we split it down and now
// need to prove something for them, try to prove the predicate for every
// possible incoming values of those Phis.
if (isImpliedViaMerge(Pred, OrigLHS, RHS, OrigFoundLHS, FoundRHS, Depth + 1))
return true;
return false;
}
static bool isKnownPredicateExtendIdiom(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// zext x u<= sext x, sext x s<= zext x
switch (Pred) {
case ICmpInst::ICMP_SGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SLE: {
// If operand >=s 0 then ZExt == SExt. If operand <s 0 then SExt <s ZExt.
const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(LHS);
const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(RHS);
if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
return true;
break;
}
case ICmpInst::ICMP_UGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_ULE: {
// If operand >=s 0 then ZExt == SExt. If operand <s 0 then ZExt <u SExt.
const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS);
const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(RHS);
if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
return true;
break;
}
default:
break;
};
return false;
}
bool
ScalarEvolution::isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
return isKnownPredicateExtendIdiom(Pred, LHS, RHS) ||
isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
}
bool
ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS) {
switch (Pred) {
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
case ICmpInst::ICMP_EQ:
case ICmpInst::ICMP_NE:
if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE:
if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS))
return true;
break;
}
// Maybe it can be proved via operations?
if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS))
return true;
return false;
}
bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
const SCEV *LHS,
const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS) {
if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
// The restriction on `FoundRHS` be lifted easily -- it exists only to
// reduce the compile time impact of this optimization.
return false;
Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
if (!Addend)
return false;
const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
// `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
// antecedent "`FoundLHS` `Pred` `FoundRHS`".
ConstantRange FoundLHSRange =
ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
// Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));
// We can also compute the range of values for `LHS` that satisfy the
// consequent, "`LHS` `Pred` `RHS`":
const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
ConstantRange SatisfyingLHSRange =
ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
// The antecedent implies the consequent if every value of `LHS` that
// satisfies the antecedent also satisfies the consequent.
return SatisfyingLHSRange.contains(LHSRange);
}
bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
bool IsSigned, bool NoWrap) {
assert(isKnownPositive(Stride) && "Positive stride expected!");
if (NoWrap) return false;
unsigned BitWidth = getTypeSizeInBits(RHS->getType());
const SCEV *One = getOne(Stride->getType());
if (IsSigned) {
APInt MaxRHS = getSignedRangeMax(RHS);
APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
// SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS);
}
APInt MaxRHS = getUnsignedRangeMax(RHS);
APInt MaxValue = APInt::getMaxValue(BitWidth);
APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
// UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS);
}
bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
bool IsSigned, bool NoWrap) {
if (NoWrap) return false;
unsigned BitWidth = getTypeSizeInBits(RHS->getType());
const SCEV *One = getOne(Stride->getType());
if (IsSigned) {
APInt MinRHS = getSignedRangeMin(RHS);
APInt MinValue = APInt::getSignedMinValue(BitWidth);
APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
// SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS);
}
APInt MinRHS = getUnsignedRangeMin(RHS);
APInt MinValue = APInt::getMinValue(BitWidth);
APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
// UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS);
}
const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
bool Equality) {
const SCEV *One = getOne(Step->getType());
Delta = Equality ? getAddExpr(Delta, Step)
: getAddExpr(Delta, getMinusSCEV(Step, One));
return getUDivExpr(Delta, Step);
}
const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
const SCEV *Stride,
const SCEV *End,
unsigned BitWidth,
bool IsSigned) {
assert(!isKnownNonPositive(Stride) &&
"Stride is expected strictly positive!");
// Calculate the maximum backedge count based on the range of values
// permitted by Start, End, and Stride.
const SCEV *MaxBECount;
APInt MinStart =
IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);
APInt StrideForMaxBECount =
IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
// We already know that the stride is positive, so we paper over conservatism
// in our range computation by forcing StrideForMaxBECount to be at least one.
// In theory this is unnecessary, but we expect MaxBECount to be a
// SCEVConstant, and (udiv <constant> 0) is not constant folded by SCEV (there
// is nothing to constant fold it to).
APInt One(BitWidth, 1, IsSigned);
StrideForMaxBECount = APIntOps::smax(One, StrideForMaxBECount);
APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth)
: APInt::getMaxValue(BitWidth);
APInt Limit = MaxValue - (StrideForMaxBECount - 1);
// Although End can be a MAX expression we estimate MaxEnd considering only
// the case End = RHS of the loop termination condition. This is safe because
// in the other case (End - Start) is zero, leading to a zero maximum backedge
// taken count.
APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit)
: APIntOps::umin(getUnsignedRangeMax(End), Limit);
MaxBECount = computeBECount(getConstant(MaxEnd - MinStart) /* Delta */,
getConstant(StrideForMaxBECount) /* Step */,
false /* Equality */);
return MaxBECount;
}
ScalarEvolution::ExitLimit
ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
const Loop *L, bool IsSigned,
bool ControlsExit, bool AllowPredicates) {
SmallPtrSet<const SCEVPredicate *, 4> Predicates;
const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
bool PredicatedIV = false;
if (!IV && AllowPredicates) {
// Try to make this an AddRec using runtime tests, in the first X
// iterations of this loop, where X is the SCEV expression found by the
// algorithm below.
IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
PredicatedIV = true;
}
// Avoid weird loops
if (!IV || IV->getLoop() != L || !IV->isAffine())
return getCouldNotCompute();
bool NoWrap = ControlsExit &&
IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
const SCEV *Stride = IV->getStepRecurrence(*this);
bool PositiveStride = isKnownPositive(Stride);
// Avoid negative or zero stride values.
if (!PositiveStride) {
// We can compute the correct backedge taken count for loops with unknown
// strides if we can prove that the loop is not an infinite loop with side
// effects. Here's the loop structure we are trying to handle -
//
// i = start
// do {
// A[i] = i;
// i += s;
// } while (i < end);
//
// The backedge taken count for such loops is evaluated as -
// (max(end, start + stride) - start - 1) /u stride
//
// The additional preconditions that we need to check to prove correctness
// of the above formula is as follows -
//
// a) IV is either nuw or nsw depending upon signedness (indicated by the
// NoWrap flag).
// b) loop is single exit with no side effects.
//
//
// Precondition a) implies that if the stride is negative, this is a single
// trip loop. The backedge taken count formula reduces to zero in this case.
//
// Precondition b) implies that the unknown stride cannot be zero otherwise
// we have UB.
//
// The positive stride case is the same as isKnownPositive(Stride) returning
// true (original behavior of the function).
