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//===- IndVarSimplify.cpp - Induction Variable Elimination ----------------===//
// The LLVM Compiler Infrastructure
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
// This transformation analyzes and transforms the induction variables (and
// computations derived from them) into simpler forms suitable for subsequent
// analysis and transformation.
// If the trip count of a loop is computable, this pass also makes the following
// changes:
// 1. The exit condition for the loop is canonicalized to compare the
// induction value against the exit value. This turns loops like:
// 'for (i = 7; i*i < 1000; ++i)' into 'for (i = 0; i != 25; ++i)'
// 2. Any use outside of the loop of an expression derived from the indvar
// is changed to compute the derived value outside of the loop, eliminating
// the dependence on the exit value of the induction variable. If the only
// purpose of the loop is to compute the exit value of some derived
// expression, this transformation will make the loop dead.
#include "llvm/Transforms/Scalar/IndVarSimplify.h"
#include "llvm/ADT/APFloat.h"
#include "llvm/ADT/APInt.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/None.h"
#include "llvm/ADT/Optional.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/ADT/iterator_range.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionExpander.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/TargetLibraryInfo.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/IR/BasicBlock.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/IRBuilder.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/Module.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PassManager.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/ValueHandle.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/MathExtras.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Transforms/Scalar/LoopPassManager.h"
#include "llvm/Transforms/Utils/BasicBlockUtils.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Transforms/Utils/LoopUtils.h"
#include "llvm/Transforms/Utils/SimplifyIndVar.h"
#include <cassert>
#include <cstdint>
#include <utility>
using namespace llvm;
#define DEBUG_TYPE "indvars"
STATISTIC(NumWidened , "Number of indvars widened");
STATISTIC(NumReplaced , "Number of exit values replaced");
STATISTIC(NumLFTR , "Number of loop exit tests replaced");
STATISTIC(NumElimExt , "Number of IV sign/zero extends eliminated");
STATISTIC(NumElimIV , "Number of congruent IVs eliminated");
// Trip count verification can be enabled by default under NDEBUG if we
// implement a strong expression equivalence checker in SCEV. Until then, we
// use the verify-indvars flag, which may assert in some cases.
static cl::opt<bool> VerifyIndvars(
"verify-indvars", cl::Hidden,
cl::desc("Verify the ScalarEvolution result after running indvars"));
enum ReplaceExitVal { NeverRepl, OnlyCheapRepl, AlwaysRepl };
static cl::opt<ReplaceExitVal> ReplaceExitValue(
"replexitval", cl::Hidden, cl::init(OnlyCheapRepl),
cl::desc("Choose the strategy to replace exit value in IndVarSimplify"),
cl::values(clEnumValN(NeverRepl, "never", "never replace exit value"),
clEnumValN(OnlyCheapRepl, "cheap",
"only replace exit value when the cost is cheap"),
clEnumValN(AlwaysRepl, "always",
"always replace exit value whenever possible")));
static cl::opt<bool> UsePostIncrementRanges(
"indvars-post-increment-ranges", cl::Hidden,
cl::desc("Use post increment control-dependent ranges in IndVarSimplify"),
static cl::opt<bool>
DisableLFTR("disable-lftr", cl::Hidden, cl::init(false),
cl::desc("Disable Linear Function Test Replace optimization"));
namespace {
struct RewritePhi;
class IndVarSimplify {
LoopInfo *LI;
ScalarEvolution *SE;
DominatorTree *DT;
const DataLayout &DL;
TargetLibraryInfo *TLI;
const TargetTransformInfo *TTI;
SmallVector<WeakTrackingVH, 16> DeadInsts;
bool Changed = false;
bool isValidRewrite(Value *FromVal, Value *ToVal);
void handleFloatingPointIV(Loop *L, PHINode *PH);
void rewriteNonIntegerIVs(Loop *L);
void simplifyAndExtend(Loop *L, SCEVExpander &Rewriter, LoopInfo *LI);
bool canLoopBeDeleted(Loop *L, SmallVector<RewritePhi, 8> &RewritePhiSet);
void rewriteLoopExitValues(Loop *L, SCEVExpander &Rewriter);
void rewriteFirstIterationLoopExitValues(Loop *L);
Value *linearFunctionTestReplace(Loop *L, const SCEV *BackedgeTakenCount,
PHINode *IndVar, SCEVExpander &Rewriter);
void sinkUnusedInvariants(Loop *L);
Value *expandSCEVIfNeeded(SCEVExpander &Rewriter, const SCEV *S, Loop *L,
Instruction *InsertPt, Type *Ty);
IndVarSimplify(LoopInfo *LI, ScalarEvolution *SE, DominatorTree *DT,
const DataLayout &DL, TargetLibraryInfo *TLI,
TargetTransformInfo *TTI)
bool run(Loop *L);
} // end anonymous namespace
/// Return true if the SCEV expansion generated by the rewriter can replace the
/// original value. SCEV guarantees that it produces the same value, but the way
/// it is produced may be illegal IR. Ideally, this function will only be
/// called for verification.
bool IndVarSimplify::isValidRewrite(Value *FromVal, Value *ToVal) {
// If an SCEV expression subsumed multiple pointers, its expansion could
// reassociate the GEP changing the base pointer. This is illegal because the
// final address produced by a GEP chain must be inbounds relative to its
// underlying object. Otherwise basic alias analysis, among other things,
// could fail in a dangerous way. Ultimately, SCEV will be improved to avoid
// producing an expression involving multiple pointers. Until then, we must
// bail out here.
// Retrieve the pointer operand of the GEP. Don't use GetUnderlyingObject
// because it understands lcssa phis while SCEV does not.
Value *FromPtr = FromVal;
Value *ToPtr = ToVal;
if (auto *GEP = dyn_cast<GEPOperator>(FromVal)) {
FromPtr = GEP->getPointerOperand();
if (auto *GEP = dyn_cast<GEPOperator>(ToVal)) {
ToPtr = GEP->getPointerOperand();
if (FromPtr != FromVal || ToPtr != ToVal) {
// Quickly check the common case
if (FromPtr == ToPtr)
return true;
// SCEV may have rewritten an expression that produces the GEP's pointer
// operand. That's ok as long as the pointer operand has the same base
// pointer. Unlike GetUnderlyingObject(), getPointerBase() will find the
// base of a recurrence. This handles the case in which SCEV expansion
// converts a pointer type recurrence into a nonrecurrent pointer base
// indexed by an integer recurrence.
// If the GEP base pointer is a vector of pointers, abort.
if (!FromPtr->getType()->isPointerTy() || !ToPtr->getType()->isPointerTy())
return false;
const SCEV *FromBase = SE->getPointerBase(SE->getSCEV(FromPtr));
const SCEV *ToBase = SE->getPointerBase(SE->getSCEV(ToPtr));
if (FromBase == ToBase)
return true;
DEBUG(dbgs() << "INDVARS: GEP rewrite bail out "
<< *FromBase << " != " << *ToBase << "\n");
return false;
return true;
/// Determine the insertion point for this user. By default, insert immediately
/// before the user. SCEVExpander or LICM will hoist loop invariants out of the
/// loop. For PHI nodes, there may be multiple uses, so compute the nearest
/// common dominator for the incoming blocks.
static Instruction *getInsertPointForUses(Instruction *User, Value *Def,
DominatorTree *DT, LoopInfo *LI) {
PHINode *PHI = dyn_cast<PHINode>(User);
if (!PHI)
return User;
Instruction *InsertPt = nullptr;
for (unsigned i = 0, e = PHI->getNumIncomingValues(); i != e; ++i) {
if (PHI->getIncomingValue(i) != Def)
BasicBlock *InsertBB = PHI->getIncomingBlock(i);
if (!InsertPt) {
InsertPt = InsertBB->getTerminator();
InsertBB = DT->findNearestCommonDominator(InsertPt->getParent(), InsertBB);
InsertPt = InsertBB->getTerminator();
assert(InsertPt && "Missing phi operand");
auto *DefI = dyn_cast<Instruction>(Def);
if (!DefI)
return InsertPt;
assert(DT->dominates(DefI, InsertPt) && "def does not dominate all uses");
auto *L = LI->getLoopFor(DefI->getParent());
assert(!L || L->contains(LI->getLoopFor(InsertPt->getParent())));
for (auto *DTN = (*DT)[InsertPt->getParent()]; DTN; DTN = DTN->getIDom())
if (LI->getLoopFor(DTN->getBlock()) == L)
return DTN->getBlock()->getTerminator();
llvm_unreachable("DefI dominates InsertPt!");
// rewriteNonIntegerIVs and helpers. Prefer integer IVs.
/// Convert APF to an integer, if possible.
static bool ConvertToSInt(const APFloat &APF, int64_t &IntVal) {
bool isExact = false;
// See if we can convert this to an int64_t
uint64_t UIntVal;
if (APF.convertToInteger(makeMutableArrayRef(UIntVal), 64, true,
APFloat::rmTowardZero, &isExact) != APFloat::opOK ||
return false;
IntVal = UIntVal;
return true;
/// If the loop has floating induction variable then insert corresponding
/// integer induction variable if possible.
/// For example,
/// for(double i = 0; i < 10000; ++i)
/// bar(i)
/// is converted into
/// for(int i = 0; i < 10000; ++i)
/// bar((double)i);
void IndVarSimplify::handleFloatingPointIV(Loop *L, PHINode *PN) {
unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
unsigned BackEdge = IncomingEdge^1;
// Check incoming value.
auto *InitValueVal = dyn_cast<ConstantFP>(PN->getIncomingValue(IncomingEdge));
int64_t InitValue;
if (!InitValueVal || !ConvertToSInt(InitValueVal->getValueAPF(), InitValue))
// Check IV increment. Reject this PN if increment operation is not
// an add or increment value can not be represented by an integer.
auto *Incr = dyn_cast<BinaryOperator>(PN->getIncomingValue(BackEdge));
if (Incr == nullptr || Incr->getOpcode() != Instruction::FAdd) return;
// If this is not an add of the PHI with a constantfp, or if the constant fp
// is not an integer, bail out.
ConstantFP *IncValueVal = dyn_cast<ConstantFP>(Incr->getOperand(1));
int64_t IncValue;
if (IncValueVal == nullptr || Incr->getOperand(0) != PN ||
!ConvertToSInt(IncValueVal->getValueAPF(), IncValue))
// Check Incr uses. One user is PN and the other user is an exit condition
// used by the conditional terminator.
Value::user_iterator IncrUse = Incr->user_begin();
Instruction *U1 = cast<Instruction>(*IncrUse++);
if (IncrUse == Incr->user_end()) return;
Instruction *U2 = cast<Instruction>(*IncrUse++);
if (IncrUse != Incr->user_end()) return;
// Find exit condition, which is an fcmp. If it doesn't exist, or if it isn't
// only used by a branch, we can't transform it.
FCmpInst *Compare = dyn_cast<FCmpInst>(U1);
if (!Compare)
Compare = dyn_cast<FCmpInst>(U2);
if (!Compare || !Compare->hasOneUse() ||
BranchInst *TheBr = cast<BranchInst>(Compare->user_back());
// We need to verify that the branch actually controls the iteration count
// of the loop. If not, the new IV can overflow and no one will notice.
// The branch block must be in the loop and one of the successors must be out
// of the loop.
assert(TheBr->isConditional() && "Can't use fcmp if not conditional");
if (!L->contains(TheBr->getParent()) ||
(L->contains(TheBr->getSuccessor(0)) &&
// If it isn't a comparison with an integer-as-fp (the exit value), we can't
// transform it.
ConstantFP *ExitValueVal = dyn_cast<ConstantFP>(Compare->getOperand(1));
int64_t ExitValue;
if (ExitValueVal == nullptr ||
!ConvertToSInt(ExitValueVal->getValueAPF(), ExitValue))
// Find new predicate for integer comparison.
