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freebsd-dev/lib/Analysis/ScalarEvolution.cpp

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//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// 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/Optional.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/Statistic.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/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/GetElementPtrTypeIterator.h"
#include "llvm/IR/GlobalAlias.h"
#include "llvm/IR/GlobalVariable.h"
#include "llvm/IR/InstIterator.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Metadata.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/MathExtras.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Support/SaveAndRestore.h"
#include <algorithm>
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::desc("Maximum number of iterations SCEV will "
"symbolically execute a constant "
"derived loop"),
cl::init(100));
// FIXME: Enable this with XDEBUG when the test suite is clean.
static cl::opt<bool>
VerifySCEV("verify-scev",
cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
//===----------------------------------------------------------------------===//
// SCEV class definitions
//===----------------------------------------------------------------------===//
//===----------------------------------------------------------------------===//
// Implementation of the SCEV class.
//
LLVM_DUMP_METHOD
void SCEV::dump() const {
print(dbgs());
dbgs() << '\n';
}
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->getNoWrapFlags(FlagNUW))
OS << "nuw><";
if (AR->getNoWrapFlags(FlagNSW))
OS << "nsw><";
if (AR->getNoWrapFlags(FlagNW) &&
!AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
OS << "nw><";
AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ">";
return;
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr: {
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;
}
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->getNoWrapFlags(FlagNUW))
OS << "<nuw>";
if (NAry->getNoWrapFlags(FlagNSW))
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:
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()->isAllOnesValue();
return false;
}
/// isNonConstantNegative - Return true if the specified scev is negated, but
/// not a constant.
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) {}
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), Op(op), Ty(ty) {}
SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
const SCEV *op, Type *ty)
: SCEVCastExpr(ID, scTruncate, op, ty) {
assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
"Cannot truncate non-integer value!");
}
SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
const SCEV *op, Type *ty)
: SCEVCastExpr(ID, scZeroExtend, op, ty) {
assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
"Cannot zero extend non-integer value!");
}
SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
const SCEV *op, Type *ty)
: SCEVCastExpr(ID, scSignExtend, op, ty) {
assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
"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) {
// Clear this SCEVUnknown from various maps.
SE->forgetMemoizedResults(this);
// 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
//===----------------------------------------------------------------------===//
namespace {
/// SCEVComplexityCompare - Return true if the complexity of the LHS is less
/// than the complexity of the RHS. This comparator is used to canonicalize
/// expressions.
class SCEVComplexityCompare {
const LoopInfo *const LI;
public:
explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
// Return true or false if LHS is less than, or at least RHS, respectively.
bool operator()(const SCEV *LHS, const SCEV *RHS) const {
return compare(LHS, RHS) < 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.
int compare(const SCEV *LHS, const SCEV *RHS) const {
// 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;
// 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);
// Sort SCEVUnknown values with some loose heuristics. TODO: This is
// not as complete as it could be.
const Value *LV = LU->getValue(), *RV = RU->getValue();
// 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 Argument *LA = dyn_cast<Argument>(LV)) {
const Argument *RA = cast<Argument>(RV);
unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
return (int)LArgNo - (int)RArgNo;
}
// For instructions, compare their loop depth, and their operand
// count. This is pretty loose.
if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
const Instruction *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();
return (int)LNumOps - (int)RNumOps;
}
return 0;
}
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);
// Compare addrec loop depths.
const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
if (LLoop != RLoop) {
unsigned LDepth = LLoop->getLoopDepth(),
RDepth = RLoop->getLoopDepth();
if (LDepth != RDepth)
return (int)LDepth - (int)RDepth;
}
// 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) {
long X = compare(LA->getOperand(i), RA->getOperand(i));
if (X != 0)
return X;
}
return 0;
}
case scAddExpr:
case scMulExpr:
case scSMaxExpr:
case scUMaxExpr: {
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) {
if (i >= RNumOps)
return 1;
long X = compare(LC->getOperand(i), RC->getOperand(i));
if (X != 0)
return X;
}
return (int)LNumOps - (int)RNumOps;
}
case scUDivExpr: {
const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
// Lexicographically compare udiv expressions.
long X = compare(LC->getLHS(), RC->getLHS());
if (X != 0)
return X;
return compare(LC->getRHS(), RC->getRHS());
}
case scTruncate:
case scZeroExtend:
case scSignExtend: {
const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
// Compare cast expressions by operand.
return compare(LC->getOperand(), RC->getOperand());
}
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
}
llvm_unreachable("Unknown SCEV kind!");
}
};
} // end anonymous namespace
/// GroupByComplexity - 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) {
if (Ops.size() < 2) return; // Noop
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 (SCEVComplexityCompare(LI)(RHS, LHS))
std::swap(LHS, RHS);
return;
}
// Do the rough sort by complexity.
std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
// 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;
FindSCEVSize() : Size(0) {}
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;
}
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<const 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 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;
};
}
//===----------------------------------------------------------------------===//
// Simple SCEV method implementations
//===----------------------------------------------------------------------===//
/// BinomialCoefficient - 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 = Mult.lshr(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));
}
/// evaluateAtIteration - 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) {
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);
// 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);
// 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);
// trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
// eliminate all the truncates, or we replace other casts with truncates.
if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
SmallVector<const SCEV *, 4> Operands;
bool hasTrunc = false;
for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
if (!isa<SCEVCastExpr>(SA->getOperand(i)))
hasTrunc = isa<SCEVTruncateExpr>(S);
Operands.push_back(S);
}
if (!hasTrunc)
return getAddExpr(Operands);
UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
}
// trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
// eliminate all the truncates, or we replace other casts with truncates.
if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
SmallVector<const SCEV *, 4> Operands;
bool hasTrunc = false;
for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
if (!isa<SCEVCastExpr>(SM->getOperand(i)))
hasTrunc = isa<SCEVTruncateExpr>(S);
Operands.push_back(S);
}
if (!hasTrunc)
return getMulExpr(Operands);
UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
}
// 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));
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);
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->getSignedRange(Step).getSignedMax());
}
if (SE->isKnownNegative(Step)) {
*Pred = ICmpInst::ICMP_SGT;
return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
SE->getSignedRange(Step).getSignedMin());
}
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->getUnsignedRange(Step).getUnsignedMax());
}
namespace {
struct ExtendOpTraitsBase {
typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
};
// 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;
}
// 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) {
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),
(SE->*GetExtendExpr)(Step, WideTy));
if ((SE->*GetExtendExpr)(Start, WideTy) == 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) {
auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
if (!PreStart)
return (SE->*GetExtendExpr)(AR->getStart(), Ty);
return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
(SE->*GetExtendExpr)(PreStart, Ty));
}
// 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;
}
const SCEV *ScalarEvolution::getZeroExtendExpr(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);
// 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);
// 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;
// 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);
}
// 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 we have special knowledge that this addrec won't overflow,
// we don't need to do any further analysis.
if (AR->getNoWrapFlags(SCEV::FlagNUW))
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
getZeroExtendExpr(Step, Ty), 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 = getMaxBackedgeTakenCount(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());
const SCEV *RecastedMaxBECount =
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
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);
const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
const SCEV *WideMaxBECount =
getZeroExtendExpr(CastedMaxBECount, WideTy);
const SCEV *OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getZeroExtendExpr(Step, WideTy)));
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),
getZeroExtendExpr(Step, Ty), 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)));
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),
getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
}
}
// 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) -
getUnsignedRange(Step).getUnsignedMax());
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
(isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
AR->getPostIncExpr(*this), 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),
getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
}
} else if (isKnownNegative(Step)) {
const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
getSignedRange(Step).getSignedMin());
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
(isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
AR->getPostIncExpr(*this), 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),
getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
}
}
}
if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
}
}
if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
// zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
if (SA->getNoWrapFlags(SCEV::FlagNUW)) {
// 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));
return getAddExpr(Ops, SCEV::FlagNUW);
}
}
// 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);
return S;
}
const SCEV *ScalarEvolution::getSignExtendExpr(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);
// 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);
// sext(zext(x)) --> zext(x)
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
return getZeroExtendExpr(SZ->getOperand(), Ty);
// 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;
// If the input value is provably positive, build a zext instead.
if (isKnownNonNegative(Op))
return getZeroExtendExpr(Op, Ty);
// 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);
}
// sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
if (SA->getNumOperands() == 2) {
auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
if (SMul && SC1) {
if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
const APInt &C1 = SC1->getAPInt();
const APInt &C2 = SC2->getAPInt();
if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
C2.ugt(C1) && C2.isPowerOf2())
return getAddExpr(getSignExtendExpr(SC1, Ty),
getSignExtendExpr(SMul, Ty));
}
}
}
// sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
if (SA->getNoWrapFlags(SCEV::FlagNSW)) {
// 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));
return getAddExpr(Ops, SCEV::FlagNSW);
}
}
// 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 we have special knowledge that this addrec won't overflow,
// we don't need to do any further analysis.
if (AR->getNoWrapFlags(SCEV::FlagNSW))
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
getSignExtendExpr(Step, Ty), 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 = getMaxBackedgeTakenCount(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());
const SCEV *RecastedMaxBECount =
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
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);
const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
const SCEV *WideMaxBECount =
getZeroExtendExpr(CastedMaxBECount, WideTy);
const SCEV *OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getSignExtendExpr(Step, WideTy)));
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),
getSignExtendExpr(Step, Ty), 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)));
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),
getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
}
}
// 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) ||
(isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
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),
getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
}
}
// If Start and Step are constants, check if we can apply this
// transformation:
// sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
auto *SC1 = dyn_cast<SCEVConstant>(Start);
auto *SC2 = dyn_cast<SCEVConstant>(Step);
if (SC1 && SC2) {
const APInt &C1 = SC1->getAPInt();
const APInt &C2 = SC2->getAPInt();
if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
C2.isPowerOf2()) {
Start = getSignExtendExpr(Start, Ty);
const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
AR->getNoWrapFlags());
return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
}
}
if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
}
}
// 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);
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;
}
/// CollectAddOperandsWithScales - 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(std::make_pair(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(std::make_pair(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 SmallVectorImpl<const SCEV *> &Ops,
SCEV::NoWrapFlags Flags) {
using namespace std::placeholders;
typedef OverflowingBinaryOperator OBO;
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 &&
Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
// (A + C) --> (A + C)<nsw> if the addition does not sign overflow
// (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
auto NSWRegion =
ConstantRange::makeNoWrapRegion(Instruction::Add, C, OBO::NoSignedWrap);
if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
}
if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
auto NUWRegion =
ConstantRange::makeNoWrapRegion(Instruction::Add, C,
OBO::NoUnsignedWrap);
if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
}
}
return Flags;
}
/// getAddExpr - Get a canonical add expression, or something simpler if
/// possible.
const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
SCEV::NoWrapFlags Flags) {
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);
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];
}
// 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]);
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);
// 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., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
// if the contents of the resulting outer trunc fold to something simple.
for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
Type *DstType = Trunc->getType();
Type *SrcType = Trunc->getOperand()->getType();
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));
} else {
Ok = false;
break;
}
}
if (Ok) {
// Evaluate the expression in the larger type.
const SCEV *Fold = getAddExpr(LargeOps, Flags);
// If it folds to something simple, use it. Otherwise, don't.
if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
return getTruncateExpr(Fold, DstType);
}
}
// 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 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);
}
// 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)));
if (Ops.empty())
return getZero(Ty);
if (Ops.size() == 1)
return Ops[0];
return getAddExpr(Ops);
}
}
// 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);
}
const SCEV *One = getOne(Ty);
const SCEV *AddOne = getAddExpr(One, InnerMul);
const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
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);
}
// 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);
}
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);
}
const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
if (Ops.size() == 2) return OuterMul;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherMulIdx-1);
Ops.push_back(OuterMul);
return getAddExpr(Ops);
}
}
}
}
// 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 (isLoopInvariant(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());
AddRecOps[0] = getAddExpr(LIOps);
// 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);
}
// 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)
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)
if (const auto *OtherAddRec = dyn_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;
}
AddRecOps[i] = getAddExpr(AddRecOps[i],
OtherAddRec->getOperand(i));
}
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);
}
// 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.