//
// We want to make sure that the stride is truly unknown as there are edge
// cases where ScalarEvolution propagates no wrap flags to the
// post-increment/decrement IV even though the increment/decrement operation
// itself is wrapping. The computed backedge taken count may be wrong in
// such cases. This is prevented by checking that the stride is not known to
// be either positive or non-positive. For example, no wrap flags are
// propagated to the post-increment IV of this loop with a trip count of 2 -
//
// unsigned char i;
// for(i=127; i<128; i+=129)
// A[i] = i;
//
if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) ||
!loopHasNoSideEffects(L))
return getCouldNotCompute();
} else if (!Stride->isOne() &&
doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
// Avoid proven overflow cases: this will ensure that the backedge taken
// count will not generate any unsigned overflow. Relaxed no-overflow
// conditions exploit NoWrapFlags, allowing to optimize in presence of
// undefined behaviors like the case of C language.
return getCouldNotCompute();
ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
: ICmpInst::ICMP_ULT;
const SCEV *Start = IV->getStart();
const SCEV *End = RHS;
// When the RHS is not invariant, we do not know the end bound of the loop and
// cannot calculate the ExactBECount needed by ExitLimit. However, we can
// calculate the MaxBECount, given the start, stride and max value for the end
// bound of the loop (RHS), and the fact that IV does not overflow (which is
// checked above).
if (!isLoopInvariant(RHS, L)) {
const SCEV *MaxBECount = computeMaxBECountForLT(
Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
false /*MaxOrZero*/, Predicates);
}
// If the backedge is taken at least once, then it will be taken
// (End-Start)/Stride times (rounded up to a multiple of Stride), where Start
// is the LHS value of the less-than comparison the first time it is evaluated
// and End is the RHS.
const SCEV *BECountIfBackedgeTaken =
computeBECount(getMinusSCEV(End, Start), Stride, false);
// If the loop entry is guarded by the result of the backedge test of the
// first loop iteration, then we know the backedge will be taken at least
// once and so the backedge taken count is as above. If not then we use the
// expression (max(End,Start)-Start)/Stride to describe the backedge count,
// as if the backedge is taken at least once max(End,Start) is End and so the
// result is as above, and if not max(End,Start) is Start so we get a backedge
// count of zero.
const SCEV *BECount;
if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
BECount = BECountIfBackedgeTaken;
else {
End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
}
const SCEV *MaxBECount;
bool MaxOrZero = false;
if (isa<SCEVConstant>(BECount))
MaxBECount = BECount;
else if (isa<SCEVConstant>(BECountIfBackedgeTaken)) {
// If we know exactly how many times the backedge will be taken if it's
// taken at least once, then the backedge count will either be that or
// zero.
MaxBECount = BECountIfBackedgeTaken;
MaxOrZero = true;
} else {
MaxBECount = computeMaxBECountForLT(
Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
}
if (isa<SCEVCouldNotCompute>(MaxBECount) &&
!isa<SCEVCouldNotCompute>(BECount))
MaxBECount = getConstant(getUnsignedRangeMax(BECount));
return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates);
}
ScalarEvolution::ExitLimit
ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
const Loop *L, bool IsSigned,
bool ControlsExit, bool AllowPredicates) {
SmallPtrSet<const SCEVPredicate *, 4> Predicates;
// We handle only IV > Invariant
if (!isLoopInvariant(RHS, L))
return getCouldNotCompute();
const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
if (!IV && AllowPredicates)
// Try to make this an AddRec using runtime tests, in the first X
// iterations of this loop, where X is the SCEV expression found by the
// algorithm below.
IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
// Avoid weird loops
if (!IV || IV->getLoop() != L || !IV->isAffine())
return getCouldNotCompute();
bool NoWrap = ControlsExit &&
IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
// Avoid negative or zero stride values
if (!isKnownPositive(Stride))
return getCouldNotCompute();
// Avoid proven overflow cases: this will ensure that the backedge taken count
// will not generate any unsigned overflow. Relaxed no-overflow conditions
// exploit NoWrapFlags, allowing to optimize in presence of undefined
// behaviors like the case of C language.
if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
return getCouldNotCompute();
ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
: ICmpInst::ICMP_UGT;
const SCEV *Start = IV->getStart();
const SCEV *End = RHS;
if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
APInt MaxStart = IsSigned ? getSignedRangeMax(Start)
: getUnsignedRangeMax(Start);
APInt MinStride = IsSigned ? getSignedRangeMin(Stride)
: getUnsignedRangeMin(Stride);
unsigned BitWidth = getTypeSizeInBits(LHS->getType());
APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
: APInt::getMinValue(BitWidth) + (MinStride - 1);
// Although End can be a MIN expression we estimate MinEnd considering only
// the case End = RHS. This is safe because in the other case (Start - End)
// is zero, leading to a zero maximum backedge taken count.
APInt MinEnd =
IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit)
: APIntOps::umax(getUnsignedRangeMin(RHS), Limit);
const SCEV *MaxBECount = isa<SCEVConstant>(BECount)
? BECount
: computeBECount(getConstant(MaxStart - MinEnd),
getConstant(MinStride), false);
if (isa<SCEVCouldNotCompute>(MaxBECount))
MaxBECount = BECount;
return ExitLimit(BECount, MaxBECount, false, Predicates);
}
const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
ScalarEvolution &SE) const {
if (Range.isFullSet()) // Infinite loop.
return SE.getCouldNotCompute();
// If the start is a non-zero constant, shift the range to simplify things.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
if (!SC->getValue()->isZero()) {
SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
Operands[0] = SE.getZero(SC->getType());
const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
getNoWrapFlags(FlagNW));
if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
return ShiftedAddRec->getNumIterationsInRange(
Range.subtract(SC->getAPInt()), SE);
// This is strange and shouldn't happen.
return SE.getCouldNotCompute();
}
// The only time we can solve this is when we have all constant indices.
// Otherwise, we cannot determine the overflow conditions.
if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
return SE.getCouldNotCompute();
// Okay at this point we know that all elements of the chrec are constants and
// that the start element is zero.
// First check to see if the range contains zero. If not, the first
// iteration exits.
unsigned BitWidth = SE.getTypeSizeInBits(getType());
if (!Range.contains(APInt(BitWidth, 0)))
return SE.getZero(getType());
if (isAffine()) {
// If this is an affine expression then we have this situation:
// Solve {0,+,A} in Range === Ax in Range
// We know that zero is in the range. If A is positive then we know that
// the upper value of the range must be the first possible exit value.
// If A is negative then the lower of the range is the last possible loop
// value. Also note that we already checked for a full range.
APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower();
// The exit value should be (End+A)/A.
APInt ExitVal = (End + A).udiv(A);
ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
// Evaluate at the exit value. If we really did fall out of the valid
// range, then we computed our trip count, otherwise wrap around or other
// things must have happened.
ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
if (Range.contains(Val->getValue()))
return SE.getCouldNotCompute(); // Something strange happened
// Ensure that the previous value is in the range. This is a sanity check.
assert(Range.contains(
EvaluateConstantChrecAtConstant(this,
ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) &&
"Linear scev computation is off in a bad way!");
return SE.getConstant(ExitValue);
}
if (isQuadratic()) {
if (auto S = SolveQuadraticAddRecRange(this, Range, SE))
return SE.getConstant(S.getValue());
}
return SE.getCouldNotCompute();
}
const SCEVAddRecExpr *
SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const {
assert(getNumOperands() > 1 && "AddRec with zero step?");
// There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)),
// but in this case we cannot guarantee that the value returned will be an
// AddRec because SCEV does not have a fixed point where it stops
// simplification: it is legal to return ({rec1} + {rec2}). For example, it
// may happen if we reach arithmetic depth limit while simplifying. So we
// construct the returned value explicitly.