CmpInst::Predicate NewPred = CmpInst::BAD_ICMP_PREDICATE;
switch (Compare->getPredicate()) {
default: return; // Unknown comparison.
case CmpInst::FCMP_OEQ:
case CmpInst::FCMP_UEQ: NewPred = CmpInst::ICMP_EQ; break;
case CmpInst::FCMP_ONE:
case CmpInst::FCMP_UNE: NewPred = CmpInst::ICMP_NE; break;
case CmpInst::FCMP_OGT:
case CmpInst::FCMP_UGT: NewPred = CmpInst::ICMP_SGT; break;
case CmpInst::FCMP_OGE:
case CmpInst::FCMP_UGE: NewPred = CmpInst::ICMP_SGE; break;
case CmpInst::FCMP_OLT:
case CmpInst::FCMP_ULT: NewPred = CmpInst::ICMP_SLT; break;
case CmpInst::FCMP_OLE:
case CmpInst::FCMP_ULE: NewPred = CmpInst::ICMP_SLE; break;
// We convert the floating point induction variable to a signed i32 value if
// we can. This is only safe if the comparison will not overflow in a way
// that won't be trapped by the integer equivalent operations. Check for this
// now.
// TODO: We could use i64 if it is native and the range requires it.
// The start/stride/exit values must all fit in signed i32.
if (!isInt<32>(InitValue) || !isInt<32>(IncValue) || !isInt<32>(ExitValue))
// If not actually striding (add x, 0.0), avoid touching the code.
if (IncValue == 0)
// Positive and negative strides have different safety conditions.
if (IncValue > 0) {
// If we have a positive stride, we require the init to be less than the
// exit value.
if (InitValue >= ExitValue)
uint32_t Range = uint32_t(ExitValue-InitValue);
// Check for infinite loop, either:
// while (i <= Exit) or until (i > Exit)
if (NewPred == CmpInst::ICMP_SLE || NewPred == CmpInst::ICMP_SGT) {
if (++Range == 0) return; // Range overflows.
unsigned Leftover = Range % uint32_t(IncValue);
// If this is an equality comparison, we require that the strided value
// exactly land on the exit value, otherwise the IV condition will wrap
// around and do things the fp IV wouldn't.
if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
Leftover != 0)
// If the stride would wrap around the i32 before exiting, we can't
// transform the IV.
if (Leftover != 0 && int32_t(ExitValue+IncValue) < ExitValue)
} else {
// If we have a negative stride, we require the init to be greater than the
// exit value.
if (InitValue <= ExitValue)
uint32_t Range = uint32_t(InitValue-ExitValue);
// Check for infinite loop, either:
// while (i >= Exit) or until (i < Exit)
if (NewPred == CmpInst::ICMP_SGE || NewPred == CmpInst::ICMP_SLT) {
if (++Range == 0) return; // Range overflows.
unsigned Leftover = Range % uint32_t(-IncValue);
// If this is an equality comparison, we require that the strided value
// exactly land on the exit value, otherwise the IV condition will wrap
// around and do things the fp IV wouldn't.
if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
Leftover != 0)
// If the stride would wrap around the i32 before exiting, we can't
// transform the IV.
if (Leftover != 0 && int32_t(ExitValue+IncValue) > ExitValue)
IntegerType *Int32Ty = Type::getInt32Ty(PN->getContext());
// Insert new integer induction variable.
PHINode *NewPHI = PHINode::Create(Int32Ty, 2, PN->getName()+".int", PN);
NewPHI->addIncoming(ConstantInt::get(Int32Ty, InitValue),
Value *NewAdd =
BinaryOperator::CreateAdd(NewPHI, ConstantInt::get(Int32Ty, IncValue),
Incr->getName()+".int", Incr);
NewPHI->addIncoming(NewAdd, PN->getIncomingBlock(BackEdge));
ICmpInst *NewCompare = new ICmpInst(TheBr, NewPred, NewAdd,
ConstantInt::get(Int32Ty, ExitValue),
// In the following deletions, PN may become dead and may be deleted.
// Use a WeakTrackingVH to observe whether this happens.
WeakTrackingVH WeakPH = PN;
// Delete the old floating point exit comparison. The branch starts using the
// new comparison.
RecursivelyDeleteTriviallyDeadInstructions(Compare, TLI);
// Delete the old floating point increment.
RecursivelyDeleteTriviallyDeadInstructions(Incr, TLI);
// If the FP induction variable still has uses, this is because something else
// in the loop uses its value. In order to canonicalize the induction
// variable, we chose to eliminate the IV and rewrite it in terms of an
// int->fp cast.
// We give preference to sitofp over uitofp because it is faster on most
// platforms.
if (WeakPH) {
Value *Conv = new SIToFPInst(NewPHI, PN->getType(), "indvar.conv",
RecursivelyDeleteTriviallyDeadInstructions(PN, TLI);
Changed = true;
void IndVarSimplify::rewriteNonIntegerIVs(Loop *L) {
// First step. Check to see if there are any floating-point recurrences.
// If there are, change them into integer recurrences, permitting analysis by
// the SCEV routines.
BasicBlock *Header = L->getHeader();
SmallVector<WeakTrackingVH, 8> PHIs;
for (PHINode &PN : Header->phis())
for (unsigned i = 0, e = PHIs.size(); i != e; ++i)
if (PHINode *PN = dyn_cast_or_null<PHINode>(&*PHIs[i]))
handleFloatingPointIV(L, PN);
// If the loop previously had floating-point IV, ScalarEvolution
// may not have been able to compute a trip count. Now that we've done some
// re-writing, the trip count may be computable.
if (Changed)
namespace {
// Collect information about PHI nodes which can be transformed in
// rewriteLoopExitValues.
struct RewritePhi {
PHINode *PN;
// Ith incoming value.
unsigned Ith;
// Exit value after expansion.
Value *Val;
// High Cost when expansion.
bool HighCost;
RewritePhi(PHINode *P, unsigned I, Value *V, bool H)
: PN(P), Ith(I), Val(V), HighCost(H) {}
} // end anonymous namespace
Value *IndVarSimplify::expandSCEVIfNeeded(SCEVExpander &Rewriter, const SCEV *S,
Loop *L, Instruction *InsertPt,
Type *ResultTy) {
// Before expanding S into an expensive LLVM expression, see if we can use an
// already existing value as the expansion for S.
if (Value *ExistingValue = Rewriter.getExactExistingExpansion(S, InsertPt, L))
if (ExistingValue->getType() == ResultTy)
return ExistingValue;
// We didn't find anything, fall back to using SCEVExpander.
return Rewriter.expandCodeFor(S, ResultTy, InsertPt);
// rewriteLoopExitValues - Optimize IV users outside the loop.
// As a side effect, reduces the amount of IV processing within the loop.
/// Check to see if this loop has a computable loop-invariant execution count.
/// If so, this means that we can compute the final value of any expressions
/// that are recurrent in the loop, and substitute the exit values from the loop
/// into any instructions outside of the loop that use the final values of the
/// current expressions.
/// This is mostly redundant with the regular IndVarSimplify activities that
/// happen later, except that it's more powerful in some cases, because it's
/// able to brute-force evaluate arbitrary instructions as long as they have
/// constant operands at the beginning of the loop.
void IndVarSimplify::rewriteLoopExitValues(Loop *L, SCEVExpander &Rewriter) {
// Check a pre-condition.
assert(L->isRecursivelyLCSSAForm(*DT, *LI) &&
"Indvars did not preserve LCSSA!");
SmallVector<BasicBlock*, 8> ExitBlocks;
SmallVector<RewritePhi, 8> RewritePhiSet;
// Find all values that are computed inside the loop, but used outside of it.
// Because of LCSSA, these values will only occur in LCSSA PHI Nodes. Scan
// the exit blocks of the loop to find them.
for (BasicBlock *ExitBB : ExitBlocks) {
// If there are no PHI nodes in this exit block, then no values defined
// inside the loop are used on this path, skip it.
PHINode *PN = dyn_cast<PHINode>(ExitBB->begin());
if (!PN) continue;
unsigned NumPreds = PN->getNumIncomingValues();
// Iterate over all of the PHI nodes.
BasicBlock::iterator BBI = ExitBB->begin();
while ((PN = dyn_cast<PHINode>(BBI++))) {
if (PN->use_empty())
continue; // dead use, don't replace it
if (!SE->isSCEVable(PN->getType()))
// It's necessary to tell ScalarEvolution about this explicitly so that
// it can walk the def-use list and forget all SCEVs, as it may not be
// watching the PHI itself. Once the new exit value is in place, there
// may not be a def-use connection between the loop and every instruction
// which got a SCEVAddRecExpr for that loop.
// Iterate over all of the values in all the PHI nodes.
for (unsigned i = 0; i != NumPreds; ++i) {
// If the value being merged in is not integer or is not defined
// in the loop, skip it.
Value *InVal = PN->getIncomingValue(i);
if (!isa<Instruction>(InVal))
// If this pred is for a subloop, not L itself, skip it.
if (LI->getLoopFor(PN->getIncomingBlock(i)) != L)
continue; // The Block is in a subloop, skip it.
// Check that InVal is defined in the loop.
Instruction *Inst = cast<Instruction>(InVal);
if (!L->contains(Inst))
// Okay, this instruction has a user outside of the current loop
// and varies predictably *inside* the loop. Evaluate the value it
// contains when the loop exits, if possible.
const SCEV *ExitValue = SE->getSCEVAtScope(Inst, L->getParentLoop());
if (!SE->isLoopInvariant(ExitValue, L) ||
!isSafeToExpand(ExitValue, *SE))
// Computing the value outside of the loop brings no benefit if :
// - it is definitely used inside the loop in a way which can not be
// optimized away.
// - no use outside of the loop can take advantage of hoisting the
// computation out of the loop
if (ExitValue->getSCEVType()>=scMulExpr) {
unsigned NumHardInternalUses = 0;
unsigned NumSoftExternalUses = 0;
unsigned NumUses = 0;
for (auto IB = Inst->user_begin(), IE = Inst->user_end();
IB != IE && NumUses <= 6; ++IB) {
Instruction *UseInstr = cast<Instruction>(*IB);
unsigned Opc = UseInstr->getOpcode();
if (L->contains(UseInstr)) {
if (Opc == Instruction::Call || Opc == Instruction::Ret)
} else {
if (Opc == Instruction::PHI) {
// Do not count the Phi as a use. LCSSA may have inserted
// plenty of trivial ones.
for (auto PB = UseInstr->user_begin(),
PE = UseInstr->user_end();
PB != PE && NumUses <= 6; ++PB, ++NumUses) {
unsigned PhiOpc = cast<Instruction>(*PB)->getOpcode();
if (PhiOpc != Instruction::Call && PhiOpc != Instruction::Ret)
if (Opc != Instruction::Call && Opc != Instruction::Ret)
if (NumUses <= 6 && NumHardInternalUses && !NumSoftExternalUses)
bool HighCost = Rewriter.isHighCostExpansion(ExitValue, L, Inst);
Value *ExitVal =
expandSCEVIfNeeded(Rewriter, ExitValue, L, Inst, PN->getType());
DEBUG(dbgs() << "INDVARS: RLEV: AfterLoopVal = " << *ExitVal << '\n'
<< " LoopVal = " << *Inst << "\n");
if (!isValidRewrite(Inst, ExitVal)) {
// Collect all the candidate PHINodes to be rewritten.
RewritePhiSet.emplace_back(PN, i, ExitVal, HighCost);
bool LoopCanBeDel = canLoopBeDeleted(L, RewritePhiSet);
// Transformation.
for (const RewritePhi &Phi : RewritePhiSet) {
PHINode *PN = Phi.PN;
Value *ExitVal = Phi.Val;
// Only do the rewrite when the ExitValue can be expanded cheaply.
