blob: d52016806967b71f23738d1610949b712ec86f70 [file] [log] [blame]
//===- 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.
#define DEBUG_TYPE "indvars"
#include "polly/LinkAllPasses.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/BasicBlock.h"
#include "llvm/Constants.h"
#include "llvm/Instructions.h"
#include "llvm/IntrinsicInst.h"
#include "llvm/LLVMContext.h"
#include "llvm/Type.h"
#include "llvm/Analysis/Dominators.h"
#include "llvm/Analysis/IVUsers.h"
#include "llvm/Analysis/ScalarEvolutionExpander.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Support/CFG.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Transforms/Utils/BasicBlockUtils.h"
#include "llvm/Transforms/Utils/SimplifyIndVar.h"
#include "llvm/DataLayout.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
using namespace llvm;
STATISTIC(NumRemoved , "Number of aux indvars removed");
STATISTIC(NumWidened , "Number of indvars widened");
STATISTIC(NumInserted , "Number of canonical indvars added");
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");
static const bool EnableIVRewrite = true;
static const bool VerifyIndvars = false;
namespace {
class PollyIndVarSimplify : public LoopPass {
IVUsers *IU;
LoopInfo *LI;
ScalarEvolution *SE;
DominatorTree *DT;
DataLayout *TD;
SmallVector<WeakVH, 16> DeadInsts;
bool Changed;
static char ID; // Pass identification, replacement for typeid
PollyIndVarSimplify() : LoopPass(ID), IU(0), LI(0), SE(0), DT(0), TD(0),
Changed(false) {
virtual bool runOnLoop(Loop *L, LPPassManager &LPM);
virtual void getAnalysisUsage(AnalysisUsage &AU) const {
if (EnableIVRewrite)
if (EnableIVRewrite)
virtual void releaseMemory() {
bool isValidRewrite(Value *FromVal, Value *ToVal);
void HandleFloatingPointIV(Loop *L, PHINode *PH);
void RewriteNonIntegerIVs(Loop *L);
void SimplifyAndExtend(Loop *L, SCEVExpander &Rewriter, LPPassManager &LPM);
void RewriteLoopExitValues(Loop *L, SCEVExpander &Rewriter);
void RewriteIVExpressions(Loop *L, SCEVExpander &Rewriter);
Value *LinearFunctionTestReplace(Loop *L, const SCEV *BackedgeTakenCount,
PHINode *IndVar, SCEVExpander &Rewriter);
void SinkUnusedInvariants(Loop *L);
char PollyIndVarSimplify::ID = 0;
INITIALIZE_PASS_BEGIN(PollyIndVarSimplify, "polly-indvars",
"Induction Variable Simplification (Polly version)", false,
INITIALIZE_PASS_END(PollyIndVarSimplify, "polly-indvars",
"Induction Variable Simplification (Polly version)", false,
Pass *polly::createIndVarSimplifyPass() {
return new PollyIndVarSimplify();
/// isValidRewrite - 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 PollyIndVarSimplify::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 (GEPOperator *GEP = dyn_cast<GEPOperator>(FromVal)) {
FromPtr = GEP->getPointerOperand();
if (GEPOperator *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) {
PHINode *PHI = dyn_cast<PHINode>(User);
if (!PHI)
return User;
Instruction *InsertPt = 0;
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");
assert((!isa<Instruction>(Def) ||
DT->dominates(cast<Instruction>(Def), InsertPt)) &&
"def does not dominate all uses");
return InsertPt;
// RewriteNonIntegerIVs and helpers. Prefer integer IVs.
/// ConvertToSInt - Convert APF to an integer, if possible.
static bool ConvertToSInt(const APFloat &APF, int64_t &IntVal) {
bool isExact = false;
if (&APF.getSemantics() == &APFloat::PPCDoubleDouble)
return false;
// See if we can convert this to an int64_t
uint64_t UIntVal;
if (APF.convertToInteger(&UIntVal, 64, true, APFloat::rmTowardZero,
&isExact) != APFloat::opOK || !isExact)
return false;
IntVal = UIntVal;
return true;
/// HandleFloatingPointIV - 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 PollyIndVarSimplify::HandleFloatingPointIV(Loop *L, PHINode *PN) {
unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
unsigned BackEdge = IncomingEdge^1;
// Check incoming value.