SmallVector<const SCEV *, 3> Ops;
// If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and
// (this + Step) is {A+B,+,B+C,+...,+,N}.
for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i)
Ops.push_back(SE.getAddExpr(getOperand(i), getOperand(i + 1)));
// We know that the last operand is not a constant zero (otherwise it would
// have been popped out earlier). This guarantees us that if the result has
// the same last operand, then it will also not be popped out, meaning that
// the returned value will be an AddRec.
const SCEV *Last = getOperand(getNumOperands() - 1);
assert(!Last->isZero() && "Recurrency with zero step?");
Ops.push_back(Last);
return cast<SCEVAddRecExpr>(SE.getAddRecExpr(Ops, getLoop(),
SCEV::FlagAnyWrap));
}
// Return true when S contains at least an undef value.
static inline bool containsUndefs(const SCEV *S) {
return SCEVExprContains(S, [](const SCEV *S) {
if (const auto *SU = dyn_cast<SCEVUnknown>(S))
return isa<UndefValue>(SU->getValue());
return false;
});
}
namespace {
// Collect all steps of SCEV expressions.
struct SCEVCollectStrides {
ScalarEvolution &SE;
SmallVectorImpl<const SCEV *> &Strides;
SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
: SE(SE), Strides(S) {}
bool follow(const SCEV *S) {
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
Strides.push_back(AR->getStepRecurrence(SE));
return true;
}
bool isDone() const { return false; }
};
// Collect all SCEVUnknown and SCEVMulExpr expressions.
struct SCEVCollectTerms {
SmallVectorImpl<const SCEV *> &Terms;
SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {}
bool follow(const SCEV *S) {
if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) ||
isa<SCEVSignExtendExpr>(S)) {
if (!containsUndefs(S))
Terms.push_back(S);
// Stop recursion: once we collected a term, do not walk its operands.
return false;
}
// Keep looking.
return true;
}
bool isDone() const { return false; }
};
// Check if a SCEV contains an AddRecExpr.
struct SCEVHasAddRec {
bool &ContainsAddRec;
SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
ContainsAddRec = false;
}
bool follow(const SCEV *S) {
if (isa<SCEVAddRecExpr>(S)) {
ContainsAddRec = true;
// Stop recursion: once we collected a term, do not walk its operands.
return false;
}
// Keep looking.
return true;
}
bool isDone() const { return false; }
};
// Find factors that are multiplied with an expression that (possibly as a
// subexpression) contains an AddRecExpr. In the expression:
//
// 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
//
// "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
// that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
// parameters as they form a product with an induction variable.
//
// This collector expects all array size parameters to be in the same MulExpr.
// It might be necessary to later add support for collecting parameters that are
// spread over different nested MulExpr.
struct SCEVCollectAddRecMultiplies {
SmallVectorImpl<const SCEV *> &Terms;
ScalarEvolution &SE;
SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
: Terms(T), SE(SE) {}
bool follow(const SCEV *S) {
if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
bool HasAddRec = false;
SmallVector<const SCEV *, 0> Operands;
for (auto Op : Mul->operands()) {
const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op);
if (Unknown && !isa<CallInst>(Unknown->getValue())) {
Operands.push_back(Op);
} else if (Unknown) {
HasAddRec = true;
} else {
bool ContainsAddRec = false;
SCEVHasAddRec ContiansAddRec(ContainsAddRec);
visitAll(Op, ContiansAddRec);
HasAddRec |= ContainsAddRec;
}
}
if (Operands.size() == 0)
return true;
if (!HasAddRec)
return false;
Terms.push_back(SE.getMulExpr(Operands));
// Stop recursion: once we collected a term, do not walk its operands.
return false;
}
// Keep looking.
return true;
}
bool isDone() const { return false; }
};
} // end anonymous namespace
/// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
/// two places:
/// 1) The strides of AddRec expressions.
/// 2) Unknowns that are multiplied with AddRec expressions.
void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
SmallVectorImpl<const SCEV *> &Terms) {
SmallVector<const SCEV *, 4> Strides;
SCEVCollectStrides StrideCollector(*this, Strides);
visitAll(Expr, StrideCollector);
LLVM_DEBUG({
dbgs() << "Strides:\n";
for (const SCEV *S : Strides)
dbgs() << *S << "\n";
});
for (const SCEV *S : Strides) {
SCEVCollectTerms TermCollector(Terms);
visitAll(S, TermCollector);
}
LLVM_DEBUG({
dbgs() << "Terms:\n";
for (const SCEV *T : Terms)
dbgs() << *T << "\n";
});
SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
visitAll(Expr, MulCollector);
}
static bool findArrayDimensionsRec(ScalarEvolution &SE,
SmallVectorImpl<const SCEV *> &Terms,
SmallVectorImpl<const SCEV *> &Sizes) {
int Last = Terms.size() - 1;
const SCEV *Step = Terms[Last];
// End of recursion.
if (Last == 0) {
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
SmallVector<const SCEV *, 2> Qs;
for (const SCEV *Op : M->operands())
if (!isa<SCEVConstant>(Op))
Qs.push_back(Op);
Step = SE.getMulExpr(Qs);
}
Sizes.push_back(Step);
return true;
}
for (const SCEV *&Term : Terms) {
// Normalize the terms before the next call to findArrayDimensionsRec.
const SCEV *Q, *R;
SCEVDivision::divide(SE, Term, Step, &Q, &R);
// Bail out when GCD does not evenly divide one of the terms.
if (!R->isZero())
return false;
Term = Q;
}
// Remove all SCEVConstants.
Terms.erase(
remove_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); }),
Terms.end());
if (Terms.size() > 0)
if (!findArrayDimensionsRec(SE, Terms, Sizes))
return false;
Sizes.push_back(Step);
return true;
}
// Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
for (const SCEV *T : Terms)
if (SCEVExprContains(T, isa<SCEVUnknown, const SCEV *>))
return true;
return false;
}
// Return the number of product terms in S.
static inline int numberOfTerms(const SCEV *S) {
if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
return Expr->getNumOperands();
return 1;
}
static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
if (isa<SCEVConstant>(T))
return nullptr;
if (isa<SCEVUnknown>(T))
return T;
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
SmallVector<const SCEV *, 2> Factors;
for (const SCEV *Op : M->operands())
if (!isa<SCEVConstant>(Op))
Factors.push_back(Op);
return SE.getMulExpr(Factors);
}
return T;
}
/// Return the size of an element read or written by Inst.
const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
Type *Ty;
if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
Ty = Store->getValueOperand()->getType();
else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
Ty = Load->getType();
else
return nullptr;
Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
return getSizeOfExpr(ETy, Ty);
}
void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
SmallVectorImpl<const SCEV *> &Sizes,
const SCEV *ElementSize) {
if (Terms.size() < 1 || !ElementSize)
return;
// Early return when Terms do not contain parameters: we do not delinearize
// non parametric SCEVs.
if (!containsParameters(Terms))
return;
LLVM_DEBUG({
dbgs() << "Terms:\n";
for (const SCEV *T : Terms)
dbgs() << *T << "\n";
});
// Remove duplicates.
array_pod_sort(Terms.begin(), Terms.end());
Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
// Put larger terms first.
llvm::sort(Terms, [](const SCEV *LHS, const SCEV *RHS) {
return numberOfTerms(LHS) > numberOfTerms(RHS);
});
// Try to divide all terms by the element size. If term is not divisible by
// element size, proceed with the original term.
for (const SCEV *&Term : Terms) {
const SCEV *Q, *R;
SCEVDivision::divide(*this, Term, ElementSize, &Q, &R);
if (!Q->isZero())
Term = Q;
}
SmallVector<const SCEV *, 4> NewTerms;
// Remove constant factors.
for (const SCEV *T : Terms)
if (const SCEV *NewT = removeConstantFactors(*this, T))
NewTerms.push_back(NewT);
LLVM_DEBUG({
dbgs() << "Terms after sorting:\n";
for (const SCEV *T : NewTerms)
dbgs() << *T << "\n";
});
if (NewTerms.empty() || !findArrayDimensionsRec(*this, NewTerms, Sizes)) {
Sizes.clear();
return;
}
// The last element to be pushed into Sizes is the size of an element.