// If LoopCanBeDel is true, rewrite exit value aggressively.
if (ReplaceExitValue == OnlyCheapRepl && !LoopCanBeDel && Phi.HighCost) {
Changed = true;
Instruction *Inst = cast<Instruction>(PN->getIncomingValue(Phi.Ith));
PN->setIncomingValue(Phi.Ith, ExitVal);
// If this instruction is dead now, delete it. Don't do it now to avoid
// invalidating iterators.
if (isInstructionTriviallyDead(Inst, TLI))
// Replace PN with ExitVal if that is legal and does not break LCSSA.
if (PN->getNumIncomingValues() == 1 &&
LI->replacementPreservesLCSSAForm(PN, ExitVal)) {
// The insertion point instruction may have been deleted; clear it out
// so that the rewriter doesn't trip over it later.
// rewriteFirstIterationLoopExitValues: Rewrite loop exit values if we know
// they will exit at the first iteration.
/// Check to see if this loop has loop invariant conditions which lead to loop
/// exits. If so, we know that if the exit path is taken, it is at the first
/// loop iteration. This lets us predict exit values of PHI nodes that live in
/// loop header.
void IndVarSimplify::rewriteFirstIterationLoopExitValues(Loop *L) {
// Verify the input to the pass is already in LCSSA form.
SmallVector<BasicBlock *, 8> ExitBlocks;
auto *LoopHeader = L->getHeader();
assert(LoopHeader && "Invalid loop");
for (auto *ExitBB : ExitBlocks) {
// If there are no more PHI nodes in this exit block, then no more
// values defined inside the loop are used on this path.
for (PHINode &PN : ExitBB->phis()) {
for (unsigned IncomingValIdx = 0, E = PN.getNumIncomingValues();
IncomingValIdx != E; ++IncomingValIdx) {
auto *IncomingBB = PN.getIncomingBlock(IncomingValIdx);
// We currently only support loop exits from loop header. If the
// incoming block is not loop header, we need to recursively check
// all conditions starting from loop header are loop invariants.
// Additional support might be added in the future.
if (IncomingBB != LoopHeader)
// Get condition that leads to the exit path.
auto *TermInst = IncomingBB->getTerminator();
Value *Cond = nullptr;
if (auto *BI = dyn_cast<BranchInst>(TermInst)) {
// Must be a conditional branch, otherwise the block
// should not be in the loop.
Cond = BI->getCondition();
} else if (auto *SI = dyn_cast<SwitchInst>(TermInst))
Cond = SI->getCondition();
if (!L->isLoopInvariant(Cond))
auto *ExitVal = dyn_cast<PHINode>(PN.getIncomingValue(IncomingValIdx));
// Only deal with PHIs.
if (!ExitVal)
// If ExitVal is a PHI on the loop header, then we know its
// value along this exit because the exit can only be taken
// on the first iteration.
auto *LoopPreheader = L->getLoopPreheader();
assert(LoopPreheader && "Invalid loop");
int PreheaderIdx = ExitVal->getBasicBlockIndex(LoopPreheader);
if (PreheaderIdx != -1) {
assert(ExitVal->getParent() == LoopHeader &&
"ExitVal must be in loop header");
/// Check whether it is possible to delete the loop after rewriting exit
/// value. If it is possible, ignore ReplaceExitValue and do rewriting
/// aggressively.
bool IndVarSimplify::canLoopBeDeleted(
Loop *L, SmallVector<RewritePhi, 8> &RewritePhiSet) {
BasicBlock *Preheader = L->getLoopPreheader();
// If there is no preheader, the loop will not be deleted.
if (!Preheader)
return false;
// In LoopDeletion pass Loop can be deleted when ExitingBlocks.size() > 1.
// We obviate multiple ExitingBlocks case for simplicity.
// TODO: If we see testcase with multiple ExitingBlocks can be deleted
// after exit value rewriting, we can enhance the logic here.
SmallVector<BasicBlock *, 4> ExitingBlocks;
SmallVector<BasicBlock *, 8> ExitBlocks;
if (ExitBlocks.size() > 1 || ExitingBlocks.size() > 1)
return false;
BasicBlock *ExitBlock = ExitBlocks[0];
BasicBlock::iterator BI = ExitBlock->begin();
while (PHINode *P = dyn_cast<PHINode>(BI)) {
Value *Incoming = P->getIncomingValueForBlock(ExitingBlocks[0]);
// If the Incoming value of P is found in RewritePhiSet, we know it
// could be rewritten to use a loop invariant value in transformation
// phase later. Skip it in the loop invariant check below.
bool found = false;
for (const RewritePhi &Phi : RewritePhiSet) {
unsigned i = Phi.Ith;
if (Phi.PN == P && (Phi.PN)->getIncomingValue(i) == Incoming) {
found = true;
Instruction *I;
if (!found && (I = dyn_cast<Instruction>(Incoming)))
if (!L->hasLoopInvariantOperands(I))
return false;
for (auto *BB : L->blocks())
if (llvm::any_of(*BB, [](Instruction &I) {
return I.mayHaveSideEffects();
return false;
return true;
// IV Widening - Extend the width of an IV to cover its widest uses.
namespace {
// Collect information about induction variables that are used by sign/zero
// extend operations. This information is recorded by CollectExtend and provides
// the input to WidenIV.
struct WideIVInfo {
PHINode *NarrowIV = nullptr;
// Widest integer type created [sz]ext
Type *WidestNativeType = nullptr;
// Was a sext user seen before a zext?
bool IsSigned = false;
} // end anonymous namespace
/// Update information about the induction variable that is extended by this
/// sign or zero extend operation. This is used to determine the final width of
/// the IV before actually widening it.
static void visitIVCast(CastInst *Cast, WideIVInfo &WI, ScalarEvolution *SE,
const TargetTransformInfo *TTI) {
bool IsSigned = Cast->getOpcode() == Instruction::SExt;
if (!IsSigned && Cast->getOpcode() != Instruction::ZExt)
Type *Ty = Cast->getType();
uint64_t Width = SE->getTypeSizeInBits(Ty);
if (!Cast->getModule()->getDataLayout().isLegalInteger(Width))
// Check that `Cast` actually extends the induction variable (we rely on this
// later). This takes care of cases where `Cast` is extending a truncation of
// the narrow induction variable, and thus can end up being narrower than the
// "narrow" induction variable.
uint64_t NarrowIVWidth = SE->getTypeSizeInBits(WI.NarrowIV->getType());
if (NarrowIVWidth >= Width)
// Cast is either an sext or zext up to this point.
// We should not widen an indvar if arithmetics on the wider indvar are more
// expensive than those on the narrower indvar. We check only the cost of ADD
// because at least an ADD is required to increment the induction variable. We
// could compute more comprehensively the cost of all instructions on the
// induction variable when necessary.
if (TTI &&
TTI->getArithmeticInstrCost(Instruction::Add, Ty) >
Cast->getOperand(0)->getType())) {
if (!WI.WidestNativeType) {
WI.WidestNativeType = SE->getEffectiveSCEVType(Ty);
WI.IsSigned = IsSigned;
// We extend the IV to satisfy the sign of its first user, arbitrarily.
if (WI.IsSigned != IsSigned)
if (Width > SE->getTypeSizeInBits(WI.WidestNativeType))
WI.WidestNativeType = SE->getEffectiveSCEVType(Ty);
namespace {
/// Record a link in the Narrow IV def-use chain along with the WideIV that
/// computes the same value as the Narrow IV def. This avoids caching Use*
/// pointers.
struct NarrowIVDefUse {
Instruction *NarrowDef = nullptr;
Instruction *NarrowUse = nullptr;
Instruction *WideDef = nullptr;
// True if the narrow def is never negative. Tracking this information lets
// us use a sign extension instead of a zero extension or vice versa, when
// profitable and legal.
bool NeverNegative = false;
NarrowIVDefUse(Instruction *ND, Instruction *NU, Instruction *WD,
bool NeverNegative)
: NarrowDef(ND), NarrowUse(NU), WideDef(WD),
NeverNegative(NeverNegative) {}
/// The goal of this transform is to remove sign and zero extends without
/// creating any new induction variables. To do this, it creates a new phi of
/// the wider type and redirects all users, either removing extends or inserting
/// truncs whenever we stop propagating the type.
class WidenIV {
// Parameters
PHINode *OrigPhi;
Type *WideType;
// Context
LoopInfo *LI;
Loop *L;
ScalarEvolution *SE;
DominatorTree *DT;
// Does the module have any calls to the llvm.experimental.guard intrinsic
// at all? If not we can avoid scanning instructions looking for guards.
bool HasGuards;
// Result
PHINode *WidePhi = nullptr;
Instruction *WideInc = nullptr;
const SCEV *WideIncExpr = nullptr;
SmallVectorImpl<WeakTrackingVH> &DeadInsts;
SmallPtrSet<Instruction *,16> Widened;
SmallVector<NarrowIVDefUse, 8> NarrowIVUsers;
enum ExtendKind { ZeroExtended, SignExtended, Unknown };
// A map tracking the kind of extension used to widen each narrow IV
// and narrow IV user.
// Key: pointer to a narrow IV or IV user.
// Value: the kind of extension used to widen this Instruction.
DenseMap<AssertingVH<Instruction>, ExtendKind> ExtendKindMap;
using DefUserPair = std::pair<AssertingVH<Value>, AssertingVH<Instruction>>;
// A map with control-dependent ranges for post increment IV uses. The key is
// a pair of IV def and a use of this def denoting the context. The value is
// a ConstantRange representing possible values of the def at the given
// context.
DenseMap<DefUserPair, ConstantRange> PostIncRangeInfos;
Optional<ConstantRange> getPostIncRangeInfo(Value *Def,
Instruction *UseI) {
DefUserPair Key(Def, UseI);
auto It = PostIncRangeInfos.find(Key);
return It == PostIncRangeInfos.end()
? Optional<ConstantRange>(None)
: Optional<ConstantRange>(It->second);
void calculatePostIncRanges(PHINode *OrigPhi);
void calculatePostIncRange(Instruction *NarrowDef, Instruction *NarrowUser);
void updatePostIncRangeInfo(Value *Def, Instruction *UseI, ConstantRange R) {
DefUserPair Key(Def, UseI);
auto It = PostIncRangeInfos.find(Key);
if (It == PostIncRangeInfos.end())
PostIncRangeInfos.insert({Key, R});
It->second = R.intersectWith(It->second);
WidenIV(const WideIVInfo &WI, LoopInfo *LInfo, ScalarEvolution *SEv,
DominatorTree *DTree, SmallVectorImpl<WeakTrackingVH> &DI,
bool HasGuards)
: OrigPhi(WI.NarrowIV), WideType(WI.WidestNativeType), LI(LInfo),
L(LI->getLoopFor(OrigPhi->getParent())), SE(SEv), DT(DTree),
HasGuards(HasGuards), DeadInsts(DI) {
assert(L->getHeader() == OrigPhi->getParent() && "Phi must be an IV");
ExtendKindMap[OrigPhi] = WI.IsSigned ? SignExtended : ZeroExtended;
PHINode *createWideIV(SCEVExpander &Rewriter);
Value *createExtendInst(Value *NarrowOper, Type *WideType, bool IsSigned,
Instruction *Use);
Instruction *cloneIVUser(NarrowIVDefUse DU, const SCEVAddRecExpr *WideAR);
Instruction *cloneArithmeticIVUser(NarrowIVDefUse DU,
const SCEVAddRecExpr *WideAR);
Instruction *cloneBitwiseIVUser(NarrowIVDefUse DU);
ExtendKind getExtendKind(Instruction *I);
using WidenedRecTy = std::pair<const SCEVAddRecExpr *, ExtendKind>;
WidenedRecTy getWideRecurrence(NarrowIVDefUse DU);
WidenedRecTy getExtendedOperandRecurrence(NarrowIVDefUse DU);
const SCEV *getSCEVByOpCode(const SCEV *LHS, const SCEV *RHS,
unsigned OpCode) const;
Instruction *widenIVUse(NarrowIVDefUse DU, SCEVExpander &Rewriter);
bool widenLoopCompare(NarrowIVDefUse DU);
void pushNarrowIVUsers(Instruction *NarrowDef, Instruction *WideDef);
} // end anonymous namespace
/// Perform a quick domtree based check for loop invariance assuming that V is
/// used within the loop. LoopInfo::isLoopInvariant() seems gratuitous for this
/// purpose.
static bool isLoopInvariant(Value *V, const Loop *L, const DominatorTree *DT) {
Instruction *Inst = dyn_cast<Instruction>(V);
if (!Inst)
return true;
return DT->properlyDominates(Inst->getParent(), L->getHeader());
Value *WidenIV::createExtendInst(Value *NarrowOper, Type *WideType,
bool IsSigned, Instruction *Use) {
// Set the debug location and conservative insertion point.
