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//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file contains the implementation of the scalar evolution analysis
// engine, which is used primarily to analyze expressions involving induction
// variables in loops.
//
// There are several aspects to this library. First is the representation of
// scalar expressions, which are represented as subclasses of the SCEV class.
// These classes are used to represent certain types of subexpressions that we
// can handle. We only create one SCEV of a particular shape, so
// pointer-comparisons for equality are legal.
//
// One important aspect of the SCEV objects is that they are never cyclic, even
// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
// the PHI node is one of the idioms that we can represent (e.g., a polynomial
// recurrence) then we represent it directly as a recurrence node, otherwise we
// represent it as a SCEVUnknown node.
//
// In addition to being able to represent expressions of various types, we also
// have folders that are used to build the *canonical* representation for a
// particular expression. These folders are capable of using a variety of
// rewrite rules to simplify the expressions.
//
// Once the folders are defined, we can implement the more interesting
// higher-level code, such as the code that recognizes PHI nodes of various
// types, computes the execution count of a loop, etc.
//
// TODO: We should use these routines and value representations to implement
// dependence analysis!
//
//===----------------------------------------------------------------------===//
//
// There are several good references for the techniques used in this analysis.
//
// Chains of recurrences -- a method to expedite the evaluation
// of closed-form functions
// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
//
// On computational properties of chains of recurrences
// Eugene V. Zima
//
// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
// Robert A. van Engelen
//
// Efficient Symbolic Analysis for Optimizing Compilers
// Robert A. van Engelen
//
// Using the chains of recurrences algebra for data dependence testing and
// induction variable substitution
// MS Thesis, Johnie Birch
//
//===----------------------------------------------------------------------===//
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/ADT/APInt.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/DepthFirstIterator.h"
#include "llvm/ADT/EquivalenceClasses.h"
#include "llvm/ADT/FoldingSet.h"
#include "llvm/ADT/None.h"
#include "llvm/ADT/Optional.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/ScopeExit.h"
#include "llvm/ADT/Sequence.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/ADT/StringRef.h"
#include "llvm/Analysis/AssumptionCache.h"
#include "llvm/Analysis/ConstantFolding.h"
#include "llvm/Analysis/InstructionSimplify.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/TargetLibraryInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/Config/llvm-config.h"
#include "llvm/IR/Argument.h"
#include "llvm/IR/BasicBlock.h"
#include "llvm/IR/CFG.h"
#include "llvm/IR/CallSite.h"
#include "llvm/IR/Constant.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/DerivedTypes.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/GlobalAlias.h"
#include "llvm/IR/GlobalValue.h"
#include "llvm/IR/GlobalVariable.h"
#include "llvm/IR/InstIterator.h"
#include "llvm/IR/InstrTypes.h"
#include "llvm/IR/Instruction.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/Intrinsics.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Metadata.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/Type.h"
#include "llvm/IR/Use.h"
#include "llvm/IR/User.h"
#include "llvm/IR/Value.h"
#include "llvm/IR/Verifier.h"
#include "llvm/InitializePasses.h"
#include "llvm/Pass.h"
#include "llvm/Support/Casting.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/KnownBits.h"
#include "llvm/Support/SaveAndRestore.h"
#include "llvm/Support/raw_ostream.h"
#include <algorithm>
#include <cassert>
#include <climits>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <map>
#include <memory>
#include <tuple>
#include <utility>
#include <vector>
using namespace llvm;
#define DEBUG_TYPE "scalar-evolution"
STATISTIC(NumArrayLenItCounts,
"Number of trip counts computed with array length");
STATISTIC(NumTripCountsComputed,
"Number of loops with predictable loop counts");
STATISTIC(NumTripCountsNotComputed,
"Number of loops without predictable loop counts");
STATISTIC(NumBruteForceTripCountsComputed,
"Number of loops with trip counts computed by force");
static cl::opt<unsigned>
MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
cl::ZeroOrMore,
cl::desc("Maximum number of iterations SCEV will "
"symbolically execute a constant "
"derived loop"),
cl::init(100));
// FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
static cl::opt<bool> VerifySCEV(
"verify-scev", cl::Hidden,
cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
static cl::opt<bool> VerifySCEVStrict(
"verify-scev-strict", cl::Hidden,
cl::desc("Enable stricter verification with -verify-scev is passed"));
static cl::opt<bool>
VerifySCEVMap("verify-scev-maps", cl::Hidden,
cl::desc("Verify no dangling value in ScalarEvolution's "
"ExprValueMap (slow)"));
static cl::opt<bool> VerifyIR(
"scev-verify-ir", cl::Hidden,
cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
cl::init(false));
static cl::opt<unsigned> MulOpsInlineThreshold(
"scev-mulops-inline-threshold", cl::Hidden,
cl::desc("Threshold for inlining multiplication operands into a SCEV"),
cl::init(32));
static cl::opt<unsigned> AddOpsInlineThreshold(
"scev-addops-inline-threshold", cl::Hidden,
cl::desc("Threshold for inlining addition operands into a SCEV"),
cl::init(500));
static cl::opt<unsigned> MaxSCEVCompareDepth(
"scalar-evolution-max-scev-compare-depth", cl::Hidden,
cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
cl::init(32));
static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
"scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
cl::init(2));
static cl::opt<unsigned> MaxValueCompareDepth(
"scalar-evolution-max-value-compare-depth", cl::Hidden,
cl::desc("Maximum depth of recursive value complexity comparisons"),
cl::init(2));
static cl::opt<unsigned>
MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
cl::desc("Maximum depth of recursive arithmetics"),
cl::init(32));
static cl::opt<unsigned> MaxConstantEvolvingDepth(
"scalar-evolution-max-constant-evolving-depth", cl::Hidden,
cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
static cl::opt<unsigned>
MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
cl::init(8));
static cl::opt<unsigned>
MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
cl::desc("Max coefficients in AddRec during evolving"),
cl::init(8));
static cl::opt<unsigned>
HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
cl::desc("Size of the expression which is considered huge"),
cl::init(4096));
static cl::opt<bool>
ClassifyExpressions("scalar-evolution-classify-expressions",
cl::Hidden, cl::init(true),
cl::desc("When printing analysis, include information on every instruction"));
//===----------------------------------------------------------------------===//
// SCEV class definitions
//===----------------------------------------------------------------------===//
//===----------------------------------------------------------------------===//
// Implementation of the SCEV class.
//
#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
LLVM_DUMP_METHOD void SCEV::dump() const {
print(dbgs());
dbgs() << '\n';
}
#endif
void SCEV::print(raw_ostream &OS) const {
switch (static_cast<SCEVTypes>(getSCEVType())) {
case scConstant:
cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
return;
case scTruncate: {
const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
const SCEV *Op = Trunc->getOperand();
OS << "(trunc " << *Op->getType() << " " << *Op << " to "
<< *Trunc->getType() << ")";
return;
}
case scZeroExtend: {
const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
const SCEV *Op = ZExt->getOperand();
OS << "(zext " << *Op->getType() << " " << *Op << " to "
<< *ZExt->getType() << ")";
return;
}
case scSignExtend: {
const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
const SCEV *Op = SExt->getOperand();
OS << "(sext " << *Op->getType() << " " << *Op << " to "
<< *SExt->getType() << ")";
return;
}
case scAddRecExpr: {
const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
OS << "{" << *AR->getOperand(0);
for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
OS << ",+," << *AR->getOperand(i);
OS << "}<";
if (AR->hasNoUnsignedWrap())
OS << "nuw><";
if (AR->hasNoSignedWrap())
OS << "nsw><";
if (AR->hasNoSelfWrap() &&
!AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
OS << "nw><";
AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ">";
return;
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr: {
const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
const char *OpStr = nullptr;
switch (NAry->getSCEVType()) {
case scAddExpr: OpStr = " + "; break;
case scMulExpr: OpStr = " * "; break;
case scUMaxExpr: OpStr = " umax "; break;
case scSMaxExpr: OpStr = " smax "; break;
case scUMinExpr:
OpStr = " umin ";
break;
case scSMinExpr:
OpStr = " smin ";
break;
}
OS << "(";
for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
I != E; ++I) {
OS << **I;
if (std::next(I) != E)
OS << OpStr;
}
OS << ")";
switch (NAry->getSCEVType()) {
case scAddExpr:
case scMulExpr:
if (NAry->hasNoUnsignedWrap())
OS << "<nuw>";
if (NAry->hasNoSignedWrap())
OS << "<nsw>";
}
return;
}
case scUDivExpr: {
const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
return;
}
case scUnknown: {
const SCEVUnknown *U = cast<SCEVUnknown>(this);
Type *AllocTy;
if (U->isSizeOf(AllocTy)) {
OS << "sizeof(" << *AllocTy << ")";
return;
}
if (U->isAlignOf(AllocTy)) {
OS << "alignof(" << *AllocTy << ")";
return;
}
Type *CTy;
Constant *FieldNo;
if (U->isOffsetOf(CTy, FieldNo)) {
OS << "offsetof(" << *CTy << ", ";
FieldNo->printAsOperand(OS, false);
OS << ")";
return;
}
// Otherwise just print it normally.
U->getValue()->printAsOperand(OS, false);
return;
}
case scCouldNotCompute:
OS << "***COULDNOTCOMPUTE***";
return;
}
llvm_unreachable("Unknown SCEV kind!");
}
Type *SCEV::getType() const {
switch (static_cast<SCEVTypes>(getSCEVType())) {
case scConstant:
return cast<SCEVConstant>(this)->getType();
case scTruncate:
case scZeroExtend:
case scSignExtend:
return cast<SCEVCastExpr>(this)->getType();
case scAddRecExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
return cast<SCEVNAryExpr>(this)->getType();
case scAddExpr:
return cast<SCEVAddExpr>(this)->getType();
case scUDivExpr:
return cast<SCEVUDivExpr>(this)->getType();
case scUnknown:
return cast<SCEVUnknown>(this)->getType();
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
}
llvm_unreachable("Unknown SCEV kind!");
}
bool SCEV::isZero() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
return SC->getValue()->isZero();
return false;
}
bool SCEV::isOne() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
return SC->getValue()->isOne();
return false;
}
bool SCEV::isAllOnesValue() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
return SC->getValue()->isMinusOne();
return false;
}
bool SCEV::isNonConstantNegative() const {
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
if (!Mul) return false;
// If there is a constant factor, it will be first.
const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
if (!SC) return false;
// Return true if the value is negative, this matches things like (-42 * V).
return SC->getAPInt().isNegative();
}
SCEVCouldNotCompute::SCEVCouldNotCompute() :
SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {}
bool SCEVCouldNotCompute::classof(const SCEV *S) {
return S->getSCEVType() == scCouldNotCompute;
}
const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
FoldingSetNodeID ID;
ID.AddInteger(scConstant);
ID.AddPointer(V);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
UniqueSCEVs.InsertNode(S, IP);
return S;
}
const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
return getConstant(ConstantInt::get(getContext(), Val));
}
const SCEV *
ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
return getConstant(ConstantInt::get(ITy, V, isSigned));
}
SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
unsigned SCEVTy, const SCEV *op, Type *ty)
: SCEV(ID, SCEVTy, computeExpressionSize(op)), Op(op), Ty(ty) {}
SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
const SCEV *op, Type *ty)
: SCEVCastExpr(ID, scTruncate, op, ty) {
assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate non-integer value!");
}
SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
const SCEV *op, Type *ty)
: SCEVCastExpr(ID, scZeroExtend, op, ty) {
assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot zero extend non-integer value!");
}
SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
const SCEV *op, Type *ty)
: SCEVCastExpr(ID, scSignExtend, op, ty) {
assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot sign extend non-integer value!");
}
void SCEVUnknown::deleted() {
// Clear this SCEVUnknown from various maps.
SE->forgetMemoizedResults(this);
// Remove this SCEVUnknown from the uniquing map.
SE->UniqueSCEVs.RemoveNode(this);
// Release the value.
setValPtr(nullptr);
}
void SCEVUnknown::allUsesReplacedWith(Value *New) {
// Remove this SCEVUnknown from the uniquing map.
SE->UniqueSCEVs.RemoveNode(this);
// Update this SCEVUnknown to point to the new value. This is needed
// because there may still be outstanding SCEVs which still point to
// this SCEVUnknown.
setValPtr(New);
}
bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
if (VCE->getOpcode() == Instruction::PtrToInt)
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
if (CE->getOpcode() == Instruction::GetElementPtr &&
CE->getOperand(0)->isNullValue() &&
CE->getNumOperands() == 2)
if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
if (CI->isOne()) {
AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
->getElementType();
return true;
}
return false;
}
bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
if (VCE->getOpcode() == Instruction::PtrToInt)
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
if (CE->getOpcode() == Instruction::GetElementPtr &&
CE->getOperand(0)->isNullValue()) {
Type *Ty =
cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
if (StructType *STy = dyn_cast<StructType>(Ty))
if (!STy->isPacked() &&
CE->getNumOperands() == 3 &&
CE->getOperand(1)->isNullValue()) {
if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
if (CI->isOne() &&
STy->getNumElements() == 2 &&
STy->getElementType(0)->isIntegerTy(1)) {
AllocTy = STy->getElementType(1);
return true;
}
}
}
return false;
}
bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
if (VCE->getOpcode() == Instruction::PtrToInt)
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
if (CE->getOpcode() == Instruction::GetElementPtr &&
CE->getNumOperands() == 3 &&
CE->getOperand(0)->isNullValue() &&
CE->getOperand(1)->isNullValue()) {
Type *Ty =
cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
// Ignore vector types here so that ScalarEvolutionExpander doesn't
// emit getelementptrs that index into vectors.
if (Ty->isStructTy() || Ty->isArrayTy()) {
CTy = Ty;
FieldNo = CE->getOperand(2);
return true;
}
}
return false;
}
//===----------------------------------------------------------------------===//
// SCEV Utilities
//===----------------------------------------------------------------------===//
/// Compare the two values \p LV and \p RV in terms of their "complexity" where
/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
/// operands in SCEV expressions. \p EqCache is a set of pairs of values that
/// have been previously deemed to be "equally complex" by this routine. It is
/// intended to avoid exponential time complexity in cases like:
///
/// %a = f(%x, %y)
/// %b = f(%a, %a)
/// %c = f(%b, %b)
///
/// %d = f(%x, %y)
/// %e = f(%d, %d)
/// %f = f(%e, %e)
///
/// CompareValueComplexity(%f, %c)
///
/// Since we do not continue running this routine on expression trees once we
/// have seen unequal values, there is no need to track them in the cache.
static int
CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
const LoopInfo *const LI, Value *LV, Value *RV,
unsigned Depth) {
if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
return 0;
// Order pointer values after integer values. This helps SCEVExpander form
// GEPs.
bool LIsPointer = LV->getType()->isPointerTy(),
RIsPointer = RV->getType()->isPointerTy();
if (LIsPointer != RIsPointer)
return (int)LIsPointer - (int)RIsPointer;
// Compare getValueID values.
unsigned LID = LV->getValueID(), RID = RV->getValueID();
if (LID != RID)
return (int)LID - (int)RID;
// Sort arguments by their position.
if (const auto *LA = dyn_cast<Argument>(LV)) {
const auto *RA = cast<Argument>(RV);
unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
return (int)LArgNo - (int)RArgNo;
}
if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
const auto *RGV = cast<GlobalValue>(RV);
const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
auto LT = GV->getLinkage();
return !(GlobalValue::isPrivateLinkage(LT) ||
GlobalValue::isInternalLinkage(LT));
};
// Use the names to distinguish the two values, but only if the
// names are semantically important.
if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
return LGV->getName().compare(RGV->getName());
}
// For instructions, compare their loop depth, and their operand count. This
// is pretty loose.
if (const auto *LInst = dyn_cast<Instruction>(LV)) {
const auto *RInst = cast<Instruction>(RV);
// Compare loop depths.
const BasicBlock *LParent = LInst->getParent(),
*RParent = RInst->getParent();
if (LParent != RParent) {
unsigned LDepth = LI->getLoopDepth(LParent),
RDepth = LI->getLoopDepth(RParent);
if (LDepth != RDepth)
return (int)LDepth - (int)RDepth;
}
// Compare the number of operands.
unsigned LNumOps = LInst->getNumOperands(),
RNumOps = RInst->getNumOperands();
if (LNumOps != RNumOps)
return (int)LNumOps - (int)RNumOps;
for (unsigned Idx : seq(0u, LNumOps)) {
int Result =
CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
RInst->getOperand(Idx), Depth + 1);
if (Result != 0)
return Result;
}
}
EqCacheValue.unionSets(LV, RV);
return 0;
}
// Return negative, zero, or positive, if LHS is less than, equal to, or greater
// than RHS, respectively. A three-way result allows recursive comparisons to be
// more efficient.
static int CompareSCEVComplexity(
EquivalenceClasses<const SCEV *> &EqCacheSCEV,
EquivalenceClasses<const Value *> &EqCacheValue,
const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
DominatorTree &DT, unsigned Depth = 0) {
// Fast-path: SCEVs are uniqued so we can do a quick equality check.
if (LHS == RHS)
return 0;
// Primarily, sort the SCEVs by their getSCEVType().
unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
if (LType != RType)
return (int)LType - (int)RType;
if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS))
return 0;
// Aside from the getSCEVType() ordering, the particular ordering
// isn't very important except that it's beneficial to be consistent,
// so that (a + b) and (b + a) don't end up as different expressions.
switch (static_cast<SCEVTypes>(LType)) {
case scUnknown: {
const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
RU->getValue(), Depth + 1);
if (X == 0)
EqCacheSCEV.unionSets(LHS, RHS);
return X;
}
case scConstant: {
const SCEVConstant *LC = cast<SCEVConstant>(LHS);
const SCEVConstant *RC = cast<SCEVConstant>(RHS);
// Compare constant values.
const APInt &LA = LC->getAPInt();
const APInt &RA = RC->getAPInt();
unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
if (LBitWidth != RBitWidth)
return (int)LBitWidth - (int)RBitWidth;
return LA.ult(RA) ? -1 : 1;
}
case scAddRecExpr: {
const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
// There is always a dominance between two recs that are used by one SCEV,
// so we can safely sort recs by loop header dominance. We require such
// order in getAddExpr.
const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
if (LLoop != RLoop) {
const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
assert(LHead != RHead && "Two loops share the same header?");
if (DT.dominates(LHead, RHead))
return 1;
else
assert(DT.dominates(RHead, LHead) &&
"No dominance between recurrences used by one SCEV?");
return -1;
}
// Addrec complexity grows with operand count.
unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
if (LNumOps != RNumOps)
return (int)LNumOps - (int)RNumOps;
// Lexicographically compare.
for (unsigned i = 0; i != LNumOps; ++i) {
int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
LA->getOperand(i), RA->getOperand(i), DT,
Depth + 1);
if (X != 0)
return X;
}
EqCacheSCEV.unionSets(LHS, RHS);
return 0;
}
case scAddExpr:
case scMulExpr:
case scSMaxExpr:
case scUMaxExpr:
case scSMinExpr:
case scUMinExpr: {
const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
// Lexicographically compare n-ary expressions.
unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
if (LNumOps != RNumOps)
return (int)LNumOps - (int)RNumOps;
for (unsigned i = 0; i != LNumOps; ++i) {
int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
LC->getOperand(i), RC->getOperand(i), DT,
Depth + 1);
if (X != 0)
return X;
}
EqCacheSCEV.unionSets(LHS, RHS);
return 0;
}
case scUDivExpr: {
const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
// Lexicographically compare udiv expressions.
int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
RC->getLHS(), DT, Depth + 1);
if (X != 0)
return X;
X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
RC->getRHS(), DT, Depth + 1);
if (X == 0)
EqCacheSCEV.unionSets(LHS, RHS);
return X;
}
case scTruncate:
case scZeroExtend:
case scSignExtend: {
const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
// Compare cast expressions by operand.
int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
LC->getOperand(), RC->getOperand(), DT,
Depth + 1);
if (X == 0)
EqCacheSCEV.unionSets(LHS, RHS);
return X;
}
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
}
llvm_unreachable("Unknown SCEV kind!");
}
/// Given a list of SCEV objects, order them by their complexity, and group
/// objects of the same complexity together by value. When this routine is
/// finished, we know that any duplicates in the vector are consecutive and that
/// complexity is monotonically increasing.
///
/// Note that we go take special precautions to ensure that we get deterministic
/// results from this routine. In other words, we don't want the results of
/// this to depend on where the addresses of various SCEV objects happened to
/// land in memory.
static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
LoopInfo *LI, DominatorTree &DT) {
if (Ops.size() < 2) return; // Noop
EquivalenceClasses<const SCEV *> EqCacheSCEV;
EquivalenceClasses<const Value *> EqCacheValue;
if (Ops.size() == 2) {
// This is the common case, which also happens to be trivially simple.
// Special case it.
const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
if (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0)
std::swap(LHS, RHS);
return;
}
// Do the rough sort by complexity.
llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) {
return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT) <
0;
});
// Now that we are sorted by complexity, group elements of the same
// complexity. Note that this is, at worst, N^2, but the vector is likely to
// be extremely short in practice. Note that we take this approach because we
// do not want to depend on the addresses of the objects we are grouping.
for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
const SCEV *S = Ops[i];
unsigned Complexity = S->getSCEVType();
// If there are any objects of the same complexity and same value as this
// one, group them.
for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
if (Ops[j] == S) { // Found a duplicate.
// Move it to immediately after i'th element.
std::swap(Ops[i+1], Ops[j]);
++i; // no need to rescan it.
if (i == e-2) return; // Done!
}
}
}
}
// Returns the size of the SCEV S.
static inline int sizeOfSCEV(const SCEV *S) {
struct FindSCEVSize {
int Size = 0;
FindSCEVSize() = default;
bool follow(const SCEV *S) {
++Size;
// Keep looking at all operands of S.
return true;
}
bool isDone() const {
return false;
}
};
FindSCEVSize F;
SCEVTraversal<FindSCEVSize> ST(F);
ST.visitAll(S);
return F.Size;
}
/// Returns true if the subtree of \p S contains at least HugeExprThreshold
/// nodes.
static bool isHugeExpression(const SCEV *S) {
return S->getExpressionSize() >= HugeExprThreshold;
}
/// Returns true of \p Ops contains a huge SCEV (see definition above).
static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) {
return any_of(Ops, isHugeExpression);
}
namespace {
struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
public:
// Computes the Quotient and Remainder of the division of Numerator by
// Denominator.
static void divide(ScalarEvolution &SE, const SCEV *Numerator,
const SCEV *Denominator, const SCEV **Quotient,
const SCEV **Remainder) {
assert(Numerator && Denominator && "Uninitialized SCEV");
SCEVDivision D(SE, Numerator, Denominator);
// Check for the trivial case here to avoid having to check for it in the
// rest of the code.
if (Numerator == Denominator) {
*Quotient = D.One;
*Remainder = D.Zero;
return;
}
if (Numerator->isZero()) {
*Quotient = D.Zero;
*Remainder = D.Zero;
return;
}
// A simple case when N/1. The quotient is N.
if (Denominator->isOne()) {
*Quotient = Numerator;
*Remainder = D.Zero;
return;
}
// Split the Denominator when it is a product.
if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
const SCEV *Q, *R;
*Quotient = Numerator;
for (const SCEV *Op : T->operands()) {
divide(SE, *Quotient, Op, &Q, &R);
*Quotient = Q;
// Bail out when the Numerator is not divisible by one of the terms of
// the Denominator.
if (!R->isZero()) {
*Quotient = D.Zero;
*Remainder = Numerator;
return;
}
}
*Remainder = D.Zero;
return;
}
D.visit(Numerator);
*Quotient = D.Quotient;
*Remainder = D.Remainder;
}
// Except in the trivial case described above, we do not know how to divide
// Expr by Denominator for the following functions with empty implementation.
void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
void visitSMinExpr(const SCEVSMinExpr *Numerator) {}
void visitUMinExpr(const SCEVUMinExpr *Numerator) {}
void visitUnknown(const SCEVUnknown *Numerator) {}
void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
void visitConstant(const SCEVConstant *Numerator) {
if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
APInt NumeratorVal = Numerator->getAPInt();
APInt DenominatorVal = D->getAPInt();
uint32_t NumeratorBW = NumeratorVal.getBitWidth();
uint32_t DenominatorBW = DenominatorVal.getBitWidth();
if (NumeratorBW > DenominatorBW)
DenominatorVal = DenominatorVal.sext(NumeratorBW);
else if (NumeratorBW < DenominatorBW)
NumeratorVal = NumeratorVal.sext(DenominatorBW);
APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
Quotient = SE.getConstant(QuotientVal);
Remainder = SE.getConstant(RemainderVal);
return;
}
}
void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
const SCEV *StartQ, *StartR, *StepQ, *StepR;
if (!Numerator->isAffine())
return cannotDivide(Numerator);
divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
// Bail out if the types do not match.
Type *Ty = Denominator->getType();
if (Ty != StartQ->getType() || Ty != StartR->getType() ||
Ty != StepQ->getType() || Ty != StepR->getType())
return cannotDivide(Numerator);
Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
Numerator->getNoWrapFlags());
Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
Numerator->getNoWrapFlags());
}
void visitAddExpr(const SCEVAddExpr *Numerator) {
SmallVector<const SCEV *, 2> Qs, Rs;
Type *Ty = Denominator->getType();
for (const SCEV *Op : Numerator->operands()) {
const SCEV *Q, *R;
divide(SE, Op, Denominator, &Q, &R);
// Bail out if types do not match.
if (Ty != Q->getType() || Ty != R->getType())
return cannotDivide(Numerator);
Qs.push_back(Q);
Rs.push_back(R);
}
if (Qs.size() == 1) {
Quotient = Qs[0];
Remainder = Rs[0];
return;
}
Quotient = SE.getAddExpr(Qs);
Remainder = SE.getAddExpr(Rs);
}
void visitMulExpr(const SCEVMulExpr *Numerator) {
SmallVector<const SCEV *, 2> Qs;
Type *Ty = Denominator->getType();
bool FoundDenominatorTerm = false;
for (const SCEV *Op : Numerator->operands()) {
// Bail out if types do not match.
if (Ty != Op->getType())
return cannotDivide(Numerator);
if (FoundDenominatorTerm) {
Qs.push_back(Op);
continue;
}
// Check whether Denominator divides one of the product operands.
const SCEV *Q, *R;
divide(SE, Op, Denominator, &Q, &R);
if (!R->isZero()) {
Qs.push_back(Op);
continue;
}
// Bail out if types do not match.
if (Ty != Q->getType())
return cannotDivide(Numerator);
FoundDenominatorTerm = true;
Qs.push_back(Q);
}
if (FoundDenominatorTerm) {
Remainder = Zero;
if (Qs.size() == 1)
Quotient = Qs[0];
else
Quotient = SE.getMulExpr(Qs);
return;
}
if (!isa<SCEVUnknown>(Denominator))
return cannotDivide(Numerator);
// The Remainder is obtained by replacing Denominator by 0 in Numerator.
ValueToValueMap RewriteMap;
RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
cast<SCEVConstant>(Zero)->getValue();
Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
if (Remainder->isZero()) {
// The Quotient is obtained by replacing Denominator by 1 in Numerator.
RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
cast<SCEVConstant>(One)->getValue();
Quotient =
SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
return;
}
// Quotient is (Numerator - Remainder) divided by Denominator.
const SCEV *Q, *R;
const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
// This SCEV does not seem to simplify: fail the division here.
if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
return cannotDivide(Numerator);
divide(SE, Diff, Denominator, &Q, &R);
if (R != Zero)
return cannotDivide(Numerator);
Quotient = Q;
}
private:
SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
const SCEV *Denominator)
: SE(S), Denominator(Denominator) {
Zero = SE.getZero(Denominator->getType());
One = SE.getOne(Denominator->getType());
// We generally do not know how to divide Expr by Denominator. We
// initialize the division to a "cannot divide" state to simplify the rest
// of the code.
cannotDivide(Numerator);
}
// Convenience function for giving up on the division. We set the quotient to
// be equal to zero and the remainder to be equal to the numerator.
void cannotDivide(const SCEV *Numerator) {
Quotient = Zero;
Remainder = Numerator;
}
ScalarEvolution &SE;
const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
};
} // end anonymous namespace
//===----------------------------------------------------------------------===//
// Simple SCEV method implementations
//===----------------------------------------------------------------------===//
/// Compute BC(It, K). The result has width W. Assume, K > 0.
static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
ScalarEvolution &SE,
Type *ResultTy) {
// Handle the simplest case efficiently.
if (K == 1)
return SE.getTruncateOrZeroExtend(It, ResultTy);
// We are using the following formula for BC(It, K):
//
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
//
// Suppose, W is the bitwidth of the return value. We must be prepared for
// overflow. Hence, we must assure that the result of our computation is
// equal to the accurate one modulo 2^W. Unfortunately, division isn't
// safe in modular arithmetic.
//
// However, this code doesn't use exactly that formula; the formula it uses
// is something like the following, where T is the number of factors of 2 in
// K! (i.e. trailing zeros in the binary representation of K!), and ^ is
// exponentiation:
//
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
//
// This formula is trivially equivalent to the previous formula. However,
// this formula can be implemented much more efficiently. The trick is that
// K! / 2^T is odd, and exact division by an odd number *is* safe in modular
// arithmetic. To do exact division in modular arithmetic, all we have
// to do is multiply by the inverse. Therefore, this step can be done at
// width W.
//
// The next issue is how to safely do the division by 2^T. The way this
// is done is by doing the multiplication step at a width of at least W + T
// bits. This way, the bottom W+T bits of the product are accurate. Then,
// when we perform the division by 2^T (which is equivalent to a right shift
// by T), the bottom W bits are accurate. Extra bits are okay; they'll get
// truncated out after the division by 2^T.
//
// In comparison to just directly using the first formula, this technique
// is much more efficient; using the first formula requires W * K bits,
// but this formula less than W + K bits. Also, the first formula requires
// a division step, whereas this formula only requires multiplies and shifts.
//
// It doesn't matter whether the subtraction step is done in the calculation
// width or the input iteration count's width; if the subtraction overflows,
// the result must be zero anyway. We prefer here to do it in the width of
// the induction variable because it helps a lot for certain cases; CodeGen
// isn't smart enough to ignore the overflow, which leads to much less
// efficient code if the width of the subtraction is wider than the native
// register width.
//
// (It's possible to not widen at all by pulling out factors of 2 before
// the multiplication; for example, K=2 can be calculated as
// It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
// extra arithmetic, so it's not an obvious win, and it gets
// much more complicated for K > 3.)
// Protection from insane SCEVs; this bound is conservative,
// but it probably doesn't matter.
if (K > 1000)
return SE.getCouldNotCompute();
unsigned W = SE.getTypeSizeInBits(ResultTy);
// Calculate K! / 2^T and T; we divide out the factors of two before
// multiplying for calculating K! / 2^T to avoid overflow.
// Other overflow doesn't matter because we only care about the bottom
// W bits of the result.
APInt OddFactorial(W, 1);
unsigned T = 1;
for (unsigned i = 3; i <= K; ++i) {
APInt Mult(W, i);
unsigned TwoFactors = Mult.countTrailingZeros();
T += TwoFactors;
Mult.lshrInPlace(TwoFactors);
OddFactorial *= Mult;
}
// We need at least W + T bits for the multiplication step
unsigned CalculationBits = W + T;
// Calculate 2^T, at width T+W.
APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
// Calculate the multiplicative inverse of K! / 2^T;
// this multiplication factor will perform the exact division by
// K! / 2^T.
APInt Mod = APInt::getSignedMinValue(W+1);
APInt MultiplyFactor = OddFactorial.zext(W+1);
MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
MultiplyFactor = MultiplyFactor.trunc(W);
// Calculate the product, at width T+W
IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
CalculationBits);
const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
for (unsigned i = 1; i != K; ++i) {
const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
Dividend = SE.getMulExpr(Dividend,
SE.getTruncateOrZeroExtend(S, CalculationTy));
}
// Divide by 2^T
const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
// Truncate the result, and divide by K! / 2^T.
return SE.getMulExpr(SE.getConstant(MultiplyFactor),
SE.getTruncateOrZeroExtend(DivResult, ResultTy));
}
/// Return the value of this chain of recurrences at the specified iteration
/// number. We can evaluate this recurrence by multiplying each element in the
/// chain by the binomial coefficient corresponding to it. In other words, we
/// can evaluate {A,+,B,+,C,+,D} as:
///
/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
///
/// where BC(It, k) stands for binomial coefficient.
const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
ScalarEvolution &SE) const {
const SCEV *Result = getStart();
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
// The computation is correct in the face of overflow provided that the
// multiplication is performed _after_ the evaluation of the binomial
// coefficient.
const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
if (isa<SCEVCouldNotCompute>(Coeff))
return Coeff;
Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
}
return Result;
}
//===----------------------------------------------------------------------===//
// SCEV Expression folder implementations
//===----------------------------------------------------------------------===//
const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
"This is not a truncating conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
FoldingSetNodeID ID;
ID.AddInteger(scTruncate);
ID.AddPointer(Op);
ID.AddPointer(Ty);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
// Fold if the operand is constant.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getConstant(
cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
// trunc(trunc(x)) --> trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
return getTruncateExpr(ST->getOperand(), Ty, Depth + 1);
// trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1);
// trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1);
if (Depth > MaxCastDepth) {
SCEV *S =
new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
// trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
// trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
// if after transforming we have at most one truncate, not counting truncates
// that replace other casts.
if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
auto *CommOp = cast<SCEVCommutativeExpr>(Op);
SmallVector<const SCEV *, 4> Operands;
unsigned numTruncs = 0;
for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
++i) {
const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1);
if (!isa<SCEVCastExpr>(CommOp->getOperand(i)) && isa<SCEVTruncateExpr>(S))
numTruncs++;
Operands.push_back(S);
}
if (numTruncs < 2) {
if (isa<SCEVAddExpr>(Op))
return getAddExpr(Operands);
else if (isa<SCEVMulExpr>(Op))
return getMulExpr(Operands);
else
llvm_unreachable("Unexpected SCEV type for Op.");
}
// Although we checked in the beginning that ID is not in the cache, it is
// possible that during recursion and different modification ID was inserted
// into the cache. So if we find it, just return it.
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
return S;
}
// If the input value is a chrec scev, truncate the chrec's operands.
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *Op : AddRec->operands())
Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1));
return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
}
// The cast wasn't folded; create an explicit cast node. We can reuse
// the existing insert position since if we get here, we won't have
// made any changes which would invalidate it.
SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
// Get the limit of a recurrence such that incrementing by Step cannot cause
// signed overflow as long as the value of the recurrence within the
// loop does not exceed this limit before incrementing.
static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
ICmpInst::Predicate *Pred,
ScalarEvolution *SE) {
unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
if (SE->isKnownPositive(Step)) {
*Pred = ICmpInst::ICMP_SLT;
return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
SE->getSignedRangeMax(Step));
}
if (SE->isKnownNegative(Step)) {
*Pred = ICmpInst::ICMP_SGT;
return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
SE->getSignedRangeMin(Step));
}
return nullptr;
}
// Get the limit of a recurrence such that incrementing by Step cannot cause
// unsigned overflow as long as the value of the recurrence within the loop does
// not exceed this limit before incrementing.
static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
ICmpInst::Predicate *Pred,
ScalarEvolution *SE) {
unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
*Pred = ICmpInst::ICMP_ULT;
return SE->getConstant(APInt::getMinValue(BitWidth) -
SE->getUnsignedRangeMax(Step));
}
namespace {
struct ExtendOpTraitsBase {
typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
unsigned);
};
// Used to make code generic over signed and unsigned overflow.
template <typename ExtendOp> struct ExtendOpTraits {
// Members present:
//
// static const SCEV::NoWrapFlags WrapType;
//
// static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
//
// static const SCEV *getOverflowLimitForStep(const SCEV *Step,
// ICmpInst::Predicate *Pred,
// ScalarEvolution *SE);
};
template <>
struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
static const GetExtendExprTy GetExtendExpr;
static const SCEV *getOverflowLimitForStep(const SCEV *Step,
ICmpInst::Predicate *Pred,
ScalarEvolution *SE) {
return getSignedOverflowLimitForStep(Step, Pred, SE);
}
};
const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
template <>
struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
static const GetExtendExprTy GetExtendExpr;
static const SCEV *getOverflowLimitForStep(const SCEV *Step,
ICmpInst::Predicate *Pred,
ScalarEvolution *SE) {
return getUnsignedOverflowLimitForStep(Step, Pred, SE);
}
};
const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
} // end anonymous namespace
// The recurrence AR has been shown to have no signed/unsigned wrap or something
// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
// easily prove NSW/NUW for its preincrement or postincrement sibling. This
// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
// expression "Step + sext/zext(PreIncAR)" is congruent with
// "sext/zext(PostIncAR)"
template <typename ExtendOpTy>
static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
ScalarEvolution *SE, unsigned Depth) {
auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
const Loop *L = AR->getLoop();
const SCEV *Start = AR->getStart();
const SCEV *Step = AR->getStepRecurrence(*SE);
// Check for a simple looking step prior to loop entry.
const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
if (!SA)
return nullptr;
// Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
// subtraction is expensive. For this purpose, perform a quick and dirty
// difference, by checking for Step in the operand list.
SmallVector<const SCEV *, 4> DiffOps;
for (const SCEV *Op : SA->operands())
if (Op != Step)
DiffOps.push_back(Op);
if (DiffOps.size() == SA->getNumOperands())
return nullptr;
// Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
// `Step`:
// 1. NSW/NUW flags on the step increment.
auto PreStartFlags =
ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
// "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
// "S+X does not sign/unsign-overflow".
//
const SCEV *BECount = SE->getBackedgeTakenCount(L);
if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
!isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
return PreStart;
// 2. Direct overflow check on the step operation's expression.
unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
const SCEV *OperandExtendedStart =
SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
(SE->*GetExtendExpr)(Step, WideTy, Depth));
if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
if (PreAR && AR->getNoWrapFlags(WrapType)) {
// If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
// or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
// `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
}
return PreStart;
}
// 3. Loop precondition.
ICmpInst::Predicate Pred;
const SCEV *OverflowLimit =
ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
if (OverflowLimit &&
SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
return PreStart;
return nullptr;
}
// Get the normalized zero or sign extended expression for this AddRec's Start.
template <typename ExtendOpTy>
static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
ScalarEvolution *SE,
unsigned Depth) {
auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
if (!PreStart)
return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
Depth),
(SE->*GetExtendExpr)(PreStart, Ty, Depth));
}
// Try to prove away overflow by looking at "nearby" add recurrences. A
// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
//
// Formally:
//
// {S,+,X} == {S-T,+,X} + T
// => Ext({S,+,X}) == Ext({S-T,+,X} + T)
//
// If ({S-T,+,X} + T) does not overflow ... (1)
//
// RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
//
// If {S-T,+,X} does not overflow ... (2)
//
// RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
// == {Ext(S-T)+Ext(T),+,Ext(X)}
//
// If (S-T)+T does not overflow ... (3)
//
// RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
// == {Ext(S),+,Ext(X)} == LHS
//
// Thus, if (1), (2) and (3) are true for some T, then
// Ext({S,+,X}) == {Ext(S),+,Ext(X)}
//
// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
// does not overflow" restricted to the 0th iteration. Therefore we only need
// to check for (1) and (2).
//
// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
// is `Delta` (defined below).
template <typename ExtendOpTy>
bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
const SCEV *Step,
const Loop *L) {
auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
// We restrict `Start` to a constant to prevent SCEV from spending too much
// time here. It is correct (but more expensive) to continue with a
// non-constant `Start` and do a general SCEV subtraction to compute
// `PreStart` below.
const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
if (!StartC)
return false;
APInt StartAI = StartC->getAPInt();
for (unsigned Delta : {-2, -1, 1, 2}) {
const SCEV *PreStart = getConstant(StartAI - Delta);
FoldingSetNodeID ID;
ID.AddInteger(scAddRecExpr);
ID.AddPointer(PreStart);
ID.AddPointer(Step);
ID.AddPointer(L);
void *IP = nullptr;
const auto *PreAR =
static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
// Give up if we don't already have the add recurrence we need because
// actually constructing an add recurrence is relatively expensive.
if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
DeltaS, &Pred, this);
if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
return true;
}
}
return false;
}
// Finds an integer D for an expression (C + x + y + ...) such that the top
// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
// the (C + x + y + ...) expression is \p WholeAddExpr.
static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
const SCEVConstant *ConstantTerm,
const SCEVAddExpr *WholeAddExpr) {
const APInt C = ConstantTerm->getAPInt();
const unsigned BitWidth = C.getBitWidth();
// Find number of trailing zeros of (x + y + ...) w/o the C first:
uint32_t TZ = BitWidth;
for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I)));
if (TZ) {
// Set D to be as many least significant bits of C as possible while still
// guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
}
return APInt(BitWidth, 0);
}
// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
const APInt &ConstantStart,
const SCEV *Step) {
const unsigned BitWidth = ConstantStart.getBitWidth();
const uint32_t TZ = SE.GetMinTrailingZeros(Step);
if (TZ)
return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
: ConstantStart;
return APInt(BitWidth, 0);
}
const SCEV *
ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
"This is not an extending conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
// Fold if the operand is constant.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getConstant(
cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
// zext(zext(x)) --> zext(x)
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
// Before doing any expensive analysis, check to see if we've already
// computed a SCEV for this Op and Ty.