Sizes.push_back(ElementSize);
LLVM_DEBUG({
dbgs() << "Sizes:\n";
for (const SCEV *S : Sizes)
dbgs() << *S << "\n";
});
}
void ScalarEvolution::computeAccessFunctions(
const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
SmallVectorImpl<const SCEV *> &Sizes) {
// Early exit in case this SCEV is not an affine multivariate function.
if (Sizes.empty())
return;
if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
if (!AR->isAffine())
return;
const SCEV *Res = Expr;
int Last = Sizes.size() - 1;
for (int i = Last; i >= 0; i--) {
const SCEV *Q, *R;
SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
LLVM_DEBUG({
dbgs() << "Res: " << *Res << "\n";
dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
dbgs() << "Res divided by Sizes[i]:\n";
dbgs() << "Quotient: " << *Q << "\n";
dbgs() << "Remainder: " << *R << "\n";
});
Res = Q;
// Do not record the last subscript corresponding to the size of elements in
// the array.
if (i == Last) {
// Bail out if the remainder is too complex.
if (isa<SCEVAddRecExpr>(R)) {
Subscripts.clear();
Sizes.clear();
return;
}
continue;
}
// Record the access function for the current subscript.
Subscripts.push_back(R);
}
// Also push in last position the remainder of the last division: it will be
// the access function of the innermost dimension.
Subscripts.push_back(Res);
std::reverse(Subscripts.begin(), Subscripts.end());
LLVM_DEBUG({
dbgs() << "Subscripts:\n";
for (const SCEV *S : Subscripts)
dbgs() << *S << "\n";
});
}
/// Splits the SCEV into two vectors of SCEVs representing the subscripts and
/// sizes of an array access. Returns the remainder of the delinearization that
/// is the offset start of the array. The SCEV->delinearize algorithm computes
/// the multiples of SCEV coefficients: that is a pattern matching of sub
/// expressions in the stride and base of a SCEV corresponding to the
/// computation of a GCD (greatest common divisor) of base and stride. When
/// SCEV->delinearize fails, it returns the SCEV unchanged.
///
/// For example: when analyzing the memory access A[i][j][k] in this loop nest
///
/// void foo(long n, long m, long o, double A[n][m][o]) {
///
/// for (long i = 0; i < n; i++)
/// for (long j = 0; j < m; j++)
/// for (long k = 0; k < o; k++)
/// A[i][j][k] = 1.0;
/// }
///
/// the delinearization input is the following AddRec SCEV:
///
/// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
///
/// From this SCEV, we are able to say that the base offset of the access is %A
/// because it appears as an offset that does not divide any of the strides in
/// the loops:
///
/// CHECK: Base offset: %A
///
/// and then SCEV->delinearize determines the size of some of the dimensions of
/// the array as these are the multiples by which the strides are happening:
///
/// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
///
/// Note that the outermost dimension remains of UnknownSize because there are
/// no strides that would help identifying the size of the last dimension: when
/// the array has been statically allocated, one could compute the size of that
/// dimension by dividing the overall size of the array by the size of the known
/// dimensions: %m * %o * 8.
///
/// Finally delinearize provides the access functions for the array reference
/// that does correspond to A[i][j][k] of the above C testcase:
///
/// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
///
/// The testcases are checking the output of a function pass:
/// DelinearizationPass that walks through all loads and stores of a function
/// asking for the SCEV of the memory access with respect to all enclosing
/// loops, calling SCEV->delinearize on that and printing the results.
void ScalarEvolution::delinearize(const SCEV *Expr,
SmallVectorImpl<const SCEV *> &Subscripts,
SmallVectorImpl<const SCEV *> &Sizes,
const SCEV *ElementSize) {
// First step: collect parametric terms.
SmallVector<const SCEV *, 4> Terms;
collectParametricTerms(Expr, Terms);
if (Terms.empty())
return;
// Second step: find subscript sizes.
findArrayDimensions(Terms, Sizes, ElementSize);
if (Sizes.empty())
return;
// Third step: compute the access functions for each subscript.
computeAccessFunctions(Expr, Subscripts, Sizes);
if (Subscripts.empty())
return;
LLVM_DEBUG({
dbgs() << "succeeded to delinearize " << *Expr << "\n";
dbgs() << "ArrayDecl[UnknownSize]";
for (const SCEV *S : Sizes)
dbgs() << "[" << *S << "]";
dbgs() << "\nArrayRef";
for (const SCEV *S : Subscripts)
dbgs() << "[" << *S << "]";
dbgs() << "\n";
});
}
bool ScalarEvolution::getIndexExpressionsFromGEP(
const GetElementPtrInst *GEP, SmallVectorImpl<const SCEV *> &Subscripts,
SmallVectorImpl<int> &Sizes) {
assert(Subscripts.empty() && Sizes.empty() &&
"Expected output lists to be empty on entry to this function.");
assert(GEP && "getIndexExpressionsFromGEP called with a null GEP");
Type *Ty = GEP->getPointerOperandType();
bool DroppedFirstDim = false;
for (unsigned i = 1; i < GEP->getNumOperands(); i++) {
const SCEV *Expr = getSCEV(GEP->getOperand(i));
if (i == 1) {
if (auto *PtrTy = dyn_cast<PointerType>(Ty)) {
Ty = PtrTy->getElementType();
} else if (auto *ArrayTy = dyn_cast<ArrayType>(Ty)) {
Ty = ArrayTy->getElementType();
} else {
Subscripts.clear();
Sizes.clear();
return false;
}
if (auto *Const = dyn_cast<SCEVConstant>(Expr))
if (Const->getValue()->isZero()) {
DroppedFirstDim = true;
continue;
}
Subscripts.push_back(Expr);
continue;
}
auto *ArrayTy = dyn_cast<ArrayType>(Ty);
if (!ArrayTy) {
Subscripts.clear();
Sizes.clear();
return false;
}
Subscripts.push_back(Expr);
if (!(DroppedFirstDim && i == 2))
Sizes.push_back(ArrayTy->getNumElements());
Ty = ArrayTy->getElementType();
}
return !Subscripts.empty();
}
//===----------------------------------------------------------------------===//
// SCEVCallbackVH Class Implementation
//===----------------------------------------------------------------------===//
void ScalarEvolution::SCEVCallbackVH::deleted() {
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->eraseValueFromMap(getValPtr());
// this now dangles!
}
void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
// Forget all the expressions associated with users of the old value,
// so that future queries will recompute the expressions using the new
// value.
Value *Old = getValPtr();
SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
SmallPtrSet<User *, 8> Visited;
while (!Worklist.empty()) {
User *U = Worklist.pop_back_val();
// Deleting the Old value will cause this to dangle. Postpone
// that until everything else is done.
if (U == Old)
continue;
if (!Visited.insert(U).second)
continue;
if (PHINode *PN = dyn_cast<PHINode>(U))
SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->eraseValueFromMap(U);
Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
}
// Delete the Old value.
if (PHINode *PN = dyn_cast<PHINode>(Old))
SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->eraseValueFromMap(Old);
// this now dangles!
}
ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
: CallbackVH(V), SE(se) {}
//===----------------------------------------------------------------------===//
// ScalarEvolution Class Implementation
//===----------------------------------------------------------------------===//
ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
AssumptionCache &AC, DominatorTree &DT,
LoopInfo &LI)
: F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64),
LoopDispositions(64), BlockDispositions(64) {
// To use guards for proving predicates, we need to scan every instruction in
// relevant basic blocks, and not just terminators. Doing this is a waste of
// time if the IR does not actually contain any calls to
// @llvm.experimental.guard, so do a quick check and remember this beforehand.