IRBuilder<> Builder(Use);
// Hoist the insertion point into loop preheaders as far as possible.
for (const Loop *L = LI->getLoopFor(Use->getParent());
L && L->getLoopPreheader() && isLoopInvariant(NarrowOper, L, DT);
L = L->getParentLoop())
return IsSigned ? Builder.CreateSExt(NarrowOper, WideType) :
Builder.CreateZExt(NarrowOper, WideType);
/// Instantiate a wide operation to replace a narrow operation. This only needs
/// to handle operations that can evaluation to SCEVAddRec. It can safely return
/// 0 for any operation we decide not to clone.
Instruction *WidenIV::cloneIVUser(NarrowIVDefUse DU,
const SCEVAddRecExpr *WideAR) {
unsigned Opcode = DU.NarrowUse->getOpcode();
switch (Opcode) {
return nullptr;
case Instruction::Add:
case Instruction::Mul:
case Instruction::UDiv:
case Instruction::Sub:
return cloneArithmeticIVUser(DU, WideAR);
case Instruction::And:
case Instruction::Or:
case Instruction::Xor:
case Instruction::Shl:
case Instruction::LShr:
case Instruction::AShr:
return cloneBitwiseIVUser(DU);
Instruction *WidenIV::cloneBitwiseIVUser(NarrowIVDefUse DU) {
Instruction *NarrowUse = DU.NarrowUse;
Instruction *NarrowDef = DU.NarrowDef;
Instruction *WideDef = DU.WideDef;
DEBUG(dbgs() << "Cloning bitwise IVUser: " << *NarrowUse << "\n");
// Replace NarrowDef operands with WideDef. Otherwise, we don't know anything
// about the narrow operand yet so must insert a [sz]ext. It is probably loop
// invariant and will be folded or hoisted. If it actually comes from a
// widened IV, it should be removed during a future call to widenIVUse.
bool IsSigned = getExtendKind(NarrowDef) == SignExtended;
Value *LHS = (NarrowUse->getOperand(0) == NarrowDef)
? WideDef
: createExtendInst(NarrowUse->getOperand(0), WideType,
IsSigned, NarrowUse);
Value *RHS = (NarrowUse->getOperand(1) == NarrowDef)
? WideDef
: createExtendInst(NarrowUse->getOperand(1), WideType,
IsSigned, NarrowUse);
auto *NarrowBO = cast<BinaryOperator>(NarrowUse);
auto *WideBO = BinaryOperator::Create(NarrowBO->getOpcode(), LHS, RHS,
IRBuilder<> Builder(NarrowUse);
return WideBO;
Instruction *WidenIV::cloneArithmeticIVUser(NarrowIVDefUse DU,
const SCEVAddRecExpr *WideAR) {
Instruction *NarrowUse = DU.NarrowUse;
Instruction *NarrowDef = DU.NarrowDef;
Instruction *WideDef = DU.WideDef;
DEBUG(dbgs() << "Cloning arithmetic IVUser: " << *NarrowUse << "\n");
unsigned IVOpIdx = (NarrowUse->getOperand(0) == NarrowDef) ? 0 : 1;
// We're trying to find X such that
// Widen(NarrowDef `op` NonIVNarrowDef) == WideAR == WideDef `op.wide` X
// We guess two solutions to X, sext(NonIVNarrowDef) and zext(NonIVNarrowDef),
// and check using SCEV if any of them are correct.
// Returns true if extending NonIVNarrowDef according to `SignExt` is a
// correct solution to X.
auto GuessNonIVOperand = [&](bool SignExt) {
const SCEV *WideLHS;
const SCEV *WideRHS;
auto GetExtend = [this, SignExt](const SCEV *S, Type *Ty) {
if (SignExt)
return SE->getSignExtendExpr(S, Ty);
return SE->getZeroExtendExpr(S, Ty);
if (IVOpIdx == 0) {
WideLHS = SE->getSCEV(WideDef);
const SCEV *NarrowRHS = SE->getSCEV(NarrowUse->getOperand(1));
WideRHS = GetExtend(NarrowRHS, WideType);
} else {
const SCEV *NarrowLHS = SE->getSCEV(NarrowUse->getOperand(0));
WideLHS = GetExtend(NarrowLHS, WideType);
WideRHS = SE->getSCEV(WideDef);
// WideUse is "WideDef `op.wide` X" as described in the comment.
const SCEV *WideUse = nullptr;
switch (NarrowUse->getOpcode()) {
llvm_unreachable("No other possibility!");
case Instruction::Add:
WideUse = SE->getAddExpr(WideLHS, WideRHS);
case Instruction::Mul:
WideUse = SE->getMulExpr(WideLHS, WideRHS);
case Instruction::UDiv:
WideUse = SE->getUDivExpr(WideLHS, WideRHS);
case Instruction::Sub:
WideUse = SE->getMinusSCEV(WideLHS, WideRHS);
return WideUse == WideAR;
bool SignExtend = getExtendKind(NarrowDef) == SignExtended;
if (!GuessNonIVOperand(SignExtend)) {
SignExtend = !SignExtend;
if (!GuessNonIVOperand(SignExtend))
return nullptr;
Value *LHS = (NarrowUse->getOperand(0) == NarrowDef)
? WideDef
: createExtendInst(NarrowUse->getOperand(0), WideType,
SignExtend, NarrowUse);
Value *RHS = (NarrowUse->getOperand(1) == NarrowDef)
? WideDef
: createExtendInst(NarrowUse->getOperand(1), WideType,
SignExtend, NarrowUse);
auto *NarrowBO = cast<BinaryOperator>(NarrowUse);
auto *WideBO = BinaryOperator::Create(NarrowBO->getOpcode(), LHS, RHS,
IRBuilder<> Builder(NarrowUse);
return WideBO;
WidenIV::ExtendKind WidenIV::getExtendKind(Instruction *I) {
auto It = ExtendKindMap.find(I);
assert(It != ExtendKindMap.end() && "Instruction not yet extended!");
return It->second;
const SCEV *WidenIV::getSCEVByOpCode(const SCEV *LHS, const SCEV *RHS,
unsigned OpCode) const {
if (OpCode == Instruction::Add)
return SE->getAddExpr(LHS, RHS);
if (OpCode == Instruction::Sub)
return SE->getMinusSCEV(LHS, RHS);
if (OpCode == Instruction::Mul)
return SE->getMulExpr(LHS, RHS);
llvm_unreachable("Unsupported opcode.");
/// No-wrap operations can transfer sign extension of their result to their
/// operands. Generate the SCEV value for the widened operation without
/// actually modifying the IR yet. If the expression after extending the
/// operands is an AddRec for this loop, return the AddRec and the kind of
/// extension used.
WidenIV::WidenedRecTy WidenIV::getExtendedOperandRecurrence(NarrowIVDefUse DU) {
// Handle the common case of add<nsw/nuw>
const unsigned OpCode = DU.NarrowUse->getOpcode();
// Only Add/Sub/Mul instructions supported yet.
if (OpCode != Instruction::Add && OpCode != Instruction::Sub &&
OpCode != Instruction::Mul)
return {nullptr, Unknown};
// One operand (NarrowDef) has already been extended to WideDef. Now determine
// if extending the other will lead to a recurrence.
const unsigned ExtendOperIdx =
DU.NarrowUse->getOperand(0) == DU.NarrowDef ? 1 : 0;
assert(DU.NarrowUse->getOperand(1-ExtendOperIdx) == DU.NarrowDef && "bad DU");
const SCEV *ExtendOperExpr = nullptr;
const OverflowingBinaryOperator *OBO =
ExtendKind ExtKind = getExtendKind(DU.NarrowDef);
if (ExtKind == SignExtended && OBO->hasNoSignedWrap())
ExtendOperExpr = SE->getSignExtendExpr(
SE->getSCEV(DU.NarrowUse->getOperand(ExtendOperIdx)), WideType);
else if(ExtKind == ZeroExtended && OBO->hasNoUnsignedWrap())
ExtendOperExpr = SE->getZeroExtendExpr(
SE->getSCEV(DU.NarrowUse->getOperand(ExtendOperIdx)), WideType);
return {nullptr, Unknown};
// When creating this SCEV expr, don't apply the current operations NSW or NUW
// flags. This instruction may be guarded by control flow that the no-wrap
// behavior depends on. Non-control-equivalent instructions can be mapped to
// the same SCEV expression, and it would be incorrect to transfer NSW/NUW
// semantics to those operations.
const SCEV *lhs = SE->getSCEV(DU.WideDef);
const SCEV *rhs = ExtendOperExpr;
// Let's swap operands to the initial order for the case of non-commutative
// operations, like SUB. See PR21014.
if (ExtendOperIdx == 0)
std::swap(lhs, rhs);
const SCEVAddRecExpr *AddRec =
dyn_cast<SCEVAddRecExpr>(getSCEVByOpCode(lhs, rhs, OpCode));
if (!AddRec || AddRec->getLoop() != L)
return {nullptr, Unknown};
return {AddRec, ExtKind};
/// Is this instruction potentially interesting for further simplification after
/// widening it's type? In other words, can the extend be safely hoisted out of
/// the loop with SCEV reducing the value to a recurrence on the same loop. If
/// so, return the extended recurrence and the kind of extension used. Otherwise
/// return {nullptr, Unknown}.
WidenIV::WidenedRecTy WidenIV::getWideRecurrence(NarrowIVDefUse DU) {
if (!SE->isSCEVable(DU.NarrowUse->getType()))
return {nullptr, Unknown};
const SCEV *NarrowExpr = SE->getSCEV(DU.NarrowUse);
if (SE->getTypeSizeInBits(NarrowExpr->getType()) >=
SE->getTypeSizeInBits(WideType)) {
// NarrowUse implicitly widens its operand. e.g. a gep with a narrow
// index. So don't follow this use.
return {nullptr, Unknown};
const SCEV *WideExpr;
ExtendKind ExtKind;
if (DU.NeverNegative) {
WideExpr = SE->getSignExtendExpr(NarrowExpr, WideType);
if (isa<SCEVAddRecExpr>(WideExpr))
ExtKind = SignExtended;
else {
WideExpr = SE->getZeroExtendExpr(NarrowExpr, WideType);
ExtKind = ZeroExtended;
} else if (getExtendKind(DU.NarrowDef) == SignExtended) {
WideExpr = SE->getSignExtendExpr(NarrowExpr, WideType);
ExtKind = SignExtended;
} else {
WideExpr = SE->getZeroExtendExpr(NarrowExpr, WideType);
ExtKind = ZeroExtended;
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(WideExpr);
if (!AddRec || AddRec->getLoop() != L)
return {nullptr, Unknown};
return {AddRec, ExtKind};
/// This IV user cannot be widen. Replace this use of the original narrow IV
/// with a truncation of the new wide IV to isolate and eliminate the narrow IV.
static void truncateIVUse(NarrowIVDefUse DU, DominatorTree *DT, LoopInfo *LI) {
DEBUG(dbgs() << "INDVARS: Truncate IV " << *DU.WideDef
<< " for user " << *DU.NarrowUse << "\n");
IRBuilder<> Builder(
getInsertPointForUses(DU.NarrowUse, DU.NarrowDef, DT, LI));
Value *Trunc = Builder.CreateTrunc(DU.WideDef, DU.NarrowDef->getType());
DU.NarrowUse->replaceUsesOfWith(DU.NarrowDef, Trunc);
/// If the narrow use is a compare instruction, then widen the compare
// (and possibly the other operand). The extend operation is hoisted into the
// loop preheader as far as possible.
bool WidenIV::widenLoopCompare(NarrowIVDefUse DU) {
ICmpInst *Cmp = dyn_cast<ICmpInst>(DU.NarrowUse);
if (!Cmp)
return false;
// We can legally widen the comparison in the following two cases:
// - The signedness of the IV extension and comparison match
// - The narrow IV is always positive (and thus its sign extension is equal
// to its zero extension). For instance, let's say we're zero extending
// %narrow for the following use
// icmp slt i32 %narrow, %val ... (A)
// and %narrow is always positive. Then
// (A) == icmp slt i32 sext(%narrow), sext(%val)
// == icmp slt i32 zext(%narrow), sext(%val)
bool IsSigned = getExtendKind(DU.NarrowDef) == SignExtended;
if (!(DU.NeverNegative || IsSigned == Cmp->isSigned()))
return false;
Value *Op = Cmp->getOperand(Cmp->getOperand(0) == DU.NarrowDef ? 1 : 0);
unsigned CastWidth = SE->getTypeSizeInBits(Op->getType());
unsigned IVWidth = SE->getTypeSizeInBits(WideType);
assert(CastWidth <= IVWidth && "Unexpected width while widening compare.");
// Widen the compare instruction.