FoldingSetNodeID ID;
ID.AddInteger(scZeroExtend);
ID.AddPointer(Op);
ID.AddPointer(Ty);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
if (Depth > MaxCastDepth) {
SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
// zext(trunc(x)) --> zext(x) or x or trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
// It's possible the bits taken off by the truncate were all zero bits. If
// so, we should be able to simplify this further.
const SCEV *X = ST->getOperand();
ConstantRange CR = getUnsignedRange(X);
unsigned TruncBits = getTypeSizeInBits(ST->getType());
unsigned NewBits = getTypeSizeInBits(Ty);
if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
CR.zextOrTrunc(NewBits)))
return getTruncateOrZeroExtend(X, Ty, Depth);
}
// If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can zero extend all of the
// operands (often constants). This allows analysis of something like
// this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
if (AR->isAffine()) {
const SCEV *Start = AR->getStart();
const SCEV *Step = AR->getStepRecurrence(*this);
unsigned BitWidth = getTypeSizeInBits(AR->getType());
const Loop *L = AR->getLoop();
if (!AR->hasNoUnsignedWrap()) {
auto NewFlags = proveNoWrapViaConstantRanges(AR);
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
}
// If we have special knowledge that this addrec won't overflow,
// we don't need to do any further analysis.
if (AR->hasNoUnsignedWrap())
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
// Check whether the backedge-taken count is SCEVCouldNotCompute.
// Note that this serves two purposes: It filters out loops that are
// simply not analyzable, and it covers the case where this code is
// being called from within backedge-taken count analysis, such that
// attempting to ask for the backedge-taken count would likely result
// in infinite recursion. In the later case, the analysis code will
// cope with a conservative value, and it will take care to purge
// that value once it has finished.
const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
// Manually compute the final value for AR, checking for
// overflow.
// Check whether the backedge-taken count can be losslessly casted to
// the addrec's type. The count is always unsigned.
const SCEV *CastedMaxBECount =
getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
CastedMaxBECount, MaxBECount->getType(), Depth);
if (MaxBECount == RecastedMaxBECount) {
Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
// Check whether Start+Step*MaxBECount has no unsigned overflow.
const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
SCEV::FlagAnyWrap, Depth + 1);
const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
SCEV::FlagAnyWrap,
Depth + 1),
WideTy, Depth + 1);
const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
const SCEV *WideMaxBECount =
getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
const SCEV *OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getZeroExtendExpr(Step, WideTy, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
if (ZAdd == OperandExtendedAdd) {
// Cache knowledge of AR NUW, which is propagated to this AddRec.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
// Similar to above, only this time treat the step value as signed.
// This covers loops that count down.
OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getSignExtendExpr(Step, WideTy, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
if (ZAdd == OperandExtendedAdd) {
// Cache knowledge of AR NW, which is propagated to this AddRec.
// Negative step causes unsigned wrap, but it still can't self-wrap.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
}
}
// Normally, in the cases we can prove no-overflow via a
// backedge guarding condition, we can also compute a backedge
// taken count for the loop. The exceptions are assumptions and
// guards present in the loop -- SCEV is not great at exploiting
// these to compute max backedge taken counts, but can still use
// these to prove lack of overflow. Use this fact to avoid
// doing extra work that may not pay off.
if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
!AC.assumptions().empty()) {
// If the backedge is guarded by a comparison with the pre-inc
// value the addrec is safe. Also, if the entry is guarded by
// a comparison with the start value and the backedge is
// guarded by a comparison with the post-inc value, the addrec
// is safe.
if (isKnownPositive(Step)) {
const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
getUnsignedRangeMax(Step));
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
// Cache knowledge of AR NUW, which is propagated to this
// AddRec.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
} else if (isKnownNegative(Step)) {
const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
getSignedRangeMin(Step));
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
// Cache knowledge of AR NW, which is propagated to this
// AddRec. Negative step causes unsigned wrap, but it
// still can't self-wrap.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
}
}
// zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
// if D + (C - D + Step * n) could be proven to not unsigned wrap
// where D maximizes the number of trailing zeros of (C - D + Step * n)
if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
const APInt &C = SC->getAPInt();
const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
if (D != 0) {
const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
const SCEV *SResidual =
getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
return getAddExpr(SZExtD, SZExtR,
(SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
Depth + 1);
}
}
if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
return getAddRecExpr(
getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
}
}
// zext(A % B) --> zext(A) % zext(B)
{
const SCEV *LHS;
const SCEV *RHS;
if (matchURem(Op, LHS, RHS))
return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
getZeroExtendExpr(RHS, Ty, Depth + 1));
}
// zext(A / B) --> zext(A) / zext(B).
if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
// zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
if (SA->hasNoUnsignedWrap()) {
// If the addition does not unsign overflow then we can, by definition,
// commute the zero extension with the addition operation.
SmallVector<const SCEV *, 4> Ops;
for (const auto *Op : SA->operands())
Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
}
// zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
// if D + (C - D + x + y + ...) could be proven to not unsigned wrap
// where D maximizes the number of trailing zeros of (C - D + x + y + ...)
//
// Often address arithmetics contain expressions like
// (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
// This transformation is useful while proving that such expressions are
// equal or differ by a small constant amount, see LoadStoreVectorizer pass.
if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
if (D != 0) {
const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
const SCEV *SResidual =
getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
return getAddExpr(SZExtD, SZExtR,
(SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
Depth + 1);
}
}
}
if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
// zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
if (SM->hasNoUnsignedWrap()) {
// If the multiply does not unsign overflow then we can, by definition,
// commute the zero extension with the multiply operation.
SmallVector<const SCEV *, 4> Ops;
for (const auto *Op : SM->operands())
Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
}
// zext(2^K * (trunc X to iN)) to iM ->
// 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
//
// Proof:
//
// zext(2^K * (trunc X to iN)) to iM
// = zext((trunc X to iN) << K) to iM
// = zext((trunc X to i{N-K}) << K)<nuw> to iM
// (because shl removes the top K bits)
// = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
// = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
//
if (SM->getNumOperands() == 2)
if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0)))
if (MulLHS->getAPInt().isPowerOf2())
if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) {
int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) -
MulLHS->getAPInt().logBase2();
Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
return getMulExpr(
getZeroExtendExpr(MulLHS, Ty),
getZeroExtendExpr(
getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty),
SCEV::FlagNUW, Depth + 1);
}
}
// The cast wasn't folded; create an explicit cast node.
// Recompute the insert position, as it may have been invalidated.
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
const SCEV *
ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
"This is not an extending conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
// Fold if the operand is constant.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getConstant(
cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
// sext(sext(x)) --> sext(x)
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
// sext(zext(x)) --> zext(x)
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
// Before doing any expensive analysis, check to see if we've already
// computed a SCEV for this Op and Ty.
FoldingSetNodeID ID;
ID.AddInteger(scSignExtend);
ID.AddPointer(Op);
ID.AddPointer(Ty);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
// Limit recursion depth.
if (Depth > MaxCastDepth) {
SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
// sext(trunc(x)) --> sext(x) or x or trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
// It's possible the bits taken off by the truncate were all sign bits. If
// so, we should be able to simplify this further.
const SCEV *X = ST->getOperand();
ConstantRange CR = getSignedRange(X);
unsigned TruncBits = getTypeSizeInBits(ST->getType());
unsigned NewBits = getTypeSizeInBits(Ty);
if (CR.truncate(TruncBits).signExtend(NewBits).contains(
CR.sextOrTrunc(NewBits)))
return getTruncateOrSignExtend(X, Ty, Depth);
}
if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
// sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
if (SA->hasNoSignedWrap()) {
// If the addition does not sign overflow then we can, by definition,
// commute the sign extension with the addition operation.
SmallVector<const SCEV *, 4> Ops;
for (const auto *Op : SA->operands())
Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
}
// sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
// if D + (C - D + x + y + ...) could be proven to not signed wrap
// where D maximizes the number of trailing zeros of (C - D + x + y + ...)
//
// For instance, this will bring two seemingly different expressions:
// 1 + sext(5 + 20 * %x + 24 * %y) and
// sext(6 + 20 * %x + 24 * %y)
// to the same form:
// 2 + sext(4 + 20 * %x + 24 * %y)
if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
if (D != 0) {
const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
const SCEV *SResidual =
getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
return getAddExpr(SSExtD, SSExtR,
(SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
Depth + 1);
}
}
}
// If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can sign extend all of the
// operands (often constants). This allows analysis of something like
// this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
if (AR->isAffine()) {
const SCEV *Start = AR->getStart();
const SCEV *Step = AR->getStepRecurrence(*this);
unsigned BitWidth = getTypeSizeInBits(AR->getType());
const Loop *L = AR->getLoop();
if (!AR->hasNoSignedWrap()) {
auto NewFlags = proveNoWrapViaConstantRanges(AR);
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
}
// If we have special knowledge that this addrec won't overflow,
// we don't need to do any further analysis.
if (AR->hasNoSignedWrap())
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
// Check whether the backedge-taken count is SCEVCouldNotCompute.
// Note that this serves two purposes: It filters out loops that are
// simply not analyzable, and it covers the case where this code is
// being called from within backedge-taken count analysis, such that
// attempting to ask for the backedge-taken count would likely result
// in infinite recursion. In the later case, the analysis code will
// cope with a conservative value, and it will take care to purge
// that value once it has finished.
const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
// Manually compute the final value for AR, checking for
// overflow.
// Check whether the backedge-taken count can be losslessly casted to
// the addrec's type. The count is always unsigned.
const SCEV *CastedMaxBECount =
getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
CastedMaxBECount, MaxBECount->getType(), Depth);
if (MaxBECount == RecastedMaxBECount) {
Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
// Check whether Start+Step*MaxBECount has no signed overflow.
const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
SCEV::FlagAnyWrap, Depth + 1);
const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
SCEV::FlagAnyWrap,
Depth + 1),
WideTy, Depth + 1);
const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
const SCEV *WideMaxBECount =
getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
const SCEV *OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getSignExtendExpr(Step, WideTy, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
if (SAdd == OperandExtendedAdd) {
// Cache knowledge of AR NSW, which is propagated to this AddRec.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
// Similar to above, only this time treat the step value as unsigned.
// This covers loops that count up with an unsigned step.
OperandExtendedAdd =
getAddExpr(WideStart,
getMulExpr(WideMaxBECount,
getZeroExtendExpr(Step, WideTy, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
if (SAdd == OperandExtendedAdd) {
// If AR wraps around then
//
// abs(Step) * MaxBECount > unsigned-max(AR->getType())
// => SAdd != OperandExtendedAdd
//
// Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
// (SAdd == OperandExtendedAdd => AR is NW)
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
// Return the expression with the addrec on the outside.
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
Depth + 1),
getZeroExtendExpr(Step, Ty, Depth + 1), L,
AR->getNoWrapFlags());
}
}
}
// Normally, in the cases we can prove no-overflow via a
// backedge guarding condition, we can also compute a backedge
// taken count for the loop. The exceptions are assumptions and
// guards present in the loop -- SCEV is not great at exploiting
// these to compute max backedge taken counts, but can still use
// these to prove lack of overflow. Use this fact to avoid
// doing extra work that may not pay off.
if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
!AC.assumptions().empty()) {
// If the backedge is guarded by a comparison with the pre-inc
// value the addrec is safe. Also, if the entry is guarded by
// a comparison with the start value and the backedge is
// guarded by a comparison with the post-inc value, the addrec
// is safe.
ICmpInst::Predicate Pred;
const SCEV *OverflowLimit =
getSignedOverflowLimitForStep(Step, &Pred, this);
if (OverflowLimit &&
(isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
// Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
}
}
// sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
// if D + (C - D + Step * n) could be proven to not signed wrap
// where D maximizes the number of trailing zeros of (C - D + Step * n)
if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
const APInt &C = SC->getAPInt();
const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
if (D != 0) {
const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
const SCEV *SResidual =
getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
return getAddExpr(SSExtD, SSExtR,
(SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
Depth + 1);
}
}
if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
return getAddRecExpr(
getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
}
}
// If the input value is provably positive and we could not simplify
// away the sext build a zext instead.
if (isKnownNonNegative(Op))
return getZeroExtendExpr(Op, Ty, Depth + 1);
// The cast wasn't folded; create an explicit cast node.
// Recompute the insert position, as it may have been invalidated.
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
/// getAnyExtendExpr - Return a SCEV for the given operand extended with
/// unspecified bits out to the given type.
const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
Type *Ty) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
"This is not an extending conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
// Sign-extend negative constants.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
if (SC->getAPInt().isNegative())
return getSignExtendExpr(Op, Ty);
// Peel off a truncate cast.
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
const SCEV *NewOp = T->getOperand();
if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
return getAnyExtendExpr(NewOp, Ty);
return getTruncateOrNoop(NewOp, Ty);
}
// Next try a zext cast. If the cast is folded, use it.
const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
if (!isa<SCEVZeroExtendExpr>(ZExt))
return ZExt;
// Next try a sext cast. If the cast is folded, use it.
const SCEV *SExt = getSignExtendExpr(Op, Ty);
if (!isa<SCEVSignExtendExpr>(SExt))
return SExt;
// Force the cast to be folded into the operands of an addrec.
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
SmallVector<const SCEV *, 4> Ops;
for (const SCEV *Op : AR->operands())
Ops.push_back(getAnyExtendExpr(Op, Ty));
return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
}
// If the expression is obviously signed, use the sext cast value.
if (isa<SCEVSMaxExpr>(Op))
return SExt;
// Absent any other information, use the zext cast value.
return ZExt;
}
/// Process the given Ops list, which is a list of operands to be added under
/// the given scale, update the given map. This is a helper function for
/// getAddRecExpr. As an example of what it does, given a sequence of operands
/// that would form an add expression like this:
///
/// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
///
/// where A and B are constants, update the map with these values:
///
/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
///
/// and add 13 + A*B*29 to AccumulatedConstant.
/// This will allow getAddRecExpr to produce this:
///
/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
///
/// This form often exposes folding opportunities that are hidden in
/// the original operand list.
///
/// Return true iff it appears that any interesting folding opportunities
/// may be exposed. This helps getAddRecExpr short-circuit extra work in
/// the common case where no interesting opportunities are present, and
/// is also used as a check to avoid infinite recursion.
static bool
CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
SmallVectorImpl<const SCEV *> &NewOps,
APInt &AccumulatedConstant,
const SCEV *const *Ops, size_t NumOperands,
const APInt &Scale,
ScalarEvolution &SE) {
bool Interesting = false;
// Iterate over the add operands. They are sorted, with constants first.
unsigned i = 0;
while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
++i;
// Pull a buried constant out to the outside.
if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
Interesting = true;
AccumulatedConstant += Scale * C->getAPInt();
}
// Next comes everything else. We're especially interested in multiplies
// here, but they're in the middle, so just visit the rest with one loop.
for (; i != NumOperands; ++i) {
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
APInt NewScale =
Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
// A multiplication of a constant with another add; recurse.
const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
Interesting |=
CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
Add->op_begin(), Add->getNumOperands(),
NewScale, SE);
} else {
// A multiplication of a constant with some other value. Update
// the map.
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
const SCEV *Key = SE.getMulExpr(MulOps);
auto Pair = M.insert({Key, NewScale});
if (Pair.second) {
NewOps.push_back(Pair.first->first);
} else {
Pair.first->second += NewScale;
// The map already had an entry for this value, which may indicate
// a folding opportunity.
Interesting = true;
}
}
} else {
// An ordinary operand. Update the map.
std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
M.insert({Ops[i], Scale});
if (Pair.second) {
NewOps.push_back(Pair.first->first);
} else {
Pair.first->second += Scale;
// The map already had an entry for this value, which may indicate
// a folding opportunity.
Interesting = true;
}
}
}
return Interesting;
}
// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
// `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
// can't-overflow flags for the operation if possible.
static SCEV::NoWrapFlags
StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
const ArrayRef<const SCEV *> Ops,
SCEV::NoWrapFlags Flags) {
using namespace std::placeholders;
using OBO = OverflowingBinaryOperator;
bool CanAnalyze =
Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
(void)CanAnalyze;
assert(CanAnalyze && "don't call from other places!");
int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
SCEV::NoWrapFlags SignOrUnsignWrap =
ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
// If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
auto IsKnownNonNegative = [&](const SCEV *S) {
return SE->isKnownNonNegative(S);
};
if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
Flags =
ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
if (SignOrUnsignWrap != SignOrUnsignMask &&
(Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
isa<SCEVConstant>(Ops[0])) {
auto Opcode = [&] {
switch (Type) {
case scAddExpr:
return Instruction::Add;
case scMulExpr:
return Instruction::Mul;
default:
llvm_unreachable("Unexpected SCEV op.");
}
}();
const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
// (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
Opcode, C, OBO::NoSignedWrap);
if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
}
// (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
Opcode, C, OBO::NoUnsignedWrap);
if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
}
}
return Flags;
}
bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
}
/// Get a canonical add expression, or something simpler if possible.
const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
SCEV::NoWrapFlags Flags,
unsigned Depth) {
assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
"only nuw or nsw allowed");
assert(!Ops.empty() && "Cannot get empty add!");
if (Ops.size() == 1) return Ops[0];
#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVAddExpr operand types don't match!");
#endif
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI, DT);
Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
++Idx;
assert(Idx < Ops.size());
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
if (Ops.size() == 2) return Ops[0];
Ops.erase(Ops.begin()+1); // Erase the folded element
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant zero being added, strip it off.
if (LHSC->getValue()->isZero()) {
Ops.erase(Ops.begin());
--Idx;
}
if (Ops.size() == 1) return Ops[0];
}
// Limit recursion calls depth.
if (Depth > MaxArithDepth || hasHugeExpression(Ops))
return getOrCreateAddExpr(Ops, Flags);
// Okay, check to see if the same value occurs in the operand list more than
// once. If so, merge them together into an multiply expression. Since we
// sorted the list, these values are required to be adjacent.
Type *Ty = Ops[0]->getType();
bool FoundMatch = false;
for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
// Scan ahead to count how many equal operands there are.
unsigned Count = 2;
while (i+Count != e && Ops[i+Count] == Ops[i])
++Count;
// Merge the values into a multiply.
const SCEV *Scale = getConstant(Ty, Count);
const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
if (Ops.size() == Count)
return Mul;
Ops[i] = Mul;
Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
--i; e -= Count - 1;
FoundMatch = true;
}
if (FoundMatch)
return getAddExpr(Ops, Flags, Depth + 1);
// Check for truncates. If all the operands are truncated from the same
// type, see if factoring out the truncate would permit the result to be
// folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
// if the contents of the resulting outer trunc fold to something simple.
auto FindTruncSrcType = [&]() -> Type * {
// We're ultimately looking to fold an addrec of truncs and muls of only
// constants and truncs, so if we find any other types of SCEV
// as operands of the addrec then we bail and return nullptr here.
// Otherwise, we return the type of the operand of a trunc that we find.
if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
return T->getOperand()->getType();
if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
return T->getOperand()->getType();
}
return nullptr;
};
if (auto *SrcType = FindTruncSrcType()) {
SmallVector<const SCEV *, 8> LargeOps;
bool Ok = true;
// Check all the operands to see if they can be represented in the
// source type of the truncate.
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
if (T->getOperand()->getType() != SrcType) {
Ok = false;
break;
}
LargeOps.push_back(T->getOperand());
} else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
LargeOps.push_back(getAnyExtendExpr(C, SrcType));
} else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
SmallVector<const SCEV *, 8> LargeMulOps;
for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
if (const SCEVTruncateExpr *T =
dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
if (T->getOperand()->getType() != SrcType) {
Ok = false;
break;
}
LargeMulOps.push_back(T->getOperand());
} else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
} else {
Ok = false;
break;
}
}
if (Ok)
LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
} else {
Ok = false;
break;
}
}
if (Ok) {
// Evaluate the expression in the larger type.
const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
// If it folds to something simple, use it. Otherwise, don't.
if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
return getTruncateExpr(Fold, Ty);
}
}
// Skip past any other cast SCEVs.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
++Idx;
// If there are add operands they would be next.
if (Idx < Ops.size()) {
bool DeletedAdd = false;
while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
if (Ops.size() > AddOpsInlineThreshold ||
Add->getNumOperands() > AddOpsInlineThreshold)
break;
// If we have an add, expand the add operands onto the end of the operands
// list.
Ops.erase(Ops.begin()+Idx);
Ops.append(Add->op_begin(), Add->op_end());
DeletedAdd = true;
}
// If we deleted at least one add, we added operands to the end of the list,
// and they are not necessarily sorted. Recurse to resort and resimplify
// any operands we just acquired.
if (DeletedAdd)
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
++Idx;
// Check to see if there are any folding opportunities present with
// operands multiplied by constant values.
if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
uint64_t BitWidth = getTypeSizeInBits(Ty);
DenseMap<const SCEV *, APInt> M;
SmallVector<const SCEV *, 8> NewOps;
APInt AccumulatedConstant(BitWidth, 0);
if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
Ops.data(), Ops.size(),
APInt(BitWidth, 1), *this)) {
struct APIntCompare {
bool operator()(const APInt &LHS, const APInt &RHS) const {
return LHS.ult(RHS);
}
};
// Some interesting folding opportunity is present, so its worthwhile to
// re-generate the operands list. Group the operands by constant scale,
// to avoid multiplying by the same constant scale multiple times.
std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
for (const SCEV *NewOp : NewOps)
MulOpLists[M.find(NewOp)->second].push_back(NewOp);
// Re-generate the operands list.
Ops.clear();
if (AccumulatedConstant != 0)
Ops.push_back(getConstant(AccumulatedConstant));
for (auto &MulOp : MulOpLists)
if (MulOp.first != 0)
Ops.push_back(getMulExpr(
getConstant(MulOp.first),
getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1));
if (Ops.empty())
return getZero(Ty);
if (Ops.size() == 1)
return Ops[0];
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
}
// If we are adding something to a multiply expression, make sure the
// something is not already an operand of the multiply. If so, merge it into
// the multiply.
for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
if (isa<SCEVConstant>(MulOpSCEV))
continue;
for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
if (MulOpSCEV == Ops[AddOp]) {
// Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
if (Mul->getNumOperands() != 2) {
// If the multiply has more than two operands, we must get the
// Y*Z term.
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
Mul->op_begin()+MulOp);
MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
}
SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
SCEV::FlagAnyWrap, Depth + 1);
if (Ops.size() == 2) return OuterMul;
if (AddOp < Idx) {
Ops.erase(Ops.begin()+AddOp);
Ops.erase(Ops.begin()+Idx-1);
} else {
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+AddOp-1);
}
Ops.push_back(OuterMul);
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// Check this multiply against other multiplies being added together.
for (unsigned OtherMulIdx = Idx+1;
OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
++OtherMulIdx) {
const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
// If MulOp occurs in OtherMul, we can fold the two multiplies
// together.
for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
OMulOp != e; ++OMulOp)
if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
// Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
if (Mul->getNumOperands() != 2) {
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
Mul->op_begin()+MulOp);
MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
}
const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
if (OtherMul->getNumOperands() != 2) {
SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
OtherMul->op_begin()+OMulOp);
MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
}
SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
const SCEV *InnerMulSum =
getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
SCEV::FlagAnyWrap, Depth + 1);
if (Ops.size() == 2) return OuterMul;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherMulIdx-1);
Ops.push_back(OuterMul);
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
}
}
}
// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant. If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
++Idx;
// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
// Scan all of the other operands to this add and add them to the vector if
// they are loop invariant w.r.t. the recurrence.
SmallVector<const SCEV *, 8> LIOps;
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
const Loop *AddRecLoop = AddRec->getLoop();
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
LIOps.push_back(Ops[i]);
Ops.erase(Ops.begin()+i);
--i; --e;
}
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
// NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
LIOps.push_back(AddRec->getStart());
SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
AddRec->op_end());
// This follows from the fact that the no-wrap flags on the outer add
// expression are applicable on the 0th iteration, when the add recurrence
// will be equal to its start value.
AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
// Build the new addrec. Propagate the NUW and NSW flags if both the
// outer add and the inner addrec are guaranteed to have no overflow.
// Always propagate NW.
Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
// Otherwise, add the folded AddRec by the non-invariant parts.
for (unsigned i = 0;; ++i)
if (Ops[i] == AddRec) {
Ops[i] = NewRec;
break;
}
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// Okay, if there weren't any loop invariants to be folded, check to see if
// there are multiple AddRec's with the same loop induction variable being
// added together. If so, we can fold them.
for (unsigned OtherIdx = Idx+1;
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
++OtherIdx) {
// We expect the AddRecExpr's to be sorted in reverse dominance order,
// so that the 1st found AddRecExpr is dominated by all others.
assert(DT.dominates(
cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
AddRec->getLoop()->getHeader()) &&
"AddRecExprs are not sorted in reverse dominance order?");
if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
// Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
AddRec->op_end());
for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
++OtherIdx) {
const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
if (OtherAddRec->getLoop() == AddRecLoop) {
for (unsigned i = 0, e = OtherAddRec->getNumOperands();
i != e; ++i) {
if (i >= AddRecOps.size()) {
AddRecOps.append(OtherAddRec->op_begin()+i,
OtherAddRec->op_end());
break;
}
SmallVector<const SCEV *, 2> TwoOps = {
AddRecOps[i], OtherAddRec->getOperand(i)};
AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
}
Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
}
}
// Step size has changed, so we cannot guarantee no self-wraparound.
Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
}
// Otherwise couldn't fold anything into this recurrence. Move onto the
// next one.
}
// Okay, it looks like we really DO need an add expr. Check to see if we
// already have one, otherwise create a new one.
return getOrCreateAddExpr(Ops, Flags);
}
const SCEV *
ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scAddExpr);
for (const SCEV *Op : Ops)
ID.AddPointer(Op);
void *IP = nullptr;
SCEVAddExpr *S =
static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
if (!S) {
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
S = new (SCEVAllocator)
SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
}
S->setNoWrapFlags(Flags);
return S;
}
const SCEV *
ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
const Loop *L, SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scAddRecExpr);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
ID.AddPointer(Ops[i]);
ID.AddPointer(L);
void *IP = nullptr;
SCEVAddRecExpr *S =
static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
if (!S) {
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
S = new (SCEVAllocator)
SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
}
S->setNoWrapFlags(Flags);
return S;
}
const SCEV *
ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scMulExpr);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
ID.AddPointer(Ops[i]);
void *IP = nullptr;
SCEVMulExpr *S =
static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
if (!S) {
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
O, Ops.size());
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
}
S->setNoWrapFlags(Flags);
return S;
}
static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
uint64_t k = i*j;
if (j > 1 && k / j != i) Overflow = true;
return k;
}
/// Compute the result of "n choose k", the binomial coefficient. If an
/// intermediate computation overflows, Overflow will be set and the return will
/// be garbage. Overflow is not cleared on absence of overflow.
static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
// We use the multiplicative formula:
// n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
// At each iteration, we take the n-th term of the numeral and divide by the
// (k-n)th term of the denominator. This division will always produce an
// integral result, and helps reduce the chance of overflow in the
// intermediate computations. However, we can still overflow even when the
// final result would fit.
if (n == 0 || n == k) return 1;
if (k > n) return 0;
if (k > n/2)
k = n-k;
uint64_t r = 1;
for (uint64_t i = 1; i <= k; ++i) {
r = umul_ov(r, n-(i-1), Overflow);
r /= i;
}
return r;
}
/// Determine if any of the operands in this SCEV are a constant or if
/// any of the add or multiply expressions in this SCEV contain a constant.
static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
struct FindConstantInAddMulChain {
bool FoundConstant = false;
bool follow(const SCEV *S) {
FoundConstant |= isa<SCEVConstant>(S);
return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
}
bool isDone() const {
return FoundConstant;
}
};
FindConstantInAddMulChain F;
SCEVTraversal<FindConstantInAddMulChain> ST(F);
ST.visitAll(StartExpr);
return F.FoundConstant;
}
/// Get a canonical multiply expression, or something simpler if possible.
const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
SCEV::NoWrapFlags Flags,
unsigned Depth) {
assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
"only nuw or nsw allowed");
assert(!Ops.empty() && "Cannot get empty mul!");
if (Ops.size() == 1) return Ops[0];
#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"SCEVMulExpr operand types don't match!");
#endif
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI, DT);
Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
// Limit recursion calls depth.
if (Depth > MaxArithDepth || hasHugeExpression(Ops))
return getOrCreateMulExpr(Ops, Flags);
// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
if (Ops.size() == 2)
// C1*(C2+V) -> C1*C2 + C1*V
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
// If any of Add's ops are Adds or Muls with a constant, apply this
// transformation as well.
//
// TODO: There are some cases where this transformation is not
// profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
// this transformation should be narrowed down.
if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add))
return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
SCEV::FlagAnyWrap, Depth + 1),
getMulExpr(LHSC, Add->getOperand(1),
SCEV::FlagAnyWrap, Depth + 1),
SCEV::FlagAnyWrap, Depth + 1);
++Idx;
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
ConstantInt *Fold =
ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant one being multiplied, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
Ops.erase(Ops.begin());
--Idx;
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
// If we have a multiply of zero, it will always be zero.
return Ops[0];
} else if (Ops[0]->isAllOnesValue()) {
// If we have a mul by -1 of an add, try distributing the -1 among the
// add operands.
if (Ops.size() == 2) {
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
SmallVector<const SCEV *, 4> NewOps;
bool AnyFolded = false;
for (const SCEV *AddOp : Add->operands()) {
const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
Depth + 1);
if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
NewOps.push_back(Mul);
}
if (AnyFolded)
return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
} else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
// Negation preserves a recurrence's no self-wrap property.
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *AddRecOp : AddRec->operands())
Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
Depth + 1));
return getAddRecExpr(Operands, AddRec->getLoop(),
AddRec->getNoWrapFlags(SCEV::FlagNW));
}
}
}
if (Ops.size() == 1)
return Ops[0];
}
// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
++Idx;
// If there are mul operands inline them all into this expression.
if (Idx < Ops.size()) {
bool DeletedMul = false;
while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
if (Ops.size() > MulOpsInlineThreshold)
break;
// If we have an mul, expand the mul operands onto the end of the
// operands list.
Ops.erase(Ops.begin()+Idx);
Ops.append(Mul->op_begin(), Mul->op_end());
DeletedMul = true;
}
// If we deleted at least one mul, we added operands to the end of the
// list, and they are not necessarily sorted. Recurse to resort and
// resimplify any operands we just acquired.
if (DeletedMul)
return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant. If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
++Idx;
// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
// Scan all of the other operands to this mul and add them to the vector
// if they are loop invariant w.r.t. the recurrence.
SmallVector<const SCEV *, 8> LIOps;
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
const Loop *AddRecLoop = AddRec->getLoop();
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
LIOps.push_back(Ops[i]);
Ops.erase(Ops.begin()+i);
--i; --e;
}
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
// NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
SmallVector<const SCEV *, 4> NewOps;
NewOps.reserve(AddRec->getNumOperands());
const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
SCEV::FlagAnyWrap, Depth + 1));
// Build the new addrec. Propagate the NUW and NSW flags if both the
// outer mul and the inner addrec are guaranteed to have no overflow.
//
// No self-wrap cannot be guaranteed after changing the step size, but
// will be inferred if either NUW or NSW is true.
Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
// Otherwise, multiply the folded AddRec by the non-invariant parts.
for (unsigned i = 0;; ++i)
if (Ops[i] == AddRec) {
Ops[i] = NewRec;
break;
}
return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}
// Okay, if there weren't any loop invariants to be folded, check to see
// if there are multiple AddRec's with the same loop induction variable
// being multiplied together. If so, we can fold them.
// {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
// = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
// choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
// ]]],+,...up to x=2n}.
// Note that the arguments to choose() are always integers with values
// known at compile time, never SCEV objects.
//
// The implementation avoids pointless extra computations when the two
// addrec's are of different length (mathematically, it's equivalent to
// an infinite stream of zeros on the right).
bool OpsModified = false;
for (unsigned OtherIdx = Idx+1;
OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
++OtherIdx) {
const SCEVAddRecExpr *OtherAddRec =
dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
continue;
// Limit max number of arguments to avoid creation of unreasonably big
// SCEVAddRecs with very complex operands.
if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
MaxAddRecSize || isHugeExpression(AddRec) ||
isHugeExpression(OtherAddRec))
continue;
bool Overflow = false;
Type *Ty = AddRec->getType();
bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
SmallVector<const SCEV*, 7> AddRecOps;
for (int x = 0, xe = AddRec->getNumOperands() +
OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
SmallVector <const SCEV *, 7> SumOps;
for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
z < ze && !Overflow; ++z) {
uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
uint64_t Coeff;
if (LargerThan64Bits)
Coeff = umul_ov(Coeff1, Coeff2, Overflow);
else
Coeff = Coeff1*Coeff2;
const SCEV *CoeffTerm = getConstant(Ty, Coeff);
const SCEV *Term1 = AddRec->getOperand(y-z);
const SCEV *Term2 = OtherAddRec->getOperand(z);
SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
SCEV::FlagAnyWrap, Depth + 1));
}
}
if (SumOps.empty())
SumOps.push_back(getZero(Ty));
AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
}
if (!Overflow) {
const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRecLoop,
SCEV::FlagAnyWrap);
if (Ops.size() == 2) return NewAddRec;
Ops[Idx] = NewAddRec;
Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
OpsModified = true;
AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
if (!AddRec)
break;
}
}
if (OpsModified)
return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
// Otherwise couldn't fold anything into this recurrence. Move onto the
// next one.
}
// Okay, it looks like we really DO need an mul expr. Check to see if we
// already have one, otherwise create a new one.
return getOrCreateMulExpr(Ops, Flags);
}
/// Represents an unsigned remainder expression based on unsigned division.
const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
const SCEV *RHS) {
assert(getEffectiveSCEVType(LHS->getType()) ==
getEffectiveSCEVType(RHS->getType()) &&
"SCEVURemExpr operand types don't match!");
// Short-circuit easy cases
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
// If constant is one, the result is trivial
if (RHSC->getValue()->isOne())
return getZero(LHS->getType()); // X urem 1 --> 0
// If constant is a power of two, fold into a zext(trunc(LHS)).
if (RHSC->getAPInt().isPowerOf2()) {
Type *FullTy = LHS->getType();
Type *TruncTy =
IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
}
}
// Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
const SCEV *UDiv = getUDivExpr(LHS, RHS);
const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
}
/// Get a canonical unsigned division expression, or something simpler if
/// possible.
const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
const SCEV *RHS) {
assert(getEffectiveSCEVType(LHS->getType()) ==
getEffectiveSCEVType(RHS->getType()) &&
"SCEVUDivExpr operand types don't match!");
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
if (RHSC->getValue()->isOne())
return LHS; // X udiv 1 --> x
// If the denominator is zero, the result of the udiv is undefined. Don't
// try to analyze it, because the resolution chosen here may differ from
// the resolution chosen in other parts of the compiler.
if (!RHSC->getValue()->isZero()) {
// Determine if the division can be folded into the operands of
// its operands.
// TODO: Generalize this to non-constants by using known-bits information.
Type *Ty = LHS->getType();
unsigned LZ = RHSC->getAPInt().countLeadingZeros();
unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
// For non-power-of-two values, effectively round the value up to the
// nearest power of two.
if (!RHSC->getAPInt().isPowerOf2())
++MaxShiftAmt;
IntegerType *ExtTy =
IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
if (const SCEVConstant *Step =
dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
// {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
const APInt &StepInt = Step->getAPInt();
const APInt &DivInt = RHSC->getAPInt();
if (!StepInt.urem(DivInt) &&
getZeroExtendExpr(AR, ExtTy) ==
getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
getZeroExtendExpr(Step, ExtTy),
AR->getLoop(), SCEV::FlagAnyWrap)) {
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *Op : AR->operands())
Operands.push_back(getUDivExpr(Op, RHS));
return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
}
/// Get a canonical UDivExpr for a recurrence.
/// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
// We can currently only fold X%N if X is constant.
const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
if (StartC && !DivInt.urem(StepInt) &&
getZeroExtendExpr(AR, ExtTy) ==
getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
getZeroExtendExpr(Step, ExtTy),
AR->getLoop(), SCEV::FlagAnyWrap)) {
const APInt &StartInt = StartC->getAPInt();
const APInt &StartRem = StartInt.urem(StepInt);
if (StartRem != 0)
LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
AR->getLoop(), SCEV::FlagNW);
}
}
// (A*B)/C --> A*(B/C) if safe and B/C can be folded.
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *Op : M->operands())
Operands.push_back(getZeroExtendExpr(Op, ExtTy));
if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
// Find an operand that's safely divisible.
for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
const SCEV *Op = M->getOperand(i);
const SCEV *Div = getUDivExpr(Op, RHSC);
if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
M->op_end());
Operands[i] = Div;
return getMulExpr(Operands);
}
}
}
// (A/B)/C --> A/(B*C) if safe and B*C can be folded.
if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
if (auto *DivisorConstant =
dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
bool Overflow = false;
APInt NewRHS =
DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
if (Overflow) {
return getConstant(RHSC->getType(), 0, false);
}
return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
}
}
// (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
SmallVector<const SCEV *, 4> Operands;
for (const SCEV *Op : A->operands())
Operands.push_back(getZeroExtendExpr(Op, ExtTy));
if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
Operands.clear();
for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
if (isa<SCEVUDivExpr>(Op) ||
getMulExpr(Op, RHS) != A->getOperand(i))
break;
Operands.push_back(Op);
}
if (Operands.size() == A->getNumOperands())
return getAddExpr(Operands);
}
}
// Fold if both operands are constant.
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
Constant *LHSCV = LHSC->getValue();
Constant *RHSCV = RHSC->getValue();
return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
RHSCV)));
}
}
}
FoldingSetNodeID ID;
ID.AddInteger(scUDivExpr);
ID.AddPointer(LHS);
ID.AddPointer(RHS);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
LHS, RHS);
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
APInt A = C1->getAPInt().abs();
APInt B = C2->getAPInt().abs();
uint32_t ABW = A.getBitWidth();
uint32_t BBW = B.getBitWidth();
if (ABW > BBW)
B = B.zext(ABW);
else if (ABW < BBW)
A = A.zext(BBW);
return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
}
/// Get a canonical unsigned division expression, or something simpler if
/// possible. There is no representation for an exact udiv in SCEV IR, but we
/// can attempt to remove factors from the LHS and RHS. We can't do this when
/// it's not exact because the udiv may be clearing bits.
const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
const SCEV *RHS) {
// TODO: we could try to find factors in all sorts of things, but for now we
// just deal with u/exact (multiply, constant). See SCEVDivision towards the
// end of this file for inspiration.
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
if (!Mul || !Mul->hasNoUnsignedWrap())
return getUDivExpr(LHS, RHS);
if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
// If the mulexpr multiplies by a constant, then that constant must be the
// first element of the mulexpr.
if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
if (LHSCst == RHSCst) {
SmallVector<const SCEV *, 2> Operands;
Operands.append(Mul->op_begin() + 1, Mul->op_end());
return getMulExpr(Operands);
}
// We can't just assume that LHSCst divides RHSCst cleanly, it could be
// that there's a factor provided by one of the other terms. We need to
// check.
APInt Factor = gcd(LHSCst, RHSCst);
if (!Factor.isIntN(1)) {
LHSCst =
cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
RHSCst =
cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
SmallVector<const SCEV *, 2> Operands;
Operands.push_back(LHSCst);
Operands.append(Mul->op_begin() + 1, Mul->op_end());
LHS = getMulExpr(Operands);
RHS = RHSCst;
Mul = dyn_cast<SCEVMulExpr>(LHS);
if (!Mul)
return getUDivExactExpr(LHS, RHS);
}
}
}
for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
if (Mul->getOperand(i) == RHS) {
SmallVector<const SCEV *, 2> Operands;
Operands.append(Mul->op_begin(), Mul->op_begin() + i);
Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
return getMulExpr(Operands);
}
}
return getUDivExpr(LHS, RHS);
}
/// Get an add recurrence expression for the specified loop. Simplify the
/// expression as much as possible.
const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
const Loop *L,
SCEV::NoWrapFlags Flags) {
SmallVector<const SCEV *, 4> Operands;
Operands.push_back(Start);
if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
if (StepChrec->getLoop() == L) {
Operands.append(StepChrec->op_begin(), StepChrec->op_end());
return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
}
Operands.push_back(Step);
return getAddRecExpr(Operands, L, Flags);
}
/// Get an add recurrence expression for the specified loop. Simplify the
/// expression as much as possible.
const SCEV *
ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
const Loop *L, SCEV::NoWrapFlags Flags) {
if (Operands.size() == 1) return Operands[0];
#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
"SCEVAddRecExpr operand types don't match!");
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
assert(isLoopInvariant(Operands[i], L) &&
"SCEVAddRecExpr operand is not loop-invariant!");
#endif
if (Operands.back()->isZero()) {
Operands.pop_back();
return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
}
// It's tempting to want to call getConstantMaxBackedgeTakenCount count here and
// use that information to infer NUW and NSW flags. However, computing a
// BE count requires calling getAddRecExpr, so we may not yet have a
// meaningful BE count at this point (and if we don't, we'd be stuck
// with a SCEVCouldNotCompute as the cached BE count).
Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
// Canonicalize nested AddRecs in by nesting them in order of loop depth.
if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
const Loop *NestedLoop = NestedAR->getLoop();
if (L->contains(NestedLoop)
? (L->getLoopDepth() < NestedLoop->getLoopDepth())
: (!NestedLoop->contains(L) &&
DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
NestedAR->op_end());
Operands[0] = NestedAR->getStart();
// AddRecs require their operands be loop-invariant with respect to their
// loops. Don't perform this transformation if it would break this
// requirement.
bool AllInvariant = all_of(
Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
if (AllInvariant) {
// Create a recurrence for the outer loop with the same step size.
//
// The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
// inner recurrence has the same property.
SCEV::NoWrapFlags OuterFlags =
maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
return isLoopInvariant(Op, NestedLoop);
});
if (AllInvariant) {
// Ok, both add recurrences are valid after the transformation.
//
// The inner recurrence keeps its NW flag but only keeps NUW/NSW if
// the outer recurrence has the same property.
SCEV::NoWrapFlags InnerFlags =
maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
}
}
// Reset Operands to its original state.
Operands[0] = NestedAR;
}
}
// Okay, it looks like we really DO need an addrec expr. Check to see if we
// already have one, otherwise create a new one.
return getOrCreateAddRecExpr(Operands, L, Flags);
}
const SCEV *
ScalarEvolution::getGEPExpr(GEPOperator *GEP,
const SmallVectorImpl<const SCEV *> &IndexExprs) {
const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
// getSCEV(Base)->getType() has the same address space as Base->getType()
// because SCEV::getType() preserves the address space.
Type *IntIdxTy = getEffectiveSCEVType(BaseExpr->getType());
// FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
// instruction to its SCEV, because the Instruction may be guarded by control
// flow and the no-overflow bits may not be valid for the expression in any
// context. This can be fixed similarly to how these flags are handled for
// adds.
SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
: SCEV::FlagAnyWrap;
const SCEV *TotalOffset = getZero(IntIdxTy);
// The array size is unimportant. The first thing we do on CurTy is getting
// its element type.
Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
for (const SCEV *IndexExpr : IndexExprs) {
// Compute the (potentially symbolic) offset in bytes for this index.
if (StructType *STy = dyn_cast<StructType>(CurTy)) {
// For a struct, add the member offset.
ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
unsigned FieldNo = Index->getZExtValue();
const SCEV *FieldOffset = getOffsetOfExpr(IntIdxTy, STy, FieldNo);
// Add the field offset to the running total offset.
TotalOffset = getAddExpr(TotalOffset, FieldOffset);
// Update CurTy to the type of the field at Index.
CurTy = STy->getTypeAtIndex(Index);
} else {
// Update CurTy to its element type.
CurTy = cast<SequentialType>(CurTy)->getElementType();
// For an array, add the element offset, explicitly scaled.
const SCEV *ElementSize = getSizeOfExpr(IntIdxTy, CurTy);
// Getelementptr indices are signed.
IndexExpr = getTruncateOrSignExtend(IndexExpr, IntIdxTy);
// Multiply the index by the element size to compute the element offset.
const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
// Add the element offset to the running total offset.
TotalOffset = getAddExpr(TotalOffset, LocalOffset);
}
}
// Add the total offset from all the GEP indices to the base.
return getAddExpr(BaseExpr, TotalOffset, Wrap);
}
std::tuple<const SCEV *, FoldingSetNodeID, void *>
ScalarEvolution::findExistingSCEVInCache(int SCEVType,
ArrayRef<const SCEV *> Ops) {
FoldingSetNodeID ID;
void *IP = nullptr;
ID.AddInteger(SCEVType);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
ID.AddPointer(Ops[i]);
return std::tuple<const SCEV *, FoldingSetNodeID, void *>(
UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP);
}
const SCEV *ScalarEvolution::getMinMaxExpr(unsigned Kind,
SmallVectorImpl<const SCEV *> &Ops) {
assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!");
if (Ops.size() == 1) return Ops[0];
#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
"Operand types don't match!");
#endif
bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI, DT);
// Check if we have created the same expression before.
if (const SCEV *S = std::get<0>(findExistingSCEVInCache(Kind, Ops))) {
return S;
}
// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
++Idx;
assert(Idx < Ops.size());
auto FoldOp = [&](const APInt &LHS, const APInt &RHS) {
if (Kind == scSMaxExpr)
return APIntOps::smax(LHS, RHS);
else if (Kind == scSMinExpr)
return APIntOps::smin(LHS, RHS);
else if (Kind == scUMaxExpr)
return APIntOps::umax(LHS, RHS);
else if (Kind == scUMinExpr)
return APIntOps::umin(LHS, RHS);
llvm_unreachable("Unknown SCEV min/max opcode");
};
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
ConstantInt *Fold = ConstantInt::get(
getContext(), FoldOp(LHSC->getAPInt(), RHSC->getAPInt()));
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
bool IsMinV = LHSC->getValue()->isMinValue(IsSigned);
bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned);
if (IsMax ? IsMinV : IsMaxV) {
// If we are left with a constant minimum(/maximum)-int, strip it off.
Ops.erase(Ops.begin());
--Idx;
} else if (IsMax ? IsMaxV : IsMinV) {
// If we have a max(/min) with a constant maximum(/minimum)-int,
// it will always be the extremum.
return LHSC;
}
if (Ops.size() == 1) return Ops[0];
}
// Find the first operation of the same kind
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
++Idx;
// Check to see if one of the operands is of the same kind. If so, expand its
// operands onto our operand list, and recurse to simplify.
if (Idx < Ops.size()) {
bool DeletedAny = false;
while (Ops[Idx]->getSCEVType() == Kind) {
const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]);
Ops.erase(Ops.begin()+Idx);
Ops.append(SMME->op_begin(), SMME->op_end());
DeletedAny = true;
}
if (DeletedAny)
return getMinMaxExpr(Kind, Ops);
}
// Okay, check to see if the same value occurs in the operand list twice. If
// so, delete one. Since we sorted the list, these values are required to
// be adjacent.
llvm::CmpInst::Predicate GEPred =
IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
llvm::CmpInst::Predicate LEPred =
IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
if (Ops[i] == Ops[i + 1] ||
isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) {
// X op Y op Y --> X op Y
// X op Y --> X, if we know X, Y are ordered appropriately
Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
--i;
--e;
} else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i],
Ops[i + 1])) {
// X op Y --> Y, if we know X, Y are ordered appropriately
Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
--i;
--e;
}
}
if (Ops.size() == 1) return Ops[0];
assert(!Ops.empty() && "Reduced smax down to nothing!");
// Okay, it looks like we really DO need an expr. Check to see if we
// already have one, otherwise create a new one.
const SCEV *ExistingSCEV;
FoldingSetNodeID ID;
void *IP;
std::tie(ExistingSCEV, ID, IP) = findExistingSCEVInCache(Kind, Ops);
if (ExistingSCEV)
return ExistingSCEV;
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
SCEV *S = new (SCEVAllocator) SCEVMinMaxExpr(
ID.Intern(SCEVAllocator), static_cast<SCEVTypes>(Kind), O, Ops.size());
UniqueSCEVs.InsertNode(S, IP);
addToLoopUseLists(S);
return S;
}
const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
return getSMaxExpr(Ops);
}
const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scSMaxExpr, Ops);
}
const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
return getUMaxExpr(Ops);
}
const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scUMaxExpr, Ops);
}
const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getSMinExpr(Ops);
}
const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scSMinExpr, Ops);
}
const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getUMinExpr(Ops);
}
const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scUMinExpr, Ops);
}
const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
// We can bypass creating a target-independent
// constant expression and then folding it back into a ConstantInt.
// This is just a compile-time optimization.
return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
}
const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
StructType *STy,
unsigned FieldNo) {
// We can bypass creating a target-independent
// constant expression and then folding it back into a ConstantInt.
// This is just a compile-time optimization.
return getConstant(
IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
}
const SCEV *ScalarEvolution::getUnknown(Value *V) {
// Don't attempt to do anything other than create a SCEVUnknown object
// here. createSCEV only calls getUnknown after checking for all other
// interesting possibilities, and any other code that calls getUnknown
// is doing so in order to hide a value from SCEV canonicalization.
FoldingSetNodeID ID;
ID.AddInteger(scUnknown);
ID.AddPointer(V);
void *IP = nullptr;
if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
assert(cast<SCEVUnknown>(S)->getValue() == V &&
"Stale SCEVUnknown in uniquing map!");
return S;
}
SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
FirstUnknown);
FirstUnknown = cast<SCEVUnknown>(S);
UniqueSCEVs.InsertNode(S, IP);
return S;
}
//===----------------------------------------------------------------------===//
// Basic SCEV Analysis and PHI Idiom Recognition Code
//
/// Test if values of the given type are analyzable within the SCEV
/// framework. This primarily includes integer types, and it can optionally
/// include pointer types if the ScalarEvolution class has access to
/// target-specific information.
bool ScalarEvolution::isSCEVable(Type *Ty) const {
// Integers and pointers are always SCEVable.
return Ty->isIntOrPtrTy();
}
/// Return the size in bits of the specified type, for which isSCEVable must
/// return true.
uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!");
if (Ty->isPointerTy())
return getDataLayout().getIndexTypeSizeInBits(Ty);
return getDataLayout().getTypeSizeInBits(Ty);
}
/// Return a type with the same bitwidth as the given type and which represents
/// how SCEV will treat the given type, for which isSCEVable must return
/// true. For pointer types, this is the pointer index sized integer type.
Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!");
if (Ty->isIntegerTy())
return Ty;
// The only other support type is pointer.
assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
return getDataLayout().getIndexType(Ty);
}
Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
}
const SCEV *ScalarEvolution::getCouldNotCompute() {
return CouldNotCompute.get();
}
bool ScalarEvolution::checkValidity(const SCEV *S) const {
bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
auto *SU = dyn_cast<SCEVUnknown>(S);
return SU && SU->getValue() == nullptr;
});
return !ContainsNulls;
}
bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
HasRecMapType::iterator I = HasRecMap.find(S);
if (I != HasRecMap.end())
return I->second;
bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
HasRecMap.insert({S, FoundAddRec});
return FoundAddRec;
}
/// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
/// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
/// offset I, then return {S', I}, else return {\p S, nullptr}.
static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
const auto *Add = dyn_cast<SCEVAddExpr>(S);
if (!Add)
return {S, nullptr};
if (Add->getNumOperands() != 2)
return {S, nullptr};
auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
if (!ConstOp)
return {S, nullptr};
return {Add->getOperand(1), ConstOp->getValue()};
}
/// Return the ValueOffsetPair set for \p S. \p S can be represented
/// by the value and offset from any ValueOffsetPair in the set.
SetVector<ScalarEvolution::ValueOffsetPair> *
ScalarEvolution::getSCEVValues(const SCEV *S) {
ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
if (SI == ExprValueMap.end())
return nullptr;
#ifndef NDEBUG
if (VerifySCEVMap) {
// Check there is no dangling Value in the set returned.
for (const auto &VE : SI->second)
assert(ValueExprMap.count(VE.first));
}
#endif
return &SI->second;
}
/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
/// cannot be used separately. eraseValueFromMap should be used to remove
/// V from ValueExprMap and ExprValueMap at the same time.
void ScalarEvolution::eraseValueFromMap(Value *V) {
ValueExprMapType::iterator I = ValueExprMap.find_as(V);
if (I != ValueExprMap.end()) {
const SCEV *S = I->second;
// Remove {V, 0} from the set of ExprValueMap[S]
if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
SV->remove({V, nullptr});
// Remove {V, Offset} from the set of ExprValueMap[Stripped]
const SCEV *Stripped;
ConstantInt *Offset;
std::tie(Stripped, Offset) = splitAddExpr(S);
if (Offset != nullptr) {
if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
SV->remove({V, Offset});
}
ValueExprMap.erase(V);
}
}
/// Check whether value has nuw/nsw/exact set but SCEV does not.
/// TODO: In reality it is better to check the poison recursively
/// but this is better than nothing.
static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) {
if (auto *I = dyn_cast<Instruction>(V)) {
if (isa<OverflowingBinaryOperator>(I)) {
if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) {
if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap())
return true;
if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap())
return true;
}
} else if (isa<PossiblyExactOperator>(I) && I->isExact())
return true;
}
return false;
}
/// Return an existing SCEV if it exists, otherwise analyze the expression and
/// create a new one.
const SCEV *ScalarEvolution::getSCEV(Value *V) {
assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
const SCEV *S = getExistingSCEV(V);
if (S == nullptr) {
S = createSCEV(V);
// During PHI resolution, it is possible to create two SCEVs for the same
// V, so it is needed to double check whether V->S is inserted into
// ValueExprMap before insert S->{V, 0} into ExprValueMap.
std::pair<ValueExprMapType::iterator, bool> Pair =
ValueExprMap.insert({SCEVCallbackVH(V, this), S});
if (Pair.second && !SCEVLostPoisonFlags(S, V)) {
ExprValueMap[S].insert({V, nullptr});
// If S == Stripped + Offset, add Stripped -> {V, Offset} into
// ExprValueMap.
const SCEV *Stripped = S;
ConstantInt *Offset = nullptr;
std::tie(Stripped, Offset) = splitAddExpr(S);
// If stripped is SCEVUnknown, don't bother to save
// Stripped -> {V, offset}. It doesn't simplify and sometimes even
// increase the complexity of the expansion code.
// If V is GetElementPtrInst, don't save Stripped -> {V, offset}
// because it may generate add/sub instead of GEP in SCEV expansion.
if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
!isa<GetElementPtrInst>(V))
ExprValueMap[Stripped].insert({V, Offset});
}
}
return S;
}
const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
ValueExprMapType::iterator I = ValueExprMap.find_as(V);
if (I != ValueExprMap.end()) {
const SCEV *S = I->second;
if (checkValidity(S))
return S;
eraseValueFromMap(V);
forgetMemoizedResults(S);
}
return nullptr;
}
/// Return a SCEV corresponding to -V = -1*V
const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
SCEV::NoWrapFlags Flags) {
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
return getConstant(
cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
Type *Ty = V->getType();
Ty = getEffectiveSCEVType(Ty);
return getMulExpr(
V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
}
/// If Expr computes ~A, return A else return nullptr
static const SCEV *MatchNotExpr(const SCEV *Expr) {
const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
if (!Add || Add->getNumOperands() != 2 ||
!Add->getOperand(0)->isAllOnesValue())
return nullptr;
const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
if (!AddRHS || AddRHS->getNumOperands() != 2 ||
!AddRHS->getOperand(0)->isAllOnesValue())
return nullptr;
return AddRHS->getOperand(1);
}
/// Return a SCEV corresponding to ~V = -1-V
const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
return getConstant(
cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
// Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) {
auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
SmallVector<const SCEV *, 2> MatchedOperands;
for (const SCEV *Operand : MME->operands()) {
const SCEV *Matched = MatchNotExpr(Operand);
if (!Matched)
return (const SCEV *)nullptr;
MatchedOperands.push_back(Matched);
}
return getMinMaxExpr(
SCEVMinMaxExpr::negate(static_cast<SCEVTypes>(MME->getSCEVType())),
MatchedOperands);
};
if (const SCEV *Replaced = MatchMinMaxNegation(MME))
return Replaced;
}
Type *Ty = V->getType();
Ty = getEffectiveSCEVType(Ty);
const SCEV *AllOnes =
getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
return getMinusSCEV(AllOnes, V);
}
const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
SCEV::NoWrapFlags Flags,
unsigned Depth) {
// Fast path: X - X --> 0.
if (LHS == RHS)
return getZero(LHS->getType());
// We represent LHS - RHS as LHS + (-1)*RHS. This transformation
// makes it so that we cannot make much use of NUW.
auto AddFlags = SCEV::FlagAnyWrap;
const bool RHSIsNotMinSigned =
!getSignedRangeMin(RHS).isMinSignedValue();
if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
// Let M be the minimum representable signed value. Then (-1)*RHS
// signed-wraps if and only if RHS is M. That can happen even for
// a NSW subtraction because e.g. (-1)*M signed-wraps even though
// -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
// (-1)*RHS, we need to prove that RHS != M.
//
// If LHS is non-negative and we know that LHS - RHS does not
// signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
// either by proving that RHS > M or that LHS >= 0.
if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
AddFlags = SCEV::FlagNSW;
}
}
// FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
// RHS is NSW and LHS >= 0.
//
// The difficulty here is that the NSW flag may have been proven
// relative to a loop that is to be found in a recurrence in LHS and
// not in RHS. Applying NSW to (-1)*M may then let the NSW have a
// larger scope than intended.
auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
}
const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
unsigned Depth) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or zero extend with non-integer arguments!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
return getTruncateExpr(V, Ty, Depth);
return getZeroExtendExpr(V, Ty, Depth);
}
const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
unsigned Depth) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or zero extend with non-integer arguments!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
return getTruncateExpr(V, Ty, Depth);
return getSignExtendExpr(V, Ty, Depth);
}
const SCEV *
ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or zero extend with non-integer arguments!");
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrZeroExtend cannot truncate!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
return getZeroExtendExpr(V, Ty);
}
const SCEV *
ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or sign extend with non-integer arguments!");
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrSignExtend cannot truncate!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
return getSignExtendExpr(V, Ty);
}
const SCEV *
ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot noop or any extend with non-integer arguments!");
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
"getNoopOrAnyExtend cannot truncate!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
return getAnyExtendExpr(V, Ty);
}
const SCEV *
ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
"Cannot truncate or noop with non-integer arguments!");
assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
"getTruncateOrNoop cannot extend!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
return getTruncateExpr(V, Ty);
}
const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
const SCEV *RHS) {
const SCEV *PromotedLHS = LHS;
const SCEV *PromotedRHS = RHS;
if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
else
PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
return getUMaxExpr(PromotedLHS, PromotedRHS);
}
const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getUMinFromMismatchedTypes(Ops);
}
const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(
SmallVectorImpl<const SCEV *> &Ops) {
assert(!Ops.empty() && "At least one operand must be!");
// Trivial case.
if (Ops.size() == 1)
return Ops[0];
// Find the max type first.
Type *MaxType = nullptr;
for (auto *S : Ops)
if (MaxType)
MaxType = getWiderType(MaxType, S->getType());
else
MaxType = S->getType();
// Extend all ops to max type.
SmallVector<const SCEV *, 2> PromotedOps;
for (auto *S : Ops)
PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
// Generate umin.
return getUMinExpr(PromotedOps);
}
const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
// A pointer operand may evaluate to a nonpointer expression, such as null.
if (!V->getType()->isPointerTy())
return V;
if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
return getPointerBase(Cast->getOperand());
} else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
const SCEV *PtrOp = nullptr;
for (const SCEV *NAryOp : NAry->operands()) {
if (NAryOp->getType()->isPointerTy()) {
// Cannot find the base of an expression with multiple pointer operands.
if (PtrOp)
return V;
PtrOp = NAryOp;
}
}
if (!PtrOp)
return V;
return getPointerBase(PtrOp);
}
return V;
}
/// Push users of the given Instruction onto the given Worklist.
static void
PushDefUseChildren(Instruction *I,
SmallVectorImpl<Instruction *> &Worklist) {
// Push the def-use children onto the Worklist stack.
for (User *U : I->users())
Worklist.push_back(cast<Instruction>(U));
}
void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
SmallVector<Instruction *, 16> Worklist;
PushDefUseChildren(PN, Worklist);
SmallPtrSet<Instruction *, 8> Visited;
Visited.insert(PN);
while (!Worklist.empty()) {
Instruction *I = Worklist.pop_back_val();
if (!Visited.insert(I).second)
continue;
auto It = ValueExprMap.find_as(static_cast<Value *>(I));
if (It != ValueExprMap.end()) {
const SCEV *Old = It->second;
// Short-circuit the def-use traversal if the symbolic name
// ceases to appear in expressions.
if (Old != SymName && !hasOperand(Old, SymName))
continue;
// SCEVUnknown for a PHI either means that it has an unrecognized
// structure, it's a PHI that's in the progress of being computed
// by createNodeForPHI, or it's a single-value PHI. In the first case,
// additional loop trip count information isn't going to change anything.
// In the second case, createNodeForPHI will perform the necessary
// updates on its own when it gets to that point. In the third, we do
// want to forget the SCEVUnknown.
if (!isa<PHINode>(I) ||
!isa<SCEVUnknown>(Old) ||
(I != PN && Old == SymName)) {
eraseValueFromMap(It->first);
forgetMemoizedResults(Old);
}
}
PushDefUseChildren(I, Worklist);
}
}
namespace {
/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
/// expression in case its Loop is L. If it is not L then
/// if IgnoreOtherLoops is true then use AddRec itself
/// otherwise rewrite cannot be done.
/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
public:
static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
bool IgnoreOtherLoops = true) {
SCEVInitRewriter Rewriter(L, SE);
const SCEV *Result = Rewriter.visit(S);
if (Rewriter.hasSeenLoopVariantSCEVUnknown())
return SE.getCouldNotCompute();
return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
? SE.getCouldNotCompute()
: Result;
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
if (!SE.isLoopInvariant(Expr, L))
SeenLoopVariantSCEVUnknown = true;
return Expr;
}
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
// Only re-write AddRecExprs for this loop.
if (Expr->getLoop() == L)
return Expr->getStart();
SeenOtherLoops = true;
return Expr;
}
bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
bool hasSeenOtherLoops() { return SeenOtherLoops; }
private:
explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L) {}
const Loop *L;
bool SeenLoopVariantSCEVUnknown = false;
bool SeenOtherLoops = false;
};
/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
/// increment expression in case its Loop is L. If it is not L then
/// use AddRec itself.
/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
public:
static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
SCEVPostIncRewriter Rewriter(L, SE);
const SCEV *Result = Rewriter.visit(S);
return Rewriter.hasSeenLoopVariantSCEVUnknown()
? SE.getCouldNotCompute()
: Result;
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
if (!SE.isLoopInvariant(Expr, L))
SeenLoopVariantSCEVUnknown = true;
return Expr;
}
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
// Only re-write AddRecExprs for this loop.
if (Expr->getLoop() == L)
return Expr->getPostIncExpr(SE);
SeenOtherLoops = true;
return Expr;
}
bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
bool hasSeenOtherLoops() { return SeenOtherLoops; }
private:
explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L) {}
const Loop *L;
bool SeenLoopVariantSCEVUnknown = false;
bool SeenOtherLoops = false;
};
/// This class evaluates the compare condition by matching it against the
/// condition of loop latch. If there is a match we assume a true value
/// for the condition while building SCEV nodes.
class SCEVBackedgeConditionFolder
: public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
public:
static const SCEV *rewrite(const SCEV *S, const Loop *L,
ScalarEvolution &SE) {
bool IsPosBECond = false;
Value *BECond = nullptr;
if (BasicBlock *Latch = L->getLoopLatch()) {
BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
if (BI && BI->isConditional()) {
assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&
"Both outgoing branches should not target same header!");
BECond = BI->getCondition();
IsPosBECond = BI->getSuccessor(0) == L->getHeader();
} else {
return S;
}
}
SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
return Rewriter.visit(S);
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
const SCEV *Result = Expr;
bool InvariantF = SE.isLoopInvariant(Expr, L);
if (!InvariantF) {
Instruction *I = cast<Instruction>(Expr->getValue());
switch (I->getOpcode()) {
case Instruction::Select: {
SelectInst *SI = cast<SelectInst>(I);
Optional<const SCEV *> Res =
compareWithBackedgeCondition(SI->getCondition());
if (Res.hasValue()) {
bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
}
break;
}
default: {
Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
if (Res.hasValue())
Result = Res.getValue();
break;
}
}
}
return Result;
}
private:
explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
bool IsPosBECond, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
IsPositiveBECond(IsPosBECond) {}
Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
const Loop *L;
/// Loop back condition.
Value *BackedgeCond = nullptr;
/// Set to true if loop back is on positive branch condition.
bool IsPositiveBECond;
};
Optional<const SCEV *>
SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
// If value matches the backedge condition for loop latch,
// then return a constant evolution node based on loopback
// branch taken.
if (BackedgeCond == IC)
return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
: SE.getZero(Type::getInt1Ty(SE.getContext()));
return None;
}
class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
public:
static const SCEV *rewrite(const SCEV *S, const Loop *L,
ScalarEvolution &SE) {
SCEVShiftRewriter Rewriter(L, SE);
const SCEV *Result = Rewriter.visit(S);
return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
// Only allow AddRecExprs for this loop.
if (!SE.isLoopInvariant(Expr, L))
Valid = false;
return Expr;
}
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
if (Expr->getLoop() == L && Expr->isAffine())
return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
Valid = false;
return Expr;
}
bool isValid() { return Valid; }
private:
explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
: SCEVRewriteVisitor(SE), L(L) {}
const Loop *L;
bool Valid = true;
};
} // end anonymous namespace
SCEV::NoWrapFlags
ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
if (!AR->isAffine())
return SCEV::FlagAnyWrap;
using OBO = OverflowingBinaryOperator;
SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
if (!AR->hasNoSignedWrap()) {
ConstantRange AddRecRange = getSignedRange(AR);
ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
Instruction::Add, IncRange, OBO::NoSignedWrap);
if (NSWRegion.contains(AddRecRange))
Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
}
if (!AR->hasNoUnsignedWrap()) {
ConstantRange AddRecRange = getUnsignedRange(AR);
ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
Instruction::Add, IncRange, OBO::NoUnsignedWrap);
if (NUWRegion.contains(AddRecRange))
Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
}
return Result;
}
namespace {
/// Represents an abstract binary operation. This may exist as a
/// normal instruction or constant expression, or may have been
/// derived from an expression tree.
struct BinaryOp {
unsigned Opcode;
Value *LHS;
Value *RHS;
bool IsNSW = false;
bool IsNUW = false;
/// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
/// constant expression.
Operator *Op = nullptr;
explicit BinaryOp(Operator *Op)
: Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
Op(Op) {
if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
IsNSW = OBO->hasNoSignedWrap();
IsNUW = OBO->hasNoUnsignedWrap();
}
}
explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
bool IsNUW = false)
: Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
};
} // end anonymous namespace
/// Try to map \p V into a BinaryOp, and return \c None on failure.
static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
auto *Op = dyn_cast<Operator>(V);
if (!Op)
return None;
// Implementation detail: all the cleverness here should happen without
// creating new SCEV expressions -- our caller knowns tricks to avoid creating
// SCEV expressions when possible, and we should not break that.
switch (Op->getOpcode()) {
case Instruction::Add:
case Instruction::Sub:
case Instruction::Mul:
case Instruction::UDiv:
case Instruction::URem:
case Instruction::And:
case Instruction::Or:
case Instruction::AShr:
case Instruction::Shl:
return BinaryOp(Op);
case Instruction::Xor:
if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
// If the RHS of the xor is a signmask, then this is just an add.
// Instcombine turns add of signmask into xor as a strength reduction step.
if (RHSC->getValue().isSignMask())
return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
return BinaryOp(Op);
case Instruction::LShr:
// Turn logical shift right of a constant into a unsigned divide.
if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
// If the shift count is not less than the bitwidth, the result of
// the shift is undefined. Don't try to analyze it, because the
// resolution chosen here may differ from the resolution chosen in
// other parts of the compiler.
if (SA->getValue().ult(BitWidth)) {
Constant *X =
ConstantInt::get(SA->getContext(),
APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
}
}
return BinaryOp(Op);
case Instruction::ExtractValue: {
auto *EVI = cast<ExtractValueInst>(Op);
if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
break;
auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand());
if (!WO)
break;
Instruction::BinaryOps BinOp = WO->getBinaryOp();
bool Signed = WO->isSigned();
// TODO: Should add nuw/nsw flags for mul as well.
if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());
// Now that we know that all uses of the arithmetic-result component of
// CI are guarded by the overflow check, we can go ahead and pretend
// that the arithmetic is non-overflowing.
return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
/* IsNSW = */ Signed, /* IsNUW = */ !Signed);
}
default:
break;
}
// Recognise intrinsic loop.decrement.reg, and as this has exactly the same
// semantics as a Sub, return a binary sub expression.
if (auto *II = dyn_cast<IntrinsicInst>(V))
if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg)
return BinaryOp(Instruction::Sub, II->getOperand(0), II->getOperand(1));
return None;
}
/// Helper function to createAddRecFromPHIWithCasts. We have a phi
/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
/// follows one of the following patterns:
/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
/// If the SCEV expression of \p Op conforms with one of the expected patterns
/// we return the type of the truncation operation, and indicate whether the
/// truncated type should be treated as signed/unsigned by setting
/// \p Signed to true/false, respectively.
static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
bool &Signed, ScalarEvolution &SE) {
// The case where Op == SymbolicPHI (that is, with no type conversions on
// the way) is handled by the regular add recurrence creating logic and
// would have already been triggered in createAddRecForPHI. Reaching it here
// means that createAddRecFromPHI had failed for this PHI before (e.g.,
// because one of the other operands of the SCEVAddExpr updating this PHI is
// not invariant).
//
// Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
// this case predicates that allow us to prove that Op == SymbolicPHI will
// be added.
if (Op == SymbolicPHI)
return nullptr;
unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
if (SourceBits != NewBits)
return nullptr;
const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
if (!SExt && !ZExt)
return nullptr;
const SCEVTruncateExpr *Trunc =
SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
: dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
if (!Trunc)
return nullptr;
const SCEV *X = Trunc->getOperand();
if (X != SymbolicPHI)
return nullptr;
Signed = SExt != nullptr;
return Trunc->getType();
}
static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
if (!PN->getType()->isIntegerTy())
return nullptr;
const Loop *L = LI.getLoopFor(PN->getParent());
if (!L || L->getHeader() != PN->getParent())
return nullptr;
return L;
}
// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
// computation that updates the phi follows the following pattern:
// (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
// which correspond to a phi->trunc->sext/zext->add->phi update chain.
// If so, try to see if it can be rewritten as an AddRecExpr under some
// Predicates. If successful, return them as a pair. Also cache the results
// of the analysis.
//
// Example usage scenario:
// Say the Rewriter is called for the following SCEV:
// 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
// where:
// %X = phi i64 (%Start, %BEValue)
// It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
// and call this function with %SymbolicPHI = %X.
//
// The analysis will find that the value coming around the backedge has
// the following SCEV:
// BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
// Upon concluding that this matches the desired pattern, the function
// will return the pair {NewAddRec, SmallPredsVec} where:
// NewAddRec = {%Start,+,%Step}
// SmallPredsVec = {P1, P2, P3} as follows:
// P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
// P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
// P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
// The returned pair means that SymbolicPHI can be rewritten into NewAddRec
// under the predicates {P1,P2,P3}.
// This predicated rewrite will be cached in PredicatedSCEVRewrites:
// PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
//
// TODO's:
//
// 1) Extend the Induction descriptor to also support inductions that involve
// casts: When needed (namely, when we are called in the context of the
// vectorizer induction analysis), a Set of cast instructions will be
// populated by this method, and provided back to isInductionPHI. This is
// needed to allow the vectorizer to properly record them to be ignored by
// the cost model and to avoid vectorizing them (otherwise these casts,
// which are redundant under the runtime overflow checks, will be
// vectorized, which can be costly).
//
// 2) Support additional induction/PHISCEV patterns: We also want to support
// inductions where the sext-trunc / zext-trunc operations (partly) occur
// after the induction update operation (the induction increment):
//
// (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
// which correspond to a phi->add->trunc->sext/zext->phi update chain.
//
// (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
// which correspond to a phi->trunc->add->sext/zext->phi update chain.
//
// 3) Outline common code with createAddRecFromPHI to avoid duplication.
Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
SmallVector<const SCEVPredicate *, 3> Predicates;
// *** Part1: Analyze if we have a phi-with-cast pattern for which we can
// return an AddRec expression under some predicate.
auto *PN = cast<PHINode>(SymbolicPHI->getValue());
const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
assert(L && "Expecting an integer loop header phi");
// The loop may have multiple entrances or multiple exits; we can analyze
// this phi as an addrec if it has a unique entry value and a unique
// backedge value.
Value *BEValueV = nullptr, *StartValueV = nullptr;
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
Value *V = PN->getIncomingValue(i);
if (L->contains(PN->getIncomingBlock(i))) {
if (!BEValueV) {
BEValueV = V;
} else if (BEValueV != V) {
BEValueV = nullptr;
break;
}
} else if (!StartValueV) {
StartValueV = V;
} else if (StartValueV != V) {
StartValueV = nullptr;
break;
}
}
if (!BEValueV || !StartValueV)
return None;
const SCEV *BEValue = getSCEV(BEValueV);
// If the value coming around the backedge is an add with the symbolic
// value we just inserted, possibly with casts that we can ignore under
// an appropriate runtime guard, then we found a simple induction variable!
const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
if (!Add)
return None;
// If there is a single occurrence of the symbolic value, possibly
// casted, replace it with a recurrence.
unsigned FoundIndex = Add->getNumOperands();
Type *TruncTy = nullptr;
bool Signed;
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if ((TruncTy =
isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
if (FoundIndex == e) {
FoundIndex = i;
break;
}
if (FoundIndex == Add->getNumOperands())
return None;
// Create an add with everything but the specified operand.
SmallVector<const SCEV *, 8> Ops;
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (i != FoundIndex)
Ops.push_back(Add->getOperand(i));
const SCEV *Accum = getAddExpr(Ops);
// The runtime checks will not be valid if the step amount is
// varying inside the loop.
if (!isLoopInvariant(Accum, L))
return None;
// *** Part2: Create the predicates
// Analysis was successful: we have a phi-with-cast pattern for which we
// can return an AddRec expression under the following predicates:
//
// P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
// fits within the truncated type (does not overflow) for i = 0 to n-1.
// P2: An Equal predicate that guarantees that
// Start = (Ext ix (Trunc iy (Start) to ix) to iy)
// P3: An Equal predicate that guarantees that
// Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
//
// As we next prove, the above predicates guarantee that:
// Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
//
//
// More formally, we want to prove that:
// Expr(i+1) = Start + (i+1) * Accum
// = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
//
// Given that:
// 1) Expr(0) = Start
// 2) Expr(1) = Start + Accum
// = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
// 3) Induction hypothesis (step i):
// Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
//
// Proof:
// Expr(i+1) =
// = Start + (i+1)*Accum
// = (Start + i*Accum) + Accum
// = Expr(i) + Accum
// = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
// :: from step i
//
// = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
//
// = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
// + (Ext ix (Trunc iy (Accum) to ix) to iy)
// + Accum :: from P3
//
// = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
// + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
//
// = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
// = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
//
// By induction, the same applies to all iterations 1<=i<n:
//
// Create a truncated addrec for which we will add a no overflow check (P1).
const SCEV *StartVal = getSCEV(StartValueV);
const SCEV *PHISCEV =
getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
// PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
// ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
// will be constant.
//
// If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
// add P1.
if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
Signed ? SCEVWrapPredicate::IncrementNSSW
: SCEVWrapPredicate::IncrementNUSW;
const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
Predicates.push_back(AddRecPred);
}
// Create the Equal Predicates P2,P3:
// It is possible that the predicates P2 and/or P3 are computable at
// compile time due to StartVal and/or Accum being constants.
// If either one is, then we can check that now and escape if either P2
// or P3 is false.
// Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
// for each of StartVal and Accum
auto getExtendedExpr = [&](const SCEV *Expr,
bool CreateSignExtend) -> const SCEV * {
assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
const SCEV *ExtendedExpr =
CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
: getZeroExtendExpr(TruncatedExpr, Expr->getType());
return ExtendedExpr;
};
// Given:
// ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
// = getExtendedExpr(Expr)
// Determine whether the predicate P: Expr == ExtendedExpr
// is known to be false at compile time
auto PredIsKnownFalse = [&](const SCEV *Expr,
const SCEV *ExtendedExpr) -> bool {
return Expr != ExtendedExpr &&
isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
};
const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
if (PredIsKnownFalse(StartVal, StartExtended)) {
LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";);
return None;
}
// The Step is always Signed (because the overflow checks are either
// NSSW or NUSW)
const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
if (PredIsKnownFalse(Accum, AccumExtended)) {
LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";);
return None;
}
auto AppendPredicate = [&](const SCEV *Expr,
const SCEV *ExtendedExpr) -> void {
if (Expr != ExtendedExpr &&
!isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred);
Predicates.push_back(Pred);
}
};
AppendPredicate(StartVal, StartExtended);
AppendPredicate(Accum, AccumExtended);
// *** Part3: Predicates are ready. Now go ahead and create the new addrec in
// which the casts had been folded away. The caller can rewrite SymbolicPHI
// into NewAR if it will also add the runtime overflow checks specified in
// Predicates.
auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
std::make_pair(NewAR, Predicates);
// Remember the result of the analysis for this SCEV at this locayyytion.
PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
return PredRewrite;
}
Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
auto *PN = cast<PHINode>(SymbolicPHI->getValue());
const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
if (!L)
return None;
// Check to see if we already analyzed this PHI.
auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
if (I != PredicatedSCEVRewrites.end()) {
std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
I->second;
// Analysis was done before and failed to create an AddRec:
if (Rewrite.first == SymbolicPHI)
return None;
// Analysis was done before and succeeded to create an AddRec under
// a predicate:
assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
assert(!(Rewrite.second).empty() && "Expected to find Predicates");
return Rewrite;
}
Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
// Record in the cache that the analysis failed
if (!Rewrite) {
SmallVector<const SCEVPredicate *, 3> Predicates;
PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
return None;
}
return Rewrite;
}
// FIXME: This utility is currently required because the Rewriter currently
// does not rewrite this expression:
// {0, +, (sext ix (trunc iy to ix) to iy)}
// into {0, +, %step},
// even when the following Equal predicate exists:
// "%step == (sext ix (trunc iy to ix) to iy)".
bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
if (AR1 == AR2)
return true;
auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
!Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
return false;
return true;
};
if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
!areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
return false;
return true;
}
/// A helper function for createAddRecFromPHI to handle simple cases.
///
/// This function tries to find an AddRec expression for the simplest (yet most
/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
/// If it fails, createAddRecFromPHI will use a more general, but slow,
/// technique for finding the AddRec expression.
const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
Value *BEValueV,
Value *StartValueV) {
const Loop *L = LI.getLoopFor(PN->getParent());
assert(L && L->getHeader() == PN->getParent());
assert(BEValueV && StartValueV);
auto BO = MatchBinaryOp(BEValueV, DT);
if (!BO)
return nullptr;
if (BO->Opcode != Instruction::Add)
return nullptr;
const SCEV *Accum = nullptr;
if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
Accum = getSCEV(BO->RHS);
else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
Accum = getSCEV(BO->LHS);
if (!Accum)
return nullptr;
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (BO->IsNUW)
Flags = setFlags(Flags, SCEV::FlagNUW);
if (BO->IsNSW)
Flags = setFlags(Flags, SCEV::FlagNSW);
const SCEV *StartVal = getSCEV(StartValueV);
const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
// We can add Flags to the post-inc expression only if we
// know that it is *undefined behavior* for BEValueV to
// overflow.
if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
(void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
return PHISCEV;
}
const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
const Loop *L = LI.getLoopFor(PN->getParent());
if (!L || L->getHeader() != PN->getParent())
return nullptr;
// The loop may have multiple entrances or multiple exits; we can analyze
// this phi as an addrec if it has a unique entry value and a unique
// backedge value.
Value *BEValueV = nullptr, *StartValueV = nullptr;
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
Value *V = PN->getIncomingValue(i);
if (L->contains(PN->getIncomingBlock(i))) {
if (!BEValueV) {
BEValueV = V;
} else if (BEValueV != V) {
BEValueV = nullptr;
break;
}
} else if (!StartValueV) {
StartValueV = V;
} else if (StartValueV != V) {
StartValueV = nullptr;
break;
}
}
if (!BEValueV || !StartValueV)
return nullptr;
assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
"PHI node already processed?");
// First, try to find AddRec expression without creating a fictituos symbolic
// value for PN.
if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
return S;
// Handle PHI node value symbolically.
const SCEV *SymbolicName = getUnknown(PN);
ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
// Using this symbolic name for the PHI, analyze the value coming around
// the back-edge.
const SCEV *BEValue = getSCEV(BEValueV);
// NOTE: If BEValue is loop invariant, we know that the PHI node just
// has a special value for the first iteration of the loop.
// If the value coming around the backedge is an add with the symbolic
// value we just inserted, then we found a simple induction variable!