FoldingSetNodeID ID;
ID.AddInteger(scAddExpr);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
ID.AddPointer(Ops[i]);
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);
}
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 containsConstantSomewhere(const SCEV *StartExpr) {
SmallVector<const SCEV *, 4> Ops;
Ops.push_back(StartExpr);
while (!Ops.empty()) {
const SCEV *CurrentExpr = Ops.pop_back_val();
if (isa<SCEVConstant>(*CurrentExpr))
return true;
if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
}
}
return false;
}
/// getMulExpr - Get a canonical multiply expression, or something simpler if
/// possible.
const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
SCEV::NoWrapFlags Flags) {
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);
Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
// C1*(C2+V) -> C1*C2 + C1*V
if (Ops.size() == 2)
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.
if (Add->getNumOperands() == 2)
if (containsConstantSomewhere(Add))
return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
getMulExpr(LHSC, Add->getOperand(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()->equalsInt(1)) {
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);
if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
NewOps.push_back(Mul);
}
if (AnyFolded)
return getAddExpr(NewOps);
} 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));
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 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);
}
// 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 (isLoopInvariant(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);
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
// 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);
}
// 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;
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) {
const SCEV *Term = getZero(Ty);
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);
Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
}
}
AddRecOps.push_back(Term);
}
if (!Overflow) {
const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
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);
// 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.
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);
}
S->setNoWrapFlags(Flags);
return S;
}
/// getUDivExpr - 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()->equalsInt(1))
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/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);
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(A, B);
}
/// getUDivExactExpr - 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)
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);
}
/// getAddRecExpr - 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);
}
/// getAddRecExpr - 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 getMaxBackedgeTakenCount 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.
FoldingSetNodeID ID;
ID.AddInteger(scAddRecExpr);
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
ID.AddPointer(Operands[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 *>(Operands.size());
std::uninitialized_copy(Operands.begin(), Operands.end(), O);
S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
O, Operands.size(), L);
UniqueSCEVs.InsertNode(S, IP);
}
S->setNoWrapFlags(Flags);
return S;
}
const SCEV *
ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
const SmallVectorImpl<const SCEV *> &IndexExprs,
bool InBounds) {
// getSCEV(Base)->getType() has the same address space as Base->getType()
// because SCEV::getType() preserves the address space.
Type *IntPtrTy = 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 = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
const SCEV *TotalOffset = getZero(IntPtrTy);
// The address space is unimportant. The first thing we do on CurTy is getting
// its element type.
Type *CurTy = PointerType::getUnqual(PointeeType);
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(IntPtrTy, 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(IntPtrTy, CurTy);
// Getelementptr indices are signed.
IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
// 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);
}
const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops;
Ops.push_back(LHS);
Ops.push_back(RHS);
return getSMaxExpr(Ops);
}
const SCEV *
ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
assert(!Ops.empty() && "Cannot get empty smax!");
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 &&
"SCEVSMaxExpr operand types don't match!");
#endif
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI);
// 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!
ConstantInt *Fold = ConstantInt::get(
getContext(), APIntOps::smax(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 minimum-int, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
Ops.erase(Ops.begin());
--Idx;
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
// If we have an smax with a constant maximum-int, it will always be
// maximum-int.
return Ops[0];
}
if (Ops.size() == 1) return Ops[0];
}
// Find the first SMax
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
++Idx;
// Check to see if one of the operands is an SMax. If so, expand its operands
// onto our operand list, and recurse to simplify.
if (Idx < Ops.size()) {
bool DeletedSMax = false;
while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
Ops.erase(Ops.begin()+Idx);
Ops.append(SMax->op_begin(), SMax->op_end());
DeletedSMax = true;
}
if (DeletedSMax)
return getSMaxExpr(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.
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
// X smax Y smax Y --> X smax Y
// X smax Y --> X, if X is always greater than Y
if (Ops[i] == Ops[i+1] ||
isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
--i; --e;
} else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
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 smax expr. Check to see if we
// already have one, otherwise create a new one.
FoldingSetNodeID ID;
ID.AddInteger(scSMaxExpr);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
ID.AddPointer(Ops[i]);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
O, Ops.size());
UniqueSCEVs.InsertNode(S, IP);
return S;
}
const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops;
Ops.push_back(LHS);
Ops.push_back(RHS);
return getUMaxExpr(Ops);
}
const SCEV *
ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
assert(!Ops.empty() && "Cannot get empty umax!");
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 &&
"SCEVUMaxExpr operand types don't match!");
#endif
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI);
// 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!
ConstantInt *Fold = ConstantInt::get(
getContext(), APIntOps::umax(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 minimum-int, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
Ops.erase(Ops.begin());
--Idx;
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
// If we have an umax with a constant maximum-int, it will always be
// maximum-int.
return Ops[0];
}
if (Ops.size() == 1) return Ops[0];
}
// Find the first UMax
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
++Idx;
// Check to see if one of the operands is a UMax. If so, expand its operands
// onto our operand list, and recurse to simplify.
if (Idx < Ops.size()) {
bool DeletedUMax = false;
while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
Ops.erase(Ops.begin()+Idx);
Ops.append(UMax->op_begin(), UMax->op_end());
DeletedUMax = true;
}
if (DeletedUMax)
return getUMaxExpr(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.
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
// X umax Y umax Y --> X umax Y
// X umax Y --> X, if X is always greater than Y
if (Ops[i] == Ops[i+1] ||
isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
--i; --e;
} else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
--i; --e;
}
if (Ops.size() == 1) return Ops[0];
assert(!Ops.empty() && "Reduced umax down to nothing!");
// Okay, it looks like we really DO need a umax expr. Check to see if we
// already have one, otherwise create a new one.
FoldingSetNodeID ID;
ID.AddInteger(scUMaxExpr);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
ID.AddPointer(Ops[i]);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
O, Ops.size());
UniqueSCEVs.InsertNode(S, IP);
return S;
}
const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
const SCEV *RHS) {
// ~smax(~x, ~y) == smin(x, y).
return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
}
const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
const SCEV *RHS) {
// ~umax(~x, ~y) == umin(x, y)
return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
}
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
//
/// isSCEVable - 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->isIntegerTy() || Ty->isPointerTy();
}
/// getTypeSizeInBits - 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!");
return getDataLayout().getTypeSizeInBits(Ty);
}
/// getEffectiveSCEVType - 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-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().getIntPtrType(Ty);
}
const SCEV *ScalarEvolution::getCouldNotCompute() {
return CouldNotCompute.get();
}
bool ScalarEvolution::checkValidity(const SCEV *S) const {
// Helper class working with SCEVTraversal to figure out if a SCEV contains
// a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
// is set iff if find such SCEVUnknown.
//
struct FindInvalidSCEVUnknown {
bool FindOne;
FindInvalidSCEVUnknown() { FindOne = false; }
bool follow(const SCEV *S) {
switch (static_cast<SCEVTypes>(S->getSCEVType())) {
case scConstant:
return false;
case scUnknown:
if (!cast<SCEVUnknown>(S)->getValue())
FindOne = true;
return false;
default:
return true;
}
}
bool isDone() const { return FindOne; }
};
FindInvalidSCEVUnknown F;
SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
ST.visitAll(S);
return !F.FindOne;
}
/// getSCEV - 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);
ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
}
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;
ValueExprMap.erase(I);
}
return nullptr;
}
/// getNegativeSCEV - 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);
}
/// getNotSCEV - 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())));
Type *Ty = V->getType();
Ty = getEffectiveSCEVType(Ty);
const SCEV *AllOnes =
getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
return getMinusSCEV(AllOnes, V);
}
/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
SCEV::NoWrapFlags Flags) {
// 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 =
!getSignedRange(RHS).getSignedMin().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);
}
/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
/// input value to the specified type. If the type must be extended, it is zero
/// extended.
const SCEV *
ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
"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);
return getZeroExtendExpr(V, Ty);
}
/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
/// input value to the specified type. If the type must be extended, it is sign
/// extended.
const SCEV *
ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
Type *Ty) {
Type *SrcTy = V->getType();
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
"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);
return getSignExtendExpr(V, Ty);
}
/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
/// input value to the specified type. If the type must be extended, it is zero
/// extended. The conversion must not be narrowing.
const SCEV *
ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
"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);
}
/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
/// input value to the specified type. If the type must be extended, it is sign
/// extended. The conversion must not be narrowing.
const SCEV *
ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
"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);
}
/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
/// the input value to the specified type. If the type must be extended,
/// it is extended with unspecified bits. The conversion must not be
/// narrowing.
const SCEV *
ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
"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);
}
/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
/// input value to the specified type. The conversion must not be widening.
const SCEV *
ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
"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);
}
/// getUMaxFromMismatchedTypes - Promote the operands to the wider of
/// the types using zero-extension, and then perform a umax operation
/// with them.
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);
}
/// getUMinFromMismatchedTypes - Promote the operands to the wider of
/// the types using zero-extension, and then perform a umin operation
/// with them.
const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(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 getUMinExpr(PromotedLHS, PromotedRHS);
}
/// getPointerBase - Transitively follow the chain of pointer-type operands
/// until reaching a SCEV that does not have a single pointer operand. This
/// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
/// but corner cases do exist.