ConstantFP *InitValueVal =
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.
BinaryOperator *Incr =
if (Incr == 0 || 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 == 0 || 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::use_iterator IncrUse = Incr->use_begin();
Instruction *U1 = cast<Instruction>(*IncrUse++);
if (IncrUse == Incr->use_end()) return;
Instruction *U2 = cast<Instruction>(*IncrUse++);
if (IncrUse != Incr->use_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 == 0 || !Compare->hasOneUse() ||
BranchInst *TheBr = cast<BranchInst>(Compare->use_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 == 0 ||
!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 WeakVH to observe whether this happens.
WeakVH WeakPH = PN;
// Delete the old floating point exit comparison. The branch starts using the
// new comparison.
// Delete the old floating point increment.
// 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",
// Add a new IVUsers entry for the newly-created integer PHI.
if (IU)
Changed = true;
void PollyIndVarSimplify::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<WeakVH, 8> PHIs;
for (BasicBlock::iterator I = Header->begin();
PHINode *PN = dyn_cast<PHINode>(I); ++I)
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)
// RewriteLoopExitValues - Optimize IV users outside the loop.
// As a side effect, reduces the amount of IV processing within the loop.
/// RewriteLoopExitValues - 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 PollyIndVarSimplify::RewriteLoopExitValues(Loop *L,
SCEVExpander &Rewriter) {
// Verify the input to the pass in already in LCSSA form.
SmallVector<BasicBlock*, 8> ExitBlocks;
// 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 (unsigned i = 0, e = ExitBlocks.size(); i != e; ++i) {
BasicBlock *ExitBB = ExitBlocks[i];
// 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
// SCEV only supports integer expressions for now.
if (!PN->getType()->isIntegerTy() && !PN->getType()->isPointerTy())
// 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))
Value *ExitVal = Rewriter.expandCodeFor(ExitValue, PN->getType(), Inst);
DEBUG(dbgs() << "INDVARS: RLEV: AfterLoopVal = " << *ExitVal << '\n'
<< " LoopVal = " << *Inst << "\n");
if (!isValidRewrite(Inst, ExitVal)) {
Changed = true;
PN->setIncomingValue(i, ExitVal);
// If this instruction is dead now, delete it.
if (NumPreds == 1) {
// Completely replace a single-pred PHI. This is safe, because the
// NewVal won't be variant in the loop, so we don't need an LCSSA phi
// node anymore.
if (NumPreds != 1) {
// Clone the PHI and delete the original one. This lets IVUsers and
// any other maps purge the original user from their records.
PHINode *NewPN = cast<PHINode>(PN->clone());
// The insertion point instruction may have been deleted; clear it out
// so that the rewriter doesn't trip over it later.
// Rewrite IV users based on a canonical IV.
// Only for use with -enable-iv-rewrite.
/// FIXME: It is an extremely bad idea to indvar substitute anything more
/// complex than affine induction variables. Doing so will put expensive
/// polynomial evaluations inside of the loop, and the str reduction pass
/// currently can only reduce affine polynomials. For now just disable
/// indvar subst on anything more complex than an affine addrec, unless
/// it can be expanded to a trivial value.
static bool isSafe(const SCEV *S, const Loop *L, ScalarEvolution *SE) {
// Loop-invariant values are safe.
if (SE->isLoopInvariant(S, L)) return true;
// Affine addrecs are safe. Non-affine are not, because LSR doesn't know how
// to transform them into efficient code.
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
return AR->isAffine();
// An add is safe it all its operands are safe.
if (const SCEVCommutativeExpr *Commutative
= dyn_cast<SCEVCommutativeExpr>(S)) {
for (SCEVCommutativeExpr::op_iterator I = Commutative->op_begin(),
E = Commutative->op_end(); I != E; ++I)
if (!isSafe(*I, L, SE)) return false;
return true;
// A cast is safe if its operand is.
if (const SCEVCastExpr *C = dyn_cast<SCEVCastExpr>(S))
return isSafe(C->getOperand(), L, SE);
// A udiv is safe if its operands are.
if (const SCEVUDivExpr *UD = dyn_cast<SCEVUDivExpr>(S))
return isSafe(UD->getLHS(), L, SE) &&
isSafe(UD->getRHS(), L, SE);
// SCEVUnknown is always safe.
if (isa<SCEVUnknown>(S))
return true;
// Nothing else is safe.
return false;
void PollyIndVarSimplify::RewriteIVExpressions(Loop *L,
SCEVExpander &Rewriter) {
// Rewrite all induction variable expressions in terms of the canonical
// induction variable.