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
// If there is a single occurrence of the symbolic value, replace it
// with a recurrence.
unsigned FoundIndex = Add->getNumOperands();
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (Add->getOperand(i) == SymbolicName)
if (FoundIndex == e) {
FoundIndex = i;
break;
}
if (FoundIndex != Add->getNumOperands()) {
// Create an add with everything but the specified operand.
SmallVector<const SCEV *, 8> Ops;
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (i != FoundIndex)
Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
L, *this));
const SCEV *Accum = getAddExpr(Ops);
// This is not a valid addrec if the step amount is varying each
// loop iteration, but is not itself an addrec in this loop.
if (isLoopInvariant(Accum, L) ||
(isa<SCEVAddRecExpr>(Accum) &&
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (auto BO = MatchBinaryOp(BEValueV, DT)) {
if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
if (BO->IsNUW)
Flags = setFlags(Flags, SCEV::FlagNUW);
if (BO->IsNSW)
Flags = setFlags(Flags, SCEV::FlagNSW);
}
} else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
// If the increment is an inbounds GEP, then we know the address
// space cannot be wrapped around. We cannot make any guarantee
// about signed or unsigned overflow because pointers are
// unsigned but we may have a negative index from the base
// pointer. We can guarantee that no unsigned wrap occurs if the
// indices form a positive value.
if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
Flags = setFlags(Flags, SCEV::FlagNW);
const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
Flags = setFlags(Flags, SCEV::FlagNUW);
}
// We cannot transfer nuw and nsw flags from subtraction
// operations -- sub nuw X, Y is not the same as add nuw X, -Y
// for instance.
}
const SCEV *StartVal = getSCEV(StartValueV);
const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
// Okay, for the entire analysis of this edge we assumed the PHI
// to be symbolic. We now need to go back and purge all of the
// entries for the scalars that use the symbolic expression.
forgetSymbolicName(PN, SymbolicName);
ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
// We can add Flags to the post-inc expression only if we
// know that it is *undefined behavior* for BEValueV to
// overflow.
if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
(void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
return PHISCEV;
}
}
} else {
// Otherwise, this could be a loop like this:
// i = 0; for (j = 1; ..; ++j) { .... i = j; }
// In this case, j = {1,+,1} and BEValue is j.
// Because the other in-value of i (0) fits the evolution of BEValue
// i really is an addrec evolution.
//
// We can generalize this saying that i is the shifted value of BEValue
// by one iteration:
// PHI(f(0), f({1,+,1})) --> f({0,+,1})
const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
if (Shifted != getCouldNotCompute() &&
Start != getCouldNotCompute()) {
const SCEV *StartVal = getSCEV(StartValueV);
if (Start == StartVal) {
// Okay, for the entire analysis of this edge we assumed the PHI
// to be symbolic. We now need to go back and purge all of the
// entries for the scalars that use the symbolic expression.
forgetSymbolicName(PN, SymbolicName);
ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
return Shifted;
}
}
}
// Remove the temporary PHI node SCEV that has been inserted while intending
// to create an AddRecExpr for this PHI node. We can not keep this temporary
// as it will prevent later (possibly simpler) SCEV expressions to be added
// to the ValueExprMap.
eraseValueFromMap(PN);
return nullptr;
}
// Checks if the SCEV S is available at BB. S is considered available at BB
// if S can be materialized at BB without introducing a fault.
static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
BasicBlock *BB) {
struct CheckAvailable {
bool TraversalDone = false;
bool Available = true;
const Loop *L = nullptr; // The loop BB is in (can be nullptr)
BasicBlock *BB = nullptr;
DominatorTree &DT;
CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
: L(L), BB(BB), DT(DT) {}
bool setUnavailable() {
TraversalDone = true;
Available = false;
return false;
}
bool follow(const SCEV *S) {
switch (S->getSCEVType()) {
case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
// These expressions are available if their operand(s) is/are.
return true;
case scAddRecExpr: {
// We allow add recurrences that are on the loop BB is in, or some
// outer loop. This guarantees availability because the value of the
// add recurrence at BB is simply the "current" value of the induction
// variable. We can relax this in the future; for instance an add
// recurrence on a sibling dominating loop is also available at BB.
const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
if (L && (ARLoop == L || ARLoop->contains(L)))
return true;
return setUnavailable();
}
case scUnknown: {
// For SCEVUnknown, we check for simple dominance.
const auto *SU = cast<SCEVUnknown>(S);
Value *V = SU->getValue();
if (isa<Argument>(V))
return false;
if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
return false;
return setUnavailable();
}
case scUDivExpr:
case scCouldNotCompute:
// We do not try to smart about these at all.
return setUnavailable();
}
llvm_unreachable("switch should be fully covered!");
}
bool isDone() { return TraversalDone; }
};
CheckAvailable CA(L, BB, DT);
SCEVTraversal<CheckAvailable> ST(CA);
ST.visitAll(S);
return CA.Available;
}
// Try to match a control flow sequence that branches out at BI and merges back
// at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
// match.
static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
Value *&C, Value *&LHS, Value *&RHS) {
C = BI->getCondition();
BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
if (!LeftEdge.isSingleEdge())
return false;
assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
Use &LeftUse = Merge->getOperandUse(0);
Use &RightUse = Merge->getOperandUse(1);
if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
LHS = LeftUse;
RHS = RightUse;
return true;
}
if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
LHS = RightUse;
RHS = LeftUse;
return true;
}
return false;
}
const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
auto IsReachable =
[&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
const Loop *L = LI.getLoopFor(PN->getParent());
// We don't want to break LCSSA, even in a SCEV expression tree.
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
return nullptr;
// Try to match
//
// br %cond, label %left, label %right
// left:
// br label %merge
// right:
// br label %merge
// merge:
// V = phi [ %x, %left ], [ %y, %right ]
//
// as "select %cond, %x, %y"
BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
assert(IDom && "At least the entry block should dominate PN");
auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
if (BI && BI->isConditional() &&
BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
}
return nullptr;
}
const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
if (const SCEV *S = createAddRecFromPHI(PN))
return S;
if (const SCEV *S = createNodeFromSelectLikePHI(PN))
return S;
// If the PHI has a single incoming value, follow that value, unless the
// PHI's incoming blocks are in a different loop, in which case doing so
// risks breaking LCSSA form. Instcombine would normally zap these, but
// it doesn't have DominatorTree information, so it may miss cases.
if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
if (LI.replacementPreservesLCSSAForm(PN, V))
return getSCEV(V);
// If it's not a loop phi, we can't handle it yet.
return getUnknown(PN);
}
const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
Value *Cond,
Value *TrueVal,
Value *FalseVal) {
// Handle "constant" branch or select. This can occur for instance when a
// loop pass transforms an inner loop and moves on to process the outer loop.
if (auto *CI = dyn_cast<ConstantInt>(Cond))
return getSCEV(CI->isOne() ? TrueVal : FalseVal);
// Try to match some simple smax or umax patterns.
auto *ICI = dyn_cast<ICmpInst>(Cond);
if (!ICI)
return getUnknown(I);
Value *LHS = ICI->getOperand(0);
Value *RHS = ICI->getOperand(1);
switch (ICI->getPredicate()) {
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
// a >s b ? a+x : b+x -> smax(a, b)+x
// a >s b ? b+x : a+x -> smin(a, b)+x
if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
const SCEV *LA = getSCEV(TrueVal);
const SCEV *RA = getSCEV(FalseVal);
const SCEV *LDiff = getMinusSCEV(LA, LS);
const SCEV *RDiff = getMinusSCEV(RA, RS);
if (LDiff == RDiff)
return getAddExpr(getSMaxExpr(LS, RS), LDiff);
LDiff = getMinusSCEV(LA, RS);
RDiff = getMinusSCEV(RA, LS);
if (LDiff == RDiff)
return getAddExpr(getSMinExpr(LS, RS), LDiff);
}
break;
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
// a >u b ? a+x : b+x -> umax(a, b)+x
// a >u b ? b+x : a+x -> umin(a, b)+x
if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
const SCEV *LA = getSCEV(TrueVal);
const SCEV *RA = getSCEV(FalseVal);
const SCEV *LDiff = getMinusSCEV(LA, LS);
const SCEV *RDiff = getMinusSCEV(RA, RS);
if (LDiff == RDiff)
return getAddExpr(getUMaxExpr(LS, RS), LDiff);
LDiff = getMinusSCEV(LA, RS);
RDiff = getMinusSCEV(RA, LS);
if (LDiff == RDiff)
return getAddExpr(getUMinExpr(LS, RS), LDiff);
}
break;
case ICmpInst::ICMP_NE:
// n != 0 ? n+x : 1+x -> umax(n, 1)+x
if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
const SCEV *One = getOne(I->getType());
const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
const SCEV *LA = getSCEV(TrueVal);
const SCEV *RA = getSCEV(FalseVal);
const SCEV *LDiff = getMinusSCEV(LA, LS);
const SCEV *RDiff = getMinusSCEV(RA, One);
if (LDiff == RDiff)
return getAddExpr(getUMaxExpr(One, LS), LDiff);
}
break;
case ICmpInst::ICMP_EQ:
// n == 0 ? 1+x : n+x -> umax(n, 1)+x
if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
const SCEV *One = getOne(I->getType());
const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
const SCEV *LA = getSCEV(TrueVal);
const SCEV *RA = getSCEV(FalseVal);
const SCEV *LDiff = getMinusSCEV(LA, One);
const SCEV *RDiff = getMinusSCEV(RA, LS);
if (LDiff == RDiff)
return getAddExpr(getUMaxExpr(One, LS), LDiff);
}
break;
default:
break;
}
return getUnknown(I);
}
/// Expand GEP instructions into add and multiply operations. This allows them
/// to be analyzed by regular SCEV code.
const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
// Don't attempt to analyze GEPs over unsized objects.
if (!GEP->getSourceElementType()->isSized())
return getUnknown(GEP);
SmallVector<const SCEV *, 4> IndexExprs;
for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
IndexExprs.push_back(getSCEV(*Index));
return getGEPExpr(GEP, IndexExprs);
}
uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
return C->getAPInt().countTrailingZeros();
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
return std::min(GetMinTrailingZeros(T->getOperand()),
(uint32_t)getTypeSizeInBits(T->getType()));
if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
return OpRes == getTypeSizeInBits(E->getOperand()->getType())
? getTypeSizeInBits(E->getType())
: OpRes;
}
if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
return OpRes == getTypeSizeInBits(E->getOperand()->getType())
? getTypeSizeInBits(E->getType())
: OpRes;
}
if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
return MinOpRes;
}
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
// The result is the sum of all operands results.
uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
uint32_t BitWidth = getTypeSizeInBits(M->getType());
for (unsigned i = 1, e = M->getNumOperands();
SumOpRes != BitWidth && i != e; ++i)
SumOpRes =
std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
return SumOpRes;
}
if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
return MinOpRes;
}
if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
return MinOpRes;
}
if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
return MinOpRes;
}
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
// For a SCEVUnknown, ask ValueTracking.
KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
return Known.countMinTrailingZeros();
}
// SCEVUDivExpr
return 0;
}
uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
auto I = MinTrailingZerosCache.find(S);
if (I != MinTrailingZerosCache.end())
return I->second;
uint32_t Result = GetMinTrailingZerosImpl(S);
auto InsertPair = MinTrailingZerosCache.insert({S, Result});
assert(InsertPair.second && "Should insert a new key");
return InsertPair.first->second;
}
/// Helper method to assign a range to V from metadata present in the IR.
static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
if (Instruction *I = dyn_cast<Instruction>(V))
if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
return getConstantRangeFromMetadata(*MD);
return None;
}
/// Determine the range for a particular SCEV. If SignHint is
/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
/// with a "cleaner" unsigned (resp. signed) representation.
const ConstantRange &
ScalarEvolution::getRangeRef(const SCEV *S,
ScalarEvolution::RangeSignHint SignHint) {
DenseMap<const SCEV *, ConstantRange> &Cache =
SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
: SignedRanges;
ConstantRange::PreferredRangeType RangeType =
SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED
? ConstantRange::Unsigned : ConstantRange::Signed;
// See if we've computed this range already.
DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
if (I != Cache.end())
return I->second;
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
return setRange(C, SignHint, ConstantRange(C->getAPInt()));
unsigned BitWidth = getTypeSizeInBits(S->getType());
ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
using OBO = OverflowingBinaryOperator;
// If the value has known zeros, the maximum value will have those known zeros
// as well.
uint32_t TZ = GetMinTrailingZeros(S);
if (TZ != 0) {
if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
ConservativeResult =
ConstantRange(APInt::getMinValue(BitWidth),
APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
else
ConservativeResult = ConstantRange(
APInt::getSignedMinValue(BitWidth),
APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
}
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
unsigned WrapType = OBO::AnyWrap;
if (Add->hasNoSignedWrap())
WrapType |= OBO::NoSignedWrap;
if (Add->hasNoUnsignedWrap())
WrapType |= OBO::NoUnsignedWrap;
for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
X = X.addWithNoWrap(getRangeRef(Add->getOperand(i), SignHint),
WrapType, RangeType);
return setRange(Add, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
return setRange(Mul, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
return setRange(SMax, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
return setRange(UMax, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVSMinExpr *SMin = dyn_cast<SCEVSMinExpr>(S)) {
ConstantRange X = getRangeRef(SMin->getOperand(0), SignHint);
for (unsigned i = 1, e = SMin->getNumOperands(); i != e; ++i)
X = X.smin(getRangeRef(SMin->getOperand(i), SignHint));
return setRange(SMin, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVUMinExpr *UMin = dyn_cast<SCEVUMinExpr>(S)) {
ConstantRange X = getRangeRef(UMin->getOperand(0), SignHint);
for (unsigned i = 1, e = UMin->getNumOperands(); i != e; ++i)
X = X.umin(getRangeRef(UMin->getOperand(i), SignHint));
return setRange(UMin, SignHint,
ConservativeResult.intersectWith(X, RangeType));
}
if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
return setRange(UDiv, SignHint,
ConservativeResult.intersectWith(X.udiv(Y), RangeType));
}
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
return setRange(ZExt, SignHint,
ConservativeResult.intersectWith(X.zeroExtend(BitWidth),
RangeType));
}
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
return setRange(SExt, SignHint,
ConservativeResult.intersectWith(X.signExtend(BitWidth),
RangeType));
}
if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
return setRange(Trunc, SignHint,
ConservativeResult.intersectWith(X.truncate(BitWidth),
RangeType));
}
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
// If there's no unsigned wrap, the value will never be less than its
// initial value.
if (AddRec->hasNoUnsignedWrap()) {
APInt UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart());
if (!UnsignedMinValue.isNullValue())
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType);
}
// If there's no signed wrap, and all the operands except initial value have
// the same sign or zero, the value won't ever be:
// 1: smaller than initial value if operands are non negative,
// 2: bigger than initial value if operands are non positive.
// For both cases, value can not cross signed min/max boundary.
if (AddRec->hasNoSignedWrap()) {
bool AllNonNeg = true;
bool AllNonPos = true;
for (unsigned i = 1, e = AddRec->getNumOperands(); i != e; ++i) {
if (!isKnownNonNegative(AddRec->getOperand(i)))
AllNonNeg = false;
if (!isKnownNonPositive(AddRec->getOperand(i)))
AllNonPos = false;
}
if (AllNonNeg)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange::getNonEmpty(getSignedRangeMin(AddRec->getStart()),
APInt::getSignedMinValue(BitWidth)),
RangeType);
else if (AllNonPos)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange::getNonEmpty(
APInt::getSignedMinValue(BitWidth),
getSignedRangeMax(AddRec->getStart()) + 1),
RangeType);
}
// TODO: non-affine addrec
if (AddRec->isAffine()) {
const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(AddRec->getLoop());
if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
auto RangeFromAffine = getRangeForAffineAR(
AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
BitWidth);
if (!RangeFromAffine.isFullSet())
ConservativeResult =
ConservativeResult.intersectWith(RangeFromAffine, RangeType);
auto RangeFromFactoring = getRangeViaFactoring(
AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
BitWidth);
if (!RangeFromFactoring.isFullSet())
ConservativeResult =
ConservativeResult.intersectWith(RangeFromFactoring, RangeType);
}
}
return setRange(AddRec, SignHint, std::move(ConservativeResult));
}
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
// Check if the IR explicitly contains !range metadata.
Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
if (MDRange.hasValue())
ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue(),
RangeType);
// Split here to avoid paying the compile-time cost of calling both
// computeKnownBits and ComputeNumSignBits. This restriction can be lifted
// if needed.
const DataLayout &DL = getDataLayout();
if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
// For a SCEVUnknown, ask ValueTracking.
KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
if (Known.getBitWidth() != BitWidth)
Known = Known.zextOrTrunc(BitWidth, true);
// If Known does not result in full-set, intersect with it.
if (Known.getMinValue() != Known.getMaxValue() + 1)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1),
RangeType);
} else {
assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
"generalize as needed!");
unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
// If the pointer size is larger than the index size type, this can cause
// NS to be larger than BitWidth. So compensate for this.
if (U->getType()->isPointerTy()) {
unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType());
int ptrIdxDiff = ptrSize - BitWidth;
if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff)
NS -= ptrIdxDiff;
}
if (NS > 1)
ConservativeResult = ConservativeResult.intersectWith(
ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1),
RangeType);
}
// A range of Phi is a subset of union of all ranges of its input.
if (const PHINode *Phi = dyn_cast<PHINode>(U->getValue())) {
// Make sure that we do not run over cycled Phis.
if (PendingPhiRanges.insert(Phi).second) {
ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
for (auto &Op : Phi->operands()) {
auto OpRange = getRangeRef(getSCEV(Op), SignHint);
RangeFromOps = RangeFromOps.unionWith(OpRange);
// No point to continue if we already have a full set.
if (RangeFromOps.isFullSet())
break;
}
ConservativeResult =
ConservativeResult.intersectWith(RangeFromOps, RangeType);
bool Erased = PendingPhiRanges.erase(Phi);
assert(Erased && "Failed to erase Phi properly?");
(void) Erased;
}
}
return setRange(U, SignHint, std::move(ConservativeResult));
}
return setRange(S, SignHint, std::move(ConservativeResult));
}
// Given a StartRange, Step and MaxBECount for an expression compute a range of
// values that the expression can take. Initially, the expression has a value
// from StartRange and then is changed by Step up to MaxBECount times. Signed
// argument defines if we treat Step as signed or unsigned.
static ConstantRange getRangeForAffineARHelper(APInt Step,
const ConstantRange &StartRange,
const APInt &MaxBECount,
unsigned BitWidth, bool Signed) {
// If either Step or MaxBECount is 0, then the expression won't change, and we
// just need to return the initial range.
if (Step == 0 || MaxBECount == 0)
return StartRange;
// If we don't know anything about the initial value (i.e. StartRange is
// FullRange), then we don't know anything about the final range either.
// Return FullRange.
if (StartRange.isFullSet())
return ConstantRange::getFull(BitWidth);
// If Step is signed and negative, then we use its absolute value, but we also
// note that we're moving in the opposite direction.
bool Descending = Signed && Step.isNegative();
if (Signed)
// This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
// abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
// This equations hold true due to the well-defined wrap-around behavior of
// APInt.
Step = Step.abs();
// Check if Offset is more than full span of BitWidth. If it is, the
// expression is guaranteed to overflow.
if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
return ConstantRange::getFull(BitWidth);
// Offset is by how much the expression can change. Checks above guarantee no
// overflow here.
APInt Offset = Step * MaxBECount;
// Minimum value of the final range will match the minimal value of StartRange
// if the expression is increasing and will be decreased by Offset otherwise.
// Maximum value of the final range will match the maximal value of StartRange
// if the expression is decreasing and will be increased by Offset otherwise.
APInt StartLower = StartRange.getLower();
APInt StartUpper = StartRange.getUpper() - 1;
APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
: (StartUpper + std::move(Offset));
// It's possible that the new minimum/maximum value will fall into the initial
// range (due to wrap around). This means that the expression can take any
// value in this bitwidth, and we have to return full range.
if (StartRange.contains(MovedBoundary))
return ConstantRange::getFull(BitWidth);
APInt NewLower =
Descending ? std::move(MovedBoundary) : std::move(StartLower);
APInt NewUpper =
Descending ? std::move(StartUpper) : std::move(MovedBoundary);
NewUpper += 1;
// No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
return ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper));
}
ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
const SCEV *Step,
const SCEV *MaxBECount,
unsigned BitWidth) {
assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
"Precondition!");
MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount);
// First, consider step signed.
ConstantRange StartSRange = getSignedRange(Start);
ConstantRange StepSRange = getSignedRange(Step);
// If Step can be both positive and negative, we need to find ranges for the
// maximum absolute step values in both directions and union them.
ConstantRange SR =
getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange,
MaxBECountValue, BitWidth, /* Signed = */ true);
SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(),
StartSRange, MaxBECountValue,
BitWidth, /* Signed = */ true));
// Next, consider step unsigned.
ConstantRange UR = getRangeForAffineARHelper(
getUnsignedRangeMax(Step), getUnsignedRange(Start),
MaxBECountValue, BitWidth, /* Signed = */ false);
// Finally, intersect signed and unsigned ranges.
return SR.intersectWith(UR, ConstantRange::Smallest);
}
ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
const SCEV *Step,
const SCEV *MaxBECount,
unsigned BitWidth) {
// RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
// == RangeOf({A,+,P}) union RangeOf({B,+,Q})
struct SelectPattern {
Value *Condition = nullptr;
APInt TrueValue;
APInt FalseValue;
explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
const SCEV *S) {
Optional<unsigned> CastOp;
APInt Offset(BitWidth, 0);
assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
"Should be!");
// Peel off a constant offset:
if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
// In the future we could consider being smarter here and handle
// {Start+Step,+,Step} too.
if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
return;
Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
S = SA->getOperand(1);
}
// Peel off a cast operation
if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
CastOp = SCast->getSCEVType();
S = SCast->getOperand();
}
using namespace llvm::PatternMatch;
auto *SU = dyn_cast<SCEVUnknown>(S);
const APInt *TrueVal, *FalseVal;
if (!SU ||
!match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
m_APInt(FalseVal)))) {
Condition = nullptr;
return;
}
TrueValue = *TrueVal;
FalseValue = *FalseVal;
// Re-apply the cast we peeled off earlier
if (CastOp.hasValue())
switch (*CastOp) {
default:
llvm_unreachable("Unknown SCEV cast type!");
case scTruncate:
TrueValue = TrueValue.trunc(BitWidth);
FalseValue = FalseValue.trunc(BitWidth);
break;
case scZeroExtend:
TrueValue = TrueValue.zext(BitWidth);
FalseValue = FalseValue.zext(BitWidth);
break;
case scSignExtend:
TrueValue = TrueValue.sext(BitWidth);
FalseValue = FalseValue.sext(BitWidth);
break;
}
// Re-apply the constant offset we peeled off earlier
TrueValue += Offset;
FalseValue += Offset;
}
bool isRecognized() { return Condition != nullptr; }
};
SelectPattern StartPattern(*this, BitWidth, Start);
if (!StartPattern.isRecognized())
return ConstantRange::getFull(BitWidth);
SelectPattern StepPattern(*this, BitWidth, Step);
if (!StepPattern.isRecognized())
return ConstantRange::getFull(BitWidth);
if (StartPattern.Condition != StepPattern.Condition) {
// We don't handle this case today; but we could, by considering four
// possibilities below instead of two. I'm not sure if there are cases where
// that will help over what getRange already does, though.
return ConstantRange::getFull(BitWidth);
}
// NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
// construct arbitrary general SCEV expressions here. This function is called
// from deep in the call stack, and calling getSCEV (on a sext instruction,
// say) can end up caching a suboptimal value.
// FIXME: without the explicit `this` receiver below, MSVC errors out with
// C2352 and C2512 (otherwise it isn't needed).
const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
ConstantRange TrueRange =
this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
ConstantRange FalseRange =
this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
return TrueRange.unionWith(FalseRange);
}
SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
const BinaryOperator *BinOp = cast<BinaryOperator>(V);
// Return early if there are no flags to propagate to the SCEV.
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (BinOp->hasNoUnsignedWrap())
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
if (BinOp->hasNoSignedWrap())
Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
if (Flags == SCEV::FlagAnyWrap)
return SCEV::FlagAnyWrap;
return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
}
bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
// Here we check that I is in the header of the innermost loop containing I,
// since we only deal with instructions in the loop header. The actual loop we
// need to check later will come from an add recurrence, but getting that
// requires computing the SCEV of the operands, which can be expensive. This
// check we can do cheaply to rule out some cases early.
Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
if (InnermostContainingLoop == nullptr ||
InnermostContainingLoop->getHeader() != I->getParent())
return false;
// Only proceed if we can prove that I does not yield poison.
if (!programUndefinedIfFullPoison(I))
return false;
// At this point we know that if I is executed, then it does not wrap
// according to at least one of NSW or NUW. If I is not executed, then we do
// not know if the calculation that I represents would wrap. Multiple
// instructions can map to the same SCEV. If we apply NSW or NUW from I to
// the SCEV, we must guarantee no wrapping for that SCEV also when it is
// derived from other instructions that map to the same SCEV. We cannot make
// that guarantee for cases where I is not executed. So we need to find the
// loop that I is considered in relation to and prove that I is executed for
// every iteration of that loop. That implies that the value that I
// calculates does not wrap anywhere in the loop, so then we can apply the
// flags to the SCEV.
//
// We check isLoopInvariant to disambiguate in case we are adding recurrences
// from different loops, so that we know which loop to prove that I is
// executed in.
for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
// I could be an extractvalue from a call to an overflow intrinsic.
// TODO: We can do better here in some cases.
if (!isSCEVable(I->getOperand(OpIndex)->getType()))
return false;
const SCEV *Op = getSCEV(I->getOperand(OpIndex));
if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
bool AllOtherOpsLoopInvariant = true;
for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
++OtherOpIndex) {
if (OtherOpIndex != OpIndex) {
const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
AllOtherOpsLoopInvariant = false;
break;
}
}
}
if (AllOtherOpsLoopInvariant &&
isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
return true;
}
}
return false;
}
bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
// If we know that \c I can never be poison period, then that's enough.
if (isSCEVExprNeverPoison(I))
return true;
// For an add recurrence specifically, we assume that infinite loops without
// side effects are undefined behavior, and then reason as follows:
//
// If the add recurrence is poison in any iteration, it is poison on all
// future iterations (since incrementing poison yields poison). If the result
// of the add recurrence is fed into the loop latch condition and the loop
// does not contain any throws or exiting blocks other than the latch, we now
// have the ability to "choose" whether the backedge is taken or not (by
// choosing a sufficiently evil value for the poison feeding into the branch)
// for every iteration including and after the one in which \p I first became
// poison. There are two possibilities (let's call the iteration in which \p
// I first became poison as K):
//
// 1. In the set of iterations including and after K, the loop body executes
// no side effects. In this case executing the backege an infinte number
// of times will yield undefined behavior.
//
// 2. In the set of iterations including and after K, the loop body executes
// at least one side effect. In this case, that specific instance of side
// effect is control dependent on poison, which also yields undefined
// behavior.
auto *ExitingBB = L->getExitingBlock();
auto *LatchBB = L->getLoopLatch();
if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
return false;
SmallPtrSet<const Instruction *, 16> Pushed;
SmallVector<const Instruction *, 8> PoisonStack;
// We start by assuming \c I, the post-inc add recurrence, is poison. Only
// things that are known to be fully poison under that assumption go on the
// PoisonStack.
Pushed.insert(I);
PoisonStack.push_back(I);
bool LatchControlDependentOnPoison = false;
while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
const Instruction *Poison = PoisonStack.pop_back_val();
for (auto *PoisonUser : Poison->users()) {
if (propagatesFullPoison(cast<Instruction>(PoisonUser))) {
if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
PoisonStack.push_back(cast<Instruction>(PoisonUser));
} else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
assert(BI->isConditional() && "Only possibility!");
if (BI->getParent() == LatchBB) {
LatchControlDependentOnPoison = true;
break;
}
}
}
}
return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
}
ScalarEvolution::LoopProperties
ScalarEvolution::getLoopProperties(const Loop *L) {
using LoopProperties = ScalarEvolution::LoopProperties;
auto Itr = LoopPropertiesCache.find(L);
if (Itr == LoopPropertiesCache.end()) {
auto HasSideEffects = [](Instruction *I) {
if (auto *SI = dyn_cast<StoreInst>(I))
return !SI->isSimple();
return I->mayHaveSideEffects();
};
LoopProperties LP = {/* HasNoAbnormalExits */ true,
/*HasNoSideEffects*/ true};
for (auto *BB : L->getBlocks())
for (auto &I : *BB) {
if (!isGuaranteedToTransferExecutionToSuccessor(&I))
LP.HasNoAbnormalExits = false;
if (HasSideEffects(&I))
LP.HasNoSideEffects = false;
if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
break; // We're already as pessimistic as we can get.
}
auto InsertPair = LoopPropertiesCache.insert({L, LP});
assert(InsertPair.second && "We just checked!");
Itr = InsertPair.first;
}
return Itr->second;
}
const SCEV *ScalarEvolution::createSCEV(Value *V) {
if (!isSCEVable(V->getType()))
return getUnknown(V);
if (Instruction *I = dyn_cast<Instruction>(V)) {
// Don't attempt to analyze instructions in blocks that aren't
// reachable. Such instructions don't matter, and they aren't required
// to obey basic rules for definitions dominating uses which this
// analysis depends on.
if (!DT.isReachableFromEntry(I->getParent()))
return getUnknown(UndefValue::get(V->getType()));
} else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
return getConstant(CI);
else if (isa<ConstantPointerNull>(V))
return getZero(V->getType());
else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
else if (!isa<ConstantExpr>(V))
return getUnknown(V);
Operator *U = cast<Operator>(V);
if (auto BO = MatchBinaryOp(U, DT)) {
switch (BO->Opcode) {
case Instruction::Add: {
// The simple thing to do would be to just call getSCEV on both operands
// and call getAddExpr with the result. However if we're looking at a
// bunch of things all added together, this can be quite inefficient,
// because it leads to N-1 getAddExpr calls for N ultimate operands.
// Instead, gather up all the operands and make a single getAddExpr call.
// LLVM IR canonical form means we need only traverse the left operands.
SmallVector<const SCEV *, 4> AddOps;
do {
if (BO->Op) {
if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
AddOps.push_back(OpSCEV);
break;
}
// If a NUW or NSW flag can be applied to the SCEV for this
// addition, then compute the SCEV for this addition by itself
// with a separate call to getAddExpr. We need to do that
// instead of pushing the operands of the addition onto AddOps,
// since the flags are only known to apply to this particular
// addition - they may not apply to other additions that can be
// formed with operands from AddOps.
const SCEV *RHS = getSCEV(BO->RHS);
SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
if (Flags != SCEV::FlagAnyWrap) {
const SCEV *LHS = getSCEV(BO->LHS);
if (BO->Opcode == Instruction::Sub)
AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
else
AddOps.push_back(getAddExpr(LHS, RHS, Flags));
break;
}
}
if (BO->Opcode == Instruction::Sub)
AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
else
AddOps.push_back(getSCEV(BO->RHS));
auto NewBO = MatchBinaryOp(BO->LHS, DT);
if (!NewBO || (NewBO->Opcode != Instruction::Add &&
NewBO->Opcode != Instruction::Sub)) {
AddOps.push_back(getSCEV(BO->LHS));
break;
}
BO = NewBO;
} while (true);
return getAddExpr(AddOps);
}
case Instruction::Mul: {
SmallVector<const SCEV *, 4> MulOps;
do {
if (BO->Op) {
if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
MulOps.push_back(OpSCEV);
break;
}
SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
if (Flags != SCEV::FlagAnyWrap) {
MulOps.push_back(
getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
break;
}
}
MulOps.push_back(getSCEV(BO->RHS));
auto NewBO = MatchBinaryOp(BO->LHS, DT);
if (!NewBO || NewBO->Opcode != Instruction::Mul) {
MulOps.push_back(getSCEV(BO->LHS));
break;
}
BO = NewBO;
} while (true);
return getMulExpr(MulOps);
}
case Instruction::UDiv:
return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
case Instruction::URem:
return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
case Instruction::Sub: {
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (BO->Op)
Flags = getNoWrapFlagsFromUB(BO->Op);
return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
}
case Instruction::And:
// For an expression like x&255 that merely masks off the high bits,
// use zext(trunc(x)) as the SCEV expression.
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
if (CI->isZero())
return getSCEV(BO->RHS);
if (CI->isMinusOne())
return getSCEV(BO->LHS);
const APInt &A = CI->getValue();
// Instcombine's ShrinkDemandedConstant may strip bits out of
// constants, obscuring what would otherwise be a low-bits mask.
// Use computeKnownBits to compute what ShrinkDemandedConstant
// knew about to reconstruct a low-bits mask value.
unsigned LZ = A.countLeadingZeros();
unsigned TZ = A.countTrailingZeros();
unsigned BitWidth = A.getBitWidth();
KnownBits Known(BitWidth);
computeKnownBits(BO->LHS, Known, getDataLayout(),
0, &AC, nullptr, &DT);
APInt EffectiveMask =
APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ));
const SCEV *LHS = getSCEV(BO->LHS);
const SCEV *ShiftedLHS = nullptr;
if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) {
if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) {
// For an expression like (x * 8) & 8, simplify the multiply.
unsigned MulZeros = OpC->getAPInt().countTrailingZeros();
unsigned GCD = std::min(MulZeros, TZ);
APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD);
SmallVector<const SCEV*, 4> MulOps;
MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD)));
MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end());
auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags());
ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt));
}
}
if (!ShiftedLHS)
ShiftedLHS = getUDivExpr(LHS, MulCount);
return getMulExpr(
getZeroExtendExpr(
getTruncateExpr(ShiftedLHS,
IntegerType::get(getContext(), BitWidth - LZ - TZ)),
BO->LHS->getType()),
MulCount);
}
}
break;
case Instruction::Or:
// If the RHS of the Or is a constant, we may have something like:
// X*4+1 which got turned into X*4|1. Handle this as an Add so loop
// optimizations will transparently handle this case.
//
// In order for this transformation to be safe, the LHS must be of the
// form X*(2^n) and the Or constant must be less than 2^n.
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
const SCEV *LHS = getSCEV(BO->LHS);
const APInt &CIVal = CI->getValue();
if (GetMinTrailingZeros(LHS) >=
(CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
// Build a plain add SCEV.
const SCEV *S = getAddExpr(LHS, getSCEV(CI));
// If the LHS of the add was an addrec and it has no-wrap flags,
// transfer the no-wrap flags, since an or won't introduce a wrap.
if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
OldAR->getNoWrapFlags());
}
return S;
}
}
break;
case Instruction::Xor:
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
// If the RHS of xor is -1, then this is a not operation.
if (CI->isMinusOne())
return getNotSCEV(getSCEV(BO->LHS));
// Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
// This is a variant of the check for xor with -1, and it handles
// the case where instcombine has trimmed non-demanded bits out
// of an xor with -1.
if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
if (LBO->getOpcode() == Instruction::And &&
LCI->getValue() == CI->getValue())
if (const SCEVZeroExtendExpr *Z =
dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
Type *UTy = BO->LHS->getType();
const SCEV *Z0 = Z->getOperand();
Type *Z0Ty = Z0->getType();
unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
// If C is a low-bits mask, the zero extend is serving to
// mask off the high bits. Complement the operand and
// re-apply the zext.
if (CI->getValue().isMask(Z0TySize))
return getZeroExtendExpr(getNotSCEV(Z0), UTy);
// If C is a single bit, it may be in the sign-bit position
// before the zero-extend. In this case, represent the xor
// using an add, which is equivalent, and re-apply the zext.
APInt Trunc = CI->getValue().trunc(Z0TySize);
if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
Trunc.isSignMask())
return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
UTy);
}
}
break;
case Instruction::Shl:
// Turn shift left of a constant amount into a multiply.
if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
// If the shift count is not less than the bitwidth, the result of
// the shift is undefined. Don't try to analyze it, because the
// resolution chosen here may differ from the resolution chosen in
// other parts of the compiler.
if (SA->getValue().uge(BitWidth))
break;
// It is currently not resolved how to interpret NSW for left
// shift by BitWidth - 1, so we avoid applying flags in that
// case. Remove this check (or this comment) once the situation
// is resolved. See
// http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
// and http://reviews.llvm.org/D8890 .
auto Flags = SCEV::FlagAnyWrap;
if (BO->Op && SA->getValue().ult(BitWidth - 1))
Flags = getNoWrapFlagsFromUB(BO->Op);
Constant *X = ConstantInt::get(
getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
}
break;
case Instruction::AShr: {
// AShr X, C, where C is a constant.
ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS);
if (!CI)
break;
Type *OuterTy = BO->LHS->getType();
uint64_t BitWidth = getTypeSizeInBits(OuterTy);
// If the shift count is not less than the bitwidth, the result of
// the shift is undefined. Don't try to analyze it, because the
// resolution chosen here may differ from the resolution chosen in
// other parts of the compiler.
if (CI->getValue().uge(BitWidth))
break;
if (CI->isZero())
return getSCEV(BO->LHS); // shift by zero --> noop
uint64_t AShrAmt = CI->getZExtValue();
Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt);
Operator *L = dyn_cast<Operator>(BO->LHS);
if (L && L->getOpcode() == Instruction::Shl) {
// X = Shl A, n
// Y = AShr X, m
// Both n and m are constant.
const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0));
if (L->getOperand(1) == BO->RHS)
// For a two-shift sext-inreg, i.e. n = m,
// use sext(trunc(x)) as the SCEV expression.
return getSignExtendExpr(
getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy);
ConstantInt *ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1));
if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) {
uint64_t ShlAmt = ShlAmtCI->getZExtValue();
if (ShlAmt > AShrAmt) {
// When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
// expression. We already checked that ShlAmt < BitWidth, so
// the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
// ShlAmt - AShrAmt < Amt.
APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt,
ShlAmt - AShrAmt);
return getSignExtendExpr(
getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy),
getConstant(Mul)), OuterTy);
}
}
}
break;
}
}
}
switch (U->getOpcode()) {
case Instruction::Trunc:
return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
case Instruction::ZExt:
return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
case Instruction::SExt:
if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) {
// The NSW flag of a subtract does not always survive the conversion to
// A + (-1)*B. By pushing sign extension onto its operands we are much
// more likely to preserve NSW and allow later AddRec optimisations.
//
// NOTE: This is effectively duplicating this logic from getSignExtend:
// sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
// but by that point the NSW information has potentially been lost.
if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
Type *Ty = U->getType();
auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
return getMinusSCEV(V1, V2, SCEV::FlagNSW);
}
}
return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
case Instruction::BitCast:
// BitCasts are no-op casts so we just eliminate the cast.
if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
return getSCEV(U->getOperand(0));
break;
// It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
// lead to pointer expressions which cannot safely be expanded to GEPs,
// because ScalarEvolution doesn't respect the GEP aliasing rules when
// simplifying integer expressions.
case Instruction::GetElementPtr:
return createNodeForGEP(cast<GEPOperator>(U));
case Instruction::PHI:
return createNodeForPHI(cast<PHINode>(U));
case Instruction::Select:
// U can also be a select constant expr, which let fall through. Since
// createNodeForSelect only works for a condition that is an `ICmpInst`, and
// constant expressions cannot have instructions as operands, we'd have
// returned getUnknown for a select constant expressions anyway.
if (isa<Instruction>(U))
return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
U->getOperand(1), U->getOperand(2));
break;
case Instruction::Call:
case Instruction::Invoke:
if (Value *RV = CallSite(U).getReturnedArgOperand())
return getSCEV(RV);
break;
}
return getUnknown(V);
}
//===----------------------------------------------------------------------===//
// Iteration Count Computation Code
//
static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
if (!ExitCount)
return 0;
ConstantInt *ExitConst = ExitCount->getValue();
// Guard against huge trip counts.
if (ExitConst->getValue().getActiveBits() > 32)
return 0;
// In case of integer overflow, this returns 0, which is correct.
return ((unsigned)ExitConst->getZExtValue()) + 1;
}
unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
if (BasicBlock *ExitingBB = L->getExitingBlock())
return getSmallConstantTripCount(L, ExitingBB);
// No trip count information for multiple exits.
return 0;
}
unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L,
BasicBlock *ExitingBlock) {
assert(ExitingBlock && "Must pass a non-null exiting block!");
assert(L->isLoopExiting(ExitingBlock) &&
"Exiting block must actually branch out of the loop!");
const SCEVConstant *ExitCount =
dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
return getConstantTripCount(ExitCount);
}
unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) {
const auto *MaxExitCount =
dyn_cast<SCEVConstant>(getConstantMaxBackedgeTakenCount(L));
return getConstantTripCount(MaxExitCount);
}
unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
if (BasicBlock *ExitingBB = L->getExitingBlock())
return getSmallConstantTripMultiple(L, ExitingBB);
// No trip multiple information for multiple exits.
return 0;
}
/// Returns the largest constant divisor of the trip count of this loop as a
/// normal unsigned value, if possible. This means that the actual trip count is
/// always a multiple of the returned value (don't forget the trip count could
/// very well be zero as well!).