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;
}
/// PushDefUseChildren - 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));
}
/// ForgetSymbolicValue - This looks up computed SCEV values for all
/// instructions that depend on the given instruction and removes them from
/// the ValueExprMapType map if they reference SymName. This is used during PHI
/// resolution.
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)) {
forgetMemoizedResults(Old);
ValueExprMap.erase(It);
}
}
PushDefUseChildren(I, Worklist);
}
}
namespace {
class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
public:
static const SCEV *rewrite(const SCEV *Scev, const Loop *L,
ScalarEvolution &SE) {
SCEVInitRewriter Rewriter(L, SE);
const SCEV *Result = Rewriter.visit(Scev);
return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
}
SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L), Valid(true) {}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
Valid = false;
return Expr;
}
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
// Only allow AddRecExprs for this loop.
if (Expr->getLoop() == L)
return Expr->getStart();
Valid = false;
return Expr;
}
bool isValid() { return Valid; }
private:
const Loop *L;
bool Valid;
};
class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
public:
static const SCEV *rewrite(const SCEV *Scev, const Loop *L,
ScalarEvolution &SE) {
SCEVShiftRewriter Rewriter(L, SE);
const SCEV *Result = Rewriter.visit(Scev);
return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
}
SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L), Valid(true) {}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
// Only allow AddRecExprs for this loop.
if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
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:
const Loop *L;
bool Valid;
};
} // end anonymous namespace
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) {
// While we are analyzing this PHI node, handle its value symbolically.
const SCEV *SymbolicName = getUnknown(PN);
assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
"PHI node already processed?");
ValueExprMap.insert(std::make_pair(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(Add->getOperand(i));
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 the increment doesn't overflow, then neither the addrec nor
// the post-increment will overflow.
if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
if (OBO->getOperand(0) == PN) {
if (OBO->hasNoUnsignedWrap())
Flags = setFlags(Flags, SCEV::FlagNUW);
if (OBO->hasNoSignedWrap())
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);
// Since the no-wrap flags are on the increment, they apply to the
// post-incremented value as well.
if (isLoopInvariant(Accum, L))
(void)getAddRecExpr(getAddExpr(StartVal, Accum), 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;
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);
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;
}
}
}
}
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:
// 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) {
if (PN->getNumIncomingValues() == 2) {
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);
// fall through
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);
// fall through
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);
}
/// createNodeForGEP - Expand GEP instructions into add and multiply
/// operations. This allows them to be analyzed by regular SCEV code.
///
const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
Value *Base = GEP->getOperand(0);
// Don't attempt to analyze GEPs over unsized objects.
if (!Base->getType()->getPointerElementType()->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->getSourceElementType(), getSCEV(Base), IndexExprs,
GEP->isInBounds());
}
/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
/// guaranteed to end in (at every loop iteration). It is, at the same time,
/// the minimum number of times S is divisible by 2. For example, given {4,+,8}
/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
uint32_t
ScalarEvolution::GetMinTrailingZeros(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.
unsigned BitWidth = getTypeSizeInBits(U->getType());
APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
nullptr, &DT);
return Zeros.countTrailingOnes();
}
// SCEVUDivExpr
return 0;
}
/// GetRangeFromMetadata - 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;
}
/// getRange - 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.
///
ConstantRange
ScalarEvolution::getRange(const SCEV *S,
ScalarEvolution::RangeSignHint SignHint) {
DenseMap<const SCEV *, ConstantRange> &Cache =
SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
: SignedRanges;
// 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);
// 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 = getRange(Add->getOperand(0), SignHint);
for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
X = X.add(getRange(Add->getOperand(i), SignHint));
return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
}
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
ConstantRange X = getRange(Mul->getOperand(0), SignHint);
for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
X = X.multiply(getRange(Mul->getOperand(i), SignHint));
return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
}
if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
ConstantRange X = getRange(SMax->getOperand(0), SignHint);
for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
X = X.smax(getRange(SMax->getOperand(i), SignHint));
return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
}
if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
ConstantRange X = getRange(UMax->getOperand(0), SignHint);
for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
X = X.umax(getRange(UMax->getOperand(i), SignHint));
return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
}
if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
ConstantRange X = getRange(UDiv->getLHS(), SignHint);
ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
return setRange(UDiv, SignHint,
ConservativeResult.intersectWith(X.udiv(Y)));
}
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
ConstantRange X = getRange(ZExt->getOperand(), SignHint);
return setRange(ZExt, SignHint,
ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
}
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
ConstantRange X = getRange(SExt->getOperand(), SignHint);
return setRange(SExt, SignHint,
ConservativeResult.intersectWith(X.signExtend(BitWidth)));
}
if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
ConstantRange X = getRange(Trunc->getOperand(), SignHint);
return setRange(Trunc, SignHint,
ConservativeResult.intersectWith(X.truncate(BitWidth)));
}
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->getNoWrapFlags(SCEV::FlagNUW))
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
if (!C->getValue()->isZero())
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
// If there's no signed wrap, and all the operands have the same sign or
// zero, the value won't ever change sign.
if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
bool AllNonNeg = true;
bool AllNonPos = true;
for (unsigned i = 0, 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(APInt(BitWidth, 0),
APInt::getSignedMinValue(BitWidth)));
else if (AllNonPos)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange(APInt::getSignedMinValue(BitWidth),
APInt(BitWidth, 1)));
}
// TODO: non-affine addrec
if (AddRec->isAffine()) {
Type *Ty = AddRec->getType();
const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
// Check for overflow. This must be done with ConstantRange arithmetic
// because we could be called from within the ScalarEvolution overflow
// checking code.
MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
ConstantRange ZExtMaxBECountRange =
MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
const SCEV *Start = AddRec->getStart();
const SCEV *Step = AddRec->getStepRecurrence(*this);
ConstantRange StepSRange = getSignedRange(Step);
ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
ConstantRange StartURange = getUnsignedRange(Start);
ConstantRange EndURange =
StartURange.add(MaxBECountRange.multiply(StepSRange));
// Check for unsigned overflow.
ConstantRange ZExtStartURange =
StartURange.zextOrTrunc(BitWidth * 2 + 1);
ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
ZExtEndURange) {
APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
EndURange.getUnsignedMin());
APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
EndURange.getUnsignedMax());
bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
if (!IsFullRange)
ConservativeResult =
ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
}
ConstantRange StartSRange = getSignedRange(Start);
ConstantRange EndSRange =
StartSRange.add(MaxBECountRange.multiply(StepSRange));
// Check for signed overflow. This must be done with ConstantRange
// arithmetic because we could be called from within the ScalarEvolution
// overflow checking code.
ConstantRange SExtStartSRange =
StartSRange.sextOrTrunc(BitWidth * 2 + 1);
ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
SExtEndSRange) {
APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
EndSRange.getSignedMin());
APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
EndSRange.getSignedMax());
bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
if (!IsFullRange)
ConservativeResult =
ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
}
}
}
return setRange(AddRec, SignHint, 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());
// 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.
APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
if (Ones != ~Zeros + 1)
ConservativeResult =
ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
} else {
assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
"generalize as needed!");
unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
if (NS > 1)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
}
return setRange(U, SignHint, ConservativeResult);
}
return setRange(S, SignHint, ConservativeResult);
}
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;
}
// Here we check that BinOp is in the header of the innermost loop
// containing BinOp, 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(BinOp->getParent());
if (innermostContainingLoop == nullptr ||
innermostContainingLoop->getHeader() != BinOp->getParent())
return SCEV::FlagAnyWrap;
// Only proceed if we can prove that BinOp does not yield poison.
if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
// At this point we know that if V is executed, then it does not wrap
// according to at least one of NSW or NUW. If V is not executed, then we do
// not know if the calculation that V represents would wrap. Multiple
// instructions can map to the same SCEV. If we apply NSW or NUW from V 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 V is not executed. So we need to find the
// loop that V is considered in relation to and prove that V is executed for
// every iteration of that loop. That implies that the value that V
// 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 two
// recurrences from different loops, so that we know which loop to prove
// that V is executed in.
for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
const int OtherOpIndex = 1 - OpIndex;
const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
return Flags;
}
}
return SCEV::FlagAnyWrap;
}
/// createSCEV - We know that there is no SCEV for the specified value. Analyze
/// the expression.
///
const SCEV *ScalarEvolution::createSCEV(Value *V) {
if (!isSCEVable(V->getType()))
return getUnknown(V);
unsigned Opcode = Instruction::UserOp1;
if (Instruction *I = dyn_cast<Instruction>(V)) {
Opcode = I->getOpcode();
// 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(V);
} else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
Opcode = CE->getOpcode();
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->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
else
return getUnknown(V);
Operator *U = cast<Operator>(V);
switch (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;
for (Value *Op = U;; Op = U->getOperand(0)) {
U = dyn_cast<Operator>(Op);
unsigned Opcode = U ? U->getOpcode() : 0;
if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
assert(Op != V && "V should be an add");
AddOps.push_back(getSCEV(Op));
break;
}
if (auto *OpSCEV = getExistingSCEV(U)) {
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(U->getOperand(1));
SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
if (Flags != SCEV::FlagAnyWrap) {
const SCEV *LHS = getSCEV(U->getOperand(0));
if (Opcode == Instruction::Sub)
AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
else
AddOps.push_back(getAddExpr(LHS, RHS, Flags));
break;
}
if (Opcode == Instruction::Sub)
AddOps.push_back(getNegativeSCEV(RHS));
else
AddOps.push_back(RHS);
}
return getAddExpr(AddOps);
}
case Instruction::Mul: {
SmallVector<const SCEV *, 4> MulOps;
for (Value *Op = U;; Op = U->getOperand(0)) {
U = dyn_cast<Operator>(Op);
if (!U || U->getOpcode() != Instruction::Mul) {
assert(Op != V && "V should be a mul");
MulOps.push_back(getSCEV(Op));
break;
}
if (auto *OpSCEV = getExistingSCEV(U)) {
MulOps.push_back(OpSCEV);
break;
}
SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
if (Flags != SCEV::FlagAnyWrap) {
MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
getSCEV(U->getOperand(1)), Flags));
break;
}
MulOps.push_back(getSCEV(U->getOperand(1)));
}
return getMulExpr(MulOps);
}
case Instruction::UDiv:
return getUDivExpr(getSCEV(U->getOperand(0)),
getSCEV(U->getOperand(1)));
case Instruction::Sub:
return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
getNoWrapFlagsFromUB(U));
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>(U->getOperand(1))) {
if (CI->isNullValue())
return getSCEV(U->getOperand(1));
if (CI->isAllOnesValue())
return getSCEV(U->getOperand(0));
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();
APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
computeKnownBits(U->getOperand(0), KnownZero, KnownOne, getDataLayout(),
0, &AC, nullptr, &DT);
APInt EffectiveMask =
APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
const SCEV *MulCount = getConstant(
ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
return getMulExpr(
getZeroExtendExpr(
getTruncateExpr(
getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
IntegerType::get(getContext(), BitWidth - LZ - TZ)),
U->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>(U->getOperand(1))) {
const SCEV *LHS = getSCEV(U->getOperand(0));
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>(U->getOperand(1))) {
// If the RHS of the xor is a signbit, then this is just an add.