// If there were induction variables of other sizes or offsets, manually
// add the offsets to the primary induction variable and cast, avoiding
// the need for the code evaluation methods to insert induction variables
// of different sizes.
for (IVUsers::iterator UI = IU->begin(), E = IU->end(); UI != E; ++UI) {
Value *Op = UI->getOperandValToReplace();
Type *UseTy = Op->getType();
Instruction *User = UI->getUser();
// Compute the final addrec to expand into code.
const SCEV *AR = IU->getReplacementExpr(*UI);
// Evaluate the expression out of the loop, if possible.
if (!L->contains(UI->getUser())) {
const SCEV *ExitVal = SE->getSCEVAtScope(AR, L->getParentLoop());
if (SE->isLoopInvariant(ExitVal, L))
AR = ExitVal;
// FIXME: It is an extremely bad idea to indvar substitute anything more
// complex than affine induction variables. Doing so will put expensive
// polynomial evaluations inside of the loop, and the str reduction pass
// currently can only reduce affine polynomials. For now just disable
// indvar subst on anything more complex than an affine addrec, unless
// it can be expanded to a trivial value.
if (!isSafe(AR, L, SE))
// Determine the insertion point for this user. By default, insert
// immediately before the user. The SCEVExpander class will automatically
// 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.
Instruction *InsertPt = getInsertPointForUses(User, Op, DT);
// Now expand it into actual Instructions and patch it into place.
Value *NewVal = Rewriter.expandCodeFor(AR, UseTy, InsertPt);
DEBUG(dbgs() << "INDVARS: Rewrote IV '" << *AR << "' " << *Op << '\n'
<< " into = " << *NewVal << "\n");
if (!isValidRewrite(Op, NewVal)) {
// Inform ScalarEvolution that this value is changing. The change doesn't
// affect its value, but it does potentially affect which use lists the
// value will be on after the replacement, which affects ScalarEvolution's
// ability to walk use lists and drop dangling pointers when a value is
// deleted.
// Patch the new value into place.
if (Op->hasName())
if (Instruction *NewValI = dyn_cast<Instruction>(NewVal))
User->replaceUsesOfWith(Op, NewVal);
Changed = true;
// The old value may be dead now.
// 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;
Type *WidestNativeType; // Widest integer type created [sz]ext
bool IsSigned; // Was an sext user seen before a zext?
WideIVInfo() : NarrowIV(0), WidestNativeType(0), IsSigned(false) {}
class WideIVVisitor : public IVVisitor {
ScalarEvolution *SE;
const DataLayout *TD;
WideIVInfo WI;
WideIVVisitor(PHINode *NarrowIV, ScalarEvolution *SCEV,
const DataLayout *TData) :
SE(SCEV), TD(TData) { WI.NarrowIV = NarrowIV; }
// Implement the interface used by simplifyUsersOfIV.
virtual void visitCast(CastInst *Cast);
/// visitCast - 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.