///
/// Returns 1 if the trip count is unknown or not guaranteed to be the
/// multiple of a constant (which is also the case if the trip count is simply
/// constant, use getSmallConstantTripCount for that case), Will also return 1
/// if the trip count is very large (>= 2^32).
///
/// As explained in the comments for getSmallConstantTripCount, this assumes
/// that control exits the loop via ExitingBlock.
unsigned
ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
BasicBlock *ExitingBlock) {
assert(ExitingBlock && "Must pass a non-null exiting block!");
assert(L->isLoopExiting(ExitingBlock) &&
"Exiting block must actually branch out of the loop!");
const SCEV *ExitCount = getExitCount(L, ExitingBlock);
if (ExitCount == getCouldNotCompute())
return 1;
// Get the trip count from the BE count by adding 1.
const SCEV *TCExpr = getAddExpr(ExitCount, getOne(ExitCount->getType()));
const SCEVConstant *TC = dyn_cast<SCEVConstant>(TCExpr);
if (!TC)
// Attempt to factor more general cases. Returns the greatest power of
// two divisor. If overflow happens, the trip count expression is still
// divisible by the greatest power of 2 divisor returned.
return 1U << std::min((uint32_t)31, GetMinTrailingZeros(TCExpr));
ConstantInt *Result = TC->getValue();
// Guard against huge trip counts (this requires checking
// for zero to handle the case where the trip count == -1 and the
// addition wraps).
if (!Result || Result->getValue().getActiveBits() > 32 ||
Result->getValue().getActiveBits() == 0)
return 1;
return (unsigned)Result->getZExtValue();
}
const SCEV *ScalarEvolution::getExitCount(const Loop *L,
BasicBlock *ExitingBlock,
ExitCountKind Kind) {
switch (Kind) {
case Exact:
return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
case ConstantMaximum:
return getBackedgeTakenInfo(L).getMax(ExitingBlock, this);
};
llvm_unreachable("Invalid ExitCountKind!");
}
const SCEV *
ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
SCEVUnionPredicate &Preds) {
return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds);
}
const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L,
ExitCountKind Kind) {
switch (Kind) {
case Exact:
return getBackedgeTakenInfo(L).getExact(L, this);
case ConstantMaximum:
return getBackedgeTakenInfo(L).getMax(this);
};
llvm_unreachable("Invalid ExitCountKind!");
}
bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
return getBackedgeTakenInfo(L).isMaxOrZero(this);
}
/// Push PHI nodes in the header of the given loop onto the given Worklist.
static void
PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
BasicBlock *Header = L->getHeader();
// Push all Loop-header PHIs onto the Worklist stack.
for (PHINode &PN : Header->phis())
Worklist.push_back(&PN);
}
const ScalarEvolution::BackedgeTakenInfo &
ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
auto &BTI = getBackedgeTakenInfo(L);
if (BTI.hasFullInfo())
return BTI;
auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
if (!Pair.second)
return Pair.first->second;
BackedgeTakenInfo Result =
computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
}
const ScalarEvolution::BackedgeTakenInfo &
ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
// Initially insert an invalid entry for this loop. If the insertion
// succeeds, proceed to actually compute a backedge-taken count and
// update the value. The temporary CouldNotCompute value tells SCEV
// code elsewhere that it shouldn't attempt to request a new
// backedge-taken count, which could result in infinite recursion.
std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
if (!Pair.second)
return Pair.first->second;
// computeBackedgeTakenCount may allocate memory for its result. Inserting it
// into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
// must be cleared in this scope.
BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
// In product build, there are no usage of statistic.
(void)NumTripCountsComputed;
(void)NumTripCountsNotComputed;
#if LLVM_ENABLE_STATS || !defined(NDEBUG)
const SCEV *BEExact = Result.getExact(L, this);
if (BEExact != getCouldNotCompute()) {
assert(isLoopInvariant(BEExact, L) &&
isLoopInvariant(Result.getMax(this), L) &&
"Computed backedge-taken count isn't loop invariant for loop!");
++NumTripCountsComputed;
}
else if (Result.getMax(this) == getCouldNotCompute() &&
isa<PHINode>(L->getHeader()->begin())) {
// Only count loops that have phi nodes as not being computable.
++NumTripCountsNotComputed;
}
#endif // LLVM_ENABLE_STATS || !defined(NDEBUG)
// Now that we know more about the trip count for this loop, forget any
// existing SCEV values for PHI nodes in this loop since they are only
// conservative estimates made without the benefit of trip count
// information. This is similar to the code in forgetLoop, except that
// it handles SCEVUnknown PHI nodes specially.
if (Result.hasAnyInfo()) {
SmallVector<Instruction *, 16> Worklist;
PushLoopPHIs(L, Worklist);
SmallPtrSet<Instruction *, 8> Discovered;
while (!Worklist.empty()) {
Instruction *I = Worklist.pop_back_val();
ValueExprMapType::iterator It =
ValueExprMap.find_as(static_cast<Value *>(I));
if (It != ValueExprMap.end()) {
const SCEV *Old = It->second;
// SCEVUnknown for a PHI either means that it has an unrecognized
// structure, or it's a PHI that's in the progress of being computed
// by createNodeForPHI. In the former case, additional loop trip
// count information isn't going to change anything. In the later
// case, createNodeForPHI will perform the necessary updates on its
// own when it gets to that point.
if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
eraseValueFromMap(It->first);
forgetMemoizedResults(Old);
}
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
// Since we don't need to invalidate anything for correctness and we're
// only invalidating to make SCEV's results more precise, we get to stop
// early to avoid invalidating too much. This is especially important in
// cases like:
//
// %v = f(pn0, pn1) // pn0 and pn1 used through some other phi node
// loop0:
// %pn0 = phi
// ...
// loop1:
// %pn1 = phi
// ...
//
// where both loop0 and loop1's backedge taken count uses the SCEV
// expression for %v. If we don't have the early stop below then in cases
// like the above, getBackedgeTakenInfo(loop1) will clear out the trip
// count for loop0 and getBackedgeTakenInfo(loop0) will clear out the trip
// count for loop1, effectively nullifying SCEV's trip count cache.
for (auto *U : I->users())
if (auto *I = dyn_cast<Instruction>(U)) {
auto *LoopForUser = LI.getLoopFor(I->getParent());
if (LoopForUser && L->contains(LoopForUser) &&
Discovered.insert(I).second)
Worklist.push_back(I);
}
}
}
// Re-lookup the insert position, since the call to
// computeBackedgeTakenCount above could result in a
// recusive call to getBackedgeTakenInfo (on a different
// loop), which would invalidate the iterator computed
// earlier.
return BackedgeTakenCounts.find(L)->second = std::move(Result);
}
void ScalarEvolution::forgetAllLoops() {
// This method is intended to forget all info about loops. It should
// invalidate caches as if the following happened:
// - The trip counts of all loops have changed arbitrarily
// - Every llvm::Value has been updated in place to produce a different
// result.
BackedgeTakenCounts.clear();
PredicatedBackedgeTakenCounts.clear();
LoopPropertiesCache.clear();
ConstantEvolutionLoopExitValue.clear();
ValueExprMap.clear();
ValuesAtScopes.clear();
LoopDispositions.clear();
BlockDispositions.clear();
UnsignedRanges.clear();
SignedRanges.clear();
ExprValueMap.clear();
HasRecMap.clear();
MinTrailingZerosCache.clear();
PredicatedSCEVRewrites.clear();
}
void ScalarEvolution::forgetLoop(const Loop *L) {
// Drop any stored trip count value.
auto RemoveLoopFromBackedgeMap =
[](DenseMap<const Loop *, BackedgeTakenInfo> &Map, const Loop *L) {
auto BTCPos = Map.find(L);
if (BTCPos != Map.end()) {
BTCPos->second.clear();
Map.erase(BTCPos);
}
};
SmallVector<const Loop *, 16> LoopWorklist(1, L);
SmallVector<Instruction *, 32> Worklist;
SmallPtrSet<Instruction *, 16> Visited;
// Iterate over all the loops and sub-loops to drop SCEV information.
while (!LoopWorklist.empty()) {
auto *CurrL = LoopWorklist.pop_back_val();
RemoveLoopFromBackedgeMap(BackedgeTakenCounts, CurrL);
RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts, CurrL);
// Drop information about predicated SCEV rewrites for this loop.
for (auto I = PredicatedSCEVRewrites.begin();
I != PredicatedSCEVRewrites.end();) {
std::pair<const SCEV *, const Loop *> Entry = I->first;
if (Entry.second == CurrL)
PredicatedSCEVRewrites.erase(I++);
else
++I;
}
auto LoopUsersItr = LoopUsers.find(CurrL);
if (LoopUsersItr != LoopUsers.end()) {
for (auto *S : LoopUsersItr->second)
forgetMemoizedResults(S);
LoopUsers.erase(LoopUsersItr);
}
// Drop information about expressions based on loop-header PHIs.
PushLoopPHIs(CurrL, Worklist);
while (!Worklist.empty()) {
Instruction *I = Worklist.pop_back_val();
if (!Visited.insert(I).second)
continue;
ValueExprMapType::iterator It =
ValueExprMap.find_as(static_cast<Value *>(I));
if (It != ValueExprMap.end()) {
eraseValueFromMap(It->first);
forgetMemoizedResults(It->second);
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
PushDefUseChildren(I, Worklist);
}
LoopPropertiesCache.erase(CurrL);
// Forget all contained loops too, to avoid dangling entries in the
// ValuesAtScopes map.
LoopWorklist.append(CurrL->begin(), CurrL->end());
}
}
void ScalarEvolution::forgetTopmostLoop(const Loop *L) {
while (Loop *Parent = L->getParentLoop())
L = Parent;
forgetLoop(L);
}
void ScalarEvolution::forgetValue(Value *V) {
Instruction *I = dyn_cast<Instruction>(V);
if (!I) return;
// Drop information about expressions based on loop-header PHIs.
SmallVector<Instruction *, 16> Worklist;
Worklist.push_back(I);
SmallPtrSet<Instruction *, 8> Visited;
while (!Worklist.empty()) {
I = Worklist.pop_back_val();
if (!Visited.insert(I).second)
continue;
ValueExprMapType::iterator It =
ValueExprMap.find_as(static_cast<Value *>(I));
if (It != ValueExprMap.end()) {
eraseValueFromMap(It->first);
forgetMemoizedResults(It->second);
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
PushDefUseChildren(I, Worklist);
}
}
/// Get the exact loop backedge taken count considering all loop exits. A
/// computable result can only be returned for loops with all exiting blocks
/// dominating the latch. howFarToZero assumes that the limit of each loop test
/// is never skipped. This is a valid assumption as long as the loop exits via
/// that test. For precise results, it is the caller's responsibility to specify
/// the relevant loop exiting block using getExact(ExitingBlock, SE).
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getExact(const Loop *L, ScalarEvolution *SE,
SCEVUnionPredicate *Preds) const {
// If any exits were not computable, the loop is not computable.
if (!isComplete() || ExitNotTaken.empty())
return SE->getCouldNotCompute();
const BasicBlock *Latch = L->getLoopLatch();
// All exiting blocks we have collected must dominate the only backedge.
if (!Latch)
return SE->getCouldNotCompute();
// All exiting blocks we have gathered dominate loop's latch, so exact trip
// count is simply a minimum out of all these calculated exit counts.
SmallVector<const SCEV *, 2> Ops;
for (auto &ENT : ExitNotTaken) {
const SCEV *BECount = ENT.ExactNotTaken;
assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!");
assert(SE->DT.dominates(ENT.ExitingBlock, Latch) &&
"We should only have known counts for exiting blocks that dominate "
"latch!");
Ops.push_back(BECount);
if (Preds && !ENT.hasAlwaysTruePredicate())
Preds->add(ENT.Predicate.get());
assert((Preds || ENT.hasAlwaysTruePredicate()) &&
"Predicate should be always true!");
}
return SE->getUMinFromMismatchedTypes(Ops);
}
/// Get the exact not taken count for this loop exit.
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
ScalarEvolution *SE) const {
for (auto &ENT : ExitNotTaken)
if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
return ENT.ExactNotTaken;
return SE->getCouldNotCompute();
}
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getMax(BasicBlock *ExitingBlock,
ScalarEvolution *SE) const {
for (auto &ENT : ExitNotTaken)
if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
return ENT.MaxNotTaken;
return SE->getCouldNotCompute();
}
/// getMax - Get the max backedge taken count for the loop.
const SCEV *
ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
return !ENT.hasAlwaysTruePredicate();
};
if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax())
return SE->getCouldNotCompute();
assert((isa<SCEVCouldNotCompute>(getMax()) || isa<SCEVConstant>(getMax())) &&
"No point in having a non-constant max backedge taken count!");
return getMax();
}
bool ScalarEvolution::BackedgeTakenInfo::isMaxOrZero(ScalarEvolution *SE) const {
auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
return !ENT.hasAlwaysTruePredicate();
};
return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
}
bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
ScalarEvolution *SE) const {
if (getMax() && getMax() != SE->getCouldNotCompute() &&
SE->hasOperand(getMax(), S))
return true;
for (auto &ENT : ExitNotTaken)
if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
SE->hasOperand(ENT.ExactNotTaken, S))
return true;
return false;
}
ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
: ExactNotTaken(E), MaxNotTaken(E) {
assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
isa<SCEVConstant>(MaxNotTaken)) &&
"No point in having a non-constant max backedge taken count!");
}
ScalarEvolution::ExitLimit::ExitLimit(
const SCEV *E, const SCEV *M, bool MaxOrZero,
ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList)
: ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) {
assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
!isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
"Exact is not allowed to be less precise than Max");
assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
isa<SCEVConstant>(MaxNotTaken)) &&
"No point in having a non-constant max backedge taken count!");
for (auto *PredSet : PredSetList)
for (auto *P : *PredSet)
addPredicate(P);
}
ScalarEvolution::ExitLimit::ExitLimit(
const SCEV *E, const SCEV *M, bool MaxOrZero,
const SmallPtrSetImpl<const SCEVPredicate *> &PredSet)
: ExitLimit(E, M, MaxOrZero, {&PredSet}) {
assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
isa<SCEVConstant>(MaxNotTaken)) &&
"No point in having a non-constant max backedge taken count!");
}
ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M,
bool MaxOrZero)
: ExitLimit(E, M, MaxOrZero, None) {
assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
isa<SCEVConstant>(MaxNotTaken)) &&
"No point in having a non-constant max backedge taken count!");
}
/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
/// computable exit into a persistent ExitNotTakenInfo array.
ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo>
ExitCounts,
bool Complete, const SCEV *MaxCount, bool MaxOrZero)
: MaxAndComplete(MaxCount, Complete), MaxOrZero(MaxOrZero) {
using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
ExitNotTaken.reserve(ExitCounts.size());
std::transform(
ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken),
[&](const EdgeExitInfo &EEI) {
BasicBlock *ExitBB = EEI.first;
const ExitLimit &EL = EEI.second;
if (EL.Predicates.empty())
return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
nullptr);
std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate);
for (auto *Pred : EL.Predicates)
Predicate->add(Pred);
return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
std::move(Predicate));
});
assert((isa<SCEVCouldNotCompute>(MaxCount) || isa<SCEVConstant>(MaxCount)) &&
"No point in having a non-constant max backedge taken count!");
}
/// Invalidate this result and free the ExitNotTakenInfo array.
void ScalarEvolution::BackedgeTakenInfo::clear() {
ExitNotTaken.clear();
}
/// Compute the number of times the backedge of the specified loop will execute.
ScalarEvolution::BackedgeTakenInfo
ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
bool AllowPredicates) {
SmallVector<BasicBlock *, 8> ExitingBlocks;
L->getExitingBlocks(ExitingBlocks);
using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
SmallVector<EdgeExitInfo, 4> ExitCounts;
bool CouldComputeBECount = true;
BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
const SCEV *MustExitMaxBECount = nullptr;
const SCEV *MayExitMaxBECount = nullptr;
bool MustExitMaxOrZero = false;
// Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
// and compute maxBECount.
// Do a union of all the predicates here.
for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
BasicBlock *ExitBB = ExitingBlocks[i];
// We canonicalize untaken exits to br (constant), ignore them so that
// proving an exit untaken doesn't negatively impact our ability to reason
// about the loop as whole.
if (auto *BI = dyn_cast<BranchInst>(ExitBB->getTerminator()))
if (auto *CI = dyn_cast<ConstantInt>(BI->getCondition())) {
bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
if ((ExitIfTrue && CI->isZero()) || (!ExitIfTrue && CI->isOne()))
continue;
}
ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
assert((AllowPredicates || EL.Predicates.empty()) &&
"Predicated exit limit when predicates are not allowed!");
// 1. For each exit that can be computed, add an entry to ExitCounts.
// CouldComputeBECount is true only if all exits can be computed.
if (EL.ExactNotTaken == getCouldNotCompute())
// We couldn't compute an exact value for this exit, so
// we won't be able to compute an exact value for the loop.
CouldComputeBECount = false;
else
ExitCounts.emplace_back(ExitBB, EL);
// 2. Derive the loop's MaxBECount from each exit's max number of
// non-exiting iterations. Partition the loop exits into two kinds:
// LoopMustExits and LoopMayExits.
//
// If the exit dominates the loop latch, it is a LoopMustExit otherwise it
// is a LoopMayExit. If any computable LoopMustExit is found, then
// MaxBECount is the minimum EL.MaxNotTaken of computable
// LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
// EL.MaxNotTaken, where CouldNotCompute is considered greater than any
// computable EL.MaxNotTaken.
if (EL.MaxNotTaken != getCouldNotCompute() && Latch &&
DT.dominates(ExitBB, Latch)) {
if (!MustExitMaxBECount) {
MustExitMaxBECount = EL.MaxNotTaken;
MustExitMaxOrZero = EL.MaxOrZero;
} else {
MustExitMaxBECount =
getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken);
}
} else if (MayExitMaxBECount != getCouldNotCompute()) {
if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute())
MayExitMaxBECount = EL.MaxNotTaken;
else {
MayExitMaxBECount =
getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken);
}
}
}
const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
(MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
// The loop backedge will be taken the maximum or zero times if there's
// a single exit that must be taken the maximum or zero times.
bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
MaxBECount, MaxOrZero);
}
ScalarEvolution::ExitLimit
ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
bool AllowPredicates) {
assert(L->contains(ExitingBlock) && "Exit count for non-loop block?");
// If our exiting block does not dominate the latch, then its connection with
// loop's exit limit may be far from trivial.
const BasicBlock *Latch = L->getLoopLatch();
if (!Latch || !DT.dominates(ExitingBlock, Latch))
return getCouldNotCompute();
bool IsOnlyExit = (L->getExitingBlock() != nullptr);
Instruction *Term = ExitingBlock->getTerminator();
if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
assert(BI->isConditional() && "If unconditional, it can't be in loop!");
bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) &&
"It should have one successor in loop and one exit block!");
// Proceed to the next level to examine the exit condition expression.
return computeExitLimitFromCond(
L, BI->getCondition(), ExitIfTrue,
/*ControlsExit=*/IsOnlyExit, AllowPredicates);
}
if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) {
// For switch, make sure that there is a single exit from the loop.
BasicBlock *Exit = nullptr;
for (auto *SBB : successors(ExitingBlock))
if (!L->contains(SBB)) {
if (Exit) // Multiple exit successors.
return getCouldNotCompute();
Exit = SBB;
}
assert(Exit && "Exiting block must have at least one exit");
return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
/*ControlsExit=*/IsOnlyExit);
}
return getCouldNotCompute();
}
ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
const Loop *L, Value *ExitCond, bool ExitIfTrue,
bool ControlsExit, bool AllowPredicates) {
ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates);
return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue,
ControlsExit, AllowPredicates);
}
Optional<ScalarEvolution::ExitLimit>
ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
bool ExitIfTrue, bool ControlsExit,
bool AllowPredicates) {
(void)this->L;
(void)this->ExitIfTrue;
(void)this->AllowPredicates;
assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
this->AllowPredicates == AllowPredicates &&
"Variance in assumed invariant key components!");
auto Itr = TripCountMap.find({ExitCond, ControlsExit});
if (Itr == TripCountMap.end())
return None;
return Itr->second;
}
void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
bool ExitIfTrue,
bool ControlsExit,
bool AllowPredicates,
const ExitLimit &EL) {
assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
this->AllowPredicates == AllowPredicates &&
"Variance in assumed invariant key components!");
auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL});
assert(InsertResult.second && "Expected successful insertion!");
(void)InsertResult;
(void)ExitIfTrue;
}
ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
bool ControlsExit, bool AllowPredicates) {
if (auto MaybeEL =
Cache.find(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates))
return *MaybeEL;
ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, ExitIfTrue,
ControlsExit, AllowPredicates);
Cache.insert(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates, EL);
return EL;
}
ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
bool ControlsExit, bool AllowPredicates) {
// Check if the controlling expression for this loop is an And or Or.
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
if (BO->getOpcode() == Instruction::And) {
// Recurse on the operands of the and.
bool EitherMayExit = !ExitIfTrue;
ExitLimit EL0 = computeExitLimitFromCondCached(
Cache, L, BO->getOperand(0), ExitIfTrue,
ControlsExit && !EitherMayExit, AllowPredicates);
ExitLimit EL1 = computeExitLimitFromCondCached(
Cache, L, BO->getOperand(1), ExitIfTrue,
ControlsExit && !EitherMayExit, AllowPredicates);
// Be robust against unsimplified IR for the form "and i1 X, true"
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(1)))
return CI->isOne() ? EL0 : EL1;
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(0)))
return CI->isOne() ? EL1 : EL0;
const SCEV *BECount = getCouldNotCompute();
const SCEV *MaxBECount = getCouldNotCompute();
if (EitherMayExit) {
// Both conditions must be true for the loop to continue executing.
// Choose the less conservative count.
if (EL0.ExactNotTaken == getCouldNotCompute() ||
EL1.ExactNotTaken == getCouldNotCompute())
BECount = getCouldNotCompute();
else
BECount =
getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
if (EL0.MaxNotTaken == getCouldNotCompute())
MaxBECount = EL1.MaxNotTaken;
else if (EL1.MaxNotTaken == getCouldNotCompute())
MaxBECount = EL0.MaxNotTaken;
else
MaxBECount =
getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
} else {
// Both conditions must be true at the same time for the loop to exit.
// For now, be conservative.
if (EL0.MaxNotTaken == EL1.MaxNotTaken)
MaxBECount = EL0.MaxNotTaken;
if (EL0.ExactNotTaken == EL1.ExactNotTaken)
BECount = EL0.ExactNotTaken;
}
// There are cases (e.g. PR26207) where computeExitLimitFromCond is able
// to be more aggressive when computing BECount than when computing
// MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
// EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
// to not.
if (isa<SCEVCouldNotCompute>(MaxBECount) &&
!isa<SCEVCouldNotCompute>(BECount))
MaxBECount = getConstant(getUnsignedRangeMax(BECount));
return ExitLimit(BECount, MaxBECount, false,
{&EL0.Predicates, &EL1.Predicates});
}
if (BO->getOpcode() == Instruction::Or) {
// Recurse on the operands of the or.
bool EitherMayExit = ExitIfTrue;
ExitLimit EL0 = computeExitLimitFromCondCached(
Cache, L, BO->getOperand(0), ExitIfTrue,
ControlsExit && !EitherMayExit, AllowPredicates);
ExitLimit EL1 = computeExitLimitFromCondCached(
Cache, L, BO->getOperand(1), ExitIfTrue,
ControlsExit && !EitherMayExit, AllowPredicates);
// Be robust against unsimplified IR for the form "or i1 X, true"
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(1)))
return CI->isZero() ? EL0 : EL1;
if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(0)))
return CI->isZero() ? EL1 : EL0;
const SCEV *BECount = getCouldNotCompute();
const SCEV *MaxBECount = getCouldNotCompute();
if (EitherMayExit) {
// Both conditions must be false for the loop to continue executing.
// Choose the less conservative count.
if (EL0.ExactNotTaken == getCouldNotCompute() ||
EL1.ExactNotTaken == getCouldNotCompute())
BECount = getCouldNotCompute();
else
BECount =
getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
if (EL0.MaxNotTaken == getCouldNotCompute())
MaxBECount = EL1.MaxNotTaken;
else if (EL1.MaxNotTaken == getCouldNotCompute())
MaxBECount = EL0.MaxNotTaken;
else
MaxBECount =
getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
} else {
// Both conditions must be false at the same time for the loop to exit.
// For now, be conservative.
if (EL0.MaxNotTaken == EL1.MaxNotTaken)
MaxBECount = EL0.MaxNotTaken;
if (EL0.ExactNotTaken == EL1.ExactNotTaken)
BECount = EL0.ExactNotTaken;
}
// There are cases (e.g. PR26207) where computeExitLimitFromCond is able
// to be more aggressive when computing BECount than when computing
// MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
// EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
// to not.
if (isa<SCEVCouldNotCompute>(MaxBECount) &&
!isa<SCEVCouldNotCompute>(BECount))
MaxBECount = getConstant(getUnsignedRangeMax(BECount));
return ExitLimit(BECount, MaxBECount, false,
{&EL0.Predicates, &EL1.Predicates});
}
}
// With an icmp, it may be feasible to compute an exact backedge-taken count.
// Proceed to the next level to examine the icmp.
if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
ExitLimit EL =
computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit);
if (EL.hasFullInfo() || !AllowPredicates)
return EL;
// Try again, but use SCEV predicates this time.
return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit,
/*AllowPredicates=*/true);
}
// Check for a constant condition. These are normally stripped out by
// SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
// preserve the CFG and is temporarily leaving constant conditions
// in place.
if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
if (ExitIfTrue == !CI->getZExtValue())
// The backedge is always taken.
return getCouldNotCompute();
else
// The backedge is never taken.
return getZero(CI->getType());
}
// If it's not an integer or pointer comparison then compute it the hard way.
return computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
}
ScalarEvolution::ExitLimit
ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
ICmpInst *ExitCond,
bool ExitIfTrue,
bool ControlsExit,
bool AllowPredicates) {
// If the condition was exit on true, convert the condition to exit on false
ICmpInst::Predicate Pred;
if (!ExitIfTrue)
Pred = ExitCond->getPredicate();
else
Pred = ExitCond->getInversePredicate();
const ICmpInst::Predicate OriginalPred = Pred;
// Handle common loops like: for (X = "string"; *X; ++X)
if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
ExitLimit ItCnt =
computeLoadConstantCompareExitLimit(LI, RHS, L, Pred);
if (ItCnt.hasAnyInfo())
return ItCnt;
}
const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
// Try to evaluate any dependencies out of the loop.
LHS = getSCEVAtScope(LHS, L);
RHS = getSCEVAtScope(RHS, L);
// At this point, we would like to compute how many iterations of the
// loop the predicate will return true for these inputs.
if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
// If there is a loop-invariant, force it into the RHS.
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
}
// Simplify the operands before analyzing them.
(void)SimplifyICmpOperands(Pred, LHS, RHS);
// If we have a comparison of a chrec against a constant, try to use value
// ranges to answer this query.
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
if (AddRec->getLoop() == L) {
// Form the constant range.
ConstantRange CompRange =
ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt());
const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
}
switch (Pred) {
case ICmpInst::ICMP_NE: { // while (X != Y)
// Convert to: while (X-Y != 0)
ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
AllowPredicates);
if (EL.hasAnyInfo()) return EL;
break;
}
case ICmpInst::ICMP_EQ: { // while (X == Y)
// Convert to: while (X-Y == 0)
ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
if (EL.hasAnyInfo()) return EL;
break;
}
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_ULT: { // while (X < Y)
bool IsSigned = Pred == ICmpInst::ICMP_SLT;
ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
AllowPredicates);
if (EL.hasAnyInfo()) return EL;
break;
}
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_UGT: { // while (X > Y)
bool IsSigned = Pred == ICmpInst::ICMP_SGT;
ExitLimit EL =
howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
AllowPredicates);
if (EL.hasAnyInfo()) return EL;
break;
}
default:
break;
}
auto *ExhaustiveCount =
computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
return ExhaustiveCount;
return computeShiftCompareExitLimit(ExitCond->getOperand(0),
ExitCond->getOperand(1), L, OriginalPred);
}
ScalarEvolution::ExitLimit
ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
SwitchInst *Switch,
BasicBlock *ExitingBlock,
bool ControlsExit) {
assert(!L->contains(ExitingBlock) && "Not an exiting block!");
// Give up if the exit is the default dest of a switch.
if (Switch->getDefaultDest() == ExitingBlock)
return getCouldNotCompute();
assert(L->contains(Switch->getDefaultDest()) &&
"Default case must not exit the loop!");
const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
// while (X != Y) --> while (X-Y != 0)
ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
if (EL.hasAnyInfo())
return EL;
return getCouldNotCompute();
}
static ConstantInt *
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
ScalarEvolution &SE) {
const SCEV *InVal = SE.getConstant(C);
const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
assert(isa<SCEVConstant>(Val) &&
"Evaluation of SCEV at constant didn't fold correctly?");
return cast<SCEVConstant>(Val)->getValue();
}
/// Given an exit condition of 'icmp op load X, cst', try to see if we can
/// compute the backedge execution count.
ScalarEvolution::ExitLimit
ScalarEvolution::computeLoadConstantCompareExitLimit(
LoadInst *LI,
Constant *RHS,
const Loop *L,
ICmpInst::Predicate predicate) {
if (LI->isVolatile()) return getCouldNotCompute();
// Check to see if the loaded pointer is a getelementptr of a global.
// TODO: Use SCEV instead of manually grubbing with GEPs.
GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
if (!GEP) return getCouldNotCompute();
// Make sure that it is really a constant global we are gepping, with an
// initializer, and make sure the first IDX is really 0.
GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
!cast<Constant>(GEP->getOperand(1))->isNullValue())
return getCouldNotCompute();
// Okay, we allow one non-constant index into the GEP instruction.
Value *VarIdx = nullptr;
std::vector<Constant*> Indexes;
unsigned VarIdxNum = 0;
for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
Indexes.push_back(CI);
} else if (!isa<ConstantInt>(GEP->getOperand(i))) {
if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
VarIdx = GEP->getOperand(i);
VarIdxNum = i-2;
Indexes.push_back(nullptr);
}
// Loop-invariant loads may be a byproduct of loop optimization. Skip them.
if (!VarIdx)
return getCouldNotCompute();
// Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
// Check to see if X is a loop variant variable value now.
const SCEV *Idx = getSCEV(VarIdx);
Idx = getSCEVAtScope(Idx, L);
// We can only recognize very limited forms of loop index expressions, in
// particular, only affine AddRec's like {C1,+,C2}.
const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
!isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
!isa<SCEVConstant>(IdxExpr->getOperand(1)))
return getCouldNotCompute();
unsigned MaxSteps = MaxBruteForceIterations;
for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
ConstantInt *ItCst = ConstantInt::get(
cast<IntegerType>(IdxExpr->getType()), IterationNum);
ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
// Form the GEP offset.
Indexes[VarIdxNum] = Val;
Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
Indexes);
if (!Result) break; // Cannot compute!
// Evaluate the condition for this iteration.
Result = ConstantExpr::getICmp(predicate, Result, RHS);
if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
++NumArrayLenItCounts;
return getConstant(ItCst); // Found terminating iteration!
}
}
return getCouldNotCompute();
}
ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
if (!RHS)
return getCouldNotCompute();
const BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
return getCouldNotCompute();
const BasicBlock *Predecessor = L->getLoopPredecessor();
if (!Predecessor)
return getCouldNotCompute();
// Return true if V is of the form "LHS `shift_op` <positive constant>".
// Return LHS in OutLHS and shift_opt in OutOpCode.
auto MatchPositiveShift =
[](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
using namespace PatternMatch;
ConstantInt *ShiftAmt;
if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
OutOpCode = Instruction::LShr;
else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
OutOpCode = Instruction::AShr;
else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
OutOpCode = Instruction::Shl;
else
return false;
return ShiftAmt->getValue().isStrictlyPositive();
};
// Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
//
// loop:
// %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
// %iv.shifted = lshr i32 %iv, <positive constant>
//
// Return true on a successful match. Return the corresponding PHI node (%iv
// above) in PNOut and the opcode of the shift operation in OpCodeOut.
auto MatchShiftRecurrence =
[&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
Optional<Instruction::BinaryOps> PostShiftOpCode;
{
Instruction::BinaryOps OpC;
Value *V;
// If we encounter a shift instruction, "peel off" the shift operation,
// and remember that we did so. Later when we inspect %iv's backedge
// value, we will make sure that the backedge value uses the same
// operation.
//
// Note: the peeled shift operation does not have to be the same
// instruction as the one feeding into the PHI's backedge value. We only
// really care about it being the same *kind* of shift instruction --
// that's all that is required for our later inferences to hold.
if (MatchPositiveShift(LHS, V, OpC)) {
PostShiftOpCode = OpC;
LHS = V;
}
}
PNOut = dyn_cast<PHINode>(LHS);
if (!PNOut || PNOut->getParent() != L->getHeader())
return false;
Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
Value *OpLHS;
return
// The backedge value for the PHI node must be a shift by a positive
// amount
MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
// of the PHI node itself
OpLHS == PNOut &&
// and the kind of shift should be match the kind of shift we peeled
// off, if any.
(!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
};
PHINode *PN;
Instruction::BinaryOps OpCode;
if (!MatchShiftRecurrence(LHS, PN, OpCode))
return getCouldNotCompute();
const DataLayout &DL = getDataLayout();
// The key rationale for this optimization is that for some kinds of shift
// recurrences, the value of the recurrence "stabilizes" to either 0 or -1
// within a finite number of iterations. If the condition guarding the
// backedge (in the sense that the backedge is taken if the condition is true)
// is false for the value the shift recurrence stabilizes to, then we know
// that the backedge is taken only a finite number of times.
ConstantInt *StableValue = nullptr;
switch (OpCode) {
default:
llvm_unreachable("Impossible case!");
case Instruction::AShr: {
// {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
// bitwidth(K) iterations.
Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
KnownBits Known = computeKnownBits(FirstValue, DL, 0, nullptr,
Predecessor->getTerminator(), &DT);
auto *Ty = cast<IntegerType>(RHS->getType());
if (Known.isNonNegative())
StableValue = ConstantInt::get(Ty, 0);
else if (Known.isNegative())
StableValue = ConstantInt::get(Ty, -1, true);
else
return getCouldNotCompute();
break;
}
case Instruction::LShr:
case Instruction::Shl:
// Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
// stabilize to 0 in at most bitwidth(K) iterations.
StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
break;
}
auto *Result =
ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
assert(Result->getType()->isIntegerTy(1) &&
"Otherwise cannot be an operand to a branch instruction");
if (Result->isZeroValue()) {
unsigned BitWidth = getTypeSizeInBits(RHS->getType());
const SCEV *UpperBound =
getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
return ExitLimit(getCouldNotCompute(), UpperBound, false);
}
return getCouldNotCompute();
}
/// Return true if we can constant fold an instruction of the specified type,
/// assuming that all operands were constants.
static bool CanConstantFold(const Instruction *I) {
if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
isa<LoadInst>(I) || isa<ExtractValueInst>(I))
return true;
if (const CallInst *CI = dyn_cast<CallInst>(I))
if (const Function *F = CI->getCalledFunction())
return canConstantFoldCallTo(CI, F);
return false;
}
/// Determine whether this instruction can constant evolve within this loop
/// assuming its operands can all constant evolve.
static bool canConstantEvolve(Instruction *I, const Loop *L) {
// An instruction outside of the loop can't be derived from a loop PHI.
if (!L->contains(I)) return false;
if (isa<PHINode>(I)) {
// We don't currently keep track of the control flow needed to evaluate
// PHIs, so we cannot handle PHIs inside of loops.
return L->getHeader() == I->getParent();
}
// If we won't be able to constant fold this expression even if the operands
// are constants, bail early.
return CanConstantFold(I);
}
/// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
/// recursing through each instruction operand until reaching a loop header phi.
static PHINode *
getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
DenseMap<Instruction *, PHINode *> &PHIMap,
unsigned Depth) {
if (Depth > MaxConstantEvolvingDepth)
return nullptr;
// Otherwise, we can evaluate this instruction if all of its operands are
// constant or derived from a PHI node themselves.
PHINode *PHI = nullptr;
for (Value *Op : UseInst->operands()) {
if (isa<Constant>(Op)) continue;
Instruction *OpInst = dyn_cast<Instruction>(Op);
if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
PHINode *P = dyn_cast<PHINode>(OpInst);
if (!P)
// If this operand is already visited, reuse the prior result.
// We may have P != PHI if this is the deepest point at which the
// inconsistent paths meet.
P = PHIMap.lookup(OpInst);
if (!P) {
// Recurse and memoize the results, whether a phi is found or not.
// This recursive call invalidates pointers into PHIMap.
P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1);
PHIMap[OpInst] = P;
}
if (!P)
return nullptr; // Not evolving from PHI
if (PHI && PHI != P)
return nullptr; // Evolving from multiple different PHIs.
PHI = P;
}
// This is a expression evolving from a constant PHI!
return PHI;
}
/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
/// in the loop that V is derived from. We allow arbitrary operations along the
/// way, but the operands of an operation must either be constants or a value
/// derived from a constant PHI. If this expression does not fit with these
/// constraints, return null.
static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
Instruction *I = dyn_cast<Instruction>(V);
if (!I || !canConstantEvolve(I, L)) return nullptr;
if (PHINode *PN = dyn_cast<PHINode>(I))
return PN;
// Record non-constant instructions contained by the loop.
DenseMap<Instruction *, PHINode *> PHIMap;
return getConstantEvolvingPHIOperands(I, L, PHIMap, 0);
}
/// EvaluateExpression - Given an expression that passes the
/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
/// in the loop has the value PHIVal. If we can't fold this expression for some
/// reason, return null.
static Constant *EvaluateExpression(Value *V, const Loop *L,
DenseMap<Instruction *, Constant *> &Vals,
const DataLayout &DL,
const TargetLibraryInfo *TLI) {
// Convenient constant check, but redundant for recursive calls.
if (Constant *C = dyn_cast<Constant>(V)) return C;
Instruction *I = dyn_cast<Instruction>(V);
if (!I) return nullptr;
if (Constant *C = Vals.lookup(I)) return C;
// An instruction inside the loop depends on a value outside the loop that we
// weren't given a mapping for, or a value such as a call inside the loop.
if (!canConstantEvolve(I, L)) return nullptr;
// An unmapped PHI can be due to a branch or another loop inside this loop,
// or due to this not being the initial iteration through a loop where we
// couldn't compute the evolution of this particular PHI last time.
if (isa<PHINode>(I)) return nullptr;
std::vector<Constant*> Operands(I->getNumOperands());
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
if (!Operand) {
Operands[i] = dyn_cast<Constant>(I->getOperand(i));
if (!Operands[i]) return nullptr;
continue;
}
Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
Vals[Operand] = C;
if (!C) return nullptr;
Operands[i] = C;
}
if (CmpInst *CI = dyn_cast<CmpInst>(I))
return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
Operands[1], DL, TLI);
if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
if (!LI->isVolatile())
return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
}
return ConstantFoldInstOperands(I, Operands, DL, TLI);
}
// If every incoming value to PN except the one for BB is a specific Constant,
// return that, else return nullptr.
static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
Constant *IncomingVal = nullptr;
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
if (PN->getIncomingBlock(i) == BB)
continue;
auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
if (!CurrentVal)
return nullptr;
if (IncomingVal != CurrentVal) {
if (IncomingVal)
return nullptr;
IncomingVal = CurrentVal;
}
}
return IncomingVal;
}
/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
/// in the header of its containing loop, we know the loop executes a
/// constant number of times, and the PHI node is just a recurrence
/// involving constants, fold it.
Constant *
ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
const APInt &BEs,
const Loop *L) {
auto I = ConstantEvolutionLoopExitValue.find(PN);
if (I != ConstantEvolutionLoopExitValue.end())
return I->second;
if (BEs.ugt(MaxBruteForceIterations))
return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
DenseMap<Instruction *, Constant *> CurrentIterVals;
BasicBlock *Header = L->getHeader();
assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
return nullptr;
for (PHINode &PHI : Header->phis()) {
if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
CurrentIterVals[&PHI] = StartCST;
}
if (!CurrentIterVals.count(PN))
return RetVal = nullptr;
Value *BEValue = PN->getIncomingValueForBlock(Latch);
// Execute the loop symbolically to determine the exit value.
assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&
"BEs is <= MaxBruteForceIterations which is an 'unsigned'!");
unsigned NumIterations = BEs.getZExtValue(); // must be in range
unsigned IterationNum = 0;
const DataLayout &DL = getDataLayout();
for (; ; ++IterationNum) {
if (IterationNum == NumIterations)
return RetVal = CurrentIterVals[PN]; // Got exit value!
// Compute the value of the PHIs for the next iteration.