// Instcombine turns add of signbit into xor as a strength reduction step.
if (CI->getValue().isSignBit())
return getAddExpr(getSCEV(U->getOperand(0)),
getSCEV(U->getOperand(1)));
// If the RHS of xor is -1, then this is a not operation.
if (CI->isAllOnesValue())
return getNotSCEV(getSCEV(U->getOperand(0)));
// 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 (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
if (BO->getOpcode() == Instruction::And &&
LCI->getValue() == CI->getValue())
if (const SCEVZeroExtendExpr *Z =
dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
Type *UTy = U->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 (APIntOps::isMask(Z0TySize, CI->getValue()))
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.isSignBit())
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>(U->getOperand(1))) {
uint32_t BitWidth = cast<IntegerType>(U->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 (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
Constant *X = ConstantInt::get(getContext(),
APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
}
break;
case Instruction::LShr:
// Turn logical shift right of a constant into a unsigned divide.
if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
uint32_t BitWidth = cast<IntegerType>(U->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;
Constant *X = ConstantInt::get(getContext(),
APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
}
break;
case Instruction::AShr:
// For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
if (L->getOpcode() == Instruction::Shl &&
L->getOperand(1) == U->getOperand(1)) {
uint64_t BitWidth = getTypeSizeInBits(U->getType());
// 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;
uint64_t Amt = BitWidth - CI->getZExtValue();
if (Amt == BitWidth)
return getSCEV(L->getOperand(0)); // shift by zero --> noop
return
getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
IntegerType::get(getContext(),
Amt)),
U->getType());
}
break;
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:
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));
default: // We cannot analyze this expression.
break;
}
return getUnknown(V);
}
//===----------------------------------------------------------------------===//
// Iteration Count Computation Code
//
unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
if (BasicBlock *ExitingBB = L->getExitingBlock())
return getSmallConstantTripCount(L, ExitingBB);
// No trip count information for multiple exits.
return 0;
}
/// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
/// normal unsigned value. Returns 0 if the trip count is unknown or not
/// constant. Will also return 0 if the maximum trip count is very large (>=
/// 2^32).
///
/// This "trip count" assumes that control exits via ExitingBlock. More
/// precisely, it is the number of times that control may reach ExitingBlock
/// before taking the branch. For loops with multiple exits, it may not be the
/// number times that the loop header executes because the loop may exit
/// prematurely via another branch.
unsigned ScalarEvolution::getSmallConstantTripCount(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));
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::getSmallConstantTripMultiple(Loop *L) {
if (BasicBlock *ExitingBB = L->getExitingBlock())
return getSmallConstantTripMultiple(L, ExitingBB);
// No trip multiple information for multiple exits.
return 0;
}
/// getSmallConstantTripMultiple - 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(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 *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
// FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
// to factor simple cases.
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
TCMul = Mul->getOperand(0);
const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
if (!MulC)
return 1;
ConstantInt *Result = MulC->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();
}
// getExitCount - Get the expression for the number of loop iterations for which
// this loop is guaranteed not to exit via ExitingBlock. Otherwise return
// SCEVCouldNotCompute.
const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
}
/// getBackedgeTakenCount - If the specified loop has a predictable
/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
/// object. The backedge-taken count is the number of times the loop header
/// will be branched to from within the loop. This is one less than the
/// trip count of the loop, since it doesn't count the first iteration,
/// when the header is branched to from outside the loop.
///
/// Note that it is not valid to call this method on a loop without a
/// loop-invariant backedge-taken count (see
/// hasLoopInvariantBackedgeTakenCount).
///
const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
return getBackedgeTakenInfo(L).getExact(this);
}
/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
/// return the least SCEV value that is known never to be less than the
/// actual backedge taken count.
const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
return getBackedgeTakenInfo(L).getMax(this);
}
/// PushLoopPHIs - 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 (BasicBlock::iterator I = Header->begin();
PHINode *PN = dyn_cast<PHINode>(I); ++I)
Worklist.push_back(PN);
}
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(std::make_pair(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);
if (Result.getExact(this) != getCouldNotCompute()) {
assert(isLoopInvariant(Result.getExact(this), 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;
}
// 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> Visited;
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()) {
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)) {
forgetMemoizedResults(Old);
ValueExprMap.erase(It);
}
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
PushDefUseChildren(I, Worklist);
}
}
// 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 = Result;
}
/// forgetLoop - This method should be called by the client when it has
/// changed a loop in a way that may effect ScalarEvolution's ability to
/// compute a trip count, or if the loop is deleted.
void ScalarEvolution::forgetLoop(const Loop *L) {
// Drop any stored trip count value.
DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
BackedgeTakenCounts.find(L);
if (BTCPos != BackedgeTakenCounts.end()) {
BTCPos->second.clear();
BackedgeTakenCounts.erase(BTCPos);
}
// Drop information about expressions based on loop-header PHIs.
SmallVector<Instruction *, 16> Worklist;
PushLoopPHIs(L, Worklist);
SmallPtrSet<Instruction *, 8> Visited;
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()) {
forgetMemoizedResults(It->second);
ValueExprMap.erase(It);
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
PushDefUseChildren(I, Worklist);
}
// Forget all contained loops too, to avoid dangling entries in the
// ValuesAtScopes map.
for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
forgetLoop(*I);
}
/// forgetValue - This method should be called by the client when it has
/// changed a value in a way that may effect its value, or which may
/// disconnect it from a def-use chain linking it to a loop.
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()) {
forgetMemoizedResults(It->second);
ValueExprMap.erase(It);
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
PushDefUseChildren(I, Worklist);
}
}
/// getExact - Get the exact loop backedge taken count considering all loop
/// exits. A computable result can only be returned for loops with a single
/// exit. Returning the minimum taken count among all exits is incorrect
/// because one of the loop's exit limit's may have been skipped. 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 exit using
/// getExact(ExitingBlock, SE).
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
// If any exits were not computable, the loop is not computable.
if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
// We need exactly one computable exit.
if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
const SCEV *BECount = nullptr;
for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
ENT != nullptr; ENT = ENT->getNextExit()) {
assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
if (!BECount)
BECount = ENT->ExactNotTaken;
else if (BECount != ENT->ExactNotTaken)
return SE->getCouldNotCompute();
}
assert(BECount && "Invalid not taken count for loop exit");
return BECount;
}
/// getExact - Get the exact not taken count for this loop exit.
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
ScalarEvolution *SE) const {
for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
ENT != nullptr; ENT = ENT->getNextExit()) {
if (ENT->ExitingBlock == ExitingBlock)
return ENT->ExactNotTaken;
}
return SE->getCouldNotCompute();
}
/// getMax - Get the max backedge taken count for the loop.
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
return Max ? Max : SE->getCouldNotCompute();
}
bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
ScalarEvolution *SE) const {
if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
return true;
if (!ExitNotTaken.ExitingBlock)
return false;
for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
ENT != nullptr; ENT = ENT->getNextExit()) {
if (ENT->ExactNotTaken != SE->getCouldNotCompute()
&& SE->hasOperand(ENT->ExactNotTaken, S)) {
return true;
}
}
return false;
}
/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
/// computable exit into a persistent ExitNotTakenInfo array.
ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
if (!Complete)
ExitNotTaken.setIncomplete();
unsigned NumExits = ExitCounts.size();
if (NumExits == 0) return;
ExitNotTaken.ExitingBlock = ExitCounts[0].first;
ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
if (NumExits == 1) return;
// Handle the rare case of multiple computable exits.
ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
ExitNotTakenInfo *PrevENT = &ExitNotTaken;
for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
PrevENT->setNextExit(ENT);
ENT->ExitingBlock = ExitCounts[i].first;
ENT->ExactNotTaken = ExitCounts[i].second;
}
}
/// clear - Invalidate this result and free the ExitNotTakenInfo array.
void ScalarEvolution::BackedgeTakenInfo::clear() {
ExitNotTaken.ExitingBlock = nullptr;
ExitNotTaken.ExactNotTaken = nullptr;
delete[] ExitNotTaken.getNextExit();
}
/// computeBackedgeTakenCount - Compute the number of times the backedge
/// of the specified loop will execute.
ScalarEvolution::BackedgeTakenInfo
ScalarEvolution::computeBackedgeTakenCount(const Loop *L) {
SmallVector<BasicBlock *, 8> ExitingBlocks;
L->getExitingBlocks(ExitingBlocks);
SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
bool CouldComputeBECount = true;
BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
const SCEV *MustExitMaxBECount = nullptr;
const SCEV *MayExitMaxBECount = nullptr;
// Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
// and compute maxBECount.
for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
BasicBlock *ExitBB = ExitingBlocks[i];
ExitLimit EL = computeExitLimit(L, ExitBB);
// 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.Exact == 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.push_back(std::make_pair(ExitBB, EL.Exact));
// 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.Max of computable LoopMustExits. Otherwise,
// MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
// considered greater than any computable EL.Max.
if (EL.Max != getCouldNotCompute() && Latch &&
DT.dominates(ExitBB, Latch)) {
if (!MustExitMaxBECount)
MustExitMaxBECount = EL.Max;
else {
MustExitMaxBECount =
getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
}
} else if (MayExitMaxBECount != getCouldNotCompute()) {
if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
MayExitMaxBECount = EL.Max;
else {
MayExitMaxBECount =
getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
}
}
}
const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
(MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
}
ScalarEvolution::ExitLimit
ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
// Okay, we've chosen an exiting block. See what condition causes us to exit
// at this block and remember the exit block and whether all other targets
// lead to the loop header.
bool MustExecuteLoopHeader = true;
BasicBlock *Exit = nullptr;
for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
SI != SE; ++SI)
if (!L->contains(*SI)) {
if (Exit) // Multiple exit successors.
return getCouldNotCompute();
Exit = *SI;
} else if (*SI != L->getHeader()) {
MustExecuteLoopHeader = false;
}
// At this point, we know we have a conditional branch that determines whether
// the loop is exited. However, we don't know if the branch is executed each
// time through the loop. If not, then the execution count of the branch will
// not be equal to the trip count of the loop.
//
// Currently we check for this by checking to see if the Exit branch goes to
// the loop header. If so, we know it will always execute the same number of
// times as the loop. We also handle the case where the exit block *is* the
// loop header. This is common for un-rotated loops.