void WideIVVisitor::visitCast(CastInst *Cast) {
bool IsSigned = Cast->getOpcode() == Instruction::SExt;
if (!IsSigned && Cast->getOpcode() != Instruction::ZExt)
Type *Ty = Cast->getType();
uint64_t Width = SE->getTypeSizeInBits(Ty);
if (TD && !TD->isLegalInteger(Width))
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 {
/// NarrowIVDefUse - 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;
Instruction *NarrowUse;
Instruction *WideDef;
NarrowIVDefUse(): NarrowDef(0), NarrowUse(0), WideDef(0) {}
NarrowIVDefUse(Instruction *ND, Instruction *NU, Instruction *WD):
NarrowDef(ND), NarrowUse(NU), WideDef(WD) {}
/// WidenIV - 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;
bool IsSigned;
// Context
LoopInfo *LI;
Loop *L;
ScalarEvolution *SE;
DominatorTree *DT;
// Result
PHINode *WidePhi;
Instruction *WideInc;
const SCEV *WideIncExpr;
SmallVectorImpl<WeakVH> &DeadInsts;
SmallPtrSet<Instruction*,16> Widened;
SmallVector<NarrowIVDefUse, 8> NarrowIVUsers;
WidenIV(const WideIVInfo &WI, LoopInfo *LInfo,
ScalarEvolution *SEv, DominatorTree *DTree,
SmallVectorImpl<WeakVH> &DI) :
DeadInsts(DI) {
assert(L->getHeader() == OrigPhi->getParent() && "Phi must be an IV");
PHINode *CreateWideIV(SCEVExpander &Rewriter);
Value *getExtend(Value *NarrowOper, Type *WideType, bool IsSigned,
Instruction *Use);
Instruction *CloneIVUser(NarrowIVDefUse DU);
const SCEVAddRecExpr *GetWideRecurrence(Instruction *NarrowUse);
const SCEVAddRecExpr* GetExtendedOperandRecurrence(NarrowIVDefUse DU);
Instruction *WidenIVUse(NarrowIVDefUse DU, SCEVExpander &Rewriter);
void pushNarrowIVUsers(Instruction *NarrowDef, Instruction *WideDef);
} // anonymous namespace
/// isLoopInvariant - 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::getExtend(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);
/// CloneIVUser - 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) {
unsigned Opcode = DU.NarrowUse->getOpcode();
switch (Opcode) {
return 0;
case Instruction::Add:
case Instruction::Mul:
case Instruction::UDiv:
case Instruction::Sub:
case Instruction::And:
case Instruction::Or:
case Instruction::Xor:
case Instruction::Shl:
case Instruction::LShr:
case Instruction::AShr:
DEBUG(dbgs() << "Cloning IVUser: " << *DU.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.
Value *LHS = (DU.NarrowUse->getOperand(0) == DU.NarrowDef) ? DU.WideDef :
getExtend(DU.NarrowUse->getOperand(0), WideType, IsSigned, DU.NarrowUse);
Value *RHS = (DU.NarrowUse->getOperand(1) == DU.NarrowDef) ? DU.WideDef :
getExtend(DU.NarrowUse->getOperand(1), WideType, IsSigned, DU.NarrowUse);
BinaryOperator *NarrowBO = cast<BinaryOperator>(DU.NarrowUse);
BinaryOperator *WideBO = BinaryOperator::Create(NarrowBO->getOpcode(),
IRBuilder<> Builder(DU.NarrowUse);
if (const OverflowingBinaryOperator *OBO =
dyn_cast<OverflowingBinaryOperator>(NarrowBO)) {
if (OBO->hasNoUnsignedWrap()) WideBO->setHasNoUnsignedWrap();
if (OBO->hasNoSignedWrap()) WideBO->setHasNoSignedWrap();
return WideBO;
/// 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 it.
const SCEVAddRecExpr* WidenIV::GetExtendedOperandRecurrence(NarrowIVDefUse DU) {
// Handle the common case of add<nsw/nuw>
if (DU.NarrowUse->getOpcode() != Instruction::Add)
return 0;
// One operand (NarrowDef) has already been extended to WideDef. Now determine
// if extending the other will lead to a recurrence.
unsigned ExtendOperIdx = DU.NarrowUse->getOperand(0) == DU.NarrowDef ? 1 : 0;
assert(DU.NarrowUse->getOperand(1-ExtendOperIdx) == DU.NarrowDef && "bad DU");
const SCEV *ExtendOperExpr = 0;
const OverflowingBinaryOperator *OBO =
if (IsSigned && OBO->hasNoSignedWrap())
ExtendOperExpr = SE->getSignExtendExpr(
SE->getSCEV(DU.NarrowUse->getOperand(ExtendOperIdx)), WideType);
else if(!IsSigned && OBO->hasNoUnsignedWrap())
ExtendOperExpr = SE->getZeroExtendExpr(
SE->getSCEV(DU.NarrowUse->getOperand(ExtendOperIdx)), WideType);
return 0;
// When creating this AddExpr, 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 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(
SE->getAddExpr(SE->getSCEV(DU.WideDef), ExtendOperExpr));
if (!AddRec || AddRec->getLoop() != L)
return 0;
return AddRec;
/// GetWideRecurrence - Is this instruction potentially interesting from
/// IVUsers' perspective 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 sign or zero extended
/// recurrence. Otherwise return NULL.
const SCEVAddRecExpr *WidenIV::GetWideRecurrence(Instruction *NarrowUse) {
if (!SE->isSCEVable(NarrowUse->getType()))
return 0;
const SCEV *NarrowExpr = SE->getSCEV(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 0;
const SCEV *WideExpr = IsSigned ?