// EvaluateExpression adds non-phi values to the CurrentIterVals map.
DenseMap<Instruction *, Constant *> NextIterVals;
Constant *NextPHI =
EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
if (!NextPHI)
return nullptr; // Couldn't evaluate!
NextIterVals[PN] = NextPHI;
bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
// Also evaluate the other PHI nodes. However, we don't get to stop if we
// cease to be able to evaluate one of them or if they stop evolving,
// because that doesn't necessarily prevent us from computing PN.
SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
for (const auto &I : CurrentIterVals) {
PHINode *PHI = dyn_cast<PHINode>(I.first);
if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
PHIsToCompute.emplace_back(PHI, I.second);
}
// We use two distinct loops because EvaluateExpression may invalidate any
// iterators into CurrentIterVals.
for (const auto &I : PHIsToCompute) {
PHINode *PHI = I.first;
Constant *&NextPHI = NextIterVals[PHI];
if (!NextPHI) { // Not already computed.
Value *BEValue = PHI->getIncomingValueForBlock(Latch);
NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
}
if (NextPHI != I.second)
StoppedEvolving = false;
}
// If all entries in CurrentIterVals == NextIterVals then we can stop
// iterating, the loop can't continue to change.
if (StoppedEvolving)
return RetVal = CurrentIterVals[PN];
CurrentIterVals.swap(NextIterVals);
}
}
const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
Value *Cond,
bool ExitWhen) {
PHINode *PN = getConstantEvolvingPHI(Cond, L);
if (!PN) return getCouldNotCompute();
// If the loop is canonicalized, the PHI will have exactly two entries.
// That's the only form we support here.
if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
DenseMap<Instruction *, Constant *> CurrentIterVals;
BasicBlock *Header = L->getHeader();
assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
BasicBlock *Latch = L->getLoopLatch();
assert(Latch && "Should follow from NumIncomingValues == 2!");
for (PHINode &PHI : Header->phis()) {
if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
CurrentIterVals[&PHI] = StartCST;
}
if (!CurrentIterVals.count(PN))
return getCouldNotCompute();
// Okay, we find a PHI node that defines the trip count of this loop. Execute
// the loop symbolically to determine when the condition gets a value of
// "ExitWhen".
unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
const DataLayout &DL = getDataLayout();
for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
auto *CondVal = dyn_cast_or_null<ConstantInt>(
EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
// Couldn't symbolically evaluate.
if (!CondVal) return getCouldNotCompute();
if (CondVal->getValue() == uint64_t(ExitWhen)) {
++NumBruteForceTripCountsComputed;
return getConstant(Type::getInt32Ty(getContext()), IterationNum);
}
// Update all the PHI nodes for the next iteration.
DenseMap<Instruction *, Constant *> NextIterVals;
// Create a list of which PHIs we need to compute. We want to do this before
// calling EvaluateExpression on them because that may invalidate iterators
// into CurrentIterVals.
SmallVector<PHINode *, 8> PHIsToCompute;
for (const auto &I : CurrentIterVals) {
PHINode *PHI = dyn_cast<PHINode>(I.first);
if (!PHI || PHI->getParent() != Header) continue;
PHIsToCompute.push_back(PHI);
}
for (PHINode *PHI : PHIsToCompute) {
Constant *&NextPHI = NextIterVals[PHI];
if (NextPHI) continue; // Already computed!
Value *BEValue = PHI->getIncomingValueForBlock(Latch);
NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
}
CurrentIterVals.swap(NextIterVals);
}
// Too many iterations were needed to evaluate.
return getCouldNotCompute();
}
const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
ValuesAtScopes[V];
// Check to see if we've folded this expression at this loop before.
for (auto &LS : Values)
if (LS.first == L)
return LS.second ? LS.second : V;
Values.emplace_back(L, nullptr);
// Otherwise compute it.
const SCEV *C = computeSCEVAtScope(V, L);
for (auto &LS : reverse(ValuesAtScopes[V]))
if (LS.first == L) {
LS.second = C;
break;
}
return C;
}
/// This builds up a Constant using the ConstantExpr interface. That way, we
/// will return Constants for objects which aren't represented by a
/// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
/// Returns NULL if the SCEV isn't representable as a Constant.
static Constant *BuildConstantFromSCEV(const SCEV *V) {
switch (static_cast<SCEVTypes>(V->getSCEVType())) {
case scCouldNotCompute:
case scAddRecExpr:
break;
case scConstant:
return cast<SCEVConstant>(V)->getValue();
case scUnknown:
return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
case scSignExtend: {
const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
return ConstantExpr::getSExt(CastOp, SS->getType());
break;
}
case scZeroExtend: {
const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
return ConstantExpr::getZExt(CastOp, SZ->getType());
break;
}
case scTruncate: {
const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
return ConstantExpr::getTrunc(CastOp, ST->getType());
break;
}
case scAddExpr: {
const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
unsigned AS = PTy->getAddressSpace();
Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
C = ConstantExpr::getBitCast(C, DestPtrTy);
}
for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
if (!C2) return nullptr;
// First pointer!
if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
unsigned AS = C2->getType()->getPointerAddressSpace();
std::swap(C, C2);
Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
// The offsets have been converted to bytes. We can add bytes to an
// i8* by GEP with the byte count in the first index.
C = ConstantExpr::getBitCast(C, DestPtrTy);
}
// Don't bother trying to sum two pointers. We probably can't
// statically compute a load that results from it anyway.
if (C2->getType()->isPointerTy())
return nullptr;
if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
if (PTy->getElementType()->isStructTy())
C2 = ConstantExpr::getIntegerCast(
C2, Type::getInt32Ty(C->getContext()), true);
C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
} else
C = ConstantExpr::getAdd(C, C2);
}
return C;
}
break;
}
case scMulExpr: {
const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
// Don't bother with pointers at all.
if (C->getType()->isPointerTy()) return nullptr;
for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
if (!C2 || C2->getType()->isPointerTy()) return nullptr;
C = ConstantExpr::getMul(C, C2);
}
return C;
}
break;
}
case scUDivExpr: {
const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
if (LHS->getType() == RHS->getType())
return ConstantExpr::getUDiv(LHS, RHS);
break;
}
case scSMaxExpr:
case scUMaxExpr:
case scSMinExpr:
case scUMinExpr:
break; // TODO: smax, umax, smin, umax.
}
return nullptr;
}
const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
if (isa<SCEVConstant>(V)) return V;
// If this instruction is evolved from a constant-evolving PHI, compute the
// exit value from the loop without using SCEVs.
if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
if (PHINode *PN = dyn_cast<PHINode>(I)) {
const Loop *LI = this->LI[I->getParent()];
// Looking for loop exit value.
if (LI && LI->getParentLoop() == L &&
PN->getParent() == LI->getHeader()) {
// Okay, there is no closed form solution for the PHI node. Check
// to see if the loop that contains it has a known backedge-taken
// count. If so, we may be able to force computation of the exit
// value.
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
// This trivial case can show up in some degenerate cases where
// the incoming IR has not yet been fully simplified.
if (BackedgeTakenCount->isZero()) {
Value *InitValue = nullptr;
bool MultipleInitValues = false;
for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
if (!LI->contains(PN->getIncomingBlock(i))) {
if (!InitValue)
InitValue = PN->getIncomingValue(i);
else if (InitValue != PN->getIncomingValue(i)) {
MultipleInitValues = true;
break;
}
}
}
if (!MultipleInitValues && InitValue)
return getSCEV(InitValue);
}
// Do we have a loop invariant value flowing around the backedge
// for a loop which must execute the backedge?
if (!isa<SCEVCouldNotCompute>(BackedgeTakenCount) &&
isKnownPositive(BackedgeTakenCount) &&
PN->getNumIncomingValues() == 2) {
unsigned InLoopPred = LI->contains(PN->getIncomingBlock(0)) ? 0 : 1;
const SCEV *OnBackedge = getSCEV(PN->getIncomingValue(InLoopPred));
if (IsAvailableOnEntry(LI, DT, OnBackedge, PN->getParent()))
return OnBackedge;
}
if (auto *BTCC = dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
// Okay, we know how many times the containing loop executes. If
// this is a constant evolving PHI node, get the final value at
// the specified iteration number.
Constant *RV =
getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
if (RV) return getSCEV(RV);
}
}
// If there is a single-input Phi, evaluate it at our scope. If we can
// prove that this replacement does not break LCSSA form, use new value.
if (PN->getNumOperands() == 1) {
const SCEV *Input = getSCEV(PN->getOperand(0));
const SCEV *InputAtScope = getSCEVAtScope(Input, L);
// TODO: We can generalize it using LI.replacementPreservesLCSSAForm,
// for the simplest case just support constants.
if (isa<SCEVConstant>(InputAtScope)) return InputAtScope;
}
}
// Okay, this is an expression that we cannot symbolically evaluate
// into a SCEV. Check to see if it's possible to symbolically evaluate
// the arguments into constants, and if so, try to constant propagate the
// result. This is particularly useful for computing loop exit values.
if (CanConstantFold(I)) {
SmallVector<Constant *, 4> Operands;
bool MadeImprovement = false;
for (Value *Op : I->operands()) {
if (Constant *C = dyn_cast<Constant>(Op)) {
Operands.push_back(C);
continue;
}
// If any of the operands is non-constant and if they are
// non-integer and non-pointer, don't even try to analyze them
// with scev techniques.
if (!isSCEVable(Op->getType()))
return V;
const SCEV *OrigV = getSCEV(Op);
const SCEV *OpV = getSCEVAtScope(OrigV, L);
MadeImprovement |= OrigV != OpV;
Constant *C = BuildConstantFromSCEV(OpV);
if (!C) return V;
if (C->getType() != Op->getType())
C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
Op->getType(),
false),
C, Op->getType());
Operands.push_back(C);
}
// Check to see if getSCEVAtScope actually made an improvement.
if (MadeImprovement) {
Constant *C = nullptr;
const DataLayout &DL = getDataLayout();
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
Operands[1], DL, &TLI);
else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
if (!LI->isVolatile())
C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
} else
C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
if (!C) return V;
return getSCEV(C);
}
}
}
// This is some other type of SCEVUnknown, just return it.
return V;
}
if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
// Avoid performing the look-up in the common case where the specified
// expression has no loop-variant portions.
for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
if (OpAtScope != Comm->getOperand(i)) {
// Okay, at least one of these operands is loop variant but might be
// foldable. Build a new instance of the folded commutative expression.
SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
Comm->op_begin()+i);
NewOps.push_back(OpAtScope);
for (++i; i != e; ++i) {
OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
NewOps.push_back(OpAtScope);
}
if (isa<SCEVAddExpr>(Comm))
return getAddExpr(NewOps, Comm->getNoWrapFlags());
if (isa<SCEVMulExpr>(Comm))
return getMulExpr(NewOps, Comm->getNoWrapFlags());
if (isa<SCEVMinMaxExpr>(Comm))
return getMinMaxExpr(Comm->getSCEVType(), NewOps);
llvm_unreachable("Unknown commutative SCEV type!");
}
}
// If we got here, all operands are loop invariant.
return Comm;
}
if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
if (LHS == Div->getLHS() && RHS == Div->getRHS())
return Div; // must be loop invariant
return getUDivExpr(LHS, RHS);
}
// If this is a loop recurrence for a loop that does not contain L, then we
// are dealing with the final value computed by the loop.
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
// First, attempt to evaluate each operand.
// Avoid performing the look-up in the common case where the specified
// expression has no loop-variant portions.
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
if (OpAtScope == AddRec->getOperand(i))
continue;
// Okay, at least one of these operands is loop variant but might be
// foldable. Build a new instance of the folded commutative expression.
SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
AddRec->op_begin()+i);
NewOps.push_back(OpAtScope);
for (++i; i != e; ++i)
NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
const SCEV *FoldedRec =
getAddRecExpr(NewOps, AddRec->getLoop(),
AddRec->getNoWrapFlags(SCEV::FlagNW));
AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
// The addrec may be folded to a nonrecurrence, for example, if the
// induction variable is multiplied by zero after constant folding. Go
// ahead and return the folded value.
if (!AddRec)
return FoldedRec;
break;
}
// If the scope is outside the addrec's loop, evaluate it by using the
// loop exit value of the addrec.
if (!AddRec->getLoop()->contains(L)) {
// To evaluate this recurrence, we need to know how many times the AddRec
// loop iterates. Compute this now.
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
// Then, evaluate the AddRec.
return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
}
return AddRec;
}
if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
if (Op == Cast->getOperand())
return Cast; // must be loop invariant
return getZeroExtendExpr(Op, Cast->getType());
}
if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
if (Op == Cast->getOperand())
return Cast; // must be loop invariant
return getSignExtendExpr(Op, Cast->getType());
}
if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
if (Op == Cast->getOperand())
return Cast; // must be loop invariant
return getTruncateExpr(Op, Cast->getType());
}
llvm_unreachable("Unknown SCEV type!");
}
const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
return getSCEVAtScope(getSCEV(V), L);
}
const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const {
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S))
return stripInjectiveFunctions(ZExt->getOperand());
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S))
return stripInjectiveFunctions(SExt->getOperand());
return S;
}
/// Finds the minimum unsigned root of the following equation:
///
/// A * X = B (mod N)
///
/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
/// A and B isn't important.
///
/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
ScalarEvolution &SE) {
uint32_t BW = A.getBitWidth();
assert(BW == SE.getTypeSizeInBits(B->getType()));
assert(A != 0 && "A must be non-zero.");
// 1. D = gcd(A, N)
//
// The gcd of A and N may have only one prime factor: 2. The number of
// trailing zeros in A is its multiplicity
uint32_t Mult2 = A.countTrailingZeros();
// D = 2^Mult2
// 2. Check if B is divisible by D.
//
// B is divisible by D if and only if the multiplicity of prime factor 2 for B
// is not less than multiplicity of this prime factor for D.
if (SE.GetMinTrailingZeros(B) < Mult2)
return SE.getCouldNotCompute();
// 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
// modulo (N / D).
//
// If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
// (N / D) in general. The inverse itself always fits into BW bits, though,
// so we immediately truncate it.
APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
APInt Mod(BW + 1, 0);
Mod.setBit(BW - Mult2); // Mod = N / D
APInt I = AD.multiplicativeInverse(Mod).trunc(BW);
// 4. Compute the minimum unsigned root of the equation:
// I * (B / D) mod (N / D)
// To simplify the computation, we factor out the divide by D:
// (I * B mod N) / D
const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
}
/// For a given quadratic addrec, generate coefficients of the corresponding
/// quadratic equation, multiplied by a common value to ensure that they are
/// integers.
/// The returned value is a tuple { A, B, C, M, BitWidth }, where
/// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C
/// were multiplied by, and BitWidth is the bit width of the original addrec
/// coefficients.
/// This function returns None if the addrec coefficients are not compile-
/// time constants.
static Optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>>
GetQuadraticEquation(const SCEVAddRecExpr *AddRec) {
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: "
<< *AddRec << '\n');
// We currently can only solve this if the coefficients are constants.
if (!LC || !MC || !NC) {
LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n");
return None;
}
APInt L = LC->getAPInt();
APInt M = MC->getAPInt();
APInt N = NC->getAPInt();
assert(!N.isNullValue() && "This is not a quadratic addrec");
unsigned BitWidth = LC->getAPInt().getBitWidth();
unsigned NewWidth = BitWidth + 1;
LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: "
<< BitWidth << '\n');
// The sign-extension (as opposed to a zero-extension) here matches the
// extension used in SolveQuadraticEquationWrap (with the same motivation).
N = N.sext(NewWidth);
M = M.sext(NewWidth);
L = L.sext(NewWidth);
// The increments are M, M+N, M+2N, ..., so the accumulated values are
// L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is,
// L+M, L+2M+N, L+3M+3N, ...
// After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N.
//
// The equation Acc = 0 is then
// L + nM + n(n-1)/2 N = 0, or 2L + 2M n + n(n-1) N = 0.
// In a quadratic form it becomes:
// N n^2 + (2M-N) n + 2L = 0.
APInt A = N;
APInt B = 2 * M - A;
APInt C = 2 * L;
APInt T = APInt(NewWidth, 2);
LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << B
<< "x + " << C << ", coeff bw: " << NewWidth
<< ", multiplied by " << T << '\n');
return std::make_tuple(A, B, C, T, BitWidth);
}
/// Helper function to compare optional APInts:
/// (a) if X and Y both exist, return min(X, Y),
/// (b) if neither X nor Y exist, return None,
/// (c) if exactly one of X and Y exists, return that value.
static Optional<APInt> MinOptional(Optional<APInt> X, Optional<APInt> Y) {
if (X.hasValue() && Y.hasValue()) {
unsigned W = std::max(X->getBitWidth(), Y->getBitWidth());
APInt XW = X->sextOrSelf(W);
APInt YW = Y->sextOrSelf(W);
return XW.slt(YW) ? *X : *Y;
}
if (!X.hasValue() && !Y.hasValue())
return None;
return X.hasValue() ? *X : *Y;
}
/// Helper function to truncate an optional APInt to a given BitWidth.
/// When solving addrec-related equations, it is preferable to return a value
/// that has the same bit width as the original addrec's coefficients. If the
/// solution fits in the original bit width, truncate it (except for i1).
/// Returning a value of a different bit width may inhibit some optimizations.
///
/// In general, a solution to a quadratic equation generated from an addrec
/// may require BW+1 bits, where BW is the bit width of the addrec's
/// coefficients. The reason is that the coefficients of the quadratic
/// equation are BW+1 bits wide (to avoid truncation when converting from
/// the addrec to the equation).
static Optional<APInt> TruncIfPossible(Optional<APInt> X, unsigned BitWidth) {
if (!X.hasValue())
return None;
unsigned W = X->getBitWidth();
if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth))
return X->trunc(BitWidth);
return X;
}
/// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n
/// iterations. The values L, M, N are assumed to be signed, and they
/// should all have the same bit widths.
/// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW,
/// where BW is the bit width of the addrec's coefficients.
/// If the calculated value is a BW-bit integer (for BW > 1), it will be
/// returned as such, otherwise the bit width of the returned value may
/// be greater than BW.
///
/// This function returns None if
/// (a) the addrec coefficients are not constant, or
/// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases
/// like x^2 = 5, no integer solutions exist, in other cases an integer
/// solution may exist, but SolveQuadraticEquationWrap may fail to find it.
static Optional<APInt>
SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
APInt A, B, C, M;
unsigned BitWidth;
auto T = GetQuadraticEquation(AddRec);
if (!T.hasValue())
return None;
std::tie(A, B, C, M, BitWidth) = *T;
LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n");
Optional<APInt> X = APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth+1);
if (!X.hasValue())
return None;
ConstantInt *CX = ConstantInt::get(SE.getContext(), *X);
ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE);
if (!V->isZero())
return None;
return TruncIfPossible(X, BitWidth);
}
/// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n
/// iterations. The values M, N are assumed to be signed, and they
/// should all have the same bit widths.
/// Find the least n such that c(n) does not belong to the given range,
/// while c(n-1) does.
///
/// This function returns None if
/// (a) the addrec coefficients are not constant, or
/// (b) SolveQuadraticEquationWrap was unable to find a solution for the
/// bounds of the range.
static Optional<APInt>
SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec,
const ConstantRange &Range, ScalarEvolution &SE) {
assert(AddRec->getOperand(0)->isZero() &&
"Starting value of addrec should be 0");
LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range "
<< Range << ", addrec " << *AddRec << '\n');
// This case is handled in getNumIterationsInRange. Here we can assume that
// we start in the range.
assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) &&
"Addrec's initial value should be in range");
APInt A, B, C, M;
unsigned BitWidth;
auto T = GetQuadraticEquation(AddRec);
if (!T.hasValue())
return None;
// Be careful about the return value: there can be two reasons for not
// returning an actual number. First, if no solutions to the equations
// were found, and second, if the solutions don't leave the given range.
// The first case means that the actual solution is "unknown", the second
// means that it's known, but not valid. If the solution is unknown, we
// cannot make any conclusions.
// Return a pair: the optional solution and a flag indicating if the
// solution was found.
auto SolveForBoundary = [&](APInt Bound) -> std::pair<Optional<APInt>,bool> {
// Solve for signed overflow and unsigned overflow, pick the lower
// solution.
LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary "
<< Bound << " (before multiplying by " << M << ")\n");
Bound *= M; // The quadratic equation multiplier.
Optional<APInt> SO = None;
if (BitWidth > 1) {
LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
"signed overflow\n");
SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth);
}
LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
"unsigned overflow\n");
Optional<APInt> UO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound,
BitWidth+1);
auto LeavesRange = [&] (const APInt &X) {
ConstantInt *C0 = ConstantInt::get(SE.getContext(), X);
ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE);
if (Range.contains(V0->getValue()))
return false;
// X should be at least 1, so X-1 is non-negative.
ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1);
ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE);
if (Range.contains(V1->getValue()))
return true;
return false;
};
// If SolveQuadraticEquationWrap returns None, it means that there can
// be a solution, but the function failed to find it. We cannot treat it
// as "no solution".
if (!SO.hasValue() || !UO.hasValue())
return { None, false };
// Check the smaller value first to see if it leaves the range.
// At this point, both SO and UO must have values.
Optional<APInt> Min = MinOptional(SO, UO);
if (LeavesRange(*Min))
return { Min, true };
Optional<APInt> Max = Min == SO ? UO : SO;
if (LeavesRange(*Max))
return { Max, true };
// Solutions were found, but were eliminated, hence the "true".
return { None, true };
};
std::tie(A, B, C, M, BitWidth) = *T;
// Lower bound is inclusive, subtract 1 to represent the exiting value.
APInt Lower = Range.getLower().sextOrSelf(A.getBitWidth()) - 1;
APInt Upper = Range.getUpper().sextOrSelf(A.getBitWidth());
auto SL = SolveForBoundary(Lower);
auto SU = SolveForBoundary(Upper);
// If any of the solutions was unknown, no meaninigful conclusions can
// be made.
if (!SL.second || !SU.second)
return None;
// Claim: The correct solution is not some value between Min and Max.
//
// Justification: Assuming that Min and Max are different values, one of
// them is when the first signed overflow happens, the other is when the
// first unsigned overflow happens. Crossing the range boundary is only
// possible via an overflow (treating 0 as a special case of it, modeling
// an overflow as crossing k*2^W for some k).
//
// The interesting case here is when Min was eliminated as an invalid
// solution, but Max was not. The argument is that if there was another
// overflow between Min and Max, it would also have been eliminated if
// it was considered.
//
// For a given boundary, it is possible to have two overflows of the same
// type (signed/unsigned) without having the other type in between: this
// can happen when the vertex of the parabola is between the iterations
// corresponding to the overflows. This is only possible when the two
// overflows cross k*2^W for the same k. In such case, if the second one
// left the range (and was the first one to do so), the first overflow
// would have to enter the range, which would mean that either we had left
// the range before or that we started outside of it. Both of these cases
// are contradictions.
//
// Claim: In the case where SolveForBoundary returns None, the correct
// solution is not some value between the Max for this boundary and the
// Min of the other boundary.
//
// Justification: Assume that we had such Max_A and Min_B corresponding
// to range boundaries A and B and such that Max_A < Min_B. If there was
// a solution between Max_A and Min_B, it would have to be caused by an
// overflow corresponding to either A or B. It cannot correspond to B,
// since Min_B is the first occurrence of such an overflow. If it
// corresponded to A, it would have to be either a signed or an unsigned
// overflow that is larger than both eliminated overflows for A. But
// between the eliminated overflows and this overflow, the values would
// cover the entire value space, thus crossing the other boundary, which
// is a contradiction.
return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth);
}
ScalarEvolution::ExitLimit
ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
bool AllowPredicates) {
// This is only used for loops with a "x != y" exit test. The exit condition
// is now expressed as a single expression, V = x-y. So the exit test is
// effectively V != 0. We know and take advantage of the fact that this
// expression only being used in a comparison by zero context.
SmallPtrSet<const SCEVPredicate *, 4> Predicates;
// If the value is a constant
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
// If the value is already zero, the branch will execute zero times.
if (C->getValue()->isZero()) return C;
return getCouldNotCompute(); // Otherwise it will loop infinitely.
}
const SCEVAddRecExpr *AddRec =
dyn_cast<SCEVAddRecExpr>(stripInjectiveFunctions(V));
if (!AddRec && AllowPredicates)
// Try to make this an AddRec using runtime tests, in the first X
// iterations of this loop, where X is the SCEV expression found by the
// algorithm below.
AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
if (!AddRec || AddRec->getLoop() != L)
return getCouldNotCompute();
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
// the quadratic equation to solve it.
if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
// We can only use this value if the chrec ends up with an exact zero
// value at this index. When solving for "X*X != 5", for example, we
// should not accept a root of 2.
if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) {
const auto *R = cast<SCEVConstant>(getConstant(S.getValue()));
return ExitLimit(R, R, false, Predicates);
}
return getCouldNotCompute();
}
// Otherwise we can only handle this if it is affine.
if (!AddRec->isAffine())
return getCouldNotCompute();
// If this is an affine expression, the execution count of this branch is
// the minimum unsigned root of the following equation:
//
// Start + Step*N = 0 (mod 2^BW)
//
// equivalent to:
//
// Step*N = -Start (mod 2^BW)
//
// where BW is the common bit width of Start and Step.
// Get the initial value for the loop.
const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
// For now we handle only constant steps.
//
// TODO: Handle a nonconstant Step given AddRec<NUW>. If the
// AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
// to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
// We have not yet seen any such cases.
const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
if (!StepC || StepC->getValue()->isZero())
return getCouldNotCompute();
// For positive steps (counting up until unsigned overflow):
// N = -Start/Step (as unsigned)
// For negative steps (counting down to zero):
// N = Start/-Step
// First compute the unsigned distance from zero in the direction of Step.
bool CountDown = StepC->getAPInt().isNegative();
const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
// Handle unitary steps, which cannot wraparound.
// 1*N = -Start; -1*N = Start (mod 2^BW), so:
// N = Distance (as unsigned)
if (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne()) {
APInt MaxBECount = getUnsignedRangeMax(Distance);
// When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
// we end up with a loop whose backedge-taken count is n - 1. Detect this
// case, and see if we can improve the bound.
//
// Explicitly handling this here is necessary because getUnsignedRange
// isn't context-sensitive; it doesn't know that we only care about the
// range inside the loop.
const SCEV *Zero = getZero(Distance->getType());
const SCEV *One = getOne(Distance->getType());
const SCEV *DistancePlusOne = getAddExpr(Distance, One);
if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
// If Distance + 1 doesn't overflow, we can compute the maximum distance
// as "unsigned_max(Distance + 1) - 1".
ConstantRange CR = getUnsignedRange(DistancePlusOne);
MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
}
return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
}
// If the condition controls loop exit (the loop exits only if the expression
// is true) and the addition is no-wrap we can use unsigned divide to
// compute the backedge count. In this case, the step may not divide the
// distance, but we don't care because if the condition is "missed" the loop
// will have undefined behavior due to wrapping.
if (ControlsExit && AddRec->hasNoSelfWrap() &&
loopHasNoAbnormalExits(AddRec->getLoop())) {
const SCEV *Exact =
getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
const SCEV *Max =
Exact == getCouldNotCompute()
? Exact
: getConstant(getUnsignedRangeMax(Exact));
return ExitLimit(Exact, Max, false, Predicates);
}
// Solve the general equation.
const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(),
getNegativeSCEV(Start), *this);
const SCEV *M = E == getCouldNotCompute()
? E
: getConstant(getUnsignedRangeMax(E));
return ExitLimit(E, M, false, Predicates);
}
ScalarEvolution::ExitLimit
ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
// Loops that look like: while (X == 0) are very strange indeed. We don't
// handle them yet except for the trivial case. This could be expanded in the
// future as needed.
// If the value is a constant, check to see if it is known to be non-zero
// already. If so, the backedge will execute zero times.
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
if (!C->getValue()->isZero())
return getZero(C->getType());
return getCouldNotCompute(); // Otherwise it will loop infinitely.
}
// We could implement others, but I really doubt anyone writes loops like
// this, and if they did, they would already be constant folded.
return getCouldNotCompute();
}
std::pair<BasicBlock *, BasicBlock *>
ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
// If the block has a unique predecessor, then there is no path from the
// predecessor to the block that does not go through the direct edge
// from the predecessor to the block.
if (BasicBlock *Pred = BB->getSinglePredecessor())
return {Pred, BB};
// A loop's header is defined to be a block that dominates the loop.
// If the header has a unique predecessor outside the loop, it must be
// a block that has exactly one successor that can reach the loop.
if (Loop *L = LI.getLoopFor(BB))
return {L->getLoopPredecessor(), L->getHeader()};
return {nullptr, nullptr};
}
/// SCEV structural equivalence is usually sufficient for testing whether two
/// expressions are equal, however for the purposes of looking for a condition
/// guarding a loop, it can be useful to be a little more general, since a
/// front-end may have replicated the controlling expression.
static bool HasSameValue(const SCEV *A, const SCEV *B) {
// Quick check to see if they are the same SCEV.
if (A == B) return true;
auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
// Not all instructions that are "identical" compute the same value. For
// instance, two distinct alloca instructions allocating the same type are
// identical and do not read memory; but compute distinct values.
return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
};
// Otherwise, if they're both SCEVUnknown, it's possible that they hold
// two different instructions with the same value. Check for this case.
if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
if (ComputesEqualValues(AI, BI))
return true;
// Otherwise assume they may have a different value.
return false;
}
bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
const SCEV *&LHS, const SCEV *&RHS,
unsigned Depth) {
bool Changed = false;
// Simplifies ICMP to trivial true or false by turning it into '0 == 0' or
// '0 != 0'.
auto TrivialCase = [&](bool TriviallyTrue) {
LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE;
return true;
};
// If we hit the max recursion limit bail out.
if (Depth >= 3)
return false;
// Canonicalize a constant to the right side.
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
// Check for both operands constant.
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
if (ConstantExpr::getICmp(Pred,
LHSC->getValue(),
RHSC->getValue())->isNullValue())
return TrivialCase(false);
else
return TrivialCase(true);
}
// Otherwise swap the operands to put the constant on the right.
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
Changed = true;
}
// If we're comparing an addrec with a value which is loop-invariant in the
// addrec's loop, put the addrec on the left. Also make a dominance check,
// as both operands could be addrecs loop-invariant in each other's loop.
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
const Loop *L = AR->getLoop();
if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
Changed = true;
}
}
// If there's a constant operand, canonicalize comparisons with boundary
// cases, and canonicalize *-or-equal comparisons to regular comparisons.
if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
const APInt &RA = RC->getAPInt();
bool SimplifiedByConstantRange = false;
if (!ICmpInst::isEquality(Pred)) {
ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
if (ExactCR.isFullSet())
return TrivialCase(true);
else if (ExactCR.isEmptySet())
return TrivialCase(false);
APInt NewRHS;
CmpInst::Predicate NewPred;
if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
ICmpInst::isEquality(NewPred)) {
// We were able to convert an inequality to an equality.
Pred = NewPred;
RHS = getConstant(NewRHS);
Changed = SimplifiedByConstantRange = true;
}
}
if (!SimplifiedByConstantRange) {
switch (Pred) {
default:
break;
case ICmpInst::ICMP_EQ:
case ICmpInst::ICMP_NE:
// Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
if (!RA)
if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
if (const SCEVMulExpr *ME =
dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
ME->getOperand(0)->isAllOnesValue()) {
RHS = AE->getOperand(1);
LHS = ME->getOperand(1);
Changed = true;
}
break;
// The "Should have been caught earlier!" messages refer to the fact
// that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
// should have fired on the corresponding cases, and canonicalized the
// check to trivial case.
case ICmpInst::ICMP_UGE:
assert(!RA.isMinValue() && "Should have been caught earlier!");
Pred = ICmpInst::ICMP_UGT;
RHS = getConstant(RA - 1);
Changed = true;
break;
case ICmpInst::ICMP_ULE:
assert(!RA.isMaxValue() && "Should have been caught earlier!");
Pred = ICmpInst::ICMP_ULT;
RHS = getConstant(RA + 1);
Changed = true;
break;
case ICmpInst::ICMP_SGE:
assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
Pred = ICmpInst::ICMP_SGT;
RHS = getConstant(RA - 1);
Changed = true;
break;
case ICmpInst::ICMP_SLE:
assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
Pred = ICmpInst::ICMP_SLT;
RHS = getConstant(RA + 1);
Changed = true;
break;
}
}
}
// Check for obvious equality.
if (HasSameValue(LHS, RHS)) {
if (ICmpInst::isTrueWhenEqual(Pred))
return TrivialCase(true);
if (ICmpInst::isFalseWhenEqual(Pred))
return TrivialCase(false);
}
// If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
// adding or subtracting 1 from one of the operands.
switch (Pred) {
case ICmpInst::ICMP_SLE:
if (!getSignedRangeMax(RHS).isMaxSignedValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SLT;
Changed = true;
} else if (!getSignedRangeMin(LHS).isMinSignedValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SLT;
Changed = true;
}
break;
case ICmpInst::ICMP_SGE:
if (!getSignedRangeMin(RHS).isMinSignedValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SGT;
Changed = true;
} else if (!getSignedRangeMax(LHS).isMaxSignedValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
SCEV::FlagNSW);
Pred = ICmpInst::ICMP_SGT;
Changed = true;
}
break;
case ICmpInst::ICMP_ULE:
if (!getUnsignedRangeMax(RHS).isMaxValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
SCEV::FlagNUW);
Pred = ICmpInst::ICMP_ULT;
Changed = true;
} else if (!getUnsignedRangeMin(LHS).isMinValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
Pred = ICmpInst::ICMP_ULT;
Changed = true;
}
break;
case ICmpInst::ICMP_UGE:
if (!getUnsignedRangeMin(RHS).isMinValue()) {
RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
Pred = ICmpInst::ICMP_UGT;
Changed = true;
} else if (!getUnsignedRangeMax(LHS).isMaxValue()) {
LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
SCEV::FlagNUW);
Pred = ICmpInst::ICMP_UGT;
Changed = true;
}
break;
default:
break;
}
// TODO: More simplifications are possible here.
// Recursively simplify until we either hit a recursion limit or nothing
// changes.
if (Changed)
return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
return Changed;
}
bool ScalarEvolution::isKnownNegative(const SCEV *S) {
return getSignedRangeMax(S).isNegative();
}
bool ScalarEvolution::isKnownPositive(const SCEV *S) {
return getSignedRangeMin(S).isStrictlyPositive();
}
bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
return !getSignedRangeMin(S).isNegative();
}
bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
return !getSignedRangeMax(S).isStrictlyPositive();
}
bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
return isKnownNegative(S) || isKnownPositive(S);
}
std::pair<const SCEV *, const SCEV *>
ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) {
// Compute SCEV on entry of loop L.
const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this);
if (Start == getCouldNotCompute())
return { Start, Start };
// Compute post increment SCEV for loop L.
const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this);
assert(PostInc != getCouldNotCompute() && "Unexpected could not compute");
return { Start, PostInc };
}
bool ScalarEvolution::isKnownViaInduction(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// First collect all loops.
SmallPtrSet<const Loop *, 8> LoopsUsed;
getUsedLoops(LHS, LoopsUsed);
getUsedLoops(RHS, LoopsUsed);
if (LoopsUsed.empty())
return false;
// Domination relationship must be a linear order on collected loops.
#ifndef NDEBUG
for (auto *L1 : LoopsUsed)
for (auto *L2 : LoopsUsed)
assert((DT.dominates(L1->getHeader(), L2->getHeader()) ||
DT.dominates(L2->getHeader(), L1->getHeader())) &&
"Domination relationship is not a linear order");
#endif
const Loop *MDL =
*std::max_element(LoopsUsed.begin(), LoopsUsed.end(),
[&](const Loop *L1, const Loop *L2) {
return DT.properlyDominates(L1->getHeader(), L2->getHeader());
});
// Get init and post increment value for LHS.
auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS);
// if LHS contains unknown non-invariant SCEV then bail out.
if (SplitLHS.first == getCouldNotCompute())
return false;
assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC");
// Get init and post increment value for RHS.
auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS);
// if RHS contains unknown non-invariant SCEV then bail out.
if (SplitRHS.first == getCouldNotCompute())
return false;
assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC");
// It is possible that init SCEV contains an invariant load but it does
// not dominate MDL and is not available at MDL loop entry, so we should
// check it here.
if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) ||
!isAvailableAtLoopEntry(SplitRHS.first, MDL))
return false;
return isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first) &&
isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second,
SplitRHS.second);
}
bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// Canonicalize the inputs first.
(void)SimplifyICmpOperands(Pred, LHS, RHS);
if (isKnownViaInduction(Pred, LHS, RHS))
return true;
if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
return true;
// Otherwise see what can be done with some simple reasoning.
return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS);
}
bool ScalarEvolution::isKnownOnEveryIteration(ICmpInst::Predicate Pred,
const SCEVAddRecExpr *LHS,
const SCEV *RHS) {
const Loop *L = LHS->getLoop();
return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) &&
isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS);
}
bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
ICmpInst::Predicate Pred,
bool &Increasing) {
bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
#ifndef NDEBUG
// Verify an invariant: inverting the predicate should turn a monotonically
// increasing change to a monotonically decreasing one, and vice versa.
bool IncreasingSwapped;
bool ResultSwapped = isMonotonicPredicateImpl(
LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
assert(Result == ResultSwapped && "should be able to analyze both!");
if (ResultSwapped)
assert(Increasing == !IncreasingSwapped &&
"monotonicity should flip as we flip the predicate");
#endif
return Result;
}
bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
ICmpInst::Predicate Pred,
bool &Increasing) {
// A zero step value for LHS means the induction variable is essentially a
// loop invariant value. We don't really depend on the predicate actually
// flipping from false to true (for increasing predicates, and the other way
// around for decreasing predicates), all we care about is that *if* the
// predicate changes then it only changes from false to true.
//
// A zero step value in itself is not very useful, but there may be places
// where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
// as general as possible.
switch (Pred) {
default:
return false; // Conservative answer
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
if (!LHS->hasNoUnsignedWrap())
return false;
Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
return true;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE: {
if (!LHS->hasNoSignedWrap())
return false;
const SCEV *Step = LHS->getStepRecurrence(*this);
if (isKnownNonNegative(Step)) {
Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
return true;
}
if (isKnownNonPositive(Step)) {
Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
return true;
}
return false;
}
}
llvm_unreachable("switch has default clause!");
}
bool ScalarEvolution::isLoopInvariantPredicate(
ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
const SCEV *&InvariantRHS) {
// If there is a loop-invariant, force it into the RHS, otherwise bail out.
if (!isLoopInvariant(RHS, L)) {
if (!isLoopInvariant(LHS, L))
return false;
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
}
const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
if (!ArLHS || ArLHS->getLoop() != L)
return false;
bool Increasing;
if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
return false;
// If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
// true as the loop iterates, and the backedge is control dependent on
// "ArLHS `Pred` RHS" == true then we can reason as follows:
//
// * if the predicate was false in the first iteration then the predicate
// is never evaluated again, since the loop exits without taking the
// backedge.
// * if the predicate was true in the first iteration then it will
// continue to be true for all future iterations since it is
// monotonically increasing.
//
// For both the above possibilities, we can replace the loop varying
// predicate with its value on the first iteration of the loop (which is
// loop invariant).
//
// A similar reasoning applies for a monotonically decreasing predicate, by
// replacing true with false and false with true in the above two bullets.
auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
return false;
InvariantPred = Pred;
InvariantLHS = ArLHS->getStart();
InvariantRHS = RHS;
return true;
}
bool ScalarEvolution::isKnownPredicateViaConstantRanges(
ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
if (HasSameValue(LHS, RHS))
return ICmpInst::isTrueWhenEqual(Pred);
// This code is split out from isKnownPredicate because it is called from
// within isLoopEntryGuardedByCond.
auto CheckRanges =
[&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
.contains(RangeLHS);
};
// The check at the top of the function catches the case where the values are
// known to be equal.
if (Pred == CmpInst::ICMP_EQ)
return false;
if (Pred == CmpInst::ICMP_NE)
return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
isKnownNonZero(getMinusSCEV(LHS, RHS));
if (CmpInst::isSigned(Pred))
return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
}
bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
const SCEV *LHS,
const SCEV *RHS) {
// Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
// Return Y via OutY.
auto MatchBinaryAddToConst =
[this](const SCEV *Result, const SCEV *X, APInt &OutY,
SCEV::NoWrapFlags ExpectedFlags) {
const SCEV *NonConstOp, *ConstOp;
SCEV::NoWrapFlags FlagsPresent;
if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
!isa<SCEVConstant>(ConstOp) || NonConstOp != X)
return false;
OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
};
APInt C;
switch (Pred) {
default:
break;
case ICmpInst::ICMP_SGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SLE:
// X s<= (X + C)<nsw> if C >= 0
if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
return true;
// (X + C)<nsw> s<= X if C <= 0
if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
!C.isStrictlyPositive())
return true;
break;
case ICmpInst::ICMP_SGT:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SLT:
// X s< (X + C)<nsw> if C > 0
if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
C.isStrictlyPositive())
return true;
// (X + C)<nsw> s< X if C < 0
if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
return true;
break;
}
return false;
}
bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
const SCEV *LHS,
const SCEV *RHS) {
if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
return false;
// Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
// the stack can result in exponential time complexity.
SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
// If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
//
// To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
// isKnownPredicate. isKnownPredicate is more powerful, but also more
// expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
// interesting cases seen in practice. We can consider "upgrading" L >= 0 to
// use isKnownPredicate later if needed.
return isKnownNonNegative(RHS) &&
isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
}
bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// No need to even try if we know the module has no guards.
if (!HasGuards)
return false;
return any_of(*BB, [&](Instruction &I) {
using namespace llvm::PatternMatch;
Value *Condition;
return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
m_Value(Condition))) &&
isImpliedCond(Pred, LHS, RHS, Condition, false);
});
}
/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
/// protected by a conditional between LHS and RHS. This is used to
/// to eliminate casts.
bool
ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// Interpret a null as meaning no loop, where there is obviously no guard
// (interprocedural conditions notwithstanding).
if (!L) return true;
if (VerifyIR)
assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&
"This cannot be done on broken IR!");
if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
return true;
BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
return false;
BranchInst *LoopContinuePredicate =
dyn_cast<BranchInst>(Latch->getTerminator());
if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
isImpliedCond(Pred, LHS, RHS,
LoopContinuePredicate->getCondition(),
LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
return true;
// We don't want more than one activation of the following loops on the stack
// -- that can lead to O(n!) time complexity.
if (WalkingBEDominatingConds)
return false;
SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
// See if we can exploit a trip count to prove the predicate.
const auto &BETakenInfo = getBackedgeTakenInfo(L);
const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
if (LatchBECount != getCouldNotCompute()) {
// We know that Latch branches back to the loop header exactly
// LatchBECount times. This means the backdege condition at Latch is
// equivalent to "{0,+,1} u< LatchBECount".
Type *Ty = LatchBECount->getType();
auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
const SCEV *LoopCounter =
getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
LatchBECount))
return true;
}
// Check conditions due to any @llvm.assume intrinsics.
for (auto &AssumeVH : AC.assumptions()) {
if (!AssumeVH)
continue;
auto *CI = cast<CallInst>(AssumeVH);
if (!DT.dominates(CI, Latch->getTerminator()))
continue;
if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
return true;
}
// If the loop is not reachable from the entry block, we risk running into an
// infinite loop as we walk up into the dom tree. These loops do not matter
// anyway, so we just return a conservative answer when we see them.
if (!DT.isReachableFromEntry(L->getHeader()))
return false;
if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
return true;
for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
DTN != HeaderDTN; DTN = DTN->getIDom()) {
assert(DTN && "should reach the loop header before reaching the root!");
BasicBlock *BB = DTN->getBlock();
if (isImpliedViaGuard(BB, Pred, LHS, RHS))
return true;
BasicBlock *PBB = BB->getSinglePredecessor();
if (!PBB)
continue;
BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
if (!ContinuePredicate || !ContinuePredicate->isConditional())
continue;
Value *Condition = ContinuePredicate->getCondition();
// If we have an edge `E` within the loop body that dominates the only
// latch, the condition guarding `E` also guards the backedge. This
// reasoning works only for loops with a single latch.
BasicBlockEdge DominatingEdge(PBB, BB);
if (DominatingEdge.isSingleEdge()) {
// We're constructively (and conservatively) enumerating edges within the
// loop body that dominate the latch. The dominator tree better agree
// with us on this:
assert(DT.dominates(DominatingEdge, Latch) && "should be!");
if (isImpliedCond(Pred, LHS, RHS, Condition,
BB != ContinuePredicate->getSuccessor(0)))
return true;
}
}
return false;
}
bool
ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// Interpret a null as meaning no loop, where there is obviously no guard
// (interprocedural conditions notwithstanding).
if (!L) return false;
if (VerifyIR)
assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&
"This cannot be done on broken IR!");
// Both LHS and RHS must be available at loop entry.
assert(isAvailableAtLoopEntry(LHS, L) &&
"LHS is not available at Loop Entry");
assert(isAvailableAtLoopEntry(RHS, L) &&
"RHS is not available at Loop Entry");
if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
return true;
// If we cannot prove strict comparison (e.g. a > b), maybe we can prove
// the facts (a >= b && a != b) separately. A typical situation is when the
// non-strict comparison is known from ranges and non-equality is known from
// dominating predicates. If we are proving strict comparison, we always try
// to prove non-equality and non-strict comparison separately.
auto NonStrictPredicate = ICmpInst::getNonStrictPredicate(Pred);
const bool ProvingStrictComparison = (Pred != NonStrictPredicate);
bool ProvedNonStrictComparison = false;
bool ProvedNonEquality = false;
if (ProvingStrictComparison) {
ProvedNonStrictComparison =
isKnownViaNonRecursiveReasoning(NonStrictPredicate, LHS, RHS);
ProvedNonEquality =
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_NE, LHS, RHS);
if (ProvedNonStrictComparison && ProvedNonEquality)
return true;
}
// Try to prove (Pred, LHS, RHS) using isImpliedViaGuard.
auto ProveViaGuard = [&](BasicBlock *Block) {
if (isImpliedViaGuard(Block, Pred, LHS, RHS))
return true;
if (ProvingStrictComparison) {
if (!ProvedNonStrictComparison)
ProvedNonStrictComparison =
isImpliedViaGuard(Block, NonStrictPredicate, LHS, RHS);
if (!ProvedNonEquality)
ProvedNonEquality =
isImpliedViaGuard(Block, ICmpInst::ICMP_NE, LHS, RHS);
if (ProvedNonStrictComparison && ProvedNonEquality)
return true;
}
return false;
};
// Try to prove (Pred, LHS, RHS) using isImpliedCond.
auto ProveViaCond = [&](Value *Condition, bool Inverse) {
if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse))
return true;
if (ProvingStrictComparison) {
if (!ProvedNonStrictComparison)
ProvedNonStrictComparison =
isImpliedCond(NonStrictPredicate, LHS, RHS, Condition, Inverse);
if (!ProvedNonEquality)
ProvedNonEquality =
isImpliedCond(ICmpInst::ICMP_NE, LHS, RHS, Condition, Inverse);
if (ProvedNonStrictComparison && ProvedNonEquality)
return true;
}
return false;
};
// Starting at the loop predecessor, climb up the predecessor chain, as long
// as there are predecessors that can be found that have unique successors
// leading to the original header.
for (std::pair<BasicBlock *, BasicBlock *>
Pair(L->getLoopPredecessor(), L->getHeader());
Pair.first;
Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
if (ProveViaGuard(Pair.first))
return true;
BranchInst *LoopEntryPredicate =
dyn_cast<BranchInst>(Pair.first->getTerminator());
if (!LoopEntryPredicate ||
LoopEntryPredicate->isUnconditional())
continue;
if (ProveViaCond(LoopEntryPredicate->getCondition(),
LoopEntryPredicate->getSuccessor(0) != Pair.second))
return true;
}
// Check conditions due to any @llvm.assume intrinsics.
for (auto &AssumeVH : AC.assumptions()) {
if (!AssumeVH)
continue;
auto *CI = cast<CallInst>(AssumeVH);
if (!DT.dominates(CI, L->getHeader()))
continue;
if (ProveViaCond(CI->getArgOperand(0), false))
return true;
}
return false;
}
bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
Value *FoundCondValue,
bool Inverse) {
if (!PendingLoopPredicates.insert(FoundCondValue).second)
return false;
auto ClearOnExit =
make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); });
// Recursively handle And and Or conditions.
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
if (BO->getOpcode() == Instruction::And) {
if (!Inverse)
return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
} else if (BO->getOpcode() == Instruction::Or) {
if (Inverse)
return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
}
}
ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
if (!ICI) return false;
// Now that we found a conditional branch that dominates the loop or controls
// the loop latch. Check to see if it is the comparison we are looking for.
ICmpInst::Predicate FoundPred;
if (Inverse)
FoundPred = ICI->getInversePredicate();
else
FoundPred = ICI->getPredicate();
const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
}
bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
const SCEV *RHS,
ICmpInst::Predicate FoundPred,
const SCEV *FoundLHS,
const SCEV *FoundRHS) {
// Balance the types.
if (getTypeSizeInBits(LHS->getType()) <
getTypeSizeInBits(FoundLHS->getType())) {
if (CmpInst::isSigned(Pred)) {
LHS = getSignExtendExpr(LHS, FoundLHS->getType());
RHS = getSignExtendExpr(RHS, FoundLHS->getType());
} else {
LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
}
} else if (getTypeSizeInBits(LHS->getType()) >
getTypeSizeInBits(FoundLHS->getType())) {
if (CmpInst::isSigned(FoundPred)) {
FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
} else {
FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
}
}
// Canonicalize the query to match the way instcombine will have
// canonicalized the comparison.
if (SimplifyICmpOperands(Pred, LHS, RHS))
if (LHS == RHS)
return CmpInst::isTrueWhenEqual(Pred);
if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
if (FoundLHS == FoundRHS)
return CmpInst::isFalseWhenEqual(FoundPred);
// Check to see if we can make the LHS or RHS match.
if (LHS == FoundRHS || RHS == FoundLHS) {
if (isa<SCEVConstant>(RHS)) {
std::swap(FoundLHS, FoundRHS);
FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
} else {
std::swap(LHS, RHS);
Pred = ICmpInst::getSwappedPredicate(Pred);
}
}
// Check whether the found predicate is the same as the desired predicate.
if (FoundPred == Pred)
return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
// Check whether swapping the found predicate makes it the same as the
// desired predicate.
if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
if (isa<SCEVConstant>(RHS))
return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
else
return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
RHS, LHS, FoundLHS, FoundRHS);
}
// Unsigned comparison is the same as signed comparison when both the operands
// are non-negative.
if (CmpInst::isUnsigned(FoundPred) &&
CmpInst::getSignedPredicate(FoundPred) == Pred &&
isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
// Check if we can make progress by sharpening ranges.
if (FoundPred == ICmpInst::ICMP_NE &&
(isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
const SCEVConstant *C = nullptr;
const SCEV *V = nullptr;
if (isa<SCEVConstant>(FoundLHS)) {
C = cast<SCEVConstant>(FoundLHS);
V = FoundRHS;
} else {
C = cast<SCEVConstant>(FoundRHS);
V = FoundLHS;
}
// The guarding predicate tells us that C != V. If the known range
// of V is [C, t), we can sharpen the range to [C + 1, t). The
// range we consider has to correspond to same signedness as the
// predicate we're interested in folding.
APInt Min = ICmpInst::isSigned(Pred) ?
getSignedRangeMin(V) : getUnsignedRangeMin(V);
if (Min == C->getAPInt()) {
// Given (V >= Min && V != Min) we conclude V >= (Min + 1).
// This is true even if (Min + 1) wraps around -- in case of
// wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
APInt SharperMin = Min + 1;
switch (Pred) {
case ICmpInst::ICMP_SGE:
case ICmpInst::ICMP_UGE:
// We know V `Pred` SharperMin. If this implies LHS `Pred`
// RHS, we're done.
if (isImpliedCondOperands(Pred, LHS, RHS, V,
getConstant(SharperMin)))
return true;
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_UGT:
// We know from the range information that (V `Pred` Min ||
// V == Min). We know from the guarding condition that !(V
// == Min). This gives us
//
// V `Pred` Min || V == Min && !(V == Min)
// => V `Pred` Min
//
// If V `Pred` Min implies LHS `Pred` RHS, we're done.
if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
return true;
LLVM_FALLTHROUGH;
default:
// No change
break;
}
}
}
// Check whether the actual condition is beyond sufficient.
if (FoundPred == ICmpInst::ICMP_EQ)
if (ICmpInst::isTrueWhenEqual(Pred))
if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
return true;
if (Pred == ICmpInst::ICMP_NE)
if (!ICmpInst::isTrueWhenEqual(FoundPred))
if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
return true;
// Otherwise assume the worst.
return false;
}
bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
const SCEV *&L, const SCEV *&R,
SCEV::NoWrapFlags &Flags) {
const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
if (!AE || AE->getNumOperands() != 2)
return false;
L = AE->getOperand(0);
R = AE->getOperand(1);
Flags = AE->getNoWrapFlags();
return true;
}
Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More,
const SCEV *Less) {
// We avoid subtracting expressions here because this function is usually
// fairly deep in the call stack (i.e. is called many times).
// X - X = 0.
if (More == Less)
return APInt(getTypeSizeInBits(More->getType()), 0);
if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
const auto *LAR = cast<SCEVAddRecExpr>(Less);
const auto *MAR = cast<SCEVAddRecExpr>(More);
if (LAR->getLoop() != MAR->getLoop())
return None;
// We look at affine expressions only; not for correctness but to keep
// getStepRecurrence cheap.
if (!LAR->isAffine() || !MAR->isAffine())
return None;
if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
return None;
Less = LAR->getStart();
More = MAR->getStart();
// fall through
}
if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
const auto &M = cast<SCEVConstant>(More)->getAPInt();
const auto &L = cast<SCEVConstant>(Less)->getAPInt();
return M - L;
}
SCEV::NoWrapFlags Flags;
const SCEV *LLess = nullptr, *RLess = nullptr;
const SCEV *LMore = nullptr, *RMore = nullptr;
const SCEVConstant *C1 = nullptr, *C2 = nullptr;
// Compare (X + C1) vs X.
if (splitBinaryAdd(Less, LLess, RLess, Flags))
if ((C1 = dyn_cast<SCEVConstant>(LLess)))
if (RLess == More)
return -(C1->getAPInt());
// Compare X vs (X + C2).
if (splitBinaryAdd(More, LMore, RMore, Flags))
if ((C2 = dyn_cast<SCEVConstant>(LMore)))
if (RMore == Less)
return C2->getAPInt();
// Compare (X + C1) vs (X + C2).
if (C1 && C2 && RLess == RMore)
return C2->getAPInt() - C1->getAPInt();
return None;
}
bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS, const SCEV *FoundRHS) {
if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
return false;
const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
if (!AddRecLHS)
return false;
const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
if (!AddRecFoundLHS)
return false;
// We'd like to let SCEV reason about control dependencies, so we constrain
// both the inequalities to be about add recurrences on the same loop. This
// way we can use isLoopEntryGuardedByCond later.
const Loop *L = AddRecFoundLHS->getLoop();
if (L != AddRecLHS->getLoop())
return false;
// FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
//
// FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
// ... (2)
//
// Informal proof for (2), assuming (1) [*]:
//
// We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
//
// Then
//
// FoundLHS s< FoundRHS s< INT_MIN - C
// <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
// <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
// <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
// (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
// <=> FoundLHS + C s< FoundRHS + C
//
// [*]: (1) can be proved by ruling out overflow.
//
// [**]: This can be proved by analyzing all the four possibilities:
// (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
// (A s>= 0, B s>= 0).
//
// Note:
// Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
// will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
// = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
// s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
// neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
// C)".
Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
if (!LDiff || !RDiff || *LDiff != *RDiff)
return false;
if (LDiff->isMinValue())
return true;
APInt FoundRHSLimit;
if (Pred == CmpInst::ICMP_ULT) {
FoundRHSLimit = -(*RDiff);
} else {
assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
}
// Try to prove (1) or (2), as needed.
return isAvailableAtLoopEntry(FoundRHS, L) &&
isLoopEntryGuardedByCond(L, Pred, FoundRHS,
getConstant(FoundRHSLimit));
}
bool ScalarEvolution::isImpliedViaMerge(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS, unsigned Depth) {
const PHINode *LPhi = nullptr, *RPhi = nullptr;
auto ClearOnExit = make_scope_exit([&]() {
if (LPhi) {
bool Erased = PendingMerges.erase(LPhi);
assert(Erased && "Failed to erase LPhi!");
(void)Erased;
}
if (RPhi) {
bool Erased = PendingMerges.erase(RPhi);
assert(Erased && "Failed to erase RPhi!");
(void)Erased;
}
});
// Find respective Phis and check that they are not being pending.
if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS))
if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) {
if (!PendingMerges.insert(Phi).second)
return false;
LPhi = Phi;
}
if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS))
if (auto *Phi = dyn_cast<PHINode>(RU->getValue())) {
// If we detect a loop of Phi nodes being processed by this method, for
// example:
//
// %a = phi i32 [ %some1, %preheader ], [ %b, %latch ]
// %b = phi i32 [ %some2, %preheader ], [ %a, %latch ]
//
// we don't want to deal with a case that complex, so return conservative
// answer false.
if (!PendingMerges.insert(Phi).second)
return false;
RPhi = Phi;
}
// If none of LHS, RHS is a Phi, nothing to do here.
if (!LPhi && !RPhi)
return false;
// If there is a SCEVUnknown Phi we are interested in, make it left.
if (!LPhi) {
std::swap(LHS, RHS);
std::swap(FoundLHS, FoundRHS);
std::swap(LPhi, RPhi);
Pred = ICmpInst::getSwappedPredicate(Pred);
}
assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!");
const BasicBlock *LBB = LPhi->getParent();
const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) {
return isKnownViaNonRecursiveReasoning(Pred, S1, S2) ||
isImpliedCondOperandsViaRanges(Pred, S1, S2, FoundLHS, FoundRHS) ||
isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth);
};
if (RPhi && RPhi->getParent() == LBB) {
// Case one: RHS is also a SCEVUnknown Phi from the same basic block.
// If we compare two Phis from the same block, and for each entry block
// the predicate is true for incoming values from this block, then the
// predicate is also true for the Phis.
for (const BasicBlock *IncBB : predecessors(LBB)) {
const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB));
if (!ProvedEasily(L, R))
return false;
}
} else if (RAR && RAR->getLoop()->getHeader() == LBB) {
// Case two: RHS is also a Phi from the same basic block, and it is an
// AddRec. It means that there is a loop which has both AddRec and Unknown
// PHIs, for it we can compare incoming values of AddRec from above the loop
// and latch with their respective incoming values of LPhi.
// TODO: Generalize to handle loops with many inputs in a header.
if (LPhi->getNumIncomingValues() != 2) return false;
auto *RLoop = RAR->getLoop();
auto *Predecessor = RLoop->getLoopPredecessor();
assert(Predecessor && "Loop with AddRec with no predecessor?");
const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor));
if (!ProvedEasily(L1, RAR->getStart()))
return false;
auto *Latch = RLoop->getLoopLatch();
assert(Latch && "Loop with AddRec with no latch?");
const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch));
if (!ProvedEasily(L2, RAR->getPostIncExpr(*this)))
return false;
} else {
// In all other cases go over inputs of LHS and compare each of them to RHS,
// the predicate is true for (LHS, RHS) if it is true for all such pairs.
// At this point RHS is either a non-Phi, or it is a Phi from some block
// different from LBB.
for (const BasicBlock *IncBB : predecessors(LBB)) {
// Check that RHS is available in this block.
if (!dominates(RHS, IncBB))
return false;
const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
if (!ProvedEasily(L, RHS))
return false;
}
}
return true;
}
bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS) {
if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
return true;
if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
return true;
return isImpliedCondOperandsHelper(Pred, LHS, RHS,
FoundLHS, FoundRHS) ||
// ~x < ~y --> x > y
isImpliedCondOperandsHelper(Pred, LHS, RHS,
getNotSCEV(FoundRHS),
getNotSCEV(FoundLHS));
}
/// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values?
template <typename MinMaxExprType>
static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr,
const SCEV *Candidate) {
const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr);
if (!MinMaxExpr)
return false;
return find(MinMaxExpr->operands(), Candidate) != MinMaxExpr->op_end();
}
static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// If both sides are affine addrecs for the same loop, with equal
// steps, and we know the recurrences don't wrap, then we only
// need to check the predicate on the starting values.
if (!ICmpInst::isRelational(Pred))
return false;
const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
if (!LAR)
return false;
const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
if (!RAR)
return false;
if (LAR->getLoop() != RAR->getLoop())
return false;
if (!LAR->isAffine() || !RAR->isAffine())
return false;
if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
return false;
SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
SCEV::FlagNSW : SCEV::FlagNUW;
if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
return false;
return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
}
/// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
/// expression?
static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
switch (Pred) {
default:
return false;
case ICmpInst::ICMP_SGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SLE:
return
// min(A, ...) <= A
IsMinMaxConsistingOf<SCEVSMinExpr>(LHS, RHS) ||
// A <= max(A, ...)
IsMinMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
case ICmpInst::ICMP_UGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_ULE:
return
// min(A, ...) <= A
IsMinMaxConsistingOf<SCEVUMinExpr>(LHS, RHS) ||
// A <= max(A, ...)
IsMinMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
}
llvm_unreachable("covered switch fell through?!");
}
bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS,
unsigned Depth) {
assert(getTypeSizeInBits(LHS->getType()) ==
getTypeSizeInBits(RHS->getType()) &&
"LHS and RHS have different sizes?");
assert(getTypeSizeInBits(FoundLHS->getType()) ==
getTypeSizeInBits(FoundRHS->getType()) &&
"FoundLHS and FoundRHS have different sizes?");
// We want to avoid hurting the compile time with analysis of too big trees.
if (Depth > MaxSCEVOperationsImplicationDepth)
return false;
// We only want to work with ICMP_SGT comparison so far.
// TODO: Extend to ICMP_UGT?
if (Pred == ICmpInst::ICMP_SLT) {
Pred = ICmpInst::ICMP_SGT;
std::swap(LHS, RHS);
std::swap(FoundLHS, FoundRHS);
}
if (Pred != ICmpInst::ICMP_SGT)
return false;
auto GetOpFromSExt = [&](const SCEV *S) {
if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S))
return Ext->getOperand();
// TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off
// the constant in some cases.
return S;
};
// Acquire values from extensions.
auto *OrigLHS = LHS;
auto *OrigFoundLHS = FoundLHS;
LHS = GetOpFromSExt(LHS);
FoundLHS = GetOpFromSExt(FoundLHS);
// Is the SGT predicate can be proved trivially or using the found context.
auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) {
return isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGT, S1, S2) ||
isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS,
FoundRHS, Depth + 1);
};
if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) {
// We want to avoid creation of any new non-constant SCEV. Since we are
// going to compare the operands to RHS, we should be certain that we don't
// need any size extensions for this. So let's decline all cases when the
// sizes of types of LHS and RHS do not match.
// TODO: Maybe try to get RHS from sext to catch more cases?
if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType()))
return false;
// Should not overflow.
if (!LHSAddExpr->hasNoSignedWrap())
return false;
auto *LL = LHSAddExpr->getOperand(0);
auto *LR = LHSAddExpr->getOperand(1);
auto *MinusOne = getNegativeSCEV(getOne(RHS->getType()));
// Checks that S1 >= 0 && S2 > RHS, trivially or using the found context.
auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) {
return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS);
};
// Try to prove the following rule:
// (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS).
// (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS).
if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL))
return true;
} else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) {
Value *LL, *LR;
// FIXME: Once we have SDiv implemented, we can get rid of this matching.
using namespace llvm::PatternMatch;
if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) {
// Rules for division.
// We are going to perform some comparisons with Denominator and its
// derivative expressions. In general case, creating a SCEV for it may
// lead to a complex analysis of the entire graph, and in particular it
// can request trip count recalculation for the same loop. This would
// cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid
// this, we only want to create SCEVs that are constants in this section.
// So we bail if Denominator is not a constant.
if (!isa<ConstantInt>(LR))
return false;
auto *Denominator = cast<SCEVConstant>(getSCEV(LR));
// We want to make sure that LHS = FoundLHS / Denominator. If it is so,
// then a SCEV for the numerator already exists and matches with FoundLHS.
auto *Numerator = getExistingSCEV(LL);
if (!Numerator || Numerator->getType() != FoundLHS->getType())
return false;
// Make sure that the numerator matches with FoundLHS and the denominator
// is positive.
if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator))
return false;
auto *DTy = Denominator->getType();
auto *FRHSTy = FoundRHS->getType();
if (DTy->isPointerTy() != FRHSTy->isPointerTy())
// One of types is a pointer and another one is not. We cannot extend
// them properly to a wider type, so let us just reject this case.
// TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help
// to avoid this check.
return false;
// Given that:
// FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0.
auto *WTy = getWiderType(DTy, FRHSTy);
auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy);
auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy);
// Try to prove the following rule:
// (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS).
// For example, given that FoundLHS > 2. It means that FoundLHS is at
// least 3. If we divide it by Denominator < 4, we will have at least 1.
auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2));
if (isKnownNonPositive(RHS) &&
IsSGTViaContext(FoundRHSExt, DenomMinusTwo))
return true;
// Try to prove the following rule:
// (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS).
// For example, given that FoundLHS > -3. Then FoundLHS is at least -2.
// If we divide it by Denominator > 2, then:
// 1. If FoundLHS is negative, then the result is 0.
// 2. If FoundLHS is non-negative, then the result is non-negative.
// Anyways, the result is non-negative.
auto *MinusOne = getNegativeSCEV(getOne(WTy));
auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt);
if (isKnownNegative(RHS) &&
IsSGTViaContext(FoundRHSExt, NegDenomMinusOne))
return true;
}
}
// If our expression contained SCEVUnknown Phis, and we split it down and now
// need to prove something for them, try to prove the predicate for every
// possible incoming values of those Phis.
if (isImpliedViaMerge(Pred, OrigLHS, RHS, OrigFoundLHS, FoundRHS, Depth + 1))
return true;
return false;
}
static bool isKnownPredicateExtendIdiom(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
// zext x u<= sext x, sext x s<= zext x
switch (Pred) {
case ICmpInst::ICMP_SGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_SLE: {
// If operand >=s 0 then ZExt == SExt. If operand <s 0 then SExt <s ZExt.
const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(LHS);
const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(RHS);
if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
return true;
break;
}
case ICmpInst::ICMP_UGE:
std::swap(LHS, RHS);
LLVM_FALLTHROUGH;
case ICmpInst::ICMP_ULE: {
// If operand >=s 0 then ZExt == SExt. If operand <s 0 then ZExt <u SExt.
const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS);
const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(RHS);
if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
return true;
break;
}
default:
break;
};
return false;
}
bool
ScalarEvolution::isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
return isKnownPredicateExtendIdiom(Pred, LHS, RHS) ||
isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
}
bool
ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS) {
switch (Pred) {
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
case ICmpInst::ICMP_EQ:
case ICmpInst::ICMP_NE:
if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE:
if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS))
return true;
break;
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS))
return true;
break;
}
// Maybe it can be proved via operations?
if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS))
return true;
return false;
}
bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
const SCEV *LHS,
const SCEV *RHS,
const SCEV *FoundLHS,
const SCEV *FoundRHS) {
if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
// The restriction on `FoundRHS` be lifted easily -- it exists only to
// reduce the compile time impact of this optimization.
return false;
Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
if (!Addend)
return false;
const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
// `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
// antecedent "`FoundLHS` `Pred` `FoundRHS`".
ConstantRange FoundLHSRange =
ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
// Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));
// We can also compute the range of values for `LHS` that satisfy the
// consequent, "`LHS` `Pred` `RHS`":
const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
ConstantRange SatisfyingLHSRange =
ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
// The antecedent implies the consequent if every value of `LHS` that
// satisfies the antecedent also satisfies the consequent.
return SatisfyingLHSRange.contains(LHSRange);
}
bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
bool IsSigned, bool NoWrap) {
assert(isKnownPositive(Stride) && "Positive stride expected!");
if (NoWrap) return false;
unsigned BitWidth = getTypeSizeInBits(RHS->getType());
const SCEV *One = getOne(Stride->getType());
if (IsSigned) {
APInt MaxRHS = getSignedRangeMax(RHS);
APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
// SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS);
}
APInt MaxRHS = getUnsignedRangeMax(RHS);
APInt MaxValue = APInt::getMaxValue(BitWidth);
APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
// UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS);
}
bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
bool IsSigned, bool NoWrap) {
if (NoWrap) return false;
unsigned BitWidth = getTypeSizeInBits(RHS->getType());
const SCEV *One = getOne(Stride->getType());
if (IsSigned) {
APInt MinRHS = getSignedRangeMin(RHS);
APInt MinValue = APInt::getSignedMinValue(BitWidth);
APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
// SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS);
}
APInt MinRHS = getUnsignedRangeMin(RHS);
APInt MinValue = APInt::getMinValue(BitWidth);
APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
// UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS);
}
const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
bool Equality) {
const SCEV *One = getOne(Step->getType());
Delta = Equality ? getAddExpr(Delta, Step)
: getAddExpr(Delta, getMinusSCEV(Step, One));
return getUDivExpr(Delta, Step);
}
const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
const SCEV *Stride,
const SCEV *End,
unsigned BitWidth,
bool IsSigned) {
assert(!isKnownNonPositive(Stride) &&
"Stride is expected strictly positive!");
// Calculate the maximum backedge count based on the range of values
// permitted by Start, End, and Stride.
const SCEV *MaxBECount;
APInt MinStart =
IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);
APInt StrideForMaxBECount =
IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
// We already know that the stride is positive, so we paper over conservatism
// in our range computation by forcing StrideForMaxBECount to be at least one.
// In theory this is unnecessary, but we expect MaxBECount to be a
// SCEVConstant, and (udiv <constant> 0) is not constant folded by SCEV (there
// is nothing to constant fold it to).
APInt One(BitWidth, 1, IsSigned);
StrideForMaxBECount = APIntOps::smax(One, StrideForMaxBECount);
APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth)
: APInt::getMaxValue(BitWidth);
APInt Limit = MaxValue - (StrideForMaxBECount - 1);
// Although End can be a MAX expression we estimate MaxEnd considering only
// the case End = RHS of the loop termination condition. This is safe because
// in the other case (End - Start) is zero, leading to a zero maximum backedge
// taken count.
APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit)
: APIntOps::umin(getUnsignedRangeMax(End), Limit);
MaxBECount = computeBECount(getConstant(MaxEnd - MinStart) /* Delta */,
getConstant(StrideForMaxBECount) /* Step */,
false /* Equality */);
return MaxBECount;
}
ScalarEvolution::ExitLimit
ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
const Loop *L, bool IsSigned,
bool ControlsExit, bool AllowPredicates) {
SmallPtrSet<const SCEVPredicate *, 4> Predicates;
const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
bool PredicatedIV = false;
if (!IV && AllowPredicates) {
// Try to make this an AddRec using runtime tests, in the first X
// iterations of this loop, where X is the SCEV expression found by the
// algorithm below.
IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
PredicatedIV = true;
}
// Avoid weird loops
if (!IV || IV->getLoop() != L || !IV->isAffine())
return getCouldNotCompute();
bool NoWrap = ControlsExit &&
IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
const SCEV *Stride = IV->getStepRecurrence(*this);
bool PositiveStride = isKnownPositive(Stride);
// Avoid negative or zero stride values.
if (!PositiveStride) {
// We can compute the correct backedge taken count for loops with unknown
// strides if we can prove that the loop is not an infinite loop with side
// effects. Here's the loop structure we are trying to handle -
//
// i = start
// do {
// A[i] = i;
// i += s;
// } while (i < end);
//
// The backedge taken count for such loops is evaluated as -
// (max(end, start + stride) - start - 1) /u stride
//
// The additional preconditions that we need to check to prove correctness
// of the above formula is as follows -
//
// a) IV is either nuw or nsw depending upon signedness (indicated by the
// NoWrap flag).
// b) loop is single exit with no side effects.
//
//
// Precondition a) implies that if the stride is negative, this is a single
// trip loop. The backedge taken count formula reduces to zero in this case.
//
// Precondition b) implies that the unknown stride cannot be zero otherwise
// we have UB.
//
// The positive stride case is the same as isKnownPositive(Stride) returning
// true (original behavior of the function).
//
// We want to make sure that the stride is truly unknown as there are edge
// cases where ScalarEvolution propagates no wrap flags to the
// post-increment/decrement IV even though the increment/decrement operation
// itself is wrapping. The computed backedge taken count may be wrong in
// such cases. This is prevented by checking that the stride is not known to
// be either positive or non-positive. For example, no wrap flags are
// propagated to the post-increment IV of this loop with a trip count of 2 -
//
// unsigned char i;
// for(i=127; i<128; i+=129)
// A[i] = i;
//
if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) ||
!loopHasNoSideEffects(L))
return getCouldNotCompute();
} else if (!Stride->isOne() &&
doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
// Avoid proven overflow cases: this will ensure that the backedge taken
// count will not generate any unsigned overflow. Relaxed no-overflow
// conditions exploit NoWrapFlags, allowing to optimize in presence of
// undefined behaviors like the case of C language.
return getCouldNotCompute();
ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
: ICmpInst::ICMP_ULT;
const SCEV *Start = IV->getStart();
const SCEV *End = RHS;
// When the RHS is not invariant, we do not know the end bound of the loop and
// cannot calculate the ExactBECount needed by ExitLimit. However, we can
// calculate the MaxBECount, given the start, stride and max value for the end
// bound of the loop (RHS), and the fact that IV does not overflow (which is
// checked above).
if (!isLoopInvariant(RHS, L)) {
const SCEV *MaxBECount = computeMaxBECountForLT(
Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
false /*MaxOrZero*/, Predicates);
}
// If the backedge is taken at least once, then it will be taken
// (End-Start)/Stride times (rounded up to a multiple of Stride), where Start
// is the LHS value of the less-than comparison the first time it is evaluated
// and End is the RHS.
const SCEV *BECountIfBackedgeTaken =
computeBECount(getMinusSCEV(End, Start), Stride, false);
// If the loop entry is guarded by the result of the backedge test of the
// first loop iteration, then we know the backedge will be taken at least
// once and so the backedge taken count is as above. If not then we use the
// expression (max(End,Start)-Start)/Stride to describe the backedge count,
// as if the backedge is taken at least once max(End,Start) is End and so the
// result is as above, and if not max(End,Start) is Start so we get a backedge
// count of zero.
const SCEV *BECount;
if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
BECount = BECountIfBackedgeTaken;
else {
End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
}
const SCEV *MaxBECount;
bool MaxOrZero = false;
if (isa<SCEVConstant>(BECount))
MaxBECount = BECount;
else if (isa<SCEVConstant>(BECountIfBackedgeTaken)) {
// If we know exactly how many times the backedge will be taken if it's
// taken at least once, then the backedge count will either be that or
// zero.
MaxBECount = BECountIfBackedgeTaken;
MaxOrZero = true;
} else {
MaxBECount = computeMaxBECountForLT(
Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
}
if (isa<SCEVCouldNotCompute>(MaxBECount) &&
!isa<SCEVCouldNotCompute>(BECount))
MaxBECount = getConstant(getUnsignedRangeMax(BECount));
return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates);
}
ScalarEvolution::ExitLimit
ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
const Loop *L, bool IsSigned,
bool ControlsExit, bool AllowPredicates) {
SmallPtrSet<const SCEVPredicate *, 4> Predicates;
// We handle only IV > Invariant
if (!isLoopInvariant(RHS, L))
return getCouldNotCompute();
const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
if (!IV && AllowPredicates)
// Try to make this an AddRec using runtime tests, in the first X
// iterations of this loop, where X is the SCEV expression found by the
// algorithm below.
IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
// Avoid weird loops
if (!IV || IV->getLoop() != L || !IV->isAffine())
return getCouldNotCompute();
bool NoWrap = ControlsExit &&
IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
// Avoid negative or zero stride values
if (!isKnownPositive(Stride))
return getCouldNotCompute();
// Avoid proven overflow cases: this will ensure that the backedge taken count
// will not generate any unsigned overflow. Relaxed no-overflow conditions
// exploit NoWrapFlags, allowing to optimize in presence of undefined
// behaviors like the case of C language.
if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
return getCouldNotCompute();
ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
: ICmpInst::ICMP_UGT;
const SCEV *Start = IV->getStart();
const SCEV *End = RHS;
if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
APInt MaxStart = IsSigned ? getSignedRangeMax(Start)
: getUnsignedRangeMax(Start);
APInt MinStride = IsSigned ? getSignedRangeMin(Stride)
: getUnsignedRangeMin(Stride);
unsigned BitWidth = getTypeSizeInBits(LHS->getType());
APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
: APInt::getMinValue(BitWidth) + (MinStride - 1);
// Although End can be a MIN expression we estimate MinEnd considering only
// the case End = RHS. This is safe because in the other case (Start - End)
// is zero, leading to a zero maximum backedge taken count.
APInt MinEnd =
IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit)
: APIntOps::umax(getUnsignedRangeMin(RHS), Limit);
const SCEV *MaxBECount = isa<SCEVConstant>(BECount)
? BECount
: computeBECount(getConstant(MaxStart - MinEnd),
getConstant(MinStride), false);
if (isa<SCEVCouldNotCompute>(MaxBECount))
MaxBECount = BECount;
return ExitLimit(BECount, MaxBECount, false, Predicates);
}
const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
ScalarEvolution &SE) const {
if (Range.isFullSet()) // Infinite loop.
return SE.getCouldNotCompute();
// If the start is a non-zero constant, shift the range to simplify things.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
if (!SC->getValue()->isZero()) {
SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
Operands[0] = SE.getZero(SC->getType());
const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
getNoWrapFlags(FlagNW));
if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
return ShiftedAddRec->getNumIterationsInRange(
Range.subtract(SC->getAPInt()), SE);
// This is strange and shouldn't happen.
return SE.getCouldNotCompute();
}
// The only time we can solve this is when we have all constant indices.
// Otherwise, we cannot determine the overflow conditions.
if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
return SE.getCouldNotCompute();
// Okay at this point we know that all elements of the chrec are constants and
// that the start element is zero.
// First check to see if the range contains zero. If not, the first
// iteration exits.
unsigned BitWidth = SE.getTypeSizeInBits(getType());
if (!Range.contains(APInt(BitWidth, 0)))
return SE.getZero(getType());
if (isAffine()) {
// If this is an affine expression then we have this situation:
// Solve {0,+,A} in Range === Ax in Range
// We know that zero is in the range. If A is positive then we know that
// the upper value of the range must be the first possible exit value.
// If A is negative then the lower of the range is the last possible loop
// value. Also note that we already checked for a full range.
APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower();
// The exit value should be (End+A)/A.
APInt ExitVal = (End + A).udiv(A);
ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
// Evaluate at the exit value. If we really did fall out of the valid
// range, then we computed our trip count, otherwise wrap around or other
// things must have happened.
ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
if (Range.contains(Val->getValue()))
return SE.getCouldNotCompute(); // Something strange happened
// Ensure that the previous value is in the range. This is a sanity check.
assert(Range.contains(
EvaluateConstantChrecAtConstant(this,
ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) &&
"Linear scev computation is off in a bad way!");
return SE.getConstant(ExitValue);
}
if (isQuadratic()) {
if (auto S = SolveQuadraticAddRecRange(this, Range, SE))
return SE.getConstant(S.getValue());
}
return SE.getCouldNotCompute();
}
const SCEVAddRecExpr *
SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const {
assert(getNumOperands() > 1 && "AddRec with zero step?");
// There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)),
// but in this case we cannot guarantee that the value returned will be an
// AddRec because SCEV does not have a fixed point where it stops
// simplification: it is legal to return ({rec1} + {rec2}). For example, it
// may happen if we reach arithmetic depth limit while simplifying. So we
// construct the returned value explicitly.
SmallVector<const SCEV *, 3> Ops;
// If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and
// (this + Step) is {A+B,+,B+C,+...,+,N}.
for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i)
Ops.push_back(SE.getAddExpr(getOperand(i), getOperand(i + 1)));
// We know that the last operand is not a constant zero (otherwise it would
// have been popped out earlier). This guarantees us that if the result has
// the same last operand, then it will also not be popped out, meaning that
// the returned value will be an AddRec.
const SCEV *Last = getOperand(getNumOperands() - 1);
assert(!Last->isZero() && "Recurrency with zero step?");
Ops.push_back(Last);
return cast<SCEVAddRecExpr>(SE.getAddRecExpr(Ops, getLoop(),
SCEV::FlagAnyWrap));
}
// Return true when S contains at least an undef value.
static inline bool containsUndefs(const SCEV *S) {
return SCEVExprContains(S, [](const SCEV *S) {
if (const auto *SU = dyn_cast<SCEVUnknown>(S))
return isa<UndefValue>(SU->getValue());
return false;
});
}
namespace {
// Collect all steps of SCEV expressions.
struct SCEVCollectStrides {
ScalarEvolution &SE;
SmallVectorImpl<const SCEV *> &Strides;
SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
: SE(SE), Strides(S) {}
bool follow(const SCEV *S) {
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
Strides.push_back(AR->getStepRecurrence(SE));
return true;
}
bool isDone() const { return false; }
};
// Collect all SCEVUnknown and SCEVMulExpr expressions.
struct SCEVCollectTerms {
SmallVectorImpl<const SCEV *> &Terms;
SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {}
bool follow(const SCEV *S) {
if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) ||
isa<SCEVSignExtendExpr>(S)) {
if (!containsUndefs(S))
Terms.push_back(S);
// Stop recursion: once we collected a term, do not walk its operands.
return false;
}
// Keep looking.
return true;
}
bool isDone() const { return false; }
};
// Check if a SCEV contains an AddRecExpr.
struct SCEVHasAddRec {
bool &ContainsAddRec;
SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
ContainsAddRec = false;
}
bool follow(const SCEV *S) {
if (isa<SCEVAddRecExpr>(S)) {
ContainsAddRec = true;
// Stop recursion: once we collected a term, do not walk its operands.
return false;
}
// Keep looking.
return true;
}
bool isDone() const { return false; }
};
// Find factors that are multiplied with an expression that (possibly as a
// subexpression) contains an AddRecExpr. In the expression:
//
// 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
//
// "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
// that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
// parameters as they form a product with an induction variable.