//
// This pessimizes the case where a pass that preserves ScalarEvolution wants
// to _add_ guards to the module when there weren't any before, and wants
// ScalarEvolution to optimize based on those guards. For now we prefer to be
// efficient in lieu of being smart in that rather obscure case.
auto *GuardDecl = F.getParent()->getFunction(
Intrinsic::getName(Intrinsic::experimental_guard));
HasGuards = GuardDecl && !GuardDecl->use_empty();
}
ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
: F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
ValueExprMap(std::move(Arg.ValueExprMap)),
PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
PendingPhiRanges(std::move(Arg.PendingPhiRanges)),
PendingMerges(std::move(Arg.PendingMerges)),
MinTrailingZerosCache(std::move(Arg.MinTrailingZerosCache)),
BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
PredicatedBackedgeTakenCounts(
std::move(Arg.PredicatedBackedgeTakenCounts)),
ConstantEvolutionLoopExitValue(
std::move(Arg.ConstantEvolutionLoopExitValue)),
ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
LoopDispositions(std::move(Arg.LoopDispositions)),
LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
BlockDispositions(std::move(Arg.BlockDispositions)),
UnsignedRanges(std::move(Arg.UnsignedRanges)),
SignedRanges(std::move(Arg.SignedRanges)),
UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
UniquePreds(std::move(Arg.UniquePreds)),
SCEVAllocator(std::move(Arg.SCEVAllocator)),
LoopUsers(std::move(Arg.LoopUsers)),
PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
FirstUnknown(Arg.FirstUnknown) {
Arg.FirstUnknown = nullptr;
}
ScalarEvolution::~ScalarEvolution() {
// Iterate through all the SCEVUnknown instances and call their
// destructors, so that they release their references to their values.
for (SCEVUnknown *U = FirstUnknown; U;) {
SCEVUnknown *Tmp = U;
U = U->Next;
Tmp->~SCEVUnknown();
}
FirstUnknown = nullptr;
ExprValueMap.clear();
ValueExprMap.clear();
HasRecMap.clear();
// Free any extra memory created for ExitNotTakenInfo in the unlikely event
// that a loop had multiple computable exits.
for (auto &BTCI : BackedgeTakenCounts)
BTCI.second.clear();
for (auto &BTCI : PredicatedBackedgeTakenCounts)
BTCI.second.clear();
assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
assert(PendingPhiRanges.empty() && "getRangeRef garbage");
assert(PendingMerges.empty() && "isImpliedViaMerge garbage");
assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
}
bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
}
static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
const Loop *L) {
// Print all inner loops first
for (Loop *I : *L)
PrintLoopInfo(OS, SE, I);
OS << "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
SmallVector<BasicBlock *, 8> ExitingBlocks;
L->getExitingBlocks(ExitingBlocks);
if (ExitingBlocks.size() != 1)
OS << "<multiple exits> ";
if (SE->hasLoopInvariantBackedgeTakenCount(L))
OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L) << "\n";
else
OS << "Unpredictable backedge-taken count.\n";
if (ExitingBlocks.size() > 1)
for (BasicBlock *ExitingBlock : ExitingBlocks) {
OS << " exit count for " << ExitingBlock->getName() << ": "
<< *SE->getExitCount(L, ExitingBlock) << "\n";
}
OS << "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
if (!isa<SCEVCouldNotCompute>(SE->getConstantMaxBackedgeTakenCount(L))) {
OS << "max backedge-taken count is " << *SE->getConstantMaxBackedgeTakenCount(L);
if (SE->isBackedgeTakenCountMaxOrZero(L))
OS << ", actual taken count either this or zero.";
} else {
OS << "Unpredictable max backedge-taken count. ";
}
OS << "\n"
"Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
SCEVUnionPredicate Pred;
auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
if (!isa<SCEVCouldNotCompute>(PBT)) {
OS << "Predicated backedge-taken count is " << *PBT << "\n";
OS << " Predicates:\n";
Pred.print(OS, 4);
} else {
OS << "Unpredictable predicated backedge-taken count. ";
}
OS << "\n";
if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
OS << "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n";
}
}
static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
switch (LD) {
case ScalarEvolution::LoopVariant:
return "Variant";
case ScalarEvolution::LoopInvariant:
return "Invariant";
case ScalarEvolution::LoopComputable:
return "Computable";
}
llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
}
void ScalarEvolution::print(raw_ostream &OS) const {
// ScalarEvolution's implementation of the print method is to print
// out SCEV values of all instructions that are interesting. Doing
// this potentially causes it to create new SCEV objects though,
// which technically conflicts with the const qualifier. This isn't
// observable from outside the class though, so casting away the
// const isn't dangerous.
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
if (ClassifyExpressions) {
OS << "Classifying expressions for: ";
F.printAsOperand(OS, /*PrintType=*/false);
OS << "\n";
for (Instruction &I : instructions(F))
if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
OS << I << '\n';
OS << " --> ";
const SCEV *SV = SE.getSCEV(&I);
SV->print(OS);
if (!isa<SCEVCouldNotCompute>(SV)) {
OS << " U: ";
SE.getUnsignedRange(SV).print(OS);
OS << " S: ";
SE.getSignedRange(SV).print(OS);
}
const Loop *L = LI.getLoopFor(I.getParent());
const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
if (AtUse != SV) {
OS << " --> ";
AtUse->print(OS);
if (!isa<SCEVCouldNotCompute>(AtUse)) {
OS << " U: ";
SE.getUnsignedRange(AtUse).print(OS);
OS << " S: ";
SE.getSignedRange(AtUse).print(OS);
}
}
if (L) {
OS << "\t\t" "Exits: ";
const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
if (!SE.isLoopInvariant(ExitValue, L)) {
OS << "<<Unknown>>";
} else {
OS << *ExitValue;
}
bool First = true;
for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
if (First) {
OS << "\t\t" "LoopDispositions: { ";
First = false;
} else {
OS << ", ";
}
Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
}
for (auto *InnerL : depth_first(L)) {
if (InnerL == L)
continue;
if (First) {
OS << "\t\t" "LoopDispositions: { ";
First = false;
} else {
OS << ", ";
}
InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
}
OS << " }";
}
OS << "\n";
}
}
OS << "Determining loop execution counts for: ";
F.printAsOperand(OS, /*PrintType=*/false);
OS << "\n";
for (Loop *I : LI)
PrintLoopInfo(OS, &SE, I);
}
ScalarEvolution::LoopDisposition
ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
auto &Values = LoopDispositions[S];
for (auto &V : Values) {
if (V.getPointer() == L)
return V.getInt();
}
Values.emplace_back(L, LoopVariant);
LoopDisposition D = computeLoopDisposition(S, L);
auto &Values2 = LoopDispositions[S];
for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
if (V.getPointer() == L) {
V.setInt(D);
break;
}
}
return D;
}
ScalarEvolution::LoopDisposition
ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
switch (static_cast<SCEVTypes>(S->getSCEVType())) {
case scConstant:
return LoopInvariant;
case scTruncate:
case scZeroExtend:
case scSignExtend:
return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
case scAddRecExpr: {
const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
// If L is the addrec's loop, it's computable.