IRBuilder<> Builder(
getInsertPointForUses(DU.NarrowUse, DU.NarrowDef, DT, LI));
DU.NarrowUse->replaceUsesOfWith(DU.NarrowDef, DU.WideDef);
// Widen the other operand of the compare, if necessary.
if (CastWidth < IVWidth) {
Value *ExtOp = createExtendInst(Op, WideType, Cmp->isSigned(), Cmp);
DU.NarrowUse->replaceUsesOfWith(Op, ExtOp);
return true;
/// Determine whether an individual user of the narrow IV can be widened. If so,
/// return the wide clone of the user.
Instruction *WidenIV::widenIVUse(NarrowIVDefUse DU, SCEVExpander &Rewriter) {
assert(ExtendKindMap.count(DU.NarrowDef) &&
"Should already know the kind of extension used to widen NarrowDef");
// Stop traversing the def-use chain at inner-loop phis or post-loop phis.
if (PHINode *UsePhi = dyn_cast<PHINode>(DU.NarrowUse)) {
if (LI->getLoopFor(UsePhi->getParent()) != L) {
// For LCSSA phis, sink the truncate outside the loop.
// After SimplifyCFG most loop exit targets have a single predecessor.
// Otherwise fall back to a truncate within the loop.
if (UsePhi->getNumOperands() != 1)
truncateIVUse(DU, DT, LI);
else {
// Widening the PHI requires us to insert a trunc. The logical place
// for this trunc is in the same BB as the PHI. This is not possible if
// the BB is terminated by a catchswitch.
if (isa<CatchSwitchInst>(UsePhi->getParent()->getTerminator()))
return nullptr;
PHINode *WidePhi =
PHINode::Create(DU.WideDef->getType(), 1, UsePhi->getName() + ".wide",
WidePhi->addIncoming(DU.WideDef, UsePhi->getIncomingBlock(0));
IRBuilder<> Builder(&*WidePhi->getParent()->getFirstInsertionPt());
Value *Trunc = Builder.CreateTrunc(WidePhi, DU.NarrowDef->getType());
DEBUG(dbgs() << "INDVARS: Widen lcssa phi " << *UsePhi
<< " to " << *WidePhi << "\n");
return nullptr;
// This narrow use can be widened by a sext if it's non-negative or its narrow
// def was widended by a sext. Same for zext.
auto canWidenBySExt = [&]() {
return DU.NeverNegative || getExtendKind(DU.NarrowDef) == SignExtended;
auto canWidenByZExt = [&]() {
return DU.NeverNegative || getExtendKind(DU.NarrowDef) == ZeroExtended;
// Our raison d'etre! Eliminate sign and zero extension.
if ((isa<SExtInst>(DU.NarrowUse) && canWidenBySExt()) ||
(isa<ZExtInst>(DU.NarrowUse) && canWidenByZExt())) {
Value *NewDef = DU.WideDef;
if (DU.NarrowUse->getType() != WideType) {
unsigned CastWidth = SE->getTypeSizeInBits(DU.NarrowUse->getType());
unsigned IVWidth = SE->getTypeSizeInBits(WideType);
if (CastWidth < IVWidth) {
// The cast isn't as wide as the IV, so insert a Trunc.
IRBuilder<> Builder(DU.NarrowUse);
NewDef = Builder.CreateTrunc(DU.WideDef, DU.NarrowUse->getType());
else {
// A wider extend was hidden behind a narrower one. This may induce
// another round of IV widening in which the intermediate IV becomes
// dead. It should be very rare.
DEBUG(dbgs() << "INDVARS: New IV " << *WidePhi
<< " not wide enough to subsume " << *DU.NarrowUse << "\n");
DU.NarrowUse->replaceUsesOfWith(DU.NarrowDef, DU.WideDef);
NewDef = DU.NarrowUse;
if (NewDef != DU.NarrowUse) {
DEBUG(dbgs() << "INDVARS: eliminating " << *DU.NarrowUse
<< " replaced by " << *DU.WideDef << "\n");
// Now that the extend is gone, we want to expose it's uses for potential
// further simplification. We don't need to directly inform SimplifyIVUsers
// of the new users, because their parent IV will be processed later as a
// new loop phi. If we preserved IVUsers analysis, we would also want to
// push the uses of WideDef here.
// No further widening is needed. The deceased [sz]ext had done it for us.
return nullptr;
// Does this user itself evaluate to a recurrence after widening?
WidenedRecTy WideAddRec = getExtendedOperandRecurrence(DU);
if (!WideAddRec.first)
WideAddRec = getWideRecurrence(DU);
assert((WideAddRec.first == nullptr) == (WideAddRec.second == Unknown));
if (!WideAddRec.first) {
// If use is a loop condition, try to promote the condition instead of
// truncating the IV first.
if (widenLoopCompare(DU))
return nullptr;
// This user does not evaluate to a recurrence after widening, so don't
// follow it. Instead insert a Trunc to kill off the original use,
// eventually isolating the original narrow IV so it can be removed.
truncateIVUse(DU, DT, LI);
return nullptr;
// Assume block terminators cannot evaluate to a recurrence. We can't to
// insert a Trunc after a terminator if there happens to be a critical edge.
assert(DU.NarrowUse != DU.NarrowUse->getParent()->getTerminator() &&
"SCEV is not expected to evaluate a block terminator");
// Reuse the IV increment that SCEVExpander created as long as it dominates
// NarrowUse.
Instruction *WideUse = nullptr;
if (WideAddRec.first == WideIncExpr &&
Rewriter.hoistIVInc(WideInc, DU.NarrowUse))
WideUse = WideInc;
else {
WideUse = cloneIVUser(DU, WideAddRec.first);
if (!WideUse)
return nullptr;
// Evaluation of WideAddRec ensured that the narrow expression could be
// extended outside the loop without overflow. This suggests that the wide use
// evaluates to the same expression as the extended narrow use, but doesn't
// absolutely guarantee it. Hence the following failsafe check. In rare cases
// where it fails, we simply throw away the newly created wide use.
if (WideAddRec.first != SE->getSCEV(WideUse)) {
DEBUG(dbgs() << "Wide use expression mismatch: " << *WideUse
<< ": " << *SE->getSCEV(WideUse) << " != " << *WideAddRec.first << "\n");
return nullptr;
ExtendKindMap[DU.NarrowUse] = WideAddRec.second;
// Returning WideUse pushes it on the worklist.
return WideUse;
/// Add eligible users of NarrowDef to NarrowIVUsers.
void WidenIV::pushNarrowIVUsers(Instruction *NarrowDef, Instruction *WideDef) {
const SCEV *NarrowSCEV = SE->getSCEV(NarrowDef);
bool NonNegativeDef =
SE->isKnownPredicate(ICmpInst::ICMP_SGE, NarrowSCEV,
SE->getConstant(NarrowSCEV->getType(), 0));
for (User *U : NarrowDef->users()) {
Instruction *NarrowUser = cast<Instruction>(U);
// Handle data flow merges and bizarre phi cycles.
if (!Widened.insert(NarrowUser).second)
bool NonNegativeUse = false;
if (!NonNegativeDef) {
// We might have a control-dependent range information for this context.
if (auto RangeInfo = getPostIncRangeInfo(NarrowDef, NarrowUser))
NonNegativeUse = RangeInfo->getSignedMin().isNonNegative();
NarrowIVUsers.emplace_back(NarrowDef, NarrowUser, WideDef,
NonNegativeDef || NonNegativeUse);
/// Process a single induction variable. First use the SCEVExpander to create a
/// wide induction variable that evaluates to the same recurrence as the
/// original narrow IV. Then use a worklist to forward traverse the narrow IV's
/// def-use chain. After widenIVUse has processed all interesting IV users, the
/// narrow IV will be isolated for removal by DeleteDeadPHIs.
/// It would be simpler to delete uses as they are processed, but we must avoid
/// invalidating SCEV expressions.
PHINode *WidenIV::createWideIV(SCEVExpander &Rewriter) {
// Is this phi an induction variable?
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(OrigPhi));
if (!AddRec)
return nullptr;
// Widen the induction variable expression.
const SCEV *WideIVExpr = getExtendKind(OrigPhi) == SignExtended
? SE->getSignExtendExpr(AddRec, WideType)
: SE->getZeroExtendExpr(AddRec, WideType);
assert(SE->getEffectiveSCEVType(WideIVExpr->getType()) == WideType &&
"Expect the new IV expression to preserve its type");
// Can the IV be extended outside the loop without overflow?
AddRec = dyn_cast<SCEVAddRecExpr>(WideIVExpr);
if (!AddRec || AddRec->getLoop() != L)
return nullptr;
// An AddRec must have loop-invariant operands. Since this AddRec is
// materialized by a loop header phi, the expression cannot have any post-loop
// operands, so they must dominate the loop header.
SE->properlyDominates(AddRec->getStart(), L->getHeader()) &&
SE->properlyDominates(AddRec->getStepRecurrence(*SE), L->getHeader()) &&
"Loop header phi recurrence inputs do not dominate the loop");
// Iterate over IV uses (including transitive ones) looking for IV increments
// of the form 'add nsw %iv, <const>'. For each increment and each use of
// the increment calculate control-dependent range information basing on
// dominating conditions inside of the loop (e.g. a range check inside of the
// loop). Calculated ranges are stored in PostIncRangeInfos map.
// Control-dependent range information is later used to prove that a narrow
// definition is not negative (see pushNarrowIVUsers). It's difficult to do
// this on demand because when pushNarrowIVUsers needs this information some
// of the dominating conditions might be already widened.
if (UsePostIncrementRanges)
// The rewriter provides a value for the desired IV expression. This may
// either find an existing phi or materialize a new one. Either way, we
// expect a well-formed cyclic phi-with-increments. i.e. any operand not part
// of the phi-SCC dominates the loop entry.