//
// If both of those tests fail, walk up the unique predecessor chain to the
// header, stopping if there is an edge that doesn't exit the loop. If the
// header is reached, the execution count of the branch will be equal to the
// trip count of the loop.
//
// More extensive analysis could be done to handle more cases here.
//
if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
// The simple checks failed, try climbing the unique predecessor chain
// up to the header.
bool Ok = false;
for (BasicBlock *BB = ExitingBlock; BB; ) {
BasicBlock *Pred = BB->getUniquePredecessor();
if (!Pred)
return getCouldNotCompute();
TerminatorInst *PredTerm = Pred->getTerminator();
for (const BasicBlock *PredSucc : PredTerm->successors()) {
if (PredSucc == BB)
continue;
// If the predecessor has a successor that isn't BB and isn't
// outside the loop, assume the worst.
if (L->contains(PredSucc))
return getCouldNotCompute();
}
if (Pred == L->getHeader()) {
Ok = true;
break;
}
BB = Pred;
}
if (!Ok)
return getCouldNotCompute();
}
bool IsOnlyExit = (L->getExitingBlock() != nullptr);
TerminatorInst *Term = ExitingBlock->getTerminator();
if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
assert(BI->isConditional() && "If unconditional, it can't be in loop!");
// Proceed to the next level to examine the exit condition expression.
return computeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
BI->getSuccessor(1),
/*ControlsExit=*/IsOnlyExit);
}
if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
/*ControlsExit=*/IsOnlyExit);
return getCouldNotCompute();
}
/// computeExitLimitFromCond - Compute the number of times the
/// backedge of the specified loop will execute if its exit condition
/// were a conditional branch of ExitCond, TBB, and FBB.
///
/// @param ControlsExit is true if ExitCond directly controls the exit
/// branch. In this case, we can assume that the loop exits only if the
/// condition is true and can infer that failing to meet the condition prior to
/// integer wraparound results in undefined behavior.
ScalarEvolution::ExitLimit
ScalarEvolution::computeExitLimitFromCond(const Loop *L,
Value *ExitCond,
BasicBlock *TBB,
BasicBlock *FBB,
bool ControlsExit) {
// 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 = L->contains(TBB);
ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
ControlsExit && !EitherMayExit);
ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
ControlsExit && !EitherMayExit);
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.Exact == getCouldNotCompute() ||
EL1.Exact == getCouldNotCompute())
BECount = getCouldNotCompute();
else
BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
if (EL0.Max == getCouldNotCompute())
MaxBECount = EL1.Max;
else if (EL1.Max == getCouldNotCompute())
MaxBECount = EL0.Max;
else
MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
} else {
// Both conditions must be true at the same time for the loop to exit.
// For now, be conservative.
assert(L->contains(FBB) && "Loop block has no successor in loop!");
if (EL0.Max == EL1.Max)
MaxBECount = EL0.Max;
if (EL0.Exact == EL1.Exact)
BECount = EL0.Exact;
}
// 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.Exact and EL1.Exact
// to match, but for EL0.Max and EL1.Max to not.
if (isa<SCEVCouldNotCompute>(MaxBECount) &&
!isa<SCEVCouldNotCompute>(BECount))
MaxBECount = BECount;
return ExitLimit(BECount, MaxBECount);
}
if (BO->getOpcode() == Instruction::Or) {
// Recurse on the operands of the or.
bool EitherMayExit = L->contains(FBB);
ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
ControlsExit && !EitherMayExit);
ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
ControlsExit && !EitherMayExit);
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.Exact == getCouldNotCompute() ||
EL1.Exact == getCouldNotCompute())
BECount = getCouldNotCompute();
else
BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
if (EL0.Max == getCouldNotCompute())
MaxBECount = EL1.Max;
else if (EL1.Max == getCouldNotCompute())
MaxBECount = EL0.Max;
else
MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
} else {
// Both conditions must be false at the same time for the loop to exit.
// For now, be conservative.
assert(L->contains(TBB) && "Loop block has no successor in loop!");
if (EL0.Max == EL1.Max)
MaxBECount = EL0.Max;
if (EL0.Exact == EL1.Exact)
BECount = EL0.Exact;
}
return ExitLimit(BECount, MaxBECount);
}
}
// 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))
return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
// 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 (L->contains(FBB) == !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, !L->contains(TBB));
}
ScalarEvolution::ExitLimit
ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
ICmpInst *ExitCond,
BasicBlock *TBB,
BasicBlock *FBB,
bool ControlsExit) {
// If the condition was exit on true, convert the condition to exit on false
ICmpInst::Predicate Cond;
if (!L->contains(FBB))
Cond = ExitCond->getPredicate();
else
Cond = ExitCond->getInversePredicate();
// 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, Cond);
if (ItCnt.hasAnyInfo())
return ItCnt;
}
ExitLimit ShiftEL = computeShiftCompareExitLimit(
ExitCond->getOperand(0), ExitCond->getOperand(1), L, Cond);
if (ShiftEL.hasAnyInfo())
return ShiftEL;
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);
Cond = ICmpInst::getSwappedPredicate(Cond);
}
// Simplify the operands before analyzing them.
(void)SimplifyICmpOperands(Cond, 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(
ICmpInst::makeConstantRange(Cond, RHSC->getAPInt()));
const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
}
switch (Cond) {
case ICmpInst::ICMP_NE: { // while (X != Y)
// Convert to: while (X-Y != 0)
ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
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 = Cond == ICmpInst::ICMP_SLT;
ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
if (EL.hasAnyInfo()) return EL;
break;
}
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_UGT: { // while (X > Y)
bool IsSigned = Cond == ICmpInst::ICMP_SGT;
ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
if (EL.hasAnyInfo()) return EL;
break;
}
default:
break;
}
return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
}
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();
}
/// computeLoadConstantCompareExitLimit - 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 succesful 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);
bool KnownZero, KnownOne;
ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
Predecessor->getTerminator(), &DT);
auto *Ty = cast<IntegerType>(RHS->getType());
if (KnownZero)
StableValue = ConstantInt::get(Ty, 0);
else if (KnownOne)
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);
}
return getCouldNotCompute();
}
/// CanConstantFold - 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))
return true;
if (const CallInst *CI = dyn_cast<CallInst>(I))
if (const Function *F = CI->getCalledFunction())
return canConstantFoldCallTo(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) {
// 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);
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);
}
/// 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], DL);
}
return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 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 (auto &I : *Header) {
PHINode *PHI = dyn_cast<PHINode>(&I);
if (!PHI) break;
auto *StartCST = getOtherIncomingValue(PHI, Latch);
if (!StartCST) continue;
CurrentIterVals[PHI] = StartCST;
}
if (!CurrentIterVals.count(PN))
return RetVal = nullptr;
Value *BEValue = PN->getIncomingValueForBlock(Latch);
// Execute the loop symbolically to determine the exit value.
if (BEs.getActiveBits() >= 32)
return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
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 (auto &I : *Header) {
PHINode *PHI = dyn_cast<PHINode>(&I);
if (!PHI)
break;
auto *StartCST = getOtherIncomingValue(PHI, Latch);
if (!StartCST) continue;
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();
}
/// getSCEVAtScope - Return a SCEV expression for the specified value
/// at the specified scope in the program. The L value specifies a loop
/// nest to evaluate the expression at, where null is the top-level or a
/// specified loop is immediately inside of the loop.
///
/// This method can be used to compute the exit value for a variable defined
/// in a loop by querying what the value will hold in the parent loop.
///
/// In the case that a relevant loop exit value cannot be computed, the
/// original value V is returned.
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:
break; // TODO: smax, 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())) {
const Loop *LI = this->LI[I->getParent()];
if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
if (PHINode *PN = dyn_cast<PHINode>(I))
if (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);
if (const SCEVConstant *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);
}
}
// 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], DL);
} else
C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 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);
if (isa<SCEVMulExpr>(Comm))
return getMulExpr(NewOps);
if (isa<SCEVSMaxExpr>(Comm))
return getSMaxExpr(NewOps);
if (isa<SCEVUMaxExpr>(Comm))
return getUMaxExpr(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!");
}
/// getSCEVAtScope - This is a convenience function which does
/// getSCEVAtScope(getSCEV(V), L).
const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
return getSCEVAtScope(getSCEV(V), L);
}
/// SolveLinEquationWithOverflow - 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 APInt &B,
ScalarEvolution &SE) {
uint32_t BW = A.getBitWidth();
assert(BW == B.getBitWidth() && "Bit widths must be the same.");
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 (B.countTrailingZeros() < Mult2)
return SE.getCouldNotCompute();
// 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
// modulo (N / D).
//
// (N / D) may need BW+1 bits in its representation. Hence, we'll use this
// bit width during computations.
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);
// 4. Compute the minimum unsigned root of the equation:
// I * (B / D) mod (N / D)
APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
// The result is guaranteed to be less than 2^BW so we may truncate it to BW
// bits.
return SE.getConstant(Result.trunc(BW));
}
/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
/// might be the same) or two SCEVCouldNotCompute objects.
///
static std::pair<const SCEV *,const SCEV *>
SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
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));
// We currently can only solve this if the coefficients are constants.
if (!LC || !MC || !NC) {
const SCEV *CNC = SE.getCouldNotCompute();
return std::make_pair(CNC, CNC);
}
uint32_t BitWidth = LC->getAPInt().getBitWidth();
const APInt &L = LC->getAPInt();
const APInt &M = MC->getAPInt();
const APInt &N = NC->getAPInt();
APInt Two(BitWidth, 2);
APInt Four(BitWidth, 4);
{
using namespace APIntOps;
const APInt& C = L;
// Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
// The B coefficient is M-N/2
APInt B(M);
B -= sdiv(N,Two);
// The A coefficient is N/2
APInt A(N.sdiv(Two));
// Compute the B^2-4ac term.
APInt SqrtTerm(B);
SqrtTerm *= B;
SqrtTerm -= Four * (A * C);
if (SqrtTerm.isNegative()) {
// The loop is provably infinite.
const SCEV *CNC = SE.getCouldNotCompute();
return std::make_pair(CNC, CNC);
}
// Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
// integer value or else APInt::sqrt() will assert.
APInt SqrtVal(SqrtTerm.sqrt());
// Compute the two solutions for the quadratic formula.
// The divisions must be performed as signed divisions.
APInt NegB(-B);
APInt TwoA(A << 1);
if (TwoA.isMinValue()) {
const SCEV *CNC = SE.getCouldNotCompute();
return std::make_pair(CNC, CNC);
}
LLVMContext &Context = SE.getContext();
ConstantInt *Solution1 =
ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
ConstantInt *Solution2 =
ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
return std::make_pair(SE.getConstant(Solution1),
SE.getConstant(Solution2));
} // end APIntOps namespace
}
/// HowFarToZero - Return the number of times a backedge comparing the specified
/// value to zero will execute. If not computable, return CouldNotCompute.