if (AR->getLoop() == L)
return LoopComputable;
// Add recurrences are never invariant in the function-body (null loop).
if (!L)
return LoopVariant;
// Everything that is not defined at loop entry is variant.
if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader()))
return LoopVariant;
assert(!L->contains(AR->getLoop()) && "Containing loop's header does not"
" dominate the contained loop's header?");
// This recurrence is invariant w.r.t. L if AR's loop contains L.
if (AR->getLoop()->contains(L))
return LoopInvariant;
// This recurrence is variant w.r.t. L if any of its operands
// are variant.
for (auto *Op : AR->operands())
if (!isLoopInvariant(Op, L))
return LoopVariant;
// Otherwise it's loop-invariant.
return LoopInvariant;
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr: {
bool HasVarying = false;
for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
LoopDisposition D = getLoopDisposition(Op, L);
if (D == LoopVariant)
return LoopVariant;
if (D == LoopComputable)
HasVarying = true;
}
return HasVarying ? LoopComputable : LoopInvariant;
}
case scUDivExpr: {
const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
if (LD == LoopVariant)
return LoopVariant;
LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
if (RD == LoopVariant)
return LoopVariant;
return (LD == LoopInvariant && RD == LoopInvariant) ?
LoopInvariant : LoopComputable;
}
case scUnknown:
// All non-instruction values are loop invariant. All instructions are loop
// invariant if they are not contained in the specified loop.
// Instructions are never considered invariant in the function body
// (null loop) because they are defined within the "loop".
if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
return LoopInvariant;
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
}
llvm_unreachable("Unknown SCEV kind!");
}
bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
return getLoopDisposition(S, L) == LoopInvariant;
}
bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
return getLoopDisposition(S, L) == LoopComputable;
}
ScalarEvolution::BlockDisposition
ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
auto &Values = BlockDispositions[S];
for (auto &V : Values) {
if (V.getPointer() == BB)
return V.getInt();
}
Values.emplace_back(BB, DoesNotDominateBlock);
BlockDisposition D = computeBlockDisposition(S, BB);
auto &Values2 = BlockDispositions[S];
for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
if (V.getPointer() == BB) {
V.setInt(D);
break;
}
}
return D;
}
ScalarEvolution::BlockDisposition
ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
switch (static_cast<SCEVTypes>(S->getSCEVType())) {
case scConstant:
return ProperlyDominatesBlock;
case scTruncate:
case scZeroExtend:
case scSignExtend:
return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
case scAddRecExpr: {
// This uses a "dominates" query instead of "properly dominates" query
// to test for proper dominance too, because the instruction which
// produces the addrec's value is a PHI, and a PHI effectively properly
// dominates its entire containing block.
const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
if (!DT.dominates(AR->getLoop()->getHeader(), BB))
return DoesNotDominateBlock;
// Fall through into SCEVNAryExpr handling.
LLVM_FALLTHROUGH;
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr: {
const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
bool Proper = true;
for (const SCEV *NAryOp : NAry->operands()) {
BlockDisposition D = getBlockDisposition(NAryOp, BB);
if (D == DoesNotDominateBlock)
return DoesNotDominateBlock;
if (D == DominatesBlock)
Proper = false;
}
return Proper ? ProperlyDominatesBlock : DominatesBlock;
}
case scUDivExpr: {
const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
BlockDisposition LD = getBlockDisposition(LHS, BB);
if (LD == DoesNotDominateBlock)
return DoesNotDominateBlock;
BlockDisposition RD = getBlockDisposition(RHS, BB);
if (RD == DoesNotDominateBlock)
return DoesNotDominateBlock;
return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
ProperlyDominatesBlock : DominatesBlock;
}
case scUnknown:
if (Instruction *I =
dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
if (I->getParent() == BB)
return DominatesBlock;
if (DT.properlyDominates(I->getParent(), BB))
return ProperlyDominatesBlock;
return DoesNotDominateBlock;
}
return ProperlyDominatesBlock;
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
}
llvm_unreachable("Unknown SCEV kind!");
}
bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
return getBlockDisposition(S, BB) >= DominatesBlock;
}
bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
}
bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
}
bool ScalarEvolution::ExitLimit::hasOperand(const SCEV *S) const {
auto IsS = [&](const SCEV *X) { return S == X; };
auto ContainsS = [&](const SCEV *X) {
return !isa<SCEVCouldNotCompute>(X) && SCEVExprContains(X, IsS);
};
return ContainsS(ExactNotTaken) || ContainsS(MaxNotTaken);
}
void
ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
ValuesAtScopes.erase(S);
LoopDispositions.erase(S);
BlockDispositions.erase(S);
UnsignedRanges.erase(S);
SignedRanges.erase(S);
ExprValueMap.erase(S);
HasRecMap.erase(S);
MinTrailingZerosCache.erase(S);
for (auto I = PredicatedSCEVRewrites.begin();
I != PredicatedSCEVRewrites.end();) {
std::pair<const SCEV *, const Loop *> Entry = I->first;
if (Entry.first == S)
PredicatedSCEVRewrites.erase(I++);
else
++I;
}
auto RemoveSCEVFromBackedgeMap =
[S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
for (auto I = Map.begin(), E = Map.end(); I != E;) {
BackedgeTakenInfo &BEInfo = I->second;
if (BEInfo.hasOperand(S, this)) {
BEInfo.clear();
Map.erase(I++);
} else
++I;
}
};
RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
}
void
ScalarEvolution::getUsedLoops(const SCEV *S,
SmallPtrSetImpl<const Loop *> &LoopsUsed) {
struct FindUsedLoops {
FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed)
: LoopsUsed(LoopsUsed) {}
SmallPtrSetImpl<const Loop *> &LoopsUsed;
bool follow(const SCEV *S) {
if (auto *AR = dyn_cast<SCEVAddRecExpr>(S))
LoopsUsed.insert(AR->getLoop());
return true;
}
bool isDone() const { return false; }
};
FindUsedLoops F(LoopsUsed);
SCEVTraversal<FindUsedLoops>(F).visitAll(S);
}
void ScalarEvolution::addToLoopUseLists(const SCEV *S) {
SmallPtrSet<const Loop *, 8> LoopsUsed;
getUsedLoops(S, LoopsUsed);
for (auto *L : LoopsUsed)
LoopUsers[L].push_back(S);
}
void ScalarEvolution::verify() const {
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
ScalarEvolution SE2(F, TLI, AC, DT, LI);
SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end());
// Map's SCEV expressions from one ScalarEvolution "universe" to another.
struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> {
SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {}
const SCEV *visitConstant(const SCEVConstant *Constant) {
return SE.getConstant(Constant->getAPInt());
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
return SE.getUnknown(Expr->getValue());
}
const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
return SE.getCouldNotCompute();
}
};
SCEVMapper SCM(SE2);
while (!LoopStack.empty()) {
auto *L = LoopStack.pop_back_val();
LoopStack.insert(LoopStack.end(), L->begin(), L->end());
auto *CurBECount = SCM.visit(
const_cast<ScalarEvolution *>(this)->getBackedgeTakenCount(L));
auto *NewBECount = SE2.getBackedgeTakenCount(L);
if (CurBECount == SE2.getCouldNotCompute() ||
NewBECount == SE2.getCouldNotCompute()) {
// NB! This situation is legal, but is very suspicious -- whatever pass
// change the loop to make a trip count go from could not compute to
// computable or vice-versa *should have* invalidated SCEV. However, we
// choose not to assert here (for now) since we don't want false
// positives.