Instruction *InsertPt = &L->getHeader()->front();
WidePhi = cast<PHINode>(Rewriter.expandCodeFor(AddRec, WideType, InsertPt));
// Remembering the WideIV increment generated by SCEVExpander allows
// widenIVUse to reuse it when widening the narrow IV's increment. We don't
// employ a general reuse mechanism because the call above is the only call to
// SCEVExpander. Henceforth, we produce 1-to-1 narrow to wide uses.
if (BasicBlock *LatchBlock = L->getLoopLatch()) {
WideInc =
WideIncExpr = SE->getSCEV(WideInc);
// Propagate the debug location associated with the original loop increment
// to the new (widened) increment.
auto *OrigInc =
DEBUG(dbgs() << "Wide IV: " << *WidePhi << "\n");
// Traverse the def-use chain using a worklist starting at the original IV.
assert(Widened.empty() && NarrowIVUsers.empty() && "expect initial state" );
pushNarrowIVUsers(OrigPhi, WidePhi);
while (!NarrowIVUsers.empty()) {
NarrowIVDefUse DU = NarrowIVUsers.pop_back_val();
// Process a def-use edge. This may replace the use, so don't hold a
// use_iterator across it.
Instruction *WideUse = widenIVUse(DU, Rewriter);
// Follow all def-use edges from the previous narrow use.
if (WideUse)
pushNarrowIVUsers(DU.NarrowUse, WideUse);
// widenIVUse may have removed the def-use edge.
if (DU.NarrowDef->use_empty())
// Attach any debug information to the new PHI. Since OrigPhi and WidePHI
// evaluate the same recurrence, we can just copy the debug info over.
SmallVector<DbgValueInst *, 1> DbgValues;
llvm::findDbgValues(DbgValues, OrigPhi);
auto *MDPhi = MetadataAsValue::get(WidePhi->getContext(),
for (auto &DbgValue : DbgValues)
DbgValue->setOperand(0, MDPhi);
return WidePhi;
/// Calculates control-dependent range for the given def at the given context
/// by looking at dominating conditions inside of the loop
void WidenIV::calculatePostIncRange(Instruction *NarrowDef,
Instruction *NarrowUser) {
using namespace llvm::PatternMatch;
Value *NarrowDefLHS;
const APInt *NarrowDefRHS;
if (!match(NarrowDef, m_NSWAdd(m_Value(NarrowDefLHS),
m_APInt(NarrowDefRHS))) ||
auto UpdateRangeFromCondition = [&] (Value *Condition,
bool TrueDest) {
CmpInst::Predicate Pred;
Value *CmpRHS;
if (!match(Condition, m_ICmp(Pred, m_Specific(NarrowDefLHS),
CmpInst::Predicate P =
TrueDest ? Pred : CmpInst::getInversePredicate(Pred);
auto CmpRHSRange = SE->getSignedRange(SE->getSCEV(CmpRHS));
auto CmpConstrainedLHSRange =
ConstantRange::makeAllowedICmpRegion(P, CmpRHSRange);
auto NarrowDefRange =
updatePostIncRangeInfo(NarrowDef, NarrowUser, NarrowDefRange);
auto UpdateRangeFromGuards = [&](Instruction *Ctx) {
if (!HasGuards)
for (Instruction &I : make_range(Ctx->getIterator().getReverse(),
Ctx->getParent()->rend())) {
Value *C = nullptr;
if (match(&I, m_Intrinsic<Intrinsic::experimental_guard>(m_Value(C))))
UpdateRangeFromCondition(C, /*TrueDest=*/true);
BasicBlock *NarrowUserBB = NarrowUser->getParent();
// If NarrowUserBB is statically unreachable asking dominator queries may
// yield surprising results. (e.g. the block may not have a dom tree node)
if (!DT->isReachableFromEntry(NarrowUserBB))
for (auto *DTB = (*DT)[NarrowUserBB]->getIDom();
DTB = DTB->getIDom()) {
auto *BB = DTB->getBlock();
auto *TI = BB->getTerminator();
auto *BI = dyn_cast<BranchInst>(TI);
if (!BI || !BI->isConditional())
auto *TrueSuccessor = BI->getSuccessor(0);
auto *FalseSuccessor = BI->getSuccessor(1);
auto DominatesNarrowUser = [this, NarrowUser] (BasicBlockEdge BBE) {
return BBE.isSingleEdge() &&
DT->dominates(BBE, NarrowUser->getParent());
if (DominatesNarrowUser(BasicBlockEdge(BB, TrueSuccessor)))
UpdateRangeFromCondition(BI->getCondition(), /*TrueDest=*/true);
if (DominatesNarrowUser(BasicBlockEdge(BB, FalseSuccessor)))
UpdateRangeFromCondition(BI->getCondition(), /*TrueDest=*/false);
/// Calculates PostIncRangeInfos map for the given IV
void WidenIV::calculatePostIncRanges(PHINode *OrigPhi) {
SmallPtrSet<Instruction *, 16> Visited;
SmallVector<Instruction *, 6> Worklist;
while (!Worklist.empty()) {
Instruction *NarrowDef = Worklist.pop_back_val();
for (Use &U : NarrowDef->uses()) {
auto *NarrowUser = cast<Instruction>(U.getUser());
// Don't go looking outside the current loop.
auto *NarrowUserLoop = (*LI)[NarrowUser->getParent()];
if (!NarrowUserLoop || !L->contains(NarrowUserLoop))
if (!Visited.insert(NarrowUser).second)
calculatePostIncRange(NarrowDef, NarrowUser);
// Live IV Reduction - Minimize IVs live across the loop.
// Simplification of IV users based on SCEV evaluation.
namespace {
class IndVarSimplifyVisitor : public IVVisitor {
ScalarEvolution *SE;
const TargetTransformInfo *TTI;
PHINode *IVPhi;
WideIVInfo WI;
IndVarSimplifyVisitor(PHINode *IV, ScalarEvolution *SCEV,
const TargetTransformInfo *TTI,
const DominatorTree *DTree)
DT = DTree;
WI.NarrowIV = IVPhi;
// Implement the interface used by simplifyUsersOfIV.
void visitCast(CastInst *Cast) override { visitIVCast(Cast, WI, SE, TTI); }
} // end anonymous namespace
/// Iteratively perform simplification on a worklist of IV users. Each
/// successive simplification may push more users which may themselves be
/// candidates for simplification.
/// Sign/Zero extend elimination is interleaved with IV simplification.
void IndVarSimplify::simplifyAndExtend(Loop *L,
SCEVExpander &Rewriter,
LoopInfo *LI) {
SmallVector<WideIVInfo, 8> WideIVs;
auto *GuardDecl = L->getBlocks()[0]->getModule()->getFunction(
bool HasGuards = GuardDecl && !GuardDecl->use_empty();
SmallVector<PHINode*, 8> LoopPhis;
for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
// Each round of simplification iterates through the SimplifyIVUsers worklist
// for all current phis, then determines whether any IVs can be
// widened. Widening adds new phis to LoopPhis, inducing another round of
// simplification on the wide IVs.
while (!LoopPhis.empty()) {
// Evaluate as many IV expressions as possible before widening any IVs. This
// forces SCEV to set no-wrap flags before evaluating sign/zero
// extension. The first time SCEV attempts to normalize sign/zero extension,
// the result becomes final. So for the most predictable results, we delay
// evaluation of sign/zero extend evaluation until needed, and avoid running
// other SCEV based analysis prior to simplifyAndExtend.
do {
PHINode *CurrIV = LoopPhis.pop_back_val();
// Information about sign/zero extensions of CurrIV.
IndVarSimplifyVisitor Visitor(CurrIV, SE, TTI, DT);
Changed |=
simplifyUsersOfIV(CurrIV, SE, DT, LI, DeadInsts, Rewriter, &Visitor);
if (Visitor.WI.WidestNativeType) {
} while(!LoopPhis.empty());
for (; !WideIVs.empty(); WideIVs.pop_back()) {
WidenIV Widener(WideIVs.back(), LI, SE, DT, DeadInsts, HasGuards);
if (PHINode *WidePhi = Widener.createWideIV(Rewriter)) {
Changed = true;
// linearFunctionTestReplace and its kin. Rewrite the loop exit condition.
/// Return true if this loop's backedge taken count expression can be safely and
/// cheaply expanded into an instruction sequence that can be used by
/// linearFunctionTestReplace.
/// TODO: This fails for pointer-type loop counters with greater than one byte
/// strides, consequently preventing LFTR from running. For the purpose of LFTR
/// we could skip this check in the case that the LFTR loop counter (chosen by
/// FindLoopCounter) is also pointer type. Instead, we could directly convert
/// the loop test to an inequality test by checking the target data's alignment
/// of element types (given that the initial pointer value originates from or is
/// used by ABI constrained operation, as opposed to inttoptr/ptrtoint).
/// However, we don't yet have a strong motivation for converting loop tests
/// into inequality tests.
static bool canExpandBackedgeTakenCount(Loop *L, ScalarEvolution *SE,
SCEVExpander &Rewriter) {
const SCEV *BackedgeTakenCount = SE->getBackedgeTakenCount(L);
if (isa<SCEVCouldNotCompute>(BackedgeTakenCount) ||
return false;
if (!L->getExitingBlock())
return false;
// Can't rewrite non-branch yet.
if (!isa<BranchInst>(L->getExitingBlock()->getTerminator()))
return false;
if (Rewriter.isHighCostExpansion(BackedgeTakenCount, L))
return false;
return true;
/// Return the loop header phi IFF IncV adds a loop invariant value to the phi.
static PHINode *getLoopPhiForCounter(Value *IncV, Loop *L, DominatorTree *DT) {
Instruction *IncI = dyn_cast<Instruction>(IncV);
if (!IncI)
return nullptr;
switch (IncI->getOpcode()) {
case Instruction::Add:
case Instruction::Sub:
case Instruction::GetElementPtr:
// An IV counter must preserve its type.
if (IncI->getNumOperands() == 2)
return nullptr;
PHINode *Phi = dyn_cast<PHINode>(IncI->getOperand(0));
if (Phi && Phi->getParent() == L->getHeader()) {
if (isLoopInvariant(IncI->getOperand(1), L, DT))
return Phi;
return nullptr;
if (IncI->getOpcode() == Instruction::GetElementPtr)
return nullptr;
// Allow add/sub to be commuted.
Phi = dyn_cast<PHINode>(IncI->getOperand(1));
if (Phi && Phi->getParent() == L->getHeader()) {
if (isLoopInvariant(IncI->getOperand(0), L, DT))
return Phi;
return nullptr;
/// Return the compare guarding the loop latch, or NULL for unrecognized tests.
static ICmpInst *getLoopTest(Loop *L) {
assert(L->getExitingBlock() && "expected loop exit");
BasicBlock *LatchBlock = L->getLoopLatch();
// Don't bother with LFTR if the loop is not properly simplified.
if (!LatchBlock)
return nullptr;
BranchInst *BI = dyn_cast<BranchInst>(L->getExitingBlock()->getTerminator());
assert(BI && "expected exit branch");
return dyn_cast<ICmpInst>(BI->getCondition());
/// linearFunctionTestReplace policy. Return true unless we can show that the
/// current exit test is already sufficiently canonical.
static bool needsLFTR(Loop *L, DominatorTree *DT) {
// Do LFTR to simplify the exit condition to an ICMP.
ICmpInst *Cond = getLoopTest(L);
if (!Cond)
return true;
// Do LFTR to simplify the exit ICMP to EQ/NE
ICmpInst::Predicate Pred = Cond->getPredicate();
if (Pred != ICmpInst::ICMP_NE && Pred != ICmpInst::ICMP_EQ)
return true;
// Look for a loop invariant RHS
Value *LHS = Cond->getOperand(0);
Value *RHS = Cond->getOperand(1);
if (!isLoopInvariant(RHS, L, DT)) {
if (!isLoopInvariant(LHS, L, DT))
return true;
std::swap(LHS, RHS);
// Look for a simple IV counter LHS
PHINode *Phi = dyn_cast<PHINode>(LHS);
if (!Phi)
Phi = getLoopPhiForCounter(LHS, L, DT);
if (!Phi)
return true;
// Do LFTR if PHI node is defined in the loop, but is *not* a counter.
int Idx = Phi->getBasicBlockIndex(L->getLoopLatch());
if (Idx < 0)
return true;
// Do LFTR if the exit condition's IV is *not* a simple counter.