SE->getSignExtendExpr(NarrowExpr, WideType) :
SE->getZeroExtendExpr(NarrowExpr, WideType);
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(WideExpr);
if (!AddRec || AddRec->getLoop() != L)
return 0;
return AddRec;
/// WidenIVUse - 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) {
// Stop traversing the def-use chain at inner-loop phis or post-loop phis.
if (isa<PHINode>(DU.NarrowUse) &&
LI->getLoopFor(DU.NarrowUse->getParent()) != L)
return 0;
// Our raison d'etre! Eliminate sign and zero extension.
if (IsSigned ? isa<SExtInst>(DU.NarrowUse) : isa<ZExtInst>(DU.NarrowUse)) {
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 0;
// Does this user itself evaluate to a recurrence after widening?
const SCEVAddRecExpr *WideAddRec = GetWideRecurrence(DU.NarrowUse);
if (!WideAddRec) {
WideAddRec = GetExtendedOperandRecurrence(DU);
if (!WideAddRec) {
// This user does not evaluate to a recurence 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.
IRBuilder<> Builder(getInsertPointForUses(DU.NarrowUse, DU.NarrowDef, DT));
Value *Trunc = Builder.CreateTrunc(DU.WideDef, DU.NarrowDef->getType());
DU.NarrowUse->replaceUsesOfWith(DU.NarrowDef, Trunc);
return 0;
// 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 = 0;
if (WideAddRec == WideIncExpr
&& Rewriter.hoistIVInc(WideInc, DU.NarrowUse))
WideUse = WideInc;
else {
WideUse = CloneIVUser(DU);
if (!WideUse)
return 0;
// 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 != SE->getSCEV(WideUse)) {
DEBUG(dbgs() << "Wide use expression mismatch: " << *WideUse
<< ": " << *SE->getSCEV(WideUse) << " != " << *WideAddRec << "\n");
return 0;
// Returning WideUse pushes it on the worklist.
return WideUse;
/// pushNarrowIVUsers - Add eligible users of NarrowDef to NarrowIVUsers.
void WidenIV::pushNarrowIVUsers(Instruction *NarrowDef, Instruction *WideDef) {
for (Value::use_iterator UI = NarrowDef->use_begin(),
UE = NarrowDef->use_end(); UI != UE; ++UI) {
Instruction *NarrowUse = cast<Instruction>(*UI);
// Handle data flow merges and bizarre phi cycles.
if (!Widened.insert(NarrowUse))
NarrowIVUsers.push_back(NarrowIVDefUse(NarrowDef, NarrowUse, WideDef));
/// CreateWideIV - 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 NULL;
// Widen the induction variable expression.
const SCEV *WideIVExpr = IsSigned ?
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 NULL;
// 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.
assert(SE->properlyDominates(AddRec->getStart(), L->getHeader()) &&
SE->properlyDominates(AddRec->getStepRecurrence(*SE), L->getHeader())
&& "Loop header phi recurrence inputs do not dominate the loop");
// 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()->begin();
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);
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())
return WidePhi;
// Simplification of IV users based on SCEV evaluation.
/// SimplifyAndExtend - 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 PollyIndVarSimplify::SimplifyAndExtend(Loop *L,
SCEVExpander &Rewriter,
LPPassManager &LPM) {
SmallVector<WideIVInfo, 8> WideIVs;
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.
WideIVVisitor WIV(CurrIV, SE, TD);
Changed |= simplifyUsersOfIV(CurrIV, SE, &LPM, DeadInsts, &WIV);
if (WIV.WI.WidestNativeType) {
} while(!LoopPhis.empty());
for (; !WideIVs.empty(); WideIVs.pop_back()) {
WidenIV Widener(WideIVs.back(), LI, SE, DT, DeadInsts);
if (PHINode *WidePhi = Widener.CreateWideIV(Rewriter)) {
Changed = true;
// LinearFunctionTestReplace and its kin. Rewrite the loop exit condition.