continue;
}
if (containsUndefs(CurBECount) || containsUndefs(NewBECount)) {
// SCEV treats "undef" as an unknown but consistent value (i.e. it does
// not propagate undef aggressively). This means we can (and do) fail
// verification in cases where a transform makes the trip count of a loop
// go from "undef" to "undef+1" (say). The transform is fine, since in
// both cases the loop iterates "undef" times, but SCEV thinks we
// increased the trip count of the loop by 1 incorrectly.
continue;
}
if (SE.getTypeSizeInBits(CurBECount->getType()) >
SE.getTypeSizeInBits(NewBECount->getType()))
NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType());
else if (SE.getTypeSizeInBits(CurBECount->getType()) <
SE.getTypeSizeInBits(NewBECount->getType()))
CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType());
const SCEV *Delta = SE2.getMinusSCEV(CurBECount, NewBECount);
// Unless VerifySCEVStrict is set, we only compare constant deltas.
if ((VerifySCEVStrict || isa<SCEVConstant>(Delta)) && !Delta->isZero()) {
dbgs() << "Trip Count for " << *L << " Changed!\n";
dbgs() << "Old: " << *CurBECount << "\n";
dbgs() << "New: " << *NewBECount << "\n";
dbgs() << "Delta: " << *Delta << "\n";
std::abort();
}
}
}
bool ScalarEvolution::invalidate(
Function &F, const PreservedAnalyses &PA,
FunctionAnalysisManager::Invalidator &Inv) {
// Invalidate the ScalarEvolution object whenever it isn't preserved or one
// of its dependencies is invalidated.
auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
Inv.invalidate<AssumptionAnalysis>(F, PA) ||
Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
Inv.invalidate<LoopAnalysis>(F, PA);
}
AnalysisKey ScalarEvolutionAnalysis::Key;
ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
FunctionAnalysisManager &AM) {
return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
AM.getResult<AssumptionAnalysis>(F),
AM.getResult<DominatorTreeAnalysis>(F),
AM.getResult<LoopAnalysis>(F));
}
PreservedAnalyses
ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) {
AM.getResult<ScalarEvolutionAnalysis>(F).verify();
return PreservedAnalyses::all();
}
PreservedAnalyses
ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
return PreservedAnalyses::all();
}
INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
"Scalar Evolution Analysis", false, true)
INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
"Scalar Evolution Analysis", false, true)
char ScalarEvolutionWrapperPass::ID = 0;
ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
}
bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
SE.reset(new ScalarEvolution(
F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F),
getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
return false;
}
void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
SE->print(OS);
}
void ScalarEvolutionWrapperPass::verifyAnalysis() const {
if (!VerifySCEV)
return;
SE->verify();
}
void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AU.addRequiredTransitive<AssumptionCacheTracker>();
AU.addRequiredTransitive<LoopInfoWrapperPass>();
AU.addRequiredTransitive<DominatorTreeWrapperPass>();
AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
}
const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS,
const SCEV *RHS) {
FoldingSetNodeID ID;
assert(LHS->getType() == RHS->getType() &&
"Type mismatch between LHS and RHS");
// Unique this node based on the arguments
ID.AddInteger(SCEVPredicate::P_Equal);
ID.AddPointer(LHS);
ID.AddPointer(RHS);
void *IP = nullptr;
if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
return S;
SCEVEqualPredicate *Eq = new (SCEVAllocator)
SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
UniquePreds.InsertNode(Eq, IP);
return Eq;
}
const SCEVPredicate *ScalarEvolution::getWrapPredicate(
const SCEVAddRecExpr *AR,
SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
FoldingSetNodeID ID;
// Unique this node based on the arguments
ID.AddInteger(SCEVPredicate::P_Wrap);
ID.AddPointer(AR);
ID.AddInteger(AddedFlags);
void *IP = nullptr;
if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
return S;
auto *OF = new (SCEVAllocator)
SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
UniquePreds.InsertNode(OF, IP);
return OF;
}
namespace {
class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
public:
/// Rewrites \p S in the context of a loop L and the SCEV predication
/// infrastructure.
///
/// If \p Pred is non-null, the SCEV expression is rewritten to respect the
/// equivalences present in \p Pred.
///
/// If \p NewPreds is non-null, rewrite is free to add further predicates to
/// \p NewPreds such that the result will be an AddRecExpr.
static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
SCEVUnionPredicate *Pred) {
SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
return Rewriter.visit(S);
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
if (Pred) {
auto ExprPreds = Pred->getPredicatesForExpr(Expr);
for (auto *Pred : ExprPreds)
if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
if (IPred->getLHS() == Expr)
return IPred->getRHS();
}
return convertToAddRecWithPreds(Expr);
}
const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
const SCEV *Operand = visit(Expr->getOperand());
const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
if (AR && AR->getLoop() == L && AR->isAffine()) {
// This couldn't be folded because the operand didn't have the nuw
// flag. Add the nusw flag as an assumption that we could make.
const SCEV *Step = AR->getStepRecurrence(SE);
Type *Ty = Expr->getType();
if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
SE.getSignExtendExpr(Step, Ty), L,
AR->getNoWrapFlags());
}
return SE.getZeroExtendExpr(Operand, Expr->getType());
}
const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
const SCEV *Operand = visit(Expr->getOperand());
const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
if (AR && AR->getLoop() == L && AR->isAffine()) {
// This couldn't be folded because the operand didn't have the nsw
// flag. Add the nssw flag as an assumption that we could make.
const SCEV *Step = AR->getStepRecurrence(SE);
Type *Ty = Expr->getType();
if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
SE.getSignExtendExpr(Step, Ty), L,
AR->getNoWrapFlags());
}
return SE.getSignExtendExpr(Operand, Expr->getType());
}
private:
explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
SCEVUnionPredicate *Pred)
: SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
bool addOverflowAssumption(const SCEVPredicate *P) {
if (!NewPreds) {
// Check if we've already made this assumption.
return Pred && Pred->implies(P);
}
NewPreds->insert(P);
return true;
}
bool addOverflowAssumption(const SCEVAddRecExpr *AR,
SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
auto *A = SE.getWrapPredicate(AR, AddedFlags);
return addOverflowAssumption(A);
}
// If \p Expr represents a PHINode, we try to see if it can be represented
// as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible
// to add this predicate as a runtime overflow check, we return the AddRec.