///
/// 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.
ScalarEvolution::ExitLimit
ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
// 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>(V);
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()) {
std::pair<const SCEV *,const SCEV *> Roots =
SolveQuadraticEquation(AddRec, *this);
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1 && R2) {
// Pick the smallest positive root value.
if (ConstantInt *CB =
dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
R1->getValue(),
R2->getValue()))) {
if (!CB->getZExtValue())
std::swap(R1, R2); // R1 is the minimum root now.
// 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.
const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
if (Val->isZero())
return R1; // We found a quadratic root!
}
}
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()->equalsInt(0))
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()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
ConstantRange CR = getUnsignedRange(Start);
const SCEV *MaxBECount;
if (!CountDown && CR.getUnsignedMin().isMinValue())
// When counting up, the worst starting value is 1, not 0.
MaxBECount = CR.getUnsignedMax().isMinValue()
? getConstant(APInt::getMinValue(CR.getBitWidth()))
: getConstant(APInt::getMaxValue(CR.getBitWidth()));
else
MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
: -CR.getUnsignedMin());
return ExitLimit(Distance, MaxBECount);
}
// As a special case, handle the instance where Step is a positive power of
// two. In this case, determining whether Step divides Distance evenly can be
// done by counting and comparing the number of trailing zeros of Step and
// Distance.
if (!CountDown) {
const APInt &StepV = StepC->getAPInt();
// StepV.isPowerOf2() returns true if StepV is an positive power of two. It
// also returns true if StepV is maximally negative (eg, INT_MIN), but that
// case is not handled as this code is guarded by !CountDown.
if (StepV.isPowerOf2() &&
GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
// Here we've constrained the equation to be of the form
//
// 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
//
// where we're operating on a W bit wide integer domain and k is
// non-negative. The smallest unsigned solution for X is the trip count.
//
// (0) is equivalent to:
//
// 2^(N + k) * Distance' - 2^N * X = L * 2^W
// <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
// <=> 2^k * Distance' - X = L * 2^(W - N)
// <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
//
// The smallest X satisfying (1) is unsigned remainder of dividing the LHS
// by 2^(W - N).
//
// <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
//
// E.g. say we're solving
//
// 2 * Val = 2 * X (in i8) ... (3)
//
// then from (2), we get X = Val URem i8 128 (k = 0 in this case).
//
// Note: It is tempting to solve (3) by setting X = Val, but Val is not
// necessarily the smallest unsigned value of X that satisfies (3).
// E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
// is i8 1, not i8 -127
const auto *ModuloResult = getUDivExactExpr(Distance, Step);
// Since SCEV does not have a URem node, we construct one using a truncate
// and a zero extend.
unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
auto *WideTy = Distance->getType();
return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
}
}
// 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->getNoWrapFlags(SCEV::FlagNW)) {
const SCEV *Exact =
getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
return ExitLimit(Exact, Exact);
}
// Then, try to solve the above equation provided that Start is constant.
if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
return SolveLinEquationWithOverflow(StepC->getAPInt(), -StartC->getAPInt(),
*this);
return getCouldNotCompute();
}
/// HowFarToNonZero - Return the number of times a backedge checking the
/// specified value for nonzero will execute. If not computable, return
/// CouldNotCompute
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()->isNullValue())
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();
}
/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
/// (which may not be an immediate predecessor) which has exactly one
/// successor from which BB is reachable, or null if no such block is
/// found.
///
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 std::make_pair(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 std::make_pair(L->getLoopPredecessor(), L->getHeader());
return std::pair<BasicBlock *, BasicBlock *>();
}
/// HasSameValue - 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;
}
/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
/// predicate Pred. Return true iff any changes were made.
///
bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
const SCEV *&LHS, const SCEV *&RHS,
unsigned Depth) {
bool Changed = false;
// 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())
goto trivially_false;
else
goto trivially_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();
switch (Pred) {
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
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;
case ICmpInst::ICMP_UGE:
if ((RA - 1).isMinValue()) {
Pred = ICmpInst::ICMP_NE;
RHS = getConstant(RA - 1);
Changed = true;
break;
}
if (RA.isMaxValue()) {
Pred = ICmpInst::ICMP_EQ;
Changed = true;
break;
}
if (RA.isMinValue()) goto trivially_true;
Pred = ICmpInst::ICMP_UGT;
RHS = getConstant(RA - 1);
Changed = true;
break;
case ICmpInst::ICMP_ULE:
if ((RA + 1).isMaxValue()) {
Pred = ICmpInst::ICMP_NE;
RHS = getConstant(RA + 1);
Changed = true;
break;
}
if (RA.isMinValue()) {
Pred = ICmpInst::ICMP_EQ;
Changed = true;
break;
}
if (RA.isMaxValue()) goto trivially_true;
Pred = ICmpInst::ICMP_ULT;
RHS = getConstant(RA + 1);
Changed = true;
break;
case ICmpInst::ICMP_SGE:
if ((RA - 1).isMinSignedValue()) {
Pred = ICmpInst::ICMP_NE;
RHS = getConstant(RA - 1);
Changed = true;
break;
}
if (RA.isMaxSignedValue()) {
Pred = ICmpInst::ICMP_EQ;
Changed = true;
break;
}
if (RA.isMinSignedValue()) goto trivially_true;
Pred = ICmpInst::ICMP_SGT;
RHS = getConstant(RA - 1);
Changed = true;
break;
case ICmpInst::ICMP_SLE:
if ((RA + 1).isMaxSignedValue()) {
Pred = ICmpInst::ICMP_NE;
RHS = getConstant(RA + 1);
Changed = true;
break;
}
if (RA.isMinSignedValue()) {
Pred = ICmpInst::ICMP_EQ;
Changed = true;
break;
}
if (RA.isMaxSignedValue()) goto trivially_true;
Pred = ICmpInst::ICMP_SLT;
RHS = getConstant(RA + 1);
Changed = true;
break;
case ICmpInst::ICMP_UGT:
if (RA.isMinValue()) {
Pred = ICmpInst::ICMP_NE;
Changed = true;
break;
}
if ((RA + 1).isMaxValue()) {
Pred = ICmpInst::ICMP_EQ;
RHS = getConstant(RA + 1);
Changed = true;
break;
}
if (RA.isMaxValue()) goto trivially_false;
break;
case ICmpInst::ICMP_ULT:
if (RA.isMaxValue()) {
Pred = ICmpInst::ICMP_NE;
Changed = true;
break;
}
if ((RA - 1).isMinValue()) {
Pred = ICmpInst::ICMP_EQ;
RHS = getConstant(RA - 1);
Changed = true;
break;
}
if (RA.isMinValue()) goto trivially_false;
break;
case ICmpInst::ICMP_SGT:
if (RA.isMinSignedValue()) {
Pred = ICmpInst::ICMP_NE;
Changed = true;
break;
}
if ((RA + 1).isMaxSignedValue()) {
Pred = ICmpInst::ICMP_EQ;
RHS = getConstant(RA + 1);
Changed = true;
break;
}
if (RA.isMaxSignedValue()) goto trivially_false;
break;
case ICmpInst::ICMP_SLT:
if (RA.isMaxSignedValue()) {
Pred = ICmpInst::ICMP_NE;
Changed = true;
break;
}
if ((RA - 1).isMinSignedValue()) {
Pred = ICmpInst::ICMP_EQ;
RHS = getConstant(RA - 1);
Changed = true;
break;
}
if (RA.isMinSignedValue()) goto trivially_false;
break;
}
}
// Check for obvious equality.
if (HasSameValue(LHS, RHS)) {
if (ICmpInst::isTrueWhenEqual(Pred))
goto trivially_true;
if (ICmpInst::isFalseWhenEqual(Pred))
goto trivially_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 (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SLT;
Changed = true;
} else if (!getSignedRange(LHS).getSignedMin().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 (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SGT;
Changed = true;
} else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SGT;
Changed = true;
}
break;
case ICmpInst::ICMP_ULE:
if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
SCEV::FlagNUW);
Pred = ICmpInst::ICMP_ULT;
Changed = true;
} else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
Pred = ICmpInst::ICMP_ULT;
Changed = true;
}
break;
case ICmpInst::ICMP_UGE:
if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
Pred = ICmpInst::ICMP_UGT;
Changed = true;
} else if (!getUnsignedRange(LHS).getUnsignedMax().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;
trivially_true:
// Return 0 == 0.
LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
Pred = ICmpInst::ICMP_EQ;
return true;
trivially_false:
// Return 0 != 0.
LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
Pred = ICmpInst::ICMP_NE;
return true;
}
bool ScalarEvolution::isKnownNegative(const SCEV *S) {
return getSignedRange(S).getSignedMax().isNegative();
}
bool ScalarEvolution::isKnownPositive(const SCEV *S) {
return getSignedRange(S).getSignedMin().isStrictlyPositive();
}
bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
return !getSignedRange(S).getSignedMin().isNegative();
}
bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
return !getSignedRange(S).getSignedMax().isStrictlyPositive();
}
bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
return isKnownNegative(S) || isKnownPositive(S);
}
bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// Canonicalize the inputs first.
(void)SimplifyICmpOperands(Pred, LHS, RHS);
// If LHS or RHS is an addrec, check to see if the condition is true in
// every iteration of the loop.
// If LHS and RHS are both addrec, both conditions must be true in
// every iteration of the loop.
const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
bool LeftGuarded = false;
bool RightGuarded = false;
if (LAR) {
const Loop *L = LAR->getLoop();
if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
if (!RAR) return true;
LeftGuarded = true;
}
}
if (RAR) {
const Loop *L = RAR->getLoop();
if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
if (!LAR) return true;
RightGuarded = true;
}
}
if (LeftGuarded && RightGuarded)
return true;
if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
return true;
// Otherwise see what can be done with known constant ranges.
return isKnownPredicateWithRanges(Pred, LHS, 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->getNoWrapFlags(SCEV::FlagNUW))
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->getNoWrapFlags(SCEV::FlagNSW))
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::isKnownPredicateWithRanges(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.
switch (Pred) {
default:
llvm_unreachable("Unexpected ICmpInst::Predicate value!");
case ICmpInst::ICMP_SGT:
std::swap(LHS, RHS);
case ICmpInst::ICMP_SLT: {
ConstantRange LHSRange = getSignedRange(LHS);
ConstantRange RHSRange = getSignedRange(RHS);
if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
return true;
if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
return false;
break;
}
case ICmpInst::ICMP_SGE:
std::swap(LHS, RHS);
case ICmpInst::ICMP_SLE: {
ConstantRange LHSRange = getSignedRange(LHS);
ConstantRange RHSRange = getSignedRange(RHS);
if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
return true;
if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
return false;
break;
}
case ICmpInst::ICMP_UGT:
std::swap(LHS, RHS);
case ICmpInst::ICMP_ULT: {
ConstantRange LHSRange = getUnsignedRange(LHS);
ConstantRange RHSRange = getUnsignedRange(RHS);
if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
return true;
if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
return false;
break;
}
case ICmpInst::ICMP_UGE:
std::swap(LHS, RHS);
case ICmpInst::ICMP_ULE: {
ConstantRange LHSRange = getUnsignedRange(LHS);
ConstantRange RHSRange = getUnsignedRange(RHS);
if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
return true;
if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
return false;
break;
}
case ICmpInst::ICMP_NE: {
if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
return true;
if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
return true;
const SCEV *Diff = getMinusSCEV(LHS, RHS);
if (isKnownNonZero(Diff))
return true;
break;
}
case ICmpInst::ICMP_EQ:
// The check at the top of the function catches the case where
// the values are known to be equal.
break;
}
return false;
}
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);
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);
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);
}
/// 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 (isKnownPredicateWithRanges(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;
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();
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;
}
/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
/// by a conditional between LHS and RHS. This is used to help avoid max
/// expressions in loop trip counts, and to eliminate casts.