//
// This collector expects all array size parameters to be in the same MulExpr.
// It might be necessary to later add support for collecting parameters that are
// spread over different nested MulExpr.
struct SCEVCollectAddRecMultiplies {
SmallVectorImpl<const SCEV *> &Terms;
ScalarEvolution &SE;
SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
: Terms(T), SE(SE) {}
bool follow(const SCEV *S) {
if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
bool HasAddRec = false;
SmallVector<const SCEV *, 0> Operands;
for (auto Op : Mul->operands()) {
const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op);
if (Unknown && !isa<CallInst>(Unknown->getValue())) {
Operands.push_back(Op);
} else if (Unknown) {
HasAddRec = true;
} else {
bool ContainsAddRec = false;
SCEVHasAddRec ContiansAddRec(ContainsAddRec);
visitAll(Op, ContiansAddRec);
HasAddRec |= ContainsAddRec;
}
}
if (Operands.size() == 0)
return true;
if (!HasAddRec)
return false;
Terms.push_back(SE.getMulExpr(Operands));
// Stop recursion: once we collected a term, do not walk its operands.
return false;
}
// Keep looking.
return true;
}
bool isDone() const { return false; }
};
} // end anonymous namespace
/// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
/// two places:
/// 1) The strides of AddRec expressions.
/// 2) Unknowns that are multiplied with AddRec expressions.
void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
SmallVectorImpl<const SCEV *> &Terms) {
SmallVector<const SCEV *, 4> Strides;
SCEVCollectStrides StrideCollector(*this, Strides);
visitAll(Expr, StrideCollector);
LLVM_DEBUG({
dbgs() << "Strides:\n";
for (const SCEV *S : Strides)
dbgs() << *S << "\n";
});
for (const SCEV *S : Strides) {
SCEVCollectTerms TermCollector(Terms);
visitAll(S, TermCollector);
}
LLVM_DEBUG({
dbgs() << "Terms:\n";
for (const SCEV *T : Terms)
dbgs() << *T << "\n";
});
SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
visitAll(Expr, MulCollector);
}
static bool findArrayDimensionsRec(ScalarEvolution &SE,
SmallVectorImpl<const SCEV *> &Terms,
SmallVectorImpl<const SCEV *> &Sizes) {
int Last = Terms.size() - 1;
const SCEV *Step = Terms[Last];
// End of recursion.
if (Last == 0) {
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
SmallVector<const SCEV *, 2> Qs;
for (const SCEV *Op : M->operands())
if (!isa<SCEVConstant>(Op))
Qs.push_back(Op);
Step = SE.getMulExpr(Qs);
}
Sizes.push_back(Step);
return true;
}
for (const SCEV *&Term : Terms) {
// Normalize the terms before the next call to findArrayDimensionsRec.
const SCEV *Q, *R;
SCEVDivision::divide(SE, Term, Step, &Q, &R);
// Bail out when GCD does not evenly divide one of the terms.
if (!R->isZero())
return false;
Term = Q;
}
// Remove all SCEVConstants.
Terms.erase(
remove_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); }),
Terms.end());
if (Terms.size() > 0)
if (!findArrayDimensionsRec(SE, Terms, Sizes))
return false;
Sizes.push_back(Step);
return true;
}
// Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
for (const SCEV *T : Terms)
if (SCEVExprContains(T, isa<SCEVUnknown, const SCEV *>))
return true;
return false;
}
// Return the number of product terms in S.
static inline int numberOfTerms(const SCEV *S) {
if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
return Expr->getNumOperands();
return 1;
}
static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
if (isa<SCEVConstant>(T))
return nullptr;
if (isa<SCEVUnknown>(T))
return T;
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
SmallVector<const SCEV *, 2> Factors;
for (const SCEV *Op : M->operands())
if (!isa<SCEVConstant>(Op))
Factors.push_back(Op);
return SE.getMulExpr(Factors);
}
return T;
}
/// Return the size of an element read or written by Inst.
const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
Type *Ty;
if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
Ty = Store->getValueOperand()->getType();
else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
Ty = Load->getType();
else
return nullptr;
Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
return getSizeOfExpr(ETy, Ty);
}
void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
SmallVectorImpl<const SCEV *> &Sizes,
const SCEV *ElementSize) {
if (Terms.size() < 1 || !ElementSize)
return;
// Early return when Terms do not contain parameters: we do not delinearize
// non parametric SCEVs.
if (!containsParameters(Terms))
return;
LLVM_DEBUG({
dbgs() << "Terms:\n";
for (const SCEV *T : Terms)
dbgs() << *T << "\n";
});
// Remove duplicates.
array_pod_sort(Terms.begin(), Terms.end());
Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
// Put larger terms first.
llvm::sort(Terms, [](const SCEV *LHS, const SCEV *RHS) {
return numberOfTerms(LHS) > numberOfTerms(RHS);
});
// Try to divide all terms by the element size. If term is not divisible by
// element size, proceed with the original term.
for (const SCEV *&Term : Terms) {
const SCEV *Q, *R;
SCEVDivision::divide(*this, Term, ElementSize, &Q, &R);
if (!Q->isZero())
Term = Q;
}
SmallVector<const SCEV *, 4> NewTerms;
// Remove constant factors.
for (const SCEV *T : Terms)
if (const SCEV *NewT = removeConstantFactors(*this, T))
NewTerms.push_back(NewT);
LLVM_DEBUG({
dbgs() << "Terms after sorting:\n";
for (const SCEV *T : NewTerms)
dbgs() << *T << "\n";
});
if (NewTerms.empty() || !findArrayDimensionsRec(*this, NewTerms, Sizes)) {
Sizes.clear();
return;
}
// The last element to be pushed into Sizes is the size of an element.
Sizes.push_back(ElementSize);
LLVM_DEBUG({
dbgs() << "Sizes:\n";
for (const SCEV *S : Sizes)
dbgs() << *S << "\n";
});
}
void ScalarEvolution::computeAccessFunctions(
const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
SmallVectorImpl<const SCEV *> &Sizes) {
// Early exit in case this SCEV is not an affine multivariate function.
if (Sizes.empty())
return;
if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
if (!AR->isAffine())
return;
const SCEV *Res = Expr;
int Last = Sizes.size() - 1;
for (int i = Last; i >= 0; i--) {
const SCEV *Q, *R;
SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
LLVM_DEBUG({
dbgs() << "Res: " << *Res << "\n";
dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
dbgs() << "Res divided by Sizes[i]:\n";
dbgs() << "Quotient: " << *Q << "\n";
dbgs() << "Remainder: " << *R << "\n";
});
Res = Q;
// Do not record the last subscript corresponding to the size of elements in
// the array.
if (i == Last) {
// Bail out if the remainder is too complex.
if (isa<SCEVAddRecExpr>(R)) {
Subscripts.clear();
Sizes.clear();
return;
}
continue;
}
// Record the access function for the current subscript.
Subscripts.push_back(R);
}
// Also push in last position the remainder of the last division: it will be
// the access function of the innermost dimension.
Subscripts.push_back(Res);
std::reverse(Subscripts.begin(), Subscripts.end());
LLVM_DEBUG({
dbgs() << "Subscripts:\n";
for (const SCEV *S : Subscripts)
dbgs() << *S << "\n";
});
}
/// Splits the SCEV into two vectors of SCEVs representing the subscripts and
/// sizes of an array access. Returns the remainder of the delinearization that
/// is the offset start of the array. The SCEV->delinearize algorithm computes
/// the multiples of SCEV coefficients: that is a pattern matching of sub
/// expressions in the stride and base of a SCEV corresponding to the
/// computation of a GCD (greatest common divisor) of base and stride. When
/// SCEV->delinearize fails, it returns the SCEV unchanged.
///
/// For example: when analyzing the memory access A[i][j][k] in this loop nest
///
/// void foo(long n, long m, long o, double A[n][m][o]) {
///
/// for (long i = 0; i < n; i++)
/// for (long j = 0; j < m; j++)
/// for (long k = 0; k < o; k++)
/// A[i][j][k] = 1.0;
/// }
///
/// the delinearization input is the following AddRec SCEV:
///
/// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
///
/// From this SCEV, we are able to say that the base offset of the access is %A
/// because it appears as an offset that does not divide any of the strides in
/// the loops:
///
/// CHECK: Base offset: %A
///
/// and then SCEV->delinearize determines the size of some of the dimensions of
/// the array as these are the multiples by which the strides are happening:
///
/// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
///
/// Note that the outermost dimension remains of UnknownSize because there are
/// no strides that would help identifying the size of the last dimension: when
/// the array has been statically allocated, one could compute the size of that
/// dimension by dividing the overall size of the array by the size of the known
/// dimensions: %m * %o * 8.
///
/// Finally delinearize provides the access functions for the array reference
/// that does correspond to A[i][j][k] of the above C testcase:
///
/// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
///
/// The testcases are checking the output of a function pass:
/// DelinearizationPass that walks through all loads and stores of a function
/// asking for the SCEV of the memory access with respect to all enclosing
/// loops, calling SCEV->delinearize on that and printing the results.
void ScalarEvolution::delinearize(const SCEV *Expr,
SmallVectorImpl<const SCEV *> &Subscripts,
SmallVectorImpl<const SCEV *> &Sizes,
const SCEV *ElementSize) {
// First step: collect parametric terms.
SmallVector<const SCEV *, 4> Terms;
collectParametricTerms(Expr, Terms);
if (Terms.empty())
return;
// Second step: find subscript sizes.
findArrayDimensions(Terms, Sizes, ElementSize);
if (Sizes.empty())
return;
// Third step: compute the access functions for each subscript.
computeAccessFunctions(Expr, Subscripts, Sizes);
if (Subscripts.empty())
return;
LLVM_DEBUG({
dbgs() << "succeeded to delinearize " << *Expr << "\n";
dbgs() << "ArrayDecl[UnknownSize]";
for (const SCEV *S : Sizes)
dbgs() << "[" << *S << "]";
dbgs() << "\nArrayRef";
for (const SCEV *S : Subscripts)
dbgs() << "[" << *S << "]";
dbgs() << "\n";
});
}
//===----------------------------------------------------------------------===//
// SCEVCallbackVH Class Implementation
//===----------------------------------------------------------------------===//
void ScalarEvolution::SCEVCallbackVH::deleted() {
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->eraseValueFromMap(getValPtr());
// this now dangles!
}
void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
// Forget all the expressions associated with users of the old value,
// so that future queries will recompute the expressions using the new
// value.
Value *Old = getValPtr();
SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
SmallPtrSet<User *, 8> Visited;
while (!Worklist.empty()) {
User *U = Worklist.pop_back_val();
// Deleting the Old value will cause this to dangle. Postpone
// that until everything else is done.
if (U == Old)
continue;
if (!Visited.insert(U).second)
continue;
if (PHINode *PN = dyn_cast<PHINode>(U))
SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->eraseValueFromMap(U);
Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
}
// Delete the Old value.
if (PHINode *PN = dyn_cast<PHINode>(Old))
SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->eraseValueFromMap(Old);
// this now dangles!
}
ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
: CallbackVH(V), SE(se) {}
//===----------------------------------------------------------------------===//
// ScalarEvolution Class Implementation
//===----------------------------------------------------------------------===//
ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
AssumptionCache &AC, DominatorTree &DT,
LoopInfo &LI)
: F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64),
LoopDispositions(64), BlockDispositions(64) {
// To use guards for proving predicates, we need to scan every instruction in
// relevant basic blocks, and not just terminators. Doing this is a waste of
// time if the IR does not actually contain any calls to
// @llvm.experimental.guard, so do a quick check and remember this beforehand.
//
// This pessimizes the case where a pass that preserves ScalarEvolution wants
// to _add_ guards to the module when there weren't any before, and wants
// ScalarEvolution to optimize based on those guards. For now we prefer to be
// efficient in lieu of being smart in that rather obscure case.
auto *GuardDecl = F.getParent()->getFunction(
Intrinsic::getName(Intrinsic::experimental_guard));
HasGuards = GuardDecl && !GuardDecl->use_empty();
}
ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
: F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
ValueExprMap(std::move(Arg.ValueExprMap)),
PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
PendingPhiRanges(std::move(Arg.PendingPhiRanges)),
PendingMerges(std::move(Arg.PendingMerges)),
MinTrailingZerosCache(std::move(Arg.MinTrailingZerosCache)),
BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
PredicatedBackedgeTakenCounts(
std::move(Arg.PredicatedBackedgeTakenCounts)),
ConstantEvolutionLoopExitValue(
std::move(Arg.ConstantEvolutionLoopExitValue)),
ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
LoopDispositions(std::move(Arg.LoopDispositions)),
LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
BlockDispositions(std::move(Arg.BlockDispositions)),
UnsignedRanges(std::move(Arg.UnsignedRanges)),
SignedRanges(std::move(Arg.SignedRanges)),
UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
UniquePreds(std::move(Arg.UniquePreds)),
SCEVAllocator(std::move(Arg.SCEVAllocator)),
LoopUsers(std::move(Arg.LoopUsers)),
PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
FirstUnknown(Arg.FirstUnknown) {
Arg.FirstUnknown = nullptr;
}
ScalarEvolution::~ScalarEvolution() {
// Iterate through all the SCEVUnknown instances and call their
// destructors, so that they release their references to their values.
for (SCEVUnknown *U = FirstUnknown; U;) {
SCEVUnknown *Tmp = U;
U = U->Next;
Tmp->~SCEVUnknown();
}
FirstUnknown = nullptr;
ExprValueMap.clear();
ValueExprMap.clear();
HasRecMap.clear();
// Free any extra memory created for ExitNotTakenInfo in the unlikely event
// that a loop had multiple computable exits.
for (auto &BTCI : BackedgeTakenCounts)
BTCI.second.clear();
for (auto &BTCI : PredicatedBackedgeTakenCounts)
BTCI.second.clear();
assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
assert(PendingPhiRanges.empty() && "getRangeRef garbage");
assert(PendingMerges.empty() && "isImpliedViaMerge garbage");
assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
}
bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
}
static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
const Loop *L) {
// Print all inner loops first
for (Loop *I : *L)
PrintLoopInfo(OS, SE, I);
OS << "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
SmallVector<BasicBlock *, 8> ExitingBlocks;
L->getExitingBlocks(ExitingBlocks);
if (ExitingBlocks.size() != 1)
OS << "<multiple exits> ";
if (SE->hasLoopInvariantBackedgeTakenCount(L))
OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L) << "\n";
else
OS << "Unpredictable backedge-taken count.\n";
if (ExitingBlocks.size() > 1)
for (BasicBlock *ExitingBlock : ExitingBlocks) {
OS << " exit count for " << ExitingBlock->getName() << ": "
<< *SE->getExitCount(L, ExitingBlock) << "\n";
}
OS << "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
if (!isa<SCEVCouldNotCompute>(SE->getConstantMaxBackedgeTakenCount(L))) {
OS << "max backedge-taken count is " << *SE->getConstantMaxBackedgeTakenCount(L);
if (SE->isBackedgeTakenCountMaxOrZero(L))
OS << ", actual taken count either this or zero.";
} else {
OS << "Unpredictable max backedge-taken count. ";
}
OS << "\n"
"Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
SCEVUnionPredicate Pred;
auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
if (!isa<SCEVCouldNotCompute>(PBT)) {
OS << "Predicated backedge-taken count is " << *PBT << "\n";
OS << " Predicates:\n";
Pred.print(OS, 4);
} else {
OS << "Unpredictable predicated backedge-taken count. ";
}
OS << "\n";
if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
OS << "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";
OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n";
}
}
static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
switch (LD) {
case ScalarEvolution::LoopVariant:
return "Variant";
case ScalarEvolution::LoopInvariant:
return "Invariant";
case ScalarEvolution::LoopComputable:
return "Computable";
}
llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
}
void ScalarEvolution::print(raw_ostream &OS) const {
// ScalarEvolution's implementation of the print method is to print
// out SCEV values of all instructions that are interesting. Doing
// this potentially causes it to create new SCEV objects though,
// which technically conflicts with the const qualifier. This isn't
// observable from outside the class though, so casting away the
// const isn't dangerous.
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
if (ClassifyExpressions) {
OS << "Classifying expressions for: ";
F.printAsOperand(OS, /*PrintType=*/false);
OS << "\n";
for (Instruction &I : instructions(F))
if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
OS << I << '\n';
OS << " --> ";
const SCEV *SV = SE.getSCEV(&I);
SV->print(OS);
if (!isa<SCEVCouldNotCompute>(SV)) {
OS << " U: ";
SE.getUnsignedRange(SV).print(OS);
OS << " S: ";
SE.getSignedRange(SV).print(OS);
}
const Loop *L = LI.getLoopFor(I.getParent());
const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
if (AtUse != SV) {
OS << " --> ";
AtUse->print(OS);
if (!isa<SCEVCouldNotCompute>(AtUse)) {
OS << " U: ";
SE.getUnsignedRange(AtUse).print(OS);
OS << " S: ";
SE.getSignedRange(AtUse).print(OS);
}
}
if (L) {
OS << "\t\t" "Exits: ";
const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
if (!SE.isLoopInvariant(ExitValue, L)) {
OS << "<<Unknown>>";
} else {
OS << *ExitValue;
}
bool First = true;
for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
if (First) {
OS << "\t\t" "LoopDispositions: { ";
First = false;
} else {
OS << ", ";
}
Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
}
for (auto *InnerL : depth_first(L)) {
if (InnerL == L)
continue;
if (First) {
OS << "\t\t" "LoopDispositions: { ";
First = false;
} else {
OS << ", ";
}
InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
}
OS << " }";
}
OS << "\n";
}
}
OS << "Determining loop execution counts for: ";
F.printAsOperand(OS, /*PrintType=*/false);
OS << "\n";
for (Loop *I : LI)
PrintLoopInfo(OS, &SE, I);
}
ScalarEvolution::LoopDisposition
ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
auto &Values = LoopDispositions[S];
for (auto &V : Values) {
if (V.getPointer() == L)
return V.getInt();
}
Values.emplace_back(L, LoopVariant);
LoopDisposition D = computeLoopDisposition(S, L);
auto &Values2 = LoopDispositions[S];
for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
if (V.getPointer() == L) {
V.setInt(D);
break;
}
}
return D;
}
ScalarEvolution::LoopDisposition
ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
switch (static_cast<SCEVTypes>(S->getSCEVType())) {
case scConstant:
return LoopInvariant;
case scTruncate:
case scZeroExtend:
case scSignExtend:
return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
case scAddRecExpr: {
const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
// If L is the addrec's loop, it's computable.
if (AR->getLoop() == L)
return LoopComputable;
// Add recurrences are never invariant in the function-body (null loop).
if (!L)
return LoopVariant;
// Everything that is not defined at loop entry is variant.
if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader()))
return LoopVariant;
assert(!L->contains(AR->getLoop()) && "Containing loop's header does not"
" dominate the contained loop's header?");
// This recurrence is invariant w.r.t. L if AR's loop contains L.
if (AR->getLoop()->contains(L))
return LoopInvariant;
// This recurrence is variant w.r.t. L if any of its operands
// are variant.
for (auto *Op : AR->operands())
if (!isLoopInvariant(Op, L))
return LoopVariant;
// Otherwise it's loop-invariant.
return LoopInvariant;
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr: {
bool HasVarying = false;
for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
LoopDisposition D = getLoopDisposition(Op, L);
if (D == LoopVariant)
return LoopVariant;
if (D == LoopComputable)
HasVarying = true;
}
return HasVarying ? LoopComputable : LoopInvariant;
}
case scUDivExpr: {
const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
if (LD == LoopVariant)
return LoopVariant;
LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
if (RD == LoopVariant)
return LoopVariant;
return (LD == LoopInvariant && RD == LoopInvariant) ?
LoopInvariant : LoopComputable;
}
case scUnknown:
// All non-instruction values are loop invariant. All instructions are loop
// invariant if they are not contained in the specified loop.
// Instructions are never considered invariant in the function body
// (null loop) because they are defined within the "loop".
if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
return LoopInvariant;
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
}
llvm_unreachable("Unknown SCEV kind!");
}
bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
return getLoopDisposition(S, L) == LoopInvariant;
}
bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
return getLoopDisposition(S, L) == LoopComputable;
}
ScalarEvolution::BlockDisposition
ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
auto &Values = BlockDispositions[S];
for (auto &V : Values) {
if (V.getPointer() == BB)
return V.getInt();
}
Values.emplace_back(BB, DoesNotDominateBlock);
BlockDisposition D = computeBlockDisposition(S, BB);
auto &Values2 = BlockDispositions[S];
for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
if (V.getPointer() == BB) {
V.setInt(D);
break;
}
}
return D;
}
ScalarEvolution::BlockDisposition
ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
switch (static_cast<SCEVTypes>(S->getSCEVType())) {
case scConstant:
return ProperlyDominatesBlock;
case scTruncate:
case scZeroExtend:
case scSignExtend:
return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
case scAddRecExpr: {
// This uses a "dominates" query instead of "properly dominates" query
// to test for proper dominance too, because the instruction which
// produces the addrec's value is a PHI, and a PHI effectively properly
// dominates its entire containing block.
const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
if (!DT.dominates(AR->getLoop()->getHeader(), BB))
return DoesNotDominateBlock;
// Fall through into SCEVNAryExpr handling.
LLVM_FALLTHROUGH;
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr: {
const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
bool Proper = true;
for (const SCEV *NAryOp : NAry->operands()) {
BlockDisposition D = getBlockDisposition(NAryOp, BB);
if (D == DoesNotDominateBlock)
return DoesNotDominateBlock;
if (D == DominatesBlock)
Proper = false;
}
return Proper ? ProperlyDominatesBlock : DominatesBlock;
}
case scUDivExpr: {
const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
BlockDisposition LD = getBlockDisposition(LHS, BB);
if (LD == DoesNotDominateBlock)
return DoesNotDominateBlock;
BlockDisposition RD = getBlockDisposition(RHS, BB);
if (RD == DoesNotDominateBlock)
return DoesNotDominateBlock;
return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
ProperlyDominatesBlock : DominatesBlock;
}
case scUnknown:
if (Instruction *I =
dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
if (I->getParent() == BB)
return DominatesBlock;
if (DT.properlyDominates(I->getParent(), BB))
return ProperlyDominatesBlock;
return DoesNotDominateBlock;
}
return ProperlyDominatesBlock;
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
}
llvm_unreachable("Unknown SCEV kind!");
}
bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
return getBlockDisposition(S, BB) >= DominatesBlock;
}
bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
}
bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
}
bool ScalarEvolution::ExitLimit::hasOperand(const SCEV *S) const {
auto IsS = [&](const SCEV *X) { return S == X; };
auto ContainsS = [&](const SCEV *X) {
return !isa<SCEVCouldNotCompute>(X) && SCEVExprContains(X, IsS);
};
return ContainsS(ExactNotTaken) || ContainsS(MaxNotTaken);
}
void
ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
ValuesAtScopes.erase(S);
LoopDispositions.erase(S);
BlockDispositions.erase(S);
UnsignedRanges.erase(S);
SignedRanges.erase(S);
ExprValueMap.erase(S);
HasRecMap.erase(S);
MinTrailingZerosCache.erase(S);
for (auto I = PredicatedSCEVRewrites.begin();
I != PredicatedSCEVRewrites.end();) {
std::pair<const SCEV *, const Loop *> Entry = I->first;
if (Entry.first == S)
PredicatedSCEVRewrites.erase(I++);
else
++I;
}
auto RemoveSCEVFromBackedgeMap =
[S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
for (auto I = Map.begin(), E = Map.end(); I != E;) {
BackedgeTakenInfo &BEInfo = I->second;
if (BEInfo.hasOperand(S, this)) {
BEInfo.clear();
Map.erase(I++);
} else
++I;
}
};
RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
}
void
ScalarEvolution::getUsedLoops(const SCEV *S,
SmallPtrSetImpl<const Loop *> &LoopsUsed) {
struct FindUsedLoops {
FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed)
: LoopsUsed(LoopsUsed) {}
SmallPtrSetImpl<const Loop *> &LoopsUsed;
bool follow(const SCEV *S) {
if (auto *AR = dyn_cast<SCEVAddRecExpr>(S))
LoopsUsed.insert(AR->getLoop());
return true;
}
bool isDone() const { return false; }
};
FindUsedLoops F(LoopsUsed);
SCEVTraversal<FindUsedLoops>(F).visitAll(S);
}
void ScalarEvolution::addToLoopUseLists(const SCEV *S) {
SmallPtrSet<const Loop *, 8> LoopsUsed;
getUsedLoops(S, LoopsUsed);
for (auto *L : LoopsUsed)
LoopUsers[L].push_back(S);
}
void ScalarEvolution::verify() const {
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
ScalarEvolution SE2(F, TLI, AC, DT, LI);
SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end());
// Map's SCEV expressions from one ScalarEvolution "universe" to another.
struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> {
SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {}
const SCEV *visitConstant(const SCEVConstant *Constant) {
return SE.getConstant(Constant->getAPInt());
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
return SE.getUnknown(Expr->getValue());
}
const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
return SE.getCouldNotCompute();
}
};
SCEVMapper SCM(SE2);
while (!LoopStack.empty()) {
auto *L = LoopStack.pop_back_val();
LoopStack.insert(LoopStack.end(), L->begin(), L->end());
auto *CurBECount = SCM.visit(
const_cast<ScalarEvolution *>(this)->getBackedgeTakenCount(L));
auto *NewBECount = SE2.getBackedgeTakenCount(L);
if (CurBECount == SE2.getCouldNotCompute() ||
NewBECount == SE2.getCouldNotCompute()) {
// NB! This situation is legal, but is very suspicious -- whatever pass
// change the loop to make a trip count go from could not compute to
// computable or vice-versa *should have* invalidated SCEV. However, we
// choose not to assert here (for now) since we don't want false
// positives.
continue;
}
if (containsUndefs(CurBECount) || containsUndefs(NewBECount)) {
// SCEV treats "undef" as an unknown but consistent value (i.e. it does
// not propagate undef aggressively). This means we can (and do) fail
// verification in cases where a transform makes the trip count of a loop
// go from "undef" to "undef+1" (say). The transform is fine, since in
// both cases the loop iterates "undef" times, but SCEV thinks we
// increased the trip count of the loop by 1 incorrectly.
continue;
}
if (SE.getTypeSizeInBits(CurBECount->getType()) >
SE.getTypeSizeInBits(NewBECount->getType()))
NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType());
else if (SE.getTypeSizeInBits(CurBECount->getType()) <
SE.getTypeSizeInBits(NewBECount->getType()))
CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType());
const SCEV *Delta = SE2.getMinusSCEV(CurBECount, NewBECount);
// Unless VerifySCEVStrict is set, we only compare constant deltas.
if ((VerifySCEVStrict || isa<SCEVConstant>(Delta)) && !Delta->isZero()) {
dbgs() << "Trip Count for " << *L << " Changed!\n";
dbgs() << "Old: " << *CurBECount << "\n";
dbgs() << "New: " << *NewBECount << "\n";
dbgs() << "Delta: " << *Delta << "\n";
std::abort();
}
}
}
bool ScalarEvolution::invalidate(
Function &F, const PreservedAnalyses &PA,
FunctionAnalysisManager::Invalidator &Inv) {
// Invalidate the ScalarEvolution object whenever it isn't preserved or one
// of its dependencies is invalidated.
auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
Inv.invalidate<AssumptionAnalysis>(F, PA) ||
Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
Inv.invalidate<LoopAnalysis>(F, PA);
}
AnalysisKey ScalarEvolutionAnalysis::Key;
ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
FunctionAnalysisManager &AM) {
return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
AM.getResult<AssumptionAnalysis>(F),
AM.getResult<DominatorTreeAnalysis>(F),
AM.getResult<LoopAnalysis>(F));
}
PreservedAnalyses
ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) {
AM.getResult<ScalarEvolutionAnalysis>(F).verify();
return PreservedAnalyses::all();
}
PreservedAnalyses
ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
return PreservedAnalyses::all();
}
INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
"Scalar Evolution Analysis", false, true)
INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
"Scalar Evolution Analysis", false, true)
char ScalarEvolutionWrapperPass::ID = 0;
ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
}
bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
SE.reset(new ScalarEvolution(
F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F),
getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
return false;
}
void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
SE->print(OS);
}
void ScalarEvolutionWrapperPass::verifyAnalysis() const {
if (!VerifySCEV)
return;
SE->verify();
}
void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AU.addRequiredTransitive<AssumptionCacheTracker>();
AU.addRequiredTransitive<LoopInfoWrapperPass>();
AU.addRequiredTransitive<DominatorTreeWrapperPass>();
AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
}
const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS,
const SCEV *RHS) {
FoldingSetNodeID ID;
assert(LHS->getType() == RHS->getType() &&
"Type mismatch between LHS and RHS");
// Unique this node based on the arguments
ID.AddInteger(SCEVPredicate::P_Equal);
ID.AddPointer(LHS);
ID.AddPointer(RHS);
void *IP = nullptr;
if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
return S;
SCEVEqualPredicate *Eq = new (SCEVAllocator)
SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
UniquePreds.InsertNode(Eq, IP);
return Eq;
}
const SCEVPredicate *ScalarEvolution::getWrapPredicate(
const SCEVAddRecExpr *AR,
SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
FoldingSetNodeID ID;
// Unique this node based on the arguments
ID.AddInteger(SCEVPredicate::P_Wrap);
ID.AddPointer(AR);
ID.AddInteger(AddedFlags);
void *IP = nullptr;
if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
return S;
auto *OF = new (SCEVAllocator)
SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
UniquePreds.InsertNode(OF, IP);
return OF;
}
namespace {
class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
public:
/// Rewrites \p S in the context of a loop L and the SCEV predication
/// infrastructure.
///
/// If \p Pred is non-null, the SCEV expression is rewritten to respect the
/// equivalences present in \p Pred.
///
/// If \p NewPreds is non-null, rewrite is free to add further predicates to
/// \p NewPreds such that the result will be an AddRecExpr.
static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
SCEVUnionPredicate *Pred) {
SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
return Rewriter.visit(S);
}
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
if (Pred) {
auto ExprPreds = Pred->getPredicatesForExpr(Expr);
for (auto *Pred : ExprPreds)
if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
if (IPred->getLHS() == Expr)
return IPred->getRHS();
}
return convertToAddRecWithPreds(Expr);
}
const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
const SCEV *Operand = visit(Expr->getOperand());
const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
if (AR && AR->getLoop() == L && AR->isAffine()) {
// This couldn't be folded because the operand didn't have the nuw
// flag. Add the nusw flag as an assumption that we could make.
const SCEV *Step = AR->getStepRecurrence(SE);
Type *Ty = Expr->getType();
if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
SE.getSignExtendExpr(Step, Ty), L,
AR->getNoWrapFlags());
}
return SE.getZeroExtendExpr(Operand, Expr->getType());
}
const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
const SCEV *Operand = visit(Expr->getOperand());
const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
if (AR && AR->getLoop() == L && AR->isAffine()) {
// This couldn't be folded because the operand didn't have the nsw
// flag. Add the nssw flag as an assumption that we could make.
const SCEV *Step = AR->getStepRecurrence(SE);
Type *Ty = Expr->getType();
if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
SE.getSignExtendExpr(Step, Ty), L,
AR->getNoWrapFlags());
}
return SE.getSignExtendExpr(Operand, Expr->getType());
}
private:
explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
SCEVUnionPredicate *Pred)
: SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
bool addOverflowAssumption(const SCEVPredicate *P) {
if (!NewPreds) {
// Check if we've already made this assumption.
return Pred && Pred->implies(P);
}
NewPreds->insert(P);
return true;
}
bool addOverflowAssumption(const SCEVAddRecExpr *AR,
SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
auto *A = SE.getWrapPredicate(AR, AddedFlags);
return addOverflowAssumption(A);
}
// If \p Expr represents a PHINode, we try to see if it can be represented
// as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible
// to add this predicate as a runtime overflow check, we return the AddRec.
// If \p Expr does not meet these conditions (is not a PHI node, or we
// couldn't create an AddRec for it, or couldn't add the predicate), we just
// return \p Expr.
const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) {
if (!isa<PHINode>(Expr->getValue()))
return Expr;
Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr);
if (!PredicatedRewrite)
return Expr;
for (auto *P : PredicatedRewrite->second){
// Wrap predicates from outer loops are not supported.
if (auto *WP = dyn_cast<const SCEVWrapPredicate>(P)) {
auto *AR = cast<const SCEVAddRecExpr>(WP->getExpr());
if (L != AR->getLoop())
return Expr;
}
if (!addOverflowAssumption(P))
return Expr;
}
return PredicatedRewrite->first;
}
SmallPtrSetImpl<const SCEVPredicate *> *NewPreds;
SCEVUnionPredicate *Pred;
const Loop *L;
};
} // end anonymous namespace
const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
SCEVUnionPredicate &Preds) {
return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
}
const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
const SCEV *S, const Loop *L,
SmallPtrSetImpl<const SCEVPredicate *> &Preds) {
SmallPtrSet<const SCEVPredicate *, 4> TransformPreds;
S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
if (!AddRec)
return nullptr;
// Since the transformation was successful, we can now transfer the SCEV
// predicates.
for (auto *P : TransformPreds)
Preds.insert(P);
return AddRec;
}
/// SCEV predicates
SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
SCEVPredicateKind Kind)
: FastID(ID), Kind(Kind) {}
SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
const SCEV *LHS, const SCEV *RHS)
: SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {
assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match");
assert(LHS != RHS && "LHS and RHS are the same SCEV");
}
bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
if (!Op)
return false;
return Op->LHS == LHS && Op->RHS == RHS;
}
bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
}
SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
const SCEVAddRecExpr *AR,
IncrementWrapFlags Flags)
: SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
}
bool SCEVWrapPredicate::isAlwaysTrue() const {
SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
IncrementWrapFlags IFlags = Flags;
if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
IFlags = clearFlags(IFlags, IncrementNSSW);
return IFlags == IncrementAnyWrap;
}
void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
OS.indent(Depth) << *getExpr() << " Added Flags: ";
if (SCEVWrapPredicate::IncrementNUSW & getFlags())
OS << "<nusw>";
if (SCEVWrapPredicate::IncrementNSSW & getFlags())
OS << "<nssw>";
OS << "\n";
}
SCEVWrapPredicate::IncrementWrapFlags
SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
ScalarEvolution &SE) {
IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
// We can safely transfer the NSW flag as NSSW.
if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
ImpliedFlags = IncrementNSSW;
if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
// If the increment is positive, the SCEV NUW flag will also imply the
// WrapPredicate NUSW flag.
if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
if (Step->getValue()->getValue().isNonNegative())
ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
}
return ImpliedFlags;
}
/// Union predicates don't get cached so create a dummy set ID for it.
SCEVUnionPredicate::SCEVUnionPredicate()
: SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
bool SCEVUnionPredicate::isAlwaysTrue() const {
return all_of(Preds,
[](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
}
ArrayRef<const SCEVPredicate *>
SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
auto I = SCEVToPreds.find(Expr);
if (I == SCEVToPreds.end())
return ArrayRef<const SCEVPredicate *>();
return I->second;
}
bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
return all_of(Set->Preds,
[this](const SCEVPredicate *I) { return this->implies(I); });
auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
if (ScevPredsIt == SCEVToPreds.end())
return false;
auto &SCEVPreds = ScevPredsIt->second;
return any_of(SCEVPreds,
[N](const SCEVPredicate *I) { return I->implies(N); });
}
const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
for (auto Pred : Preds)
Pred->print(OS, Depth);
}
void SCEVUnionPredicate::add(const SCEVPredicate *N) {
if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
for (auto Pred : Set->Preds)
add(Pred);
return;
}
if (implies(N))
return;
const SCEV *Key = N->getExpr();
assert(Key && "Only SCEVUnionPredicate doesn't have an "
" associated expression!");
SCEVToPreds[Key].push_back(N);
Preds.push_back(N);
}
PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
Loop &L)
: SE(SE), L(L) {}
const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
const SCEV *Expr = SE.getSCEV(V);
RewriteEntry &Entry = RewriteMap[Expr];
// If we already have an entry and the version matches, return it.
if (Entry.second && Generation == Entry.first)
return Entry.second;
// We found an entry but it's stale. Rewrite the stale entry
// according to the current predicate.
if (Entry.second)
Expr = Entry.second;
const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
Entry = {Generation, NewSCEV};
return NewSCEV;
}
const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
if (!BackedgeCount) {
SCEVUnionPredicate BackedgePred;
BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
addPredicate(BackedgePred);
}
return BackedgeCount;
}
void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
if (Preds.implies(&Pred))
return;
Preds.add(&Pred);
updateGeneration();
}
const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
return Preds;
}
void PredicatedScalarEvolution::updateGeneration() {
// If the generation number wrapped recompute everything.
if (++Generation == 0) {
for (auto &II : RewriteMap) {
const SCEV *Rewritten = II.second.second;
II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
}
}
}
void PredicatedScalarEvolution::setNoOverflow(
Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
const SCEV *Expr = getSCEV(V);
const auto *AR = cast<SCEVAddRecExpr>(Expr);
auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
// Clear the statically implied flags.
Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
addPredicate(*SE.getWrapPredicate(AR, Flags));
auto II = FlagsMap.insert({V, Flags});
if (!II.second)
II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
}
bool PredicatedScalarEvolution::hasNoOverflow(
Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
const SCEV *Expr = getSCEV(V);
const auto *AR = cast<SCEVAddRecExpr>(Expr);
Flags = SCEVWrapPredicate::clearFlags(
Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
auto II = FlagsMap.find(V);
if (II != FlagsMap.end())
Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
return Flags == SCEVWrapPredicate::IncrementAnyWrap;
}
const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
const SCEV *Expr = this->getSCEV(V);
SmallPtrSet<const SCEVPredicate *, 4> NewPreds;
auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);
if (!New)
return nullptr;
for (auto *P : NewPreds)
Preds.add(P);
updateGeneration();
RewriteMap[SE.getSCEV(V)] = {Generation, New};
return New;
}
PredicatedScalarEvolution::PredicatedScalarEvolution(
const PredicatedScalarEvolution &Init)
: RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
for (auto I : Init.FlagsMap)
FlagsMap.insert(I);
}
void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
// For each block.
for (auto *BB : L.getBlocks())
for (auto &I : *BB) {
if (!SE.isSCEVable(I.getType()))
continue;
auto *Expr = SE.getSCEV(&I);
auto II = RewriteMap.find(Expr);
if (II == RewriteMap.end())
continue;
// Don't print things that are not interesting.
if (II->second.second == Expr)
continue;
OS.indent(Depth) << "[PSE]" << I << ":\n";
OS.indent(Depth + 2) << *Expr << "\n";
OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
}
}
// Match the mathematical pattern A - (A / B) * B, where A and B can be
// arbitrary expressions.
// It's not always easy, as A and B can be folded (imagine A is X / 2, and B is
// 4, A / B becomes X / 8).
bool ScalarEvolution::matchURem(const SCEV *Expr, const SCEV *&LHS,
const SCEV *&RHS) {
const auto *Add = dyn_cast<SCEVAddExpr>(Expr);
if (Add == nullptr || Add->getNumOperands() != 2)
return false;
const SCEV *A = Add->getOperand(1);
const auto *Mul = dyn_cast<SCEVMulExpr>(Add->getOperand(0));
if (Mul == nullptr)
return false;
const auto MatchURemWithDivisor = [&](const SCEV *B) {
// (SomeExpr + (-(SomeExpr / B) * B)).
if (Expr == getURemExpr(A, B)) {
LHS = A;
RHS = B;
return true;
}
return false;
};
// (SomeExpr + (-1 * (SomeExpr / B) * B)).
if (Mul->getNumOperands() == 3 && isa<SCEVConstant>(Mul->getOperand(0)))
return MatchURemWithDivisor(Mul->getOperand(1)) ||
MatchURemWithDivisor(Mul->getOperand(2));
// (SomeExpr + ((-SomeExpr / B) * B)) or (SomeExpr + ((SomeExpr / B) * -B)).
if (Mul->getNumOperands() == 2)
return MatchURemWithDivisor(Mul->getOperand(1)) ||
MatchURemWithDivisor(Mul->getOperand(0)) ||
MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(1))) ||
MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(0)));
return false;
}