// If \p Expr does not meet these conditions (is not a PHI node, or we
// couldn't create an AddRec for it, or couldn't add the predicate), we just
// return \p Expr.
const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) {
if (!isa<PHINode>(Expr->getValue()))
return Expr;
Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr);
if (!PredicatedRewrite)
return Expr;
for (auto *P : PredicatedRewrite->second){
// Wrap predicates from outer loops are not supported.
if (auto *WP = dyn_cast<const SCEVWrapPredicate>(P)) {
auto *AR = cast<const SCEVAddRecExpr>(WP->getExpr());
if (L != AR->getLoop())
return Expr;
}
if (!addOverflowAssumption(P))
return Expr;
}
return PredicatedRewrite->first;
}
SmallPtrSetImpl<const SCEVPredicate *> *NewPreds;
SCEVUnionPredicate *Pred;
const Loop *L;
};
} // end anonymous namespace
const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
SCEVUnionPredicate &Preds) {
return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
}
const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
const SCEV *S, const Loop *L,
SmallPtrSetImpl<const SCEVPredicate *> &Preds) {
SmallPtrSet<const SCEVPredicate *, 4> TransformPreds;
S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
if (!AddRec)
return nullptr;
// Since the transformation was successful, we can now transfer the SCEV
// predicates.
for (auto *P : TransformPreds)
Preds.insert(P);
return AddRec;
}
/// SCEV predicates
SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
SCEVPredicateKind Kind)
: FastID(ID), Kind(Kind) {}
SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
const SCEV *LHS, const SCEV *RHS)
: SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {
assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match");
assert(LHS != RHS && "LHS and RHS are the same SCEV");
}
bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
if (!Op)
return false;
return Op->LHS == LHS && Op->RHS == RHS;
}
bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
}
SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
const SCEVAddRecExpr *AR,
IncrementWrapFlags Flags)
: SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
}
bool SCEVWrapPredicate::isAlwaysTrue() const {
SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
IncrementWrapFlags IFlags = Flags;
if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
IFlags = clearFlags(IFlags, IncrementNSSW);
return IFlags == IncrementAnyWrap;
}
void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
OS.indent(Depth) << *getExpr() << " Added Flags: ";
if (SCEVWrapPredicate::IncrementNUSW & getFlags())
OS << "<nusw>";
if (SCEVWrapPredicate::IncrementNSSW & getFlags())
OS << "<nssw>";
OS << "\n";
}
SCEVWrapPredicate::IncrementWrapFlags
SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
ScalarEvolution &SE) {
IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
// We can safely transfer the NSW flag as NSSW.
if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
ImpliedFlags = IncrementNSSW;
if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
// If the increment is positive, the SCEV NUW flag will also imply the
// WrapPredicate NUSW flag.
if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
if (Step->getValue()->getValue().isNonNegative())
ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
}
return ImpliedFlags;
}
/// Union predicates don't get cached so create a dummy set ID for it.
SCEVUnionPredicate::SCEVUnionPredicate()
: SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
bool SCEVUnionPredicate::isAlwaysTrue() const {
return all_of(Preds,
[](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
}
ArrayRef<const SCEVPredicate *>
SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
auto I = SCEVToPreds.find(Expr);
if (I == SCEVToPreds.end())
return ArrayRef<const SCEVPredicate *>();
return I->second;
}
bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
return all_of(Set->Preds,
[this](const SCEVPredicate *I) { return this->implies(I); });
auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
if (ScevPredsIt == SCEVToPreds.end())
return false;
auto &SCEVPreds = ScevPredsIt->second;
return any_of(SCEVPreds,
[N](const SCEVPredicate *I) { return I->implies(N); });
}
const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
for (auto Pred : Preds)
Pred->print(OS, Depth);
}
void SCEVUnionPredicate::add(const SCEVPredicate *N) {
if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
for (auto Pred : Set->Preds)
add(Pred);
return;
}
if (implies(N))
return;
const SCEV *Key = N->getExpr();
assert(Key && "Only SCEVUnionPredicate doesn't have an "
" associated expression!");
SCEVToPreds[Key].push_back(N);
Preds.push_back(N);
}
PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
Loop &L)
: SE(SE), L(L) {}
const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
const SCEV *Expr = SE.getSCEV(V);
RewriteEntry &Entry = RewriteMap[Expr];
// If we already have an entry and the version matches, return it.
if (Entry.second && Generation == Entry.first)
return Entry.second;
// We found an entry but it's stale. Rewrite the stale entry
// according to the current predicate.
if (Entry.second)
Expr = Entry.second;
const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
Entry = {Generation, NewSCEV};
return NewSCEV;
}
const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
if (!BackedgeCount) {
SCEVUnionPredicate BackedgePred;
BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
addPredicate(BackedgePred);
}
return BackedgeCount;
}
void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
if (Preds.implies(&Pred))
return;
Preds.add(&Pred);
updateGeneration();
}
const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
return Preds;
}
void PredicatedScalarEvolution::updateGeneration() {
// If the generation number wrapped recompute everything.
if (++Generation == 0) {
for (auto &II : RewriteMap) {
const SCEV *Rewritten = II.second.second;
II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
}
}
}
void PredicatedScalarEvolution::setNoOverflow(
Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
const SCEV *Expr = getSCEV(V);
const auto *AR = cast<SCEVAddRecExpr>(Expr);
auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
// Clear the statically implied flags.
Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
addPredicate(*SE.getWrapPredicate(AR, Flags));
auto II = FlagsMap.insert({V, Flags});
if (!II.second)
II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
}
bool PredicatedScalarEvolution::hasNoOverflow(
Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
const SCEV *Expr = getSCEV(V);
const auto *AR = cast<SCEVAddRecExpr>(Expr);
Flags = SCEVWrapPredicate::clearFlags(
Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
auto II = FlagsMap.find(V);
if (II != FlagsMap.end())
Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
return Flags == SCEVWrapPredicate::IncrementAnyWrap;
}
const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
const SCEV *Expr = this->getSCEV(V);
SmallPtrSet<const SCEVPredicate *, 4> NewPreds;
auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);
if (!New)
return nullptr;
for (auto *P : NewPreds)
Preds.add(P);
updateGeneration();
RewriteMap[SE.getSCEV(V)] = {Generation, New};
return New;
}
PredicatedScalarEvolution::PredicatedScalarEvolution(
const PredicatedScalarEvolution &Init)
: RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
for (auto I : Init.FlagsMap)
FlagsMap.insert(I);
}
void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
// For each block.
for (auto *BB : L.getBlocks())
for (auto &I : *BB) {
if (!SE.isSCEVable(I.getType()))
continue;
auto *Expr = SE.getSCEV(&I);
auto II = RewriteMap.find(Expr);
if (II == RewriteMap.end())
continue;
// Don't print things that are not interesting.
if (II->second.second == Expr)
continue;
OS.indent(Depth) << "[PSE]" << I << ":\n";
OS.indent(Depth + 2) << *Expr << "\n";
OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
}
}
// Match the mathematical pattern A - (A / B) * B, where A and B can be
// arbitrary expressions.
// It's not always easy, as A and B can be folded (imagine A is X / 2, and B is
// 4, A / B becomes X / 8).
bool ScalarEvolution::matchURem(const SCEV *Expr, const SCEV *&LHS,
const SCEV *&RHS) {
const auto *Add = dyn_cast<SCEVAddExpr>(Expr);
if (Add == nullptr || Add->getNumOperands() != 2)
return false;
const SCEV *A = Add->getOperand(1);
const auto *Mul = dyn_cast<SCEVMulExpr>(Add->getOperand(0));
if (Mul == nullptr)
return false;
const auto MatchURemWithDivisor = [&](const SCEV *B) {
// (SomeExpr + (-(SomeExpr / B) * B)).
if (Expr == getURemExpr(A, B)) {
LHS = A;
RHS = B;
return true;
}
return false;
};
// (SomeExpr + (-1 * (SomeExpr / B) * B)).
if (Mul->getNumOperands() == 3 && isa<SCEVConstant>(Mul->getOperand(0)))
return MatchURemWithDivisor(Mul->getOperand(1)) ||
MatchURemWithDivisor(Mul->getOperand(2));
// (SomeExpr + ((-SomeExpr / B) * B)) or (SomeExpr + ((SomeExpr / B) * -B)).
if (Mul->getNumOperands() == 2)
return MatchURemWithDivisor(Mul->getOperand(1)) ||
MatchURemWithDivisor(Mul->getOperand(0)) ||
MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(1))) ||
MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(0)));
return false;
}
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