/// Check for expressions that ScalarEvolution generates to compute
/// BackedgeTakenInfo. If these expressions have not been reduced, then
/// expanding them may incur additional cost (albeit in the loop preheader).
static bool isHighCostExpansion(const SCEV *S, BranchInst *BI,
SmallPtrSet<const SCEV*, 8> &Processed,
ScalarEvolution *SE) {
if (!Processed.insert(S))
return false;
// If the backedge-taken count is a UDiv, it's very likely a UDiv that
// ScalarEvolution's HowFarToZero or HowManyLessThans produced to compute a
// precise expression, rather than a UDiv from the user's code. If we can't
// find a UDiv in the code with some simple searching, assume the former and
// forego rewriting the loop.
if (isa<SCEVUDivExpr>(S)) {
ICmpInst *OrigCond = dyn_cast<ICmpInst>(BI->getCondition());
if (!OrigCond) return true;
const SCEV *R = SE->getSCEV(OrigCond->getOperand(1));
R = SE->getMinusSCEV(R, SE->getConstant(R->getType(), 1));
if (R != S) {
const SCEV *L = SE->getSCEV(OrigCond->getOperand(0));
L = SE->getMinusSCEV(L, SE->getConstant(L->getType(), 1));
if (L != S)
return true;
if (EnableIVRewrite)
return false;
// Recurse past add expressions, which commonly occur in the
// BackedgeTakenCount. They may already exist in program code, and if not,
// they are not too expensive rematerialize.
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
for (SCEVAddExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
I != E; ++I) {
if (isHighCostExpansion(*I, BI, Processed, SE))
return true;
return false;
// HowManyLessThans uses a Max expression whenever the loop is not guarded by
// the exit condition.
if (isa<SCEVSMaxExpr>(S) || isa<SCEVUMaxExpr>(S))
return true;
// If we haven't recognized an expensive SCEV pattern, assume it's an
// expression produced by program code.
return false;
/// canExpandBackedgeTakenCount - 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) {
const SCEV *BackedgeTakenCount = SE->getBackedgeTakenCount(L);
if (isa<SCEVCouldNotCompute>(BackedgeTakenCount) ||
return false;
if (!L->getExitingBlock())
return false;
// Can't rewrite non-branch yet.
BranchInst *BI = dyn_cast<BranchInst>(L->getExitingBlock()->getTerminator());
if (!BI)
return false;
SmallPtrSet<const SCEV*, 8> Processed;
if (isHighCostExpansion(BackedgeTakenCount, BI, Processed, SE))
return false;
return true;
/// getBackedgeIVType - Get the widest type used by the loop test after peeking
/// through Truncs.
/// TODO: Unnecessary when ForceLFTR is removed.
static Type *getBackedgeIVType(Loop *L) {
if (!L->getExitingBlock())
return 0;
// Can't rewrite non-branch yet.
BranchInst *BI = dyn_cast<BranchInst>(L->getExitingBlock()->getTerminator());
if (!BI)
return 0;
ICmpInst *Cond = dyn_cast<ICmpInst>(BI->getCondition());
if (!Cond)
return 0;
Type *Ty = 0;
for(User::op_iterator OI = Cond->op_begin(), OE = Cond->op_end();
OI != OE; ++OI) {
assert((!Ty || Ty == (*OI)->getType()) && "bad icmp operand types");
TruncInst *Trunc = dyn_cast<TruncInst>(*OI);
if (!Trunc)
return Trunc->getSrcTy();
return Ty;
/// getLoopPhiForCounter - 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 0;
switch (IncI->getOpcode()) {
case Instruction::Add:
case Instruction::Sub:
case Instruction::GetElementPtr:
// An IV counter must preserve its type.
if (IncI->getNumOperands() == 2)
return 0;
PHINode *Phi = dyn_cast<PHINode>(IncI->getOperand(0));
if (Phi && Phi->getParent() == L->getHeader()) {
if (isLoopInvariant(IncI->getOperand(1), L, DT))
return Phi;
return 0;
if (IncI->getOpcode() == Instruction::GetElementPtr)
return 0;
// 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 0;
/// needsLFTR - LinearFunctionTestReplace policy. Return true unless we can show
/// that the current exit test is already sufficiently canonical.
static bool needsLFTR(Loop *L, DominatorTree *DT) {
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 false;
BranchInst *BI = dyn_cast<BranchInst>(L->getExitingBlock()->getTerminator());
assert(BI && "expected exit branch");
// Do LFTR to simplify the exit condition to an ICMP.