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 (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
// 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)) {
BranchInst *LoopEntryPredicate =
dyn_cast<BranchInst>(Pair.first->getTerminator());
if (!LoopEntryPredicate ||
LoopEntryPredicate->isUnconditional())
continue;
if (isImpliedCond(Pred, LHS, RHS,
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 (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
return true;
}
return false;
}
namespace {
/// RAII wrapper to prevent recursive application of isImpliedCond.
/// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
/// currently evaluating isImpliedCond.
struct MarkPendingLoopPredicate {
Value *Cond;
DenseSet<Value*> &LoopPreds;
bool Pending;
MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
: Cond(C), LoopPreds(LP) {
Pending = !LoopPreds.insert(Cond).second;
}
~MarkPendingLoopPredicate() {
if (!Pending)
LoopPreds.erase(Cond);
}
};
} // end anonymous namespace
/// isImpliedCond - Test whether the condition described by Pred, LHS,
/// and RHS is true whenever the given Cond value evaluates to true.
bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
Value *FoundCondValue,
bool Inverse) {
MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
if (Mark.Pending)
return false;
// 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) ?
getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
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;
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;
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;
}
bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
const SCEV *More,
APInt &C) {
// We avoid subtracting expressions here because this function is usually
// fairly deep in the call stack (i.e. is called many times).
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 false;
// We look at affine expressions only; not for correctness but to keep
// getStepRecurrence cheap.
if (!LAR->isAffine() || !MAR->isAffine())
return false;
if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
return false;
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();
C = M - L;
return true;
}
const SCEV *L, *R;
SCEV::NoWrapFlags Flags;
if (splitBinaryAdd(Less, L, R, Flags))
if (const auto *LC = dyn_cast<SCEVConstant>(L))
if (R == More) {
C = -(LC->getAPInt());
return true;
}
if (splitBinaryAdd(More, L, R, Flags))
if (const auto *LC = dyn_cast<SCEVConstant>(L))
if (R == Less) {
C = LC->getAPInt();
return true;
}
return false;
}
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)".
APInt LDiff, RDiff;
if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
!computeConstantDifference(FoundRHS, RHS, RDiff) ||
LDiff != RDiff)
return false;
if (LDiff == 0)
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 isLoopEntryGuardedByCond(L, Pred, FoundRHS,
getConstant(FoundRHSLimit));
}
/// isImpliedCondOperands - Test whether the condition described by Pred,
/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
/// and FoundRHS is 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));
}
/// 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);
}
/// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
template<typename MaxExprType>
static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
const SCEV *Candidate) {
const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
if (!MaxExpr) return false;
return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
}
/// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
template<typename MaxExprType>
static bool IsMinConsistingOf(ScalarEvolution &SE,
const SCEV *MaybeMinExpr,
const SCEV *Candidate) {
const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
if (!MaybeMaxExpr)
return false;
return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
}
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);
// fall through
case ICmpInst::ICMP_SLE:
return
// min(A, ...) <= A
IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
// A <= max(A, ...)
IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
case ICmpInst::ICMP_UGE:
std::swap(LHS, RHS);
// fall through
case ICmpInst::ICMP_ULE:
return
// min(A, ...) <= A
IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
// A <= max(A, ...)
IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
}
llvm_unreachable("covered switch fell through?!");
}
/// isImpliedCondOperandsHelper - Test whether the condition described by
/// Pred, LHS, and RHS is true whenever the condition described by Pred,
/// FoundLHS, and FoundRHS is true.
bool
ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS) {
auto IsKnownPredicateFull =
[this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
};
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 (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
return true;
break;
}
return false;
}
/// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
/// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
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;
const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
!isa<SCEVConstant>(AddLHS->getOperand(0)))
return false;
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` + `AddLHS->getOperand(0)`, we can compute a range
// for `LHS`:
APInt Addend = cast<SCEVConstant>(AddLHS->getOperand(0))->getAPInt();
ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
// We can also compute the range of values for `LHS` that satisfy the
// consequent, "`LHS` `Pred` `RHS`":
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);
}
// Verify if an linear IV with positive stride can overflow when in a
// less-than comparison, knowing the invariant term of the comparison, the
// stride and the knowledge of NSW/NUW flags on the recurrence.
bool ScalarEvolution::doesIVOverflowOnLT(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 MaxRHS = getSignedRange(RHS).getSignedMax();
APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
.getSignedMax();
// SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
}
APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
APInt MaxValue = APInt::getMaxValue(BitWidth);
APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
.getUnsignedMax();
// UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
}
// Verify if an linear IV with negative stride can overflow when in a
// greater-than comparison, knowing the invariant term of the comparison,
// the stride and the knowledge of NSW/NUW flags on the recurrence.
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 = getSignedRange(RHS).getSignedMin();
APInt MinValue = APInt::getSignedMinValue(BitWidth);
APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
.getSignedMax();
// SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
}
APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
APInt MinValue = APInt::getMinValue(BitWidth);
APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
.getUnsignedMax();
// UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
}
// Compute the backedge taken count knowing the interval difference, the
// stride and presence of the equality in the comparison.
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);
}
/// HowManyLessThans - Return the number of times a backedge containing the
/// specified less-than comparison will execute. If not computable, return
/// CouldNotCompute.
///
/// @param ControlsExit is true when the LHS < RHS condition directly controls
/// the branch (loops exits only if condition is true). In this case, we can use
/// NoWrapFlags to skip overflow checks.
ScalarEvolution::ExitLimit
ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
const Loop *L, bool IsSigned,
bool ControlsExit) {
// We handle only IV < Invariant
if (!isLoopInvariant(RHS, L))
return getCouldNotCompute();
const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
// 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);
// 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() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
return getCouldNotCompute();
ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
: ICmpInst::ICMP_ULT;
const SCEV *Start = IV->getStart();
const SCEV *End = RHS;
if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
const SCEV *Diff = getMinusSCEV(RHS, Start);
// If we have NoWrap set, then we can assume that the increment won't
// overflow, in which case if RHS - Start is a constant, we don't need to
// do a max operation since we can just figure it out statically
if (NoWrap && isa<SCEVConstant>(Diff)) {
APInt D = dyn_cast<const SCEVConstant>(Diff)->getAPInt();
if (D.isNegative())
End = Start;
} else
End = IsSigned ? getSMaxExpr(RHS, Start)
: getUMaxExpr(RHS, Start);
}
const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
: getUnsignedRange(Start).getUnsignedMin();
APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
: getUnsignedRange(Stride).getUnsignedMin();
unsigned BitWidth = getTypeSizeInBits(LHS->getType());
APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
: APInt::getMaxValue(BitWidth) - (MinStride - 1);
// Although End can be a MAX expression we estimate MaxEnd considering only
// the case End = RHS. 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(getSignedRange(RHS).getSignedMax(), Limit)
: APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
const SCEV *MaxBECount;
if (isa<SCEVConstant>(BECount))
MaxBECount = BECount;
else
MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
getConstant(MinStride), false);
if (isa<SCEVCouldNotCompute>(MaxBECount))
MaxBECount = BECount;
return ExitLimit(BECount, MaxBECount);
}
ScalarEvolution::ExitLimit
ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
const Loop *L, bool IsSigned,
bool ControlsExit) {
// We handle only IV > Invariant
if (!isLoopInvariant(RHS, L))
return getCouldNotCompute();
const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
// 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)) {
const SCEV *Diff = getMinusSCEV(RHS, Start);
// If we have NoWrap set, then we can assume that the increment won't
// overflow, in which case if RHS - Start is a constant, we don't need to
// do a max operation since we can just figure it out statically
if (NoWrap && isa<SCEVConstant>(Diff)) {
APInt D = dyn_cast<const SCEVConstant>(Diff)->getAPInt();
if (!D.isNegative())
End = Start;
} else
End = IsSigned ? getSMinExpr(RHS, Start)
: getUMinExpr(RHS, Start);
}
const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
: getUnsignedRange(Start).getUnsignedMax();
APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
: getUnsignedRange(Stride).getUnsignedMin();
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(getSignedRange(RHS).getSignedMin(), Limit)
: APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
const SCEV *MaxBECount = getCouldNotCompute();
if (isa<SCEVConstant>(BECount))
MaxBECount = BECount;
else
MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
getConstant(MinStride), false);
if (isa<SCEVCouldNotCompute>(MaxBECount))
MaxBECount = BECount;
return ExitLimit(BECount, MaxBECount);
}
/// getNumIterationsInRange - Return the number of iterations of this loop that
/// produce values in the specified constant range. Another way of looking at
/// this is that it returns the first iteration number where the value is not in
/// the condition, thus computing the exit count. If the iteration count can't
/// be computed, an instance of SCEVCouldNotCompute is returned.
const SCEV *SCEVAddRecExpr::getNumIterationsInRange(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 One(BitWidth,1);
APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
APInt End = A.sge(One) ? (Range.getUpper() - One) : 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 - One), SE)->getValue()) &&
"Linear scev computation is off in a bad way!");
return SE.getConstant(ExitValue);
} else if (isQuadratic()) {
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
// quadratic equation to solve it. To do this, we must frame our problem in
// terms of figuring out when zero is crossed, instead of when
// Range.getUpper() is crossed.
SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
// getNoWrapFlags(FlagNW)
FlagAnyWrap);
// Next, solve the constructed addrec
auto Roots = SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1) {
// Pick the smallest positive root value.
if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
if (!CB->getZExtValue())
std::swap(R1, R2); // R1 is the minimum root now.
// Make sure the root is not off by one. The returned iteration should
// not be in the range, but the previous one should be. When solving
// for "X*X < 5", for example, we should not return a root of 2.
ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
R1->getValue(),
SE);
if (Range.contains(R1Val->getValue())) {
// The next iteration must be out of the range...
ConstantInt *NextVal =
ConstantInt::get(SE.getContext(), R1->getAPInt() + 1);
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
if (!Range.contains(R1Val->getValue()))
return SE.getConstant(NextVal);
return SE.getCouldNotCompute(); // Something strange happened
}
// If R1 was not in the range, then it is a good return value. Make
// sure that R1-1 WAS in the range though, just in case.
ConstantInt *NextVal =
ConstantInt::get(SE.getContext(), R1->getAPInt() - 1);
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
if (Range.contains(R1Val->getValue()))
return R1;
return SE.getCouldNotCompute(); // Something strange happened
}
}
}
return SE.getCouldNotCompute();
}
namespace {
struct FindUndefs {
bool Found;
FindUndefs() : Found(false) {}
bool follow(const SCEV *S) {
if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
if (isa<UndefValue>(C->getValue()))
Found = true;
} else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
if (isa<UndefValue>(C->getValue()))
Found = true;
}
// Keep looking if we haven't found it yet.
return !Found;
}
bool isDone() const {
// Stop recursion if we have found an undef.
return Found;
}
};
}
// Return true when S contains at least an undef value.
static inline bool
containsUndefs(const SCEV *S) {
FindUndefs F;
SCEVTraversal<FindUndefs> ST(F);
ST.visitAll(S);
return F.Found;
}
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)) {
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()) {
if (isa<SCEVUnknown>(Op)) {
Operands.push_back(Op);
} else {
bool ContainsAddRec;
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; }
};
}
/// 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);
DEBUG({
dbgs() << "Strides:\n";
for (const SCEV *S : Strides)
dbgs() << *S << "\n";
});
for (const SCEV *S : Strides) {
SCEVCollectTerms TermCollector(Terms);
visitAll(S, TermCollector);
}
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(std::remove_if(Terms.begin(), Terms.end(), [](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 S contains at least a SCEVUnknown parameter.
static inline bool
containsParameters(const SCEV *S) {
struct FindParameter {
bool FoundParameter;
FindParameter() : FoundParameter(false) {}
bool follow(const SCEV *S) {
if (isa<SCEVUnknown>(S)) {
FoundParameter = true;
// Stop recursion: we found a parameter.
return false;
}
// Keep looking.
return true;
}
bool isDone() const {
// Stop recursion if we have found a parameter.
return FoundParameter;
}
};
FindParameter F;
SCEVTraversal<FindParameter> ST(F);
ST.visitAll(S);
return F.FoundParameter;
}
// 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 (containsParameters(T))
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);
}
/// Second step of delinearization: compute the array dimensions Sizes from the
/// set of Terms extracted from the memory access function of this SCEVAddRec.
void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
SmallVectorImpl<const SCEV *> &Sizes,
const SCEV *ElementSize) const {
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;
DEBUG({
dbgs() << "Terms:\n";
for (const SCEV *T : Terms)
dbgs() << *T << "\n";
});
// Remove duplicates.
std::sort(Terms.begin(), Terms.end());
Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
// Put larger terms first.
std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
return numberOfTerms(LHS) > numberOfTerms(RHS);
});
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
// 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(SE, 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(SE, T))
NewTerms.push_back(NewT);
DEBUG({
dbgs() << "Terms after sorting:\n";
for (const SCEV *T : NewTerms)
dbgs() << *T << "\n";
});
if (NewTerms.empty() ||
!findArrayDimensionsRec(SE, NewTerms, Sizes)) {
Sizes.clear();
return;
}
// The last element to be pushed into Sizes is the size of an element.
Sizes.push_back(ElementSize);
DEBUG({
dbgs() << "Sizes:\n";
for (const SCEV *S : Sizes)
dbgs() << *S << "\n";
});
}
/// Third step of delinearization: compute the access functions for the
/// Subscripts based on the dimensions in Sizes.
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);
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());
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;
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";
});
}
//===----------------------------------------------------------------------===//
// 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->ValueExprMap.erase(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->ValueExprMap.erase(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->ValueExprMap.erase(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()),
WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
FirstUnknown(nullptr) {}
ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
: F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
CouldNotCompute(std::move(Arg.CouldNotCompute)),
ValueExprMap(std::move(Arg.ValueExprMap)),
WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
ConstantEvolutionLoopExitValue(
std::move(Arg.ConstantEvolutionLoopExitValue)),
ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
LoopDispositions(std::move(Arg.LoopDispositions)),
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)),
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;
ValueExprMap.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();
assert(PendingLoopPredicates.empty() && "isImpliedCond 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::iterator I = L->begin(), E = L->end(); I != E; ++I)
PrintLoopInfo(OS, SE, *I);
OS << "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
SmallVector<BasicBlock *, 8> ExitBlocks;
L->getExitBlocks(ExitBlocks);
if (ExitBlocks.size() != 1)
OS << "<multiple exits> ";
if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
} else {
OS << "Unpredictable backedge-taken count. ";
}
OS << "\n"
"Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
} else {
OS << "Unpredictable max backedge-taken count. ";
}
OS << "\n";
}
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);
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;
}
}
OS << "\n";
}
OS << "Determining loop execution counts for: ";
F.printAsOperand(OS, /*PrintType=*/false);
OS << "\n";
for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
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;
// This recurrence is variant w.r.t. L if L contains AR's loop.
if (L->contains(AR->getLoop()))
return LoopVariant;
// 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: {
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.
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr: {
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 {
// Search for a SCEV expression node within an expression tree.
// Implements SCEVTraversal::Visitor.
struct SCEVSearch {
const SCEV *Node;
bool IsFound;
SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
bool follow(const SCEV *S) {
IsFound |= (S == Node);
return !IsFound;
}
bool isDone() const { return IsFound; }
};
SCEVSearch Search(Op);
visitAll(S, Search);
return Search.IsFound;
}
void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
ValuesAtScopes.erase(S);
LoopDispositions.erase(S);
BlockDispositions.erase(S);
UnsignedRanges.erase(S);
SignedRanges.erase(S);
for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
BackedgeTakenInfo &BEInfo = I->second;
if (BEInfo.hasOperand(S, this)) {
BEInfo.clear();
BackedgeTakenCounts.erase(I++);
}
else
++I;
}
}
typedef DenseMap<const Loop *, std::string> VerifyMap;
/// replaceSubString - Replaces all occurrences of From in Str with To.
static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
size_t Pos = 0;
while ((Pos = Str.find(From, Pos)) != std::string::npos) {
Str.replace(Pos, From.size(), To.data(), To.size());
Pos += To.size();
}
}
/// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
static void
getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
std::string &S = Map[L];
if (S.empty()) {
raw_string_ostream OS(S);
SE.getBackedgeTakenCount(L)->print(OS);
// false and 0 are semantically equivalent. This can happen in dead loops.
replaceSubString(OS.str(), "false", "0");
// Remove wrap flags, their use in SCEV is highly fragile.
// FIXME: Remove this when SCEV gets smarter about them.
replaceSubString(OS.str(), "<nw>", "");
replaceSubString(OS.str(), "<nsw>", "");
replaceSubString(OS.str(), "<nuw>", "");
}
for (auto *R : reverse(*L))
getLoopBackedgeTakenCounts(R, Map, SE); // recurse.
}
void ScalarEvolution::verify() const {
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
// Gather stringified backedge taken counts for all loops using SCEV's caches.
// FIXME: It would be much better to store actual values instead of strings,
// but SCEV pointers will change if we drop the caches.
VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
// Gather stringified backedge taken counts for all loops using a fresh
// ScalarEvolution object.
ScalarEvolution SE2(F, TLI, AC, DT, LI);
for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
// Now compare whether they're the same with and without caches. This allows
// verifying that no pass changed the cache.
assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
"New loops suddenly appeared!");
for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
OldE = BackedgeDumpsOld.end(),
NewI = BackedgeDumpsNew.begin();
OldI != OldE; ++OldI, ++NewI) {
assert(OldI->first == NewI->first && "Loop order changed!");
// Compare the stringified SCEVs. We don't care if undef backedgetaken count
// changes.
// FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
// means that a pass is buggy or SCEV has to learn a new pattern but is
// usually not harmful.
if (OldI->second != NewI->second &&
OldI->second.find("undef") == std::string::npos &&
NewI->second.find("undef") == std::string::npos &&
OldI->second != "***COULDNOTCOMPUTE***" &&
NewI->second != "***COULDNOTCOMPUTE***") {
dbgs() << "SCEVValidator: SCEV for loop '"
<< OldI->first->getHeader()->getName()
<< "' changed from '" << OldI->second
<< "' to '" << NewI->second << "'!\n";
std::abort();
}
}
// TODO: Verify more things.
}
char ScalarEvolutionAnalysis::PassID;
ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
AnalysisManager<Function> *AM) {
return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
AM->getResult<AssumptionAnalysis>(F),
AM->getResult<DominatorTreeAnalysis>(F),
AM->getResult<LoopAnalysis>(F));
}
PreservedAnalyses
ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *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(),
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 SCEVUnknown *LHS,
const SCEVConstant *RHS) {
FoldingSetNodeID ID;
// 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;
}
namespace {
class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
public:
static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
SCEVUnionPredicate &A) {
SCEVPredicateRewriter Rewriter(SE, A);
return Rewriter.visit(Scev);
}
SCEVPredicateRewriter(ScalarEvolution &SE, SCEVUnionPredicate &P)
: SCEVRewriteVisitor(SE), P(P) {}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
auto ExprPreds = P.getPredicatesForExpr(Expr);
for (auto *Pred : ExprPreds)
if (const auto *IPred = dyn_cast<const SCEVEqualPredicate>(Pred))
if (IPred->getLHS() == Expr)
return IPred->getRHS();
return Expr;
}
private:
SCEVUnionPredicate &P;
};
} // end anonymous namespace
const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *Scev,
SCEVUnionPredicate &Preds) {
return SCEVPredicateRewriter::rewrite(Scev, *this, Preds);
}
/// SCEV predicates
SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
SCEVPredicateKind Kind)
: FastID(ID), Kind(Kind) {}
SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
const SCEVUnknown *LHS,
const SCEVConstant *RHS)
: SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
const auto *Op = dyn_cast<const 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";
}
/// 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<const 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<const 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)
: SE(SE), Generation(0) {}
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
// acording to the current predicate.
if (Entry.second)
Expr = Entry.second;
const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, Preds);
Entry = {Generation, NewSCEV};
return NewSCEV;
}
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, Preds)};
}
}
}
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