Value *IncV = Phi->getIncomingValue(Idx);
return Phi != getLoopPhiForCounter(IncV, L, DT);
/// Recursive helper for hasConcreteDef(). Unfortunately, this currently boils
/// down to checking that all operands are constant and listing instructions
/// that may hide undef.
static bool hasConcreteDefImpl(Value *V, SmallPtrSetImpl<Value*> &Visited,
unsigned Depth) {
if (isa<Constant>(V))
return !isa<UndefValue>(V);
if (Depth >= 6)
return false;
// Conservatively handle non-constant non-instructions. For example, Arguments
// may be undef.
Instruction *I = dyn_cast<Instruction>(V);
if (!I)
return false;
// Load and return values may be undef.
if(I->mayReadFromMemory() || isa<CallInst>(I) || isa<InvokeInst>(I))
return false;
// Optimistically handle other instructions.
for (Value *Op : I->operands()) {
if (!Visited.insert(Op).second)
if (!hasConcreteDefImpl(Op, Visited, Depth+1))
return false;
return true;
/// Return true if the given value is concrete. We must prove that undef can
/// never reach it.
/// TODO: If we decide that this is a good approach to checking for undef, we
/// may factor it into a common location.
static bool hasConcreteDef(Value *V) {
SmallPtrSet<Value*, 8> Visited;
return hasConcreteDefImpl(V, Visited, 0);
/// Return true if this IV has any uses other than the (soon to be rewritten)
/// loop exit test.
static bool AlmostDeadIV(PHINode *Phi, BasicBlock *LatchBlock, Value *Cond) {
int LatchIdx = Phi->getBasicBlockIndex(LatchBlock);
Value *IncV = Phi->getIncomingValue(LatchIdx);
for (User *U : Phi->users())
if (U != Cond && U != IncV) return false;
for (User *U : IncV->users())
if (U != Cond && U != Phi) return false;
return true;
/// Find an affine IV in canonical form.
/// BECount may be an i8* pointer type. The pointer difference is already
/// valid count without scaling the address stride, so it remains a pointer
/// expression as far as SCEV is concerned.
/// Currently only valid for LFTR. See the comments on hasConcreteDef below.
/// FIXME: Accept -1 stride and set IVLimit = IVInit - BECount
/// FIXME: Accept non-unit stride as long as SCEV can reduce BECount * Stride.
/// This is difficult in general for SCEV because of potential overflow. But we
/// could at least handle constant BECounts.
static PHINode *FindLoopCounter(Loop *L, const SCEV *BECount,
ScalarEvolution *SE, DominatorTree *DT) {
uint64_t BCWidth = SE->getTypeSizeInBits(BECount->getType());
Value *Cond =
// Loop over all of the PHI nodes, looking for a simple counter.
PHINode *BestPhi = nullptr;
const SCEV *BestInit = nullptr;
BasicBlock *LatchBlock = L->getLoopLatch();
assert(LatchBlock && "needsLFTR should guarantee a loop latch");
const DataLayout &DL = L->getHeader()->getModule()->getDataLayout();
for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
PHINode *Phi = cast<PHINode>(I);
if (!SE->isSCEVable(Phi->getType()))
// Avoid comparing an integer IV against a pointer Limit.
if (BECount->getType()->isPointerTy() && !Phi->getType()->isPointerTy())
const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(Phi));
if (!AR || AR->getLoop() != L || !AR->isAffine())
// AR may be a pointer type, while BECount is an integer type.
// AR may be wider than BECount. With eq/ne tests overflow is immaterial.
// AR may not be a narrower type, or we may never exit.
uint64_t PhiWidth = SE->getTypeSizeInBits(AR->getType());
if (PhiWidth < BCWidth || !DL.isLegalInteger(PhiWidth))
const SCEV *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(*SE));
if (!Step || !Step->isOne())
int LatchIdx = Phi->getBasicBlockIndex(LatchBlock);
Value *IncV = Phi->getIncomingValue(LatchIdx);
if (getLoopPhiForCounter(IncV, L, DT) != Phi)
// Avoid reusing a potentially undef value to compute other values that may
// have originally had a concrete definition.
if (!hasConcreteDef(Phi)) {
// We explicitly allow unknown phis as long as they are already used by
// the loop test. In this case we assume that performing LFTR could not
// increase the number of undef users.
if (ICmpInst *Cond = getLoopTest(L)) {
if (Phi != getLoopPhiForCounter(Cond->getOperand(0), L, DT) &&
Phi != getLoopPhiForCounter(Cond->getOperand(1), L, DT)) {
const SCEV *Init = AR->getStart();
if (BestPhi && !AlmostDeadIV(BestPhi, LatchBlock, Cond)) {
// Don't force a live loop counter if another IV can be used.
if (AlmostDeadIV(Phi, LatchBlock, Cond))
// Prefer to count-from-zero. This is a more "canonical" counter form. It
// also prefers integer to pointer IVs.
if (BestInit->isZero() != Init->isZero()) {
if (BestInit->isZero())
// If two IVs both count from zero or both count from nonzero then the
// narrower is likely a dead phi that has been widened. Use the wider phi
// to allow the other to be eliminated.
else if (PhiWidth <= SE->getTypeSizeInBits(BestPhi->getType()))
BestPhi = Phi;
BestInit = Init;
return BestPhi;
/// Help linearFunctionTestReplace by generating a value that holds the RHS of
/// the new loop test.
static Value *genLoopLimit(PHINode *IndVar, const SCEV *IVCount, Loop *L,
SCEVExpander &Rewriter, ScalarEvolution *SE) {
const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(IndVar));
assert(AR && AR->getLoop() == L && AR->isAffine() && "bad loop counter");
const SCEV *IVInit = AR->getStart();
// IVInit may be a pointer while IVCount is an integer when FindLoopCounter
// finds a valid pointer IV. Sign extend BECount in order to materialize a
// GEP. Avoid running SCEVExpander on a new pointer value, instead reusing
// the existing GEPs whenever possible.
if (IndVar->getType()->isPointerTy() && !IVCount->getType()->isPointerTy()) {
// IVOffset will be the new GEP offset that is interpreted by GEP as a
// signed value. IVCount on the other hand represents the loop trip count,
// which is an unsigned value. FindLoopCounter only allows induction
// variables that have a positive unit stride of one. This means we don't
// have to handle the case of negative offsets (yet) and just need to zero
// extend IVCount.
Type *OfsTy = SE->getEffectiveSCEVType(IVInit->getType());
const SCEV *IVOffset = SE->getTruncateOrZeroExtend(IVCount, OfsTy);
// Expand the code for the iteration count.
assert(SE->isLoopInvariant(IVOffset, L) &&
"Computed iteration count is not loop invariant!");
BranchInst *BI = cast<BranchInst>(L->getExitingBlock()->getTerminator());
Value *GEPOffset = Rewriter.expandCodeFor(IVOffset, OfsTy, BI);
Value *GEPBase = IndVar->getIncomingValueForBlock(L->getLoopPreheader());
assert(AR->getStart() == SE->getSCEV(GEPBase) && "bad loop counter");
// We could handle pointer IVs other than i8*, but we need to compensate for
// gep index scaling. See canExpandBackedgeTakenCount comments.
->getElementType())->isOne() &&
"unit stride pointer IV must be i8*");
IRBuilder<> Builder(L->getLoopPreheader()->getTerminator());
return Builder.CreateGEP(nullptr, GEPBase, GEPOffset, "lftr.limit");
} else {
// In any other case, convert both IVInit and IVCount to integers before
// comparing. This may result in SCEV expansion of pointers, but in practice
// SCEV will fold the pointer arithmetic away as such:
// BECount = (IVEnd - IVInit - 1) => IVLimit = IVInit (postinc).
// Valid Cases: (1) both integers is most common; (2) both may be pointers
// for simple memset-style loops.
// IVInit integer and IVCount pointer would only occur if a canonical IV
// were generated on top of case #2, which is not expected.
const SCEV *IVLimit = nullptr;
// For unit stride, IVCount = Start + BECount with 2's complement overflow.
// For non-zero Start, compute IVCount here.
if (AR->getStart()->isZero())
IVLimit = IVCount;
else {
assert(AR->getStepRecurrence(*SE)->isOne() && "only handles unit stride");
const SCEV *IVInit = AR->getStart();
// For integer IVs, truncate the IV before computing IVInit + BECount.
if (SE->getTypeSizeInBits(IVInit->getType())
> SE->getTypeSizeInBits(IVCount->getType()))
IVInit = SE->getTruncateExpr(IVInit, IVCount->getType());
IVLimit = SE->getAddExpr(IVInit, IVCount);
// Expand the code for the iteration count.
BranchInst *BI = cast<BranchInst>(L->getExitingBlock()->getTerminator());
IRBuilder<> Builder(BI);
assert(SE->isLoopInvariant(IVLimit, L) &&
"Computed iteration count is not loop invariant!");
// Ensure that we generate the same type as IndVar, or a smaller integer
// type. In the presence of null pointer values, we have an integer type
// SCEV expression (IVInit) for a pointer type IV value (IndVar).
Type *LimitTy = IVCount->getType()->isPointerTy() ?
IndVar->getType() : IVCount->getType();
return Rewriter.expandCodeFor(IVLimit, LimitTy, BI);
/// This method rewrites the exit condition of the loop to be a canonical !=
/// comparison against the incremented loop induction variable. This pass is
/// able to rewrite the exit tests of any loop where the SCEV analysis can
/// determine a loop-invariant trip count of the loop, which is actually a much
/// broader range than just linear tests.
Value *IndVarSimplify::
linearFunctionTestReplace(Loop *L,
const SCEV *BackedgeTakenCount,
PHINode *IndVar,
SCEVExpander &Rewriter) {
assert(canExpandBackedgeTakenCount(L, SE, Rewriter) && "precondition");
// Initialize CmpIndVar and IVCount to their preincremented values.
Value *CmpIndVar = IndVar;
const SCEV *IVCount = BackedgeTakenCount;
assert(L->getLoopLatch() && "Loop no longer in simplified form?");
// If the exiting block is the same as the backedge block, we prefer to
// compare against the post-incremented value, otherwise we must compare
// against the preincremented value.
if (L->getExitingBlock() == L->getLoopLatch()) {
// Add one to the "backedge-taken" count to get the trip count.
// This addition may overflow, which is valid as long as the comparison is
// truncated to BackedgeTakenCount->getType().
IVCount = SE->getAddExpr(BackedgeTakenCount,
// The BackedgeTaken expression contains the number of times that the
// backedge branches to the loop header. This is one less than the
// number of times the loop executes, so use the incremented indvar.
CmpIndVar = IndVar->getIncomingValueForBlock(L->getExitingBlock());
Value *ExitCnt = genLoopLimit(IndVar, IVCount, L, Rewriter, SE);
assert(ExitCnt->getType()->isPointerTy() ==
IndVar->getType()->isPointerTy() &&
"genLoopLimit missed a cast");
// Insert a new icmp_ne or icmp_eq instruction before the branch.