ICmpInst *Cond = dyn_cast<ICmpInst>(BI->getCondition());
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 the exit condition's IV is *not* a simple counter.
Value *IncV = Phi->getIncomingValueForBlock(L->getLoopLatch());
return Phi != getLoopPhiForCounter(IncV, L, DT);
/// AlmostDeadIV - 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 (Value::use_iterator UI = Phi->use_begin(), UE = Phi->use_end();
UI != UE; ++UI) {
if (*UI != Cond && *UI != IncV) return false;
for (Value::use_iterator UI = IncV->use_begin(), UE = IncV->use_end();
UI != UE; ++UI) {
if (*UI != Cond && *UI != Phi) return false;
return true;
/// FindLoopCounter - 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.
/// 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, const DataLayout *TD) {
uint64_t BCWidth = SE->getTypeSizeInBits(BECount->getType());
Value *Cond =
// Loop over all of the PHI nodes, looking for a simple counter.
PHINode *BestPhi = 0;
const SCEV *BestInit = 0;
BasicBlock *LatchBlock = L->getLoopLatch();
assert(LatchBlock && "needsLFTR should guarantee a loop latch");
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 || (TD && !TD->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)
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.
if (PhiWidth <= SE->getTypeSizeInBits(BestPhi->getType()))
BestPhi = Phi;
BestInit = Init;
return BestPhi;
/// genLoopLimit - 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()) {
Type *OfsTy = SE->getEffectiveSCEVType(IVInit->getType());
const SCEV *IVOffset = SE->getTruncateOrSignExtend(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.
&& "unit stride pointer IV must be i8*");
IRBuilder<> Builder(L->getLoopPreheader()->getTerminator());
return Builder.CreateGEP(GEPBase, GEPOffset, "lftr.limit");
else {
// In any other case, convert both IVInit and IVCount to integers before
// comparing. This may result in SCEV expension 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; (3) IVInit is an integer and IVCount is a
// pointer may occur when enable-iv-rewrite generates a canonical IV on top
// of case #2.
const SCEV *IVLimit = 0;
// 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);
/// LinearFunctionTestReplace - 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 *PollyIndVarSimplify::
LinearFunctionTestReplace(Loop *L,
const SCEV *BackedgeTakenCount,
PHINode *IndVar,
SCEVExpander &Rewriter) {
assert(canExpandBackedgeTakenCount(L, SE) && "precondition");
// LFTR can ignore IV overflow and truncate to the width of
// BECount. This avoids materializing the add(zext(add)) expression.
Type *CntTy = !EnableIVRewrite ?
BackedgeTakenCount->getType() : IndVar->getType();
const SCEV *IVCount = BackedgeTakenCount;
// 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.
Value *CmpIndVar;
if (L->getExitingBlock() == L->getLoopLatch()) {
// Add one to the "backedge-taken" count to get the trip count.
// If this addition may overflow, we have to be more pessimistic and
// cast the induction variable before doing the add.
const SCEV *N =
SE->getAddExpr(IVCount, SE->getConstant(IVCount->getType(), 1));
if (CntTy == IVCount->getType())
IVCount = N;
else {
const SCEV *Zero = SE->getConstant(IVCount->getType(), 0);
if ((isa<SCEVConstant>(N) && !N->isZero()) ||
SE->isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, N, Zero)) {
// No overflow. Cast the sum.
IVCount = SE->getTruncateOrZeroExtend(N, CntTy);
} else {
// Potential overflow. Cast before doing the add.
IVCount = SE->getTruncateOrZeroExtend(IVCount, CntTy);
IVCount = SE->getAddExpr(IVCount, SE->getConstant(CntTy, 1));
// 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());
} else {
// We must use the preincremented value...
IVCount = SE->getTruncateOrZeroExtend(IVCount, CntTy);
CmpIndVar = IndVar;
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);
if (SE->getTypeSizeInBits(CmpIndVar->getType())
> SE->getTypeSizeInBits(ExitCnt->getType())) {
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 PollyIndVarSimplify::SinkUnusedInvariants(Loop *L) {
BasicