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//===- llvm/Analysis/IVDescriptors.cpp - IndVar Descriptors -----*- C++ -*-===//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// This file "describes" induction and recurrence variables.
#include "llvm/Analysis/IVDescriptors.h"
#include "llvm/ADT/ScopeExit.h"
#include "llvm/Analysis/BasicAliasAnalysis.h"
#include "llvm/Analysis/DemandedBits.h"
#include "llvm/Analysis/DomTreeUpdater.h"
#include "llvm/Analysis/GlobalsModRef.h"
#include "llvm/Analysis/InstructionSimplify.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Analysis/MustExecute.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionAliasAnalysis.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/Module.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/ValueHandle.h"
#include "llvm/Pass.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/KnownBits.h"
using namespace llvm;
using namespace llvm::PatternMatch;
#define DEBUG_TYPE "iv-descriptors"
bool RecurrenceDescriptor::areAllUsesIn(Instruction *I,
SmallPtrSetImpl<Instruction *> &Set) {
for (User::op_iterator Use = I->op_begin(), E = I->op_end(); Use != E; ++Use)
if (!Set.count(dyn_cast<Instruction>(*Use)))
return false;
return true;
bool RecurrenceDescriptor::isIntegerRecurrenceKind(RecurKind Kind) {
switch (Kind) {
case RecurKind::Add:
case RecurKind::Mul:
case RecurKind::Or:
case RecurKind::And:
case RecurKind::Xor:
case RecurKind::SMax:
case RecurKind::SMin:
case RecurKind::UMax:
case RecurKind::UMin:
return true;
return false;
bool RecurrenceDescriptor::isFloatingPointRecurrenceKind(RecurKind Kind) {
return (Kind != RecurKind::None) && !isIntegerRecurrenceKind(Kind);
bool RecurrenceDescriptor::isArithmeticRecurrenceKind(RecurKind Kind) {
switch (Kind) {
case RecurKind::Add:
case RecurKind::Mul:
case RecurKind::FAdd:
case RecurKind::FMul:
return true;
return false;
/// Determines if Phi may have been type-promoted. If Phi has a single user
/// that ANDs the Phi with a type mask, return the user. RT is updated to
/// account for the narrower bit width represented by the mask, and the AND
/// instruction is added to CI.
static Instruction *lookThroughAnd(PHINode *Phi, Type *&RT,
SmallPtrSetImpl<Instruction *> &Visited,
SmallPtrSetImpl<Instruction *> &CI) {
if (!Phi->hasOneUse())
return Phi;
const APInt *M = nullptr;
Instruction *I, *J = cast<Instruction>(Phi->use_begin()->getUser());
// Matches either I & 2^x-1 or 2^x-1 & I. If we find a match, we update RT
// with a new integer type of the corresponding bit width.
if (match(J, m_c_And(m_Instruction(I), m_APInt(M)))) {
int32_t Bits = (*M + 1).exactLogBase2();
if (Bits > 0) {
RT = IntegerType::get(Phi->getContext(), Bits);
return J;
return Phi;
/// Compute the minimal bit width needed to represent a reduction whose exit
/// instruction is given by Exit.
static std::pair<Type *, bool> computeRecurrenceType(Instruction *Exit,
DemandedBits *DB,
AssumptionCache *AC,
DominatorTree *DT) {
bool IsSigned = false;
const DataLayout &DL = Exit->getModule()->getDataLayout();
uint64_t MaxBitWidth = DL.getTypeSizeInBits(Exit->getType());
if (DB) {
// Use the demanded bits analysis to determine the bits that are live out
// of the exit instruction, rounding up to the nearest power of two. If the
// use of demanded bits results in a smaller bit width, we know the value
// must be positive (i.e., IsSigned = false), because if this were not the
// case, the sign bit would have been demanded.
auto Mask = DB->getDemandedBits(Exit);
MaxBitWidth = Mask.getBitWidth() - Mask.countLeadingZeros();
if (MaxBitWidth == DL.getTypeSizeInBits(Exit->getType()) && AC && DT) {
// If demanded bits wasn't able to limit the bit width, we can try to use
// value tracking instead. This can be the case, for example, if the value
// may be negative.
auto NumSignBits = ComputeNumSignBits(Exit, DL, 0, AC, nullptr, DT);
auto NumTypeBits = DL.getTypeSizeInBits(Exit->getType());
MaxBitWidth = NumTypeBits - NumSignBits;
KnownBits Bits = computeKnownBits(Exit, DL);
if (!Bits.isNonNegative()) {
// If the value is not known to be non-negative, we set IsSigned to true,
// meaning that we will use sext instructions instead of zext
// instructions to restore the original type.
IsSigned = true;
if (!Bits.isNegative())
// If the value is not known to be negative, we don't known what the
// upper bit is, and therefore, we don't know what kind of extend we
// will need. In this case, just increase the bit width by one bit and
// use sext.
if (!isPowerOf2_64(MaxBitWidth))
MaxBitWidth = NextPowerOf2(MaxBitWidth);
return std::make_pair(Type::getIntNTy(Exit->getContext(), MaxBitWidth),
/// Collect cast instructions that can be ignored in the vectorizer's cost
/// model, given a reduction exit value and the minimal type in which the
/// reduction can be represented.
static void collectCastsToIgnore(Loop *TheLoop, Instruction *Exit,
Type *RecurrenceType,
SmallPtrSetImpl<Instruction *> &Casts) {
SmallVector<Instruction *, 8> Worklist;
SmallPtrSet<Instruction *, 8> Visited;
while (!Worklist.empty()) {
Instruction *Val = Worklist.pop_back_val();
if (auto *Cast = dyn_cast<CastInst>(Val))
if (Cast->getSrcTy() == RecurrenceType) {
// If the source type of a cast instruction is equal to the recurrence
// type, it will be eliminated, and should be ignored in the vectorizer
// cost model.
// Add all operands to the work list if they are loop-varying values that
// we haven't yet visited.
for (Value *O : cast<User>(Val)->operands())
if (auto *I = dyn_cast<Instruction>(O))
if (TheLoop->contains(I) && !Visited.count(I))
bool RecurrenceDescriptor::AddReductionVar(PHINode *Phi, RecurKind Kind,
Loop *TheLoop, FastMathFlags FuncFMF,
RecurrenceDescriptor &RedDes,
DemandedBits *DB,
AssumptionCache *AC,
DominatorTree *DT) {
if (Phi->getNumIncomingValues() != 2)
return false;
// Reduction variables are only found in the loop header block.
if (Phi->getParent() != TheLoop->getHeader())
return false;
// Obtain the reduction start value from the value that comes from the loop
// preheader.
Value *RdxStart = Phi->getIncomingValueForBlock(TheLoop->getLoopPreheader());
// ExitInstruction is the single value which is used outside the loop.
// We only allow for a single reduction value to be used outside the loop.
// This includes users of the reduction, variables (which form a cycle
// which ends in the phi node).
Instruction *ExitInstruction = nullptr;
// Indicates that we found a reduction operation in our scan.
bool FoundReduxOp = false;
// We start with the PHI node and scan for all of the users of this
// instruction. All users must be instructions that can be used as reduction
// variables (such as ADD). We must have a single out-of-block user. The cycle
// must include the original PHI.
bool FoundStartPHI = false;
// To recognize min/max patterns formed by a icmp select sequence, we store
// the number of instruction we saw from the recognized min/max pattern,
// to make sure we only see exactly the two instructions.
unsigned NumCmpSelectPatternInst = 0;
InstDesc ReduxDesc(false, nullptr);
// Data used for determining if the recurrence has been type-promoted.
Type *RecurrenceType = Phi->getType();
SmallPtrSet<Instruction *, 4> CastInsts;
Instruction *Start = Phi;
bool IsSigned = false;
SmallPtrSet<Instruction *, 8> VisitedInsts;
SmallVector<Instruction *, 8> Worklist;
// Return early if the recurrence kind does not match the type of Phi. If the
// recurrence kind is arithmetic, we attempt to look through AND operations
// resulting from the type promotion performed by InstCombine. Vector
// operations are not limited to the legal integer widths, so we may be able
// to evaluate the reduction in the narrower width.
if (RecurrenceType->isFloatingPointTy()) {
if (!isFloatingPointRecurrenceKind(Kind))
return false;
} else {
if (!isIntegerRecurrenceKind(Kind))
return false;
if (isArithmeticRecurrenceKind(Kind))
Start = lookThroughAnd(Phi, RecurrenceType, VisitedInsts, CastInsts);
// Start with all flags set because we will intersect this with the reduction
// flags from all the reduction operations.
FastMathFlags FMF = FastMathFlags::getFast();
// A value in the reduction can be used:
// - By the reduction:
// - Reduction operation:
// - One use of reduction value (safe).
// - Multiple use of reduction value (not safe).
// - PHI:
// - All uses of the PHI must be the reduction (safe).
// - Otherwise, not safe.
// - By instructions outside of the loop (safe).
// * One value may have several outside users, but all outside
// uses must be of the same value.
// - By an instruction that is not part of the reduction (not safe).
// This is either:
// * An instruction type other than PHI or the reduction operation.
// * A PHI in the header other than the initial PHI.
while (!Worklist.empty()) {
Instruction *Cur = Worklist.pop_back_val();
// No Users.
// If the instruction has no users then this is a broken chain and can't be
// a reduction variable.
if (Cur->use_empty())
return false;
bool IsAPhi = isa<PHINode>(Cur);
// A header PHI use other than the original PHI.
if (Cur != Phi && IsAPhi && Cur->getParent() == Phi->getParent())
return false;
// Reductions of instructions such as Div, and Sub is only possible if the
// LHS is the reduction variable.
if (!Cur->isCommutative() && !IsAPhi && !isa<SelectInst>(Cur) &&
!isa<ICmpInst>(Cur) && !isa<FCmpInst>(Cur) &&
return false;
// Any reduction instruction must be of one of the allowed kinds. We ignore
// the starting value (the Phi or an AND instruction if the Phi has been
// type-promoted).
if (Cur != Start) {
ReduxDesc = isRecurrenceInstr(Cur, Kind, ReduxDesc, FuncFMF);
if (!ReduxDesc.isRecurrence())
return false;
// FIXME: FMF is allowed on phi, but propagation is not handled correctly.
if (isa<FPMathOperator>(ReduxDesc.getPatternInst()) && !IsAPhi) {
FastMathFlags CurFMF = ReduxDesc.getPatternInst()->getFastMathFlags();
if (auto *Sel = dyn_cast<SelectInst>(ReduxDesc.getPatternInst())) {
// Accept FMF on either fcmp or select of a min/max idiom.
// TODO: This is a hack to work-around the fact that FMF may not be
// assigned/propagated correctly. If that problem is fixed or we
// standardize on fmin/fmax via intrinsics, this can be removed.
if (auto *FCmp = dyn_cast<FCmpInst>(Sel->getCondition()))
CurFMF |= FCmp->getFastMathFlags();
FMF &= CurFMF;
// Update this reduction kind if we matched a new instruction.
// TODO: Can we eliminate the need for a 2nd InstDesc by keeping 'Kind'
// state accurate while processing the worklist?
if (ReduxDesc.getRecKind() != RecurKind::None)
Kind = ReduxDesc.getRecKind();
bool IsASelect = isa<SelectInst>(Cur);
// A conditional reduction operation must only have 2 or less uses in
// VisitedInsts.
if (IsASelect && (Kind == RecurKind::FAdd || Kind == RecurKind::FMul) &&
hasMultipleUsesOf(Cur, VisitedInsts, 2))
return false;
// A reduction operation must only have one use of the reduction value.
if (!IsAPhi && !IsASelect && !isMinMaxRecurrenceKind(Kind) &&
hasMultipleUsesOf(Cur, VisitedInsts, 1))
return false;
// All inputs to a PHI node must be a reduction value.
if (IsAPhi && Cur != Phi && !areAllUsesIn(Cur, VisitedInsts))
return false;
if (isIntMinMaxRecurrenceKind(Kind) &&
(isa<ICmpInst>(Cur) || isa<SelectInst>(Cur)))
if (isFPMinMaxRecurrenceKind(Kind) &&
(isa<FCmpInst>(Cur) || isa<SelectInst>(Cur)))
// Check whether we found a reduction operator.
FoundReduxOp |= !IsAPhi && Cur != Start;
// Process users of current instruction. Push non-PHI nodes after PHI nodes
// onto the stack. This way we are going to have seen all inputs to PHI
// nodes once we get to them.
SmallVector<Instruction *, 8> NonPHIs;
SmallVector<Instruction *, 8> PHIs;
for (User *U : Cur->users()) {
Instruction *UI = cast<Instruction>(U);
// Check if we found the exit user.
BasicBlock *Parent = UI->getParent();
if (!TheLoop->contains(Parent)) {
// If we already know this instruction is used externally, move on to
// the next user.
if (ExitInstruction == Cur)
// Exit if you find multiple values used outside or if the header phi
// node is being used. In this case the user uses the value of the
// previous iteration, in which case we would loose "VF-1" iterations of
// the reduction operation if we vectorize.
if (ExitInstruction != nullptr || Cur == Phi)
return false;
// The instruction used by an outside user must be the last instruction
// before we feed back to the reduction phi. Otherwise, we loose VF-1
// operations on the value.
if (!is_contained(Phi->operands(), Cur))
return false;
ExitInstruction = Cur;
// Process instructions only once (termination). Each reduction cycle
// value must only be used once, except by phi nodes and min/max
// reductions which are represented as a cmp followed by a select.
InstDesc IgnoredVal(false, nullptr);
if (VisitedInsts.insert(UI).second) {
if (isa<PHINode>(UI))
} else if (!isa<PHINode>(UI) &&
((!isa<FCmpInst>(UI) && !isa<ICmpInst>(UI) &&
!isa<SelectInst>(UI)) ||
(!isConditionalRdxPattern(Kind, UI).isRecurrence() &&
!isMinMaxSelectCmpPattern(UI, IgnoredVal).isRecurrence())))
return false;
// Remember that we completed the cycle.
if (UI == Phi)
FoundStartPHI = true;
Worklist.append(PHIs.begin(), PHIs.end());
Worklist.append(NonPHIs.begin(), NonPHIs.end());
// This means we have seen one but not the other instruction of the
// pattern or more than just a select and cmp.
if (isMinMaxRecurrenceKind(Kind) && NumCmpSelectPatternInst != 2)
return false;
if (!FoundStartPHI || !FoundReduxOp || !ExitInstruction)
return false;
if (Start != Phi) {
// If the starting value is not the same as the phi node, we speculatively
// looked through an 'and' instruction when evaluating a potential
// arithmetic reduction to determine if it may have been type-promoted.
// We now compute the minimal bit width that is required to represent the
// reduction. If this is the same width that was indicated by the 'and', we
// can represent the reduction in the smaller type. The 'and' instruction
// will be eliminated since it will essentially be a cast instruction that
// can be ignore in the cost model. If we compute a different type than we
// did when evaluating the 'and', the 'and' will not be eliminated, and we
// will end up with different kinds of operations in the recurrence
// expression (e.g., IntegerAND, IntegerADD). We give up if this is
// the case.
// The vectorizer relies on InstCombine to perform the actual
// type-shrinking. It does this by inserting instructions to truncate the
// exit value of the reduction to the width indicated by RecurrenceType and
// then extend this value back to the original width. If IsSigned is false,
// a 'zext' instruction will be generated; otherwise, a 'sext' will be
// used.
// TODO: We should not rely on InstCombine to rewrite the reduction in the
// smaller type. We should just generate a correctly typed expression
// to begin with.
Type *ComputedType;
std::tie(ComputedType, IsSigned) =
computeRecurrenceType(ExitInstruction, DB, AC, DT);
if (ComputedType != RecurrenceType)
return false;
// The recurrence expression will be represented in a narrower type. If
// there are any cast instructions that will be unnecessary, collect them
// in CastInsts. Note that the 'and' instruction was already included in
// this list.
// TODO: A better way to represent this may be to tag in some way all the
// instructions that are a part of the reduction. The vectorizer cost
// model could then apply the recurrence type to these instructions,
// without needing a white list of instructions to ignore.
// This may also be useful for the inloop reductions, if it can be
// kept simple enough.
collectCastsToIgnore(TheLoop, ExitInstruction, RecurrenceType, CastInsts);
// We found a reduction var if we have reached the original phi node and we
// only have a single instruction with out-of-loop users.
// The ExitInstruction(Instruction which is allowed to have out-of-loop users)
// is saved as part of the RecurrenceDescriptor.
// Save the description of this reduction variable.
RecurrenceDescriptor RD(RdxStart, ExitInstruction, Kind, FMF,
ReduxDesc.getUnsafeAlgebraInst(), RecurrenceType,
IsSigned, CastInsts);
RedDes = RD;
return true;
RecurrenceDescriptor::isMinMaxSelectCmpPattern(Instruction *I,
const InstDesc &Prev) {
assert((isa<CmpInst>(I) || isa<SelectInst>(I)) &&
"Expected a cmp or select instruction");
// We must handle the select(cmp()) as a single instruction. Advance to the
// select.
CmpInst::Predicate Pred;
if (match(I, m_OneUse(m_Cmp(Pred, m_Value(), m_Value())))) {
if (auto *Select = dyn_cast<SelectInst>(*I->user_begin()))
return InstDesc(Select, Prev.getRecKind());
// Only match select with single use cmp condition.
if (!match(I, m_Select(m_OneUse(m_Cmp(Pred, m_Value(), m_Value())), m_Value(),
return InstDesc(false, I);
// Look for a min/max pattern.
if (match(I, m_UMin(m_Value(), m_Value())))
return InstDesc(I, RecurKind::UMin);
if (match(I, m_UMax(m_Value(), m_Value())))
return InstDesc(I, RecurKind::UMax);
if (match(I, m_SMax(m_Value(), m_Value())))
return InstDesc(I, RecurKind::SMax);
if (match(I, m_SMin(m_Value(), m_Value())))
return InstDesc(I, RecurKind::SMin);
if (match(I, m_OrdFMin(m_Value(), m_Value())))
return InstDesc(I, RecurKind::FMin);
if (match(I, m_OrdFMax(m_Value(), m_Value())))
return InstDesc(I, RecurKind::FMax);
if (match(I, m_UnordFMin(m_Value(), m_Value())))
return InstDesc(I, RecurKind::FMin);
if (match(I, m_UnordFMax(m_Value(), m_Value())))
return InstDesc(I, RecurKind::FMax);
return InstDesc(false, I);
/// Returns true if the select instruction has users in the compare-and-add
/// reduction pattern below. The select instruction argument is the last one
/// in the sequence.
/// %sum.1 = phi ...
/// ...
/// %cmp = fcmp pred %0, %CFP
/// %add = fadd %0, %sum.1
/// %sum.2 = select %cmp, %add, %sum.1
RecurrenceDescriptor::isConditionalRdxPattern(RecurKind Kind, Instruction *I) {
SelectInst *SI = dyn_cast<SelectInst>(I);
if (!SI)
return InstDesc(false, I);
CmpInst *CI = dyn_cast<CmpInst>(SI->getCondition());
// Only handle single use cases for now.
if (!CI || !CI->hasOneUse())
return InstDesc(false, I);
Value *TrueVal = SI->getTrueValue();
Value *FalseVal = SI->getFalseValue();
// Handle only when either of operands of select instruction is a PHI
// node for now.
if ((isa<PHINode>(*TrueVal) && isa<PHINode>(*FalseVal)) ||
(!isa<PHINode>(*TrueVal) && !isa<PHINode>(*FalseVal)))
return InstDesc(false, I);
Instruction *I1 =
isa<PHINode>(*TrueVal) ? dyn_cast<Instruction>(FalseVal)
: dyn_cast<Instruction>(TrueVal);
if (!I1 || !I1->isBinaryOp())
return InstDesc(false, I);
Value *Op1, *Op2;
if ((m_FAdd(m_Value(Op1), m_Value(Op2)).match(I1) ||
m_FSub(m_Value(Op1), m_Value(Op2)).match(I1)) &&
return InstDesc(Kind == RecurKind::FAdd, SI);
if (m_FMul(m_Value(Op1), m_Value(Op2)).match(I1) && (I1->isFast()))
return InstDesc(Kind == RecurKind::FMul, SI);
return InstDesc(false, I);
RecurrenceDescriptor::isRecurrenceInstr(Instruction *I, RecurKind Kind,
InstDesc &Prev, FastMathFlags FMF) {
Instruction *UAI = Prev.getUnsafeAlgebraInst();
if (!UAI && isa<FPMathOperator>(I) && !I->hasAllowReassoc())
UAI = I; // Found an unsafe (unvectorizable) algebra instruction.
switch (I->getOpcode()) {
return InstDesc(false, I);
case Instruction::PHI:
return InstDesc(I, Prev.getRecKind(), Prev.getUnsafeAlgebraInst());
case Instruction::Sub:
case Instruction::Add:
return InstDesc(Kind == RecurKind::Add, I);
case Instruction::Mul:
return InstDesc(Kind == RecurKind::Mul, I);
case Instruction::And:
return InstDesc(Kind == RecurKind::And, I);
case Instruction::Or:
return InstDesc(Kind == RecurKind::Or, I);
case Instruction::Xor:
return InstDesc(Kind == RecurKind::Xor, I);
case Instruction::FDiv:
case Instruction::FMul:
return InstDesc(Kind == RecurKind::FMul, I, UAI);
case Instruction::FSub:
case Instruction::FAdd:
return InstDesc(Kind == RecurKind::FAdd, I, UAI);
case Instruction::Select:
if (Kind == RecurKind::FAdd || Kind == RecurKind::FMul)
return isConditionalRdxPattern(Kind, I);
case Instruction::FCmp:
case Instruction::ICmp:
if (isIntMinMaxRecurrenceKind(Kind) ||
(FMF.noNaNs() && FMF.noSignedZeros() &&
return isMinMaxSelectCmpPattern(I, Prev);
return InstDesc(false, I);
bool RecurrenceDescriptor::hasMultipleUsesOf(
Instruction *I, SmallPtrSetImpl<Instruction *> &Insts,
unsigned MaxNumUses) {
unsigned NumUses = 0;
for (User::op_iterator Use = I->op_begin(), E = I->op_end(); Use != E;
++Use) {
if (Insts.count(dyn_cast<Instruction>(*Use)))
if (NumUses > MaxNumUses)
return true;
return false;
bool RecurrenceDescriptor::isReductionPHI(PHINode *Phi, Loop *TheLoop,
RecurrenceDescriptor &RedDes,
DemandedBits *DB, AssumptionCache *AC,
DominatorTree *DT) {
BasicBlock *Header = TheLoop->getHeader();
Function &F = *Header->getParent();
FastMathFlags FMF;
F.getFnAttribute("no-nans-fp-math").getValueAsString() == "true");
F.getFnAttribute("no-signed-zeros-fp-math").getValueAsString() == "true");
if (AddReductionVar(Phi, RecurKind::Add, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found an ADD reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::Mul, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found a MUL reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::Or, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found an OR reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::And, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found an AND reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::Xor, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found a XOR reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::SMax, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found a SMAX reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::SMin, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found a SMIN reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::UMax, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found a UMAX reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::UMin, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found a UMIN reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::FMul, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found an FMult reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::FAdd, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found an FAdd reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::FMax, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found a float MAX reduction PHI." << *Phi << "\n");
return true;
if (AddReductionVar(Phi, RecurKind::FMin, TheLoop, FMF, RedDes, DB, AC, DT)) {
LLVM_DEBUG(dbgs() << "Found a float MIN reduction PHI." << *Phi << "\n");
return true;
// Not a reduction of known type.
return false;
bool RecurrenceDescriptor::isFirstOrderRecurrence(
PHINode *Phi, Loop *TheLoop,
DenseMap<Instruction *, Instruction *> &SinkAfter, DominatorTree *DT) {
// Ensure the phi node is in the loop header and has two incoming values.
if (Phi->getParent() != TheLoop->getHeader() ||
Phi->getNumIncomingValues() != 2)
return false;
// Ensure the loop has a preheader and a single latch block. The loop
// vectorizer will need the latch to set up the next iteration of the loop.
auto *Preheader = TheLoop->getLoopPreheader();
auto *Latch = TheLoop->getLoopLatch();
if (!Preheader || !Latch)
return false;
// Ensure the phi node's incoming blocks are the loop preheader and latch.
if (Phi->getBasicBlockIndex(Preheader) < 0 ||
Phi->getBasicBlockIndex(Latch) < 0)
return false;
// Get the previous value. The previous value comes from the latch edge while
// the initial value comes form the preheader edge.
auto *Previous = dyn_cast<Instruction>(Phi->getIncomingValueForBlock(Latch));
if (!Previous || !TheLoop->contains(Previous) || isa<PHINode>(Previous) ||
SinkAfter.count(Previous)) // Cannot rely on dominance due to motion.
return false;
// Ensure every user of the phi node is dominated by the previous value.
// The dominance requirement ensures the loop vectorizer will not need to
// vectorize the initial value prior to the first iteration of the loop.
// TODO: Consider extending this sinking to handle memory instructions and
// phis with multiple users.
// Returns true, if all users of I are dominated by DominatedBy.
auto allUsesDominatedBy = [DT](Instruction *I, Instruction *DominatedBy) {
return all_of(I->uses(), [DT, DominatedBy](Use &U) {
return DT->dominates(DominatedBy, U);
if (Phi->hasOneUse()) {
Instruction *I = Phi->user_back();
// If the user of the PHI is also the incoming value, we potentially have a
// reduction and which cannot be handled by sinking.
if (Previous == I)
return false;
// We cannot sink terminator instructions.
if (I->getParent()->getTerminator() == I)
return false;
// Do not try to sink an instruction multiple times (if multiple operands
// are first order recurrences).
// TODO: We can support this case, by sinking the instruction after the
// 'deepest' previous instruction.
if (SinkAfter.find(I) != SinkAfter.end())
return false;
if (DT->dominates(Previous, I)) // We already are good w/o sinking.
return true;
// We can sink any instruction without side effects, as long as all users
// are dominated by the instruction we are sinking after.
if (I->getParent() == Phi->getParent() && !I->mayHaveSideEffects() &&
allUsesDominatedBy(I, Previous)) {
SinkAfter[I] = Previous;
return true;
return allUsesDominatedBy(Phi, Previous);
/// This function returns the identity element (or neutral element) for
/// the operation K.