BranchInst *BI = cast<BranchInst>(L->getExitingBlock()->getTerminator());
ICmpInst::Predicate P;
if (L->contains(BI->getSuccessor(0)))
P = ICmpInst::ICMP_NE;
P = ICmpInst::ICMP_EQ;
DEBUG(dbgs() << "INDVARS: Rewriting loop exit condition to:\n"
<< " LHS:" << *CmpIndVar << '\n'
<< " op:\t"
<< (P == ICmpInst::ICMP_NE ? "!=" : "==") << "\n"
<< " RHS:\t" << *ExitCnt << "\n"
<< " IVCount:\t" << *IVCount << "\n");
IRBuilder<> Builder(BI);
// The new loop exit condition should reuse the debug location of the
// original loop exit condition.
if (auto *Cond = dyn_cast<Instruction>(BI->getCondition()))
// LFTR can ignore IV overflow and truncate to the width of
// BECount. This avoids materializing the add(zext(add)) expression.
unsigned CmpIndVarSize = SE->getTypeSizeInBits(CmpIndVar->getType());
unsigned ExitCntSize = SE->getTypeSizeInBits(ExitCnt->getType());
if (CmpIndVarSize > ExitCntSize) {
const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(SE->getSCEV(IndVar));
const SCEV *ARStart = AR->getStart();
const SCEV *ARStep = AR->getStepRecurrence(*SE);
// For constant IVCount, avoid truncation.
if (isa<SCEVConstant>(ARStart) && isa<SCEVConstant>(IVCount)) {
const APInt &Start = cast<SCEVConstant>(ARStart)->getAPInt();
APInt Count = cast<SCEVConstant>(IVCount)->getAPInt();
// Note that the post-inc value of BackedgeTakenCount may have overflowed
// above such that IVCount is now zero.
if (IVCount != BackedgeTakenCount && Count == 0) {
Count = APInt::getMaxValue(Count.getBitWidth()).zext(CmpIndVarSize);
Count = Count.zext(CmpIndVarSize);
APInt NewLimit;
if (cast<SCEVConstant>(ARStep)->getValue()->isNegative())
NewLimit = Start - Count;
NewLimit = Start + Count;
ExitCnt = ConstantInt::get(CmpIndVar->getType(), NewLimit);
DEBUG(dbgs() << " Widen RHS:\t" << *ExitCnt << "\n");
} else {
// We try to extend trip count first. If that doesn't work we truncate IV.
// Zext(trunc(IV)) == IV implies equivalence of the following two:
// Trunc(IV) == ExitCnt and IV == zext(ExitCnt). Similarly for sext. If
// one of the two holds, extend the trip count, otherwise we truncate IV.
bool Extended = false;
const SCEV *IV = SE->getSCEV(CmpIndVar);
const SCEV *ZExtTrunc =
if (ZExtTrunc == IV) {
Extended = true;
ExitCnt = Builder.CreateZExt(ExitCnt, IndVar->getType(),
} else {
const SCEV *SExtTrunc =
if (SExtTrunc == IV) {
Extended = true;
ExitCnt = Builder.CreateSExt(ExitCnt, IndVar->getType(),
if (!Extended)
CmpIndVar = Builder.CreateTrunc(CmpIndVar, ExitCnt->getType(),
Value *Cond = Builder.CreateICmp(P, CmpIndVar, ExitCnt, "exitcond");
Value *OrigCond = BI->getCondition();
// It's tempting to use replaceAllUsesWith here to fully replace the old
// comparison, but that's not immediately safe, since users of the old
// comparison may not be dominated by the new comparison. Instead, just
// update the branch to use the new comparison; in the common case this
// will make old comparison dead.
Changed = true;
return Cond;
// sinkUnusedInvariants. A late subpass to cleanup loop preheaders.
/// If there's a single exit block, sink any loop-invariant values that
/// were defined in the preheader but not used inside the loop into the
/// exit block to reduce register pressure in the loop.
void IndVarSimplify::sinkUnusedInvariants(Loop *L) {
BasicBlock *ExitBlock = L->getExitBlock();
if (!ExitBlock) return;
BasicBlock *Preheader = L->getLoopPreheader();
if (!Preheader) return;
BasicBlock::iterator InsertPt = ExitBlock->getFirstInsertionPt();
BasicBlock::iterator I(Preheader->getTerminator());
while (I != Preheader->begin()) {
// New instructions were inserted at the end of the preheader.
if (isa<PHINode>(I))
// Don't move instructions which might have side effects, since the side
// effects need to complete before instructions inside the loop. Also don't
// move instructions which might read memory, since the loop may modify
// memory. Note that it's okay if the instruction might have undefined
// behavior: LoopSimplify guarantees that the preheader dominates the exit
// block.
if (I->mayHaveSideEffects() || I->mayReadFromMemory())
// Skip debug info intrinsics.
if (isa<DbgInfoIntrinsic>(I))
// Skip eh pad instructions.
if (I->isEHPad())
// Don't sink alloca: we never want to sink static alloca's out of the
// entry block, and correctly sinking dynamic alloca's requires
// checks for stacksave/stackrestore intrinsics.
// FIXME: Refactor this check somehow?
if (isa<AllocaInst>(I))
// Determine if there is a use in or before the loop (direct or
// otherwise).
bool UsedInLoop = false;
for (Use &U : I->uses()) {
Instruction *User = cast<Instruction>(U.getUser());
BasicBlock *UseBB = User->getParent();
if (PHINode *P = dyn_cast<PHINode>(User)) {
unsigned i =
UseBB = P->getIncomingBlock(i);
if (UseBB == Preheader || L->contains(UseBB)) {
UsedInLoop = true;
// If there is, the def must remain in the preheader.
if (UsedInLoop)
// Otherwise, sink it to the exit block.
Instruction *ToMove = &*I;
bool Done = false;
if (I != Preheader->begin()) {
// Skip debug info intrinsics.
do {
} while (isa<DbgInfoIntrinsic>(I) && I != Preheader->begin());
if (isa<DbgInfoIntrinsic>(I) && I == Preheader->begin())
Done = true;
} else {
Done = true;
ToMove->moveBefore(*ExitBlock, InsertPt);
if (Done) break;
InsertPt = ToMove->getIterator();
// IndVarSimplify driver. Manage several subpasses of IV simplification.
bool IndVarSimplify::run(Loop *L) {
// We need (and expect!) the incoming loop to be in LCSSA.
assert(L->isRecursivelyLCSSAForm(*DT, *LI) &&
"LCSSA required to run indvars!");
// If LoopSimplify form is not available, stay out of trouble. Some notes:
// - LSR currently only supports LoopSimplify-form loops. Indvars'
// canonicalization can be a pessimization without LSR to "clean up"
// afterwards.
// - We depend on having a preheader; in particular,
// Loop::getCanonicalInductionVariable only supports loops with preheaders,
// and we're in trouble if we can't find the induction variable even when
// we've manually inserted one.
// - LFTR relies on having a single backedge.
if (!L->isLoopSimplifyForm())
return false;
// If there are any floating-point recurrences, attempt to
// transform them to use integer recurrences.
const SCEV *BackedgeTakenCount = SE->getBackedgeTakenCount(L);
// Create a rewriter object which we'll use to transform the code with.
SCEVExpander Rewriter(*SE, DL, "indvars");
#ifndef NDEBUG
// Eliminate redundant IV users.
// Simplification works best when run before other consumers of SCEV. We
// attempt to avoid evaluating SCEVs for sign/zero extend operations until
// other expressions involving loop IVs have been evaluated. This helps SCEV
// set no-wrap flags before normalizing sign/zero extension.
simplifyAndExtend(L, Rewriter, LI);
// Check to see if this loop has a computable loop-invariant execution count.
// If so, this means that we can compute the final value of any expressions
// that are recurrent in the loop, and substitute the exit values from the
// loop into any instructions outside of the loop that use the final values of
// the current expressions.
if (ReplaceExitValue != NeverRepl &&
rewriteLoopExitValues(L, Rewriter);
// Eliminate redundant IV cycles.
NumElimIV += Rewriter.replaceCongruentIVs(L, DT, DeadInsts);
// If we have a trip count expression, rewrite the loop's exit condition
// using it. We can currently only handle loops with a single exit.
if (!DisableLFTR && canExpandBackedgeTakenCount(L, SE, Rewriter) &&
needsLFTR(L, DT)) {
PHINode *IndVar = FindLoopCounter(L, BackedgeTakenCount, SE, DT);
if (IndVar) {
// Check preconditions for proper SCEVExpander operation. SCEV does not
// express SCEVExpander's dependencies, such as LoopSimplify. Instead any
// pass that uses the SCEVExpander must do it. This does not work well for
// loop passes because SCEVExpander makes assumptions about all loops,
// while LoopPassManager only forces the current loop to be simplified.
// FIXME: SCEV expansion has no way to bail out, so the caller must
// explicitly check any assumptions made by SCEV. Brittle.
const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(BackedgeTakenCount);
if (!AR || AR->getLoop()->getLoopPreheader())
(void)linearFunctionTestReplace(L, BackedgeTakenCount, IndVar,
// Clear the rewriter cache, because values that are in the rewriter's cache
// can be deleted in the loop below, causing the AssertingVH in the cache to
// trigger.
// Now that we're done iterating through lists, clean up any instructions
// which are now dead.
while (!DeadInsts.empty())
if (Instruction *Inst =
RecursivelyDeleteTriviallyDeadInstructions(Inst, TLI);
// The Rewriter may not be used from this point on.
// Loop-invariant instructions in the preheader that aren't used in the
// loop may be sunk below the loop to reduce register pressure.
// rewriteFirstIterationLoopExitValues does not rely on the computation of
// trip count and therefore can further simplify exit values in addition to
// rewriteLoopExitValues.
// Clean up dead instructions.
Changed |= DeleteDeadPHIs(L->getHeader(), TLI);
// Check a post-condition.
assert(L->isRecursivelyLCSSAForm(*DT, *LI) &&
"Indvars did not preserve LCSSA!");
// Verify that LFTR, and any other change have not interfered with SCEV's
// ability to compute trip count.
#ifndef NDEBUG
if (VerifyIndvars && !isa<SCEVCouldNotCompute>(BackedgeTakenCount)) {
const SCEV *NewBECount = SE->getBackedgeTakenCount(L);
if (SE->getTypeSizeInBits(BackedgeTakenCount->getType()) <
NewBECount = SE->getTruncateOrNoop(NewBECount,
BackedgeTakenCount = SE->getTruncateOrNoop(BackedgeTakenCount,
assert(BackedgeTakenCount == NewBECount && "indvars must preserve SCEV");
return Changed;
PreservedAnalyses IndVarSimplifyPass::run(Loop &L, LoopAnalysisManager &AM,
LoopStandardAnalysisResults &AR,
LPMUpdater &) {
Function *F = L.getHeader()->getParent();
const DataLayout &DL = F->getParent()->getDataLayout();
IndVarSimplify IVS(&AR.LI, &AR.SE, &AR.DT, DL, &AR.TLI, &AR.TTI);
if (!
return PreservedAnalyses::all();
auto PA = getLoopPassPreservedAnalyses();
return PA;
namespace {
struct IndVarSimplifyLegacyPass : public LoopPass {
static char ID; // Pass identification, replacement for typeid
IndVarSimplifyLegacyPass() : LoopPass(ID) {
bool runOnLoop(Loop *L, LPPassManager &LPM) override {
if (skipLoop(L))
return false;
auto *LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
auto *SE = &getAnalysis<ScalarEvolutionWrapperPass>().getSE();
auto *DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
auto *TLIP = getAnalysisIfAvailable<TargetLibraryInfoWrapperPass>();
auto *TLI = TLIP ? &TLIP->getTLI() : nullptr;
auto *TTIP = getAnalysisIfAvailable<TargetTransformInfoWrapperPass>();
auto *TTI = TTIP ? &TTIP->getTTI(*L->getHeader()->getParent()) : nullptr;
const DataLayout &DL = L->getHeader()->getModule()->getDataLayout();
IndVarSimplify IVS(LI, SE, DT, DL, TLI, TTI);
void getAnalysisUsage(AnalysisUsage &AU) const override {
} // end anonymous namespace
char IndVarSimplifyLegacyPass::ID = 0;
INITIALIZE_PASS_BEGIN(IndVarSimplifyLegacyPass, "indvars",
"Induction Variable Simplification", false, false)
INITIALIZE_PASS_END(IndVarSimplifyLegacyPass, "indvars",
"Induction Variable Simplification", false, false)
Pass *llvm::createIndVarSimplifyPass() {
return new IndVarSimplifyLegacyPass();