Constant *RecurrenceDescriptor::getRecurrenceIdentity(RecurKind K, Type *Tp) {
switch (K) {
case RecurKind::Xor:
case RecurKind::Add:
case RecurKind::Or:
// Adding, Xoring, Oring zero to a number does not change it.
return ConstantInt::get(Tp, 0);
case RecurKind::Mul:
// Multiplying a number by 1 does not change it.
return ConstantInt::get(Tp, 1);
case RecurKind::And:
// AND-ing a number with an all-1 value does not change it.
return ConstantInt::get(Tp, -1, true);
case RecurKind::FMul:
// Multiplying a number by 1 does not change it.
return ConstantFP::get(Tp, 1.0L);
case RecurKind::FAdd:
// Adding zero to a number does not change it.
return ConstantFP::get(Tp, 0.0L);
case RecurKind::UMin:
return ConstantInt::get(Tp, -1);
case RecurKind::UMax:
return ConstantInt::get(Tp, 0);
case RecurKind::SMin:
return ConstantInt::get(Tp,
case RecurKind::SMax:
return ConstantInt::get(Tp,
case RecurKind::FMin:
return ConstantFP::getInfinity(Tp, true);
case RecurKind::FMax:
return ConstantFP::getInfinity(Tp, false);
llvm_unreachable("Unknown recurrence kind");
unsigned RecurrenceDescriptor::getOpcode(RecurKind Kind) {
switch (Kind) {
case RecurKind::Add:
return Instruction::Add;
case RecurKind::Mul:
return Instruction::Mul;
case RecurKind::Or:
return Instruction::Or;
case RecurKind::And:
return Instruction::And;
case RecurKind::Xor:
return Instruction::Xor;
case RecurKind::FMul:
return Instruction::FMul;
case RecurKind::FAdd:
return Instruction::FAdd;
case RecurKind::SMax:
case RecurKind::SMin:
case RecurKind::UMax:
case RecurKind::UMin:
return Instruction::ICmp;
case RecurKind::FMax:
case RecurKind::FMin:
return Instruction::FCmp;
llvm_unreachable("Unknown recurrence operation");
SmallVector<Instruction *, 4>
RecurrenceDescriptor::getReductionOpChain(PHINode *Phi, Loop *L) const {
SmallVector<Instruction *, 4> ReductionOperations;
unsigned RedOp = getOpcode(Kind);
// Search down from the Phi to the LoopExitInstr, looking for instructions
// with a single user of the correct type for the reduction.
// Note that we check that the type of the operand is correct for each item in
// the chain, including the last (the loop exit value). This can come up from
// sub, which would otherwise be treated as an add reduction. MinMax also need
// to check for a pair of icmp/select, for which we use getNextInstruction and
// isCorrectOpcode functions to step the right number of instruction, and
// check the icmp/select pair.
// FIXME: We also do not attempt to look through Phi/Select's yet, which might
// be part of the reduction chain, or attempt to looks through And's to find a
// smaller bitwidth. Subs are also currently not allowed (which are usually
// treated as part of a add reduction) as they are expected to generally be
// more expensive than out-of-loop reductions, and need to be costed more
// carefully.
unsigned ExpectedUses = 1;
if (RedOp == Instruction::ICmp || RedOp == Instruction::FCmp)
ExpectedUses = 2;
auto getNextInstruction = [&](Instruction *Cur) {
if (RedOp == Instruction::ICmp || RedOp == Instruction::FCmp) {
// We are expecting a icmp/select pair, which we go to the next select
// instruction if we can. We already know that Cur has 2 uses.
if (isa<SelectInst>(*Cur->user_begin()))
return cast<Instruction>(*Cur->user_begin());
return cast<Instruction>(*std::next(Cur->user_begin()));
return cast<Instruction>(*Cur->user_begin());
auto isCorrectOpcode = [&](Instruction *Cur) {
if (RedOp == Instruction::ICmp || RedOp == Instruction::FCmp) {
Value *LHS, *RHS;
return SelectPatternResult::isMinOrMax(
matchSelectPattern(Cur, LHS, RHS).Flavor);
return Cur->getOpcode() == RedOp;
// The loop exit instruction we check first (as a quick test) but add last. We
// check the opcode is correct (and dont allow them to be Subs) and that they
// have expected to have the expected number of uses. They will have one use
// from the phi and one from a LCSSA value, no matter the type.
if (!isCorrectOpcode(LoopExitInstr) || !LoopExitInstr->hasNUses(2))
return {};
// Check that the Phi has one (or two for min/max) uses.
if (!Phi->hasNUses(ExpectedUses))
return {};
Instruction *Cur = getNextInstruction(Phi);
// Each other instruction in the chain should have the expected number of uses
// and be the correct opcode.
while (Cur != LoopExitInstr) {
if (!isCorrectOpcode(Cur) || !Cur->hasNUses(ExpectedUses))
return {};
Cur = getNextInstruction(Cur);
return ReductionOperations;
InductionDescriptor::InductionDescriptor(Value *Start, InductionKind K,
const SCEV *Step, BinaryOperator *BOp,
SmallVectorImpl<Instruction *> *Casts)
: StartValue(Start), IK(K), Step(Step), InductionBinOp(BOp) {
assert(IK != IK_NoInduction && "Not an induction");
// Start value type should match the induction kind and the value
// itself should not be null.
assert(StartValue && "StartValue is null");
assert((IK != IK_PtrInduction || StartValue->getType()->isPointerTy()) &&
"StartValue is not a pointer for pointer induction");
assert((IK != IK_IntInduction || StartValue->getType()->isIntegerTy()) &&
"StartValue is not an integer for integer induction");
// Check the Step Value. It should be non-zero integer value.
assert((!getConstIntStepValue() || !getConstIntStepValue()->isZero()) &&
"Step value is zero");
assert((IK != IK_PtrInduction || getConstIntStepValue()) &&
"Step value should be constant for pointer induction");
assert((IK == IK_FpInduction || Step->getType()->isIntegerTy()) &&
"StepValue is not an integer");
assert((IK != IK_FpInduction || Step->getType()->isFloatingPointTy()) &&
"StepValue is not FP for FpInduction");
assert((IK != IK_FpInduction ||
(InductionBinOp &&
(InductionBinOp->getOpcode() == Instruction::FAdd ||
InductionBinOp->getOpcode() == Instruction::FSub))) &&
"Binary opcode should be specified for FP induction");
if (Casts) {
for (auto &Inst : *Casts) {
ConstantInt *InductionDescriptor::getConstIntStepValue() const {
if (isa<SCEVConstant>(Step))
return dyn_cast<ConstantInt>(cast<SCEVConstant>(Step)->getValue());
return nullptr;
bool InductionDescriptor::isFPInductionPHI(PHINode *Phi, const Loop *TheLoop,
ScalarEvolution *SE,
InductionDescriptor &D) {
// Here we only handle FP induction variables.
assert(Phi->getType()->isFloatingPointTy() && "Unexpected Phi type");
if (TheLoop->getHeader() != Phi->getParent())
return false;
// The loop may have multiple entrances or multiple exits; we can analyze
// this phi if it has a unique entry value and a unique backedge value.
if (Phi->getNumIncomingValues() != 2)
return false;
Value *BEValue = nullptr, *StartValue = nullptr;
if (TheLoop->contains(Phi->getIncomingBlock(0))) {
BEValue = Phi->getIncomingValue(0);
StartValue = Phi->getIncomingValue(1);
} else {
assert(TheLoop->contains(Phi->getIncomingBlock(1)) &&
"Unexpected Phi node in the loop");
BEValue = Phi->getIncomingValue(1);
StartValue = Phi->getIncomingValue(0);
BinaryOperator *BOp = dyn_cast<BinaryOperator>(BEValue);
if (!BOp)
return false;
Value *Addend = nullptr;
if (BOp->getOpcode() == Instruction::FAdd) {
if (BOp->getOperand(0) == Phi)
Addend = BOp->getOperand(1);
else if (BOp->getOperand(1) == Phi)
Addend = BOp->getOperand(0);
} else if (BOp->getOpcode() == Instruction::FSub)
if (BOp->getOperand(0) == Phi)
Addend = BOp->getOperand(1);
if (!Addend)
return false;
// The addend should be loop invariant
if (auto *I = dyn_cast<Instruction>(Addend))
if (TheLoop->contains(I))
return false;
// FP Step has unknown SCEV
const SCEV *Step = SE->getUnknown(Addend);
D = InductionDescriptor(StartValue, IK_FpInduction, Step, BOp);
return true;
/// This function is called when we suspect that the update-chain of a phi node
/// (whose symbolic SCEV expression sin \p PhiScev) contains redundant casts,
/// that can be ignored. (This can happen when the PSCEV rewriter adds a runtime
/// predicate P under which the SCEV expression for the phi can be the
/// AddRecurrence \p AR; See createAddRecFromPHIWithCast). We want to find the
/// cast instructions that are involved in the update-chain of this induction.
/// A caller that adds the required runtime predicate can be free to drop these
/// cast instructions, and compute the phi using \p AR (instead of some scev
/// expression with casts).
/// For example, without a predicate the scev expression can take the following
/// form:
/// (Ext ix (Trunc iy ( Start + i*Step ) to ix) to iy)
/// It corresponds to the following IR sequence:
/// %for.body:
/// %x = phi i64 [ 0, %ph ], [ %add, %for.body ]
/// %casted_phi = "ExtTrunc i64 %x"
/// %add = add i64 %casted_phi, %step
/// where %x is given in \p PN,
/// PSE.getSCEV(%x) is equal to PSE.getSCEV(%casted_phi) under a predicate,
/// and the IR sequence that "ExtTrunc i64 %x" represents can take one of
/// several forms, for example, such as:
/// ExtTrunc1: %casted_phi = and %x, 2^n-1
/// or:
/// ExtTrunc2: %t = shl %x, m
/// %casted_phi = ashr %t, m
/// If we are able to find such sequence, we return the instructions
/// we found, namely %casted_phi and the instructions on its use-def chain up
/// to the phi (not including the phi).
static bool getCastsForInductionPHI(PredicatedScalarEvolution &PSE,
const SCEVUnknown *PhiScev,
const SCEVAddRecExpr *AR,
SmallVectorImpl<Instruction *> &CastInsts) {
assert(CastInsts.empty() && "CastInsts is expected to be empty.");
auto *PN = cast<PHINode>(PhiScev->getValue());
assert(PSE.getSCEV(PN) == AR && "Unexpected phi node SCEV expression");
const Loop *L = AR->getLoop();
// Find any cast instructions that participate in the def-use chain of
// PhiScev in the loop.
// FORNOW/TODO: We currently expect the def-use chain to include only
// two-operand instructions, where one of the operands is an invariant.
// createAddRecFromPHIWithCasts() currently does not support anything more
// involved than that, so we keep the search simple. This can be
// extended/generalized as needed.
auto getDef = [&](const Value *Val) -> Value * {
const BinaryOperator *BinOp = dyn_cast<BinaryOperator>(Val);
if (!BinOp)
return nullptr;
Value *Op0 = BinOp->getOperand(0);
Value *Op1 = BinOp->getOperand(1);
Value *Def = nullptr;
if (L->isLoopInvariant(Op0))
Def = Op1;
else if (L->isLoopInvariant(Op1))
Def = Op0;
return Def;
// Look for the instruction that defines the induction via the
// loop backedge.
BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
return false;
Value *Val = PN->getIncomingValueForBlock(Latch);
if (!Val)
return false;
// Follow the def-use chain until the induction phi is reached.
// If on the way we encounter a Value that has the same SCEV Expr as the
// phi node, we can consider the instructions we visit from that point
// as part of the cast-sequence that can be ignored.
bool InCastSequence = false;
auto *Inst = dyn_cast<Instruction>(Val);
while (Val != PN) {
// If we encountered a phi node other than PN, or if we left the loop,
// we bail out.
if (!Inst || !L->contains(Inst)) {
return false;
auto *AddRec = dyn_cast<SCEVAddRecExpr>(PSE.getSCEV(Val));
if (AddRec && PSE.areAddRecsEqualWithPreds(AddRec, AR))
InCastSequence = true;
if (InCastSequence) {
// Only the last instruction in the cast sequence is expected to have
// uses outside the induction def-use chain.
if (!CastInsts.empty())
if (!Inst->hasOneUse())
return false;
Val = getDef(Val);
if (!Val)
return false;
Inst = dyn_cast<Instruction>(Val);
return InCastSequence;
bool InductionDescriptor::isInductionPHI(PHINode *Phi, const Loop *TheLoop,
PredicatedScalarEvolution &PSE,
InductionDescriptor &D, bool Assume) {
Type *PhiTy = Phi->getType();
// Handle integer and pointer inductions variables.
// Now we handle also FP induction but not trying to make a
// recurrent expression from the PHI node in-place.
if (!PhiTy->isIntegerTy() && !PhiTy->isPointerTy() && !PhiTy->isFloatTy() &&
!PhiTy->isDoubleTy() && !PhiTy->isHalfTy())
return false;
if (PhiTy->isFloatingPointTy())
return isFPInductionPHI(Phi, TheLoop, PSE.getSE(), D);
const SCEV *PhiScev = PSE.getSCEV(Phi);
const auto *AR = dyn_cast<SCEVAddRecExpr>(PhiScev);
// We need this expression to be an AddRecExpr.
if (Assume && !AR)
AR = PSE.getAsAddRec(Phi);
if (!AR) {
LLVM_DEBUG(dbgs() << "LV: PHI is not a poly recurrence.\n");
return false;
// Record any Cast instructions that participate in the induction update
const auto *SymbolicPhi = dyn_cast<SCEVUnknown>(PhiScev);
// If we started from an UnknownSCEV, and managed to build an addRecurrence
// only after enabling Assume with PSCEV, this means we may have encountered
// cast instructions that required adding a runtime check in order to
// guarantee the correctness of the AddRecurrence respresentation of the
// induction.
if (PhiScev != AR && SymbolicPhi) {
SmallVector<Instruction *, 2> Casts;
if (getCastsForInductionPHI(PSE, SymbolicPhi, AR, Casts))
return isInductionPHI(Phi, TheLoop, PSE.getSE(), D, AR, &Casts);
return isInductionPHI(Phi, TheLoop, PSE.getSE(), D, AR);
bool InductionDescriptor::isInductionPHI(
PHINode *Phi, const Loop *TheLoop, ScalarEvolution *SE,
InductionDescriptor &D, const SCEV *Expr,
SmallVectorImpl<Instruction *> *CastsToIgnore) {
Type *PhiTy = Phi->getType();
// We only handle integer and pointer inductions variables.
if (!PhiTy->isIntegerTy() && !PhiTy->isPointerTy())
return false;
// Check that the PHI is consecutive.
const SCEV *PhiScev = Expr ? Expr : SE->getSCEV(Phi);
const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(PhiScev);
if (!AR) {
LLVM_DEBUG(dbgs() << "LV: PHI is not a poly recurrence.\n");
return false;
if (AR->getLoop() != TheLoop) {
// FIXME: We should treat this as a uniform. Unfortunately, we
// don't currently know how to handled uniform PHIs.
dbgs() << "LV: PHI is a recurrence with respect to an outer loop.\n");
return false;
Value *StartValue =
BasicBlock *Latch = AR->getLoop()->getLoopLatch();
if (!Latch)
return false;
BinaryOperator *BOp =
const SCEV *Step = AR->getStepRecurrence(*SE);
// Calculate the pointer stride and check if it is consecutive.
// The stride may be a constant or a loop invariant integer value.
const SCEVConstant *ConstStep = dyn_cast<SCEVConstant>(Step);
if (!ConstStep && !SE->isLoopInvariant(Step, TheLoop))
return false;
if (PhiTy->isIntegerTy()) {
D = InductionDescriptor(StartValue, IK_IntInduction, Step, BOp,
return true;
assert(PhiTy->isPointerTy() && "The PHI must be a pointer");
// Pointer induction should be a constant.
if (!ConstStep)
return false;
ConstantInt *CV = ConstStep->getValue();
Type *PointerElementType = PhiTy->getPointerElementType();
// The pointer stride cannot be determined if the pointer element type is not
// sized.
if (!PointerElementType->isSized())
return false;
const DataLayout &DL = Phi->getModule()->getDataLayout();
int64_t Size = static_cast<int64_t>(DL.getTypeAllocSize(PointerElementType));
if (!Size)
return false;
int64_t CVSize = CV->getSExtValue();
if (CVSize % Size)
return false;
auto *StepValue =
SE->getConstant(CV->getType(), CVSize / Size, true /* signed */);
D = InductionDescriptor(StartValue, IK_PtrInduction, StepValue, BOp);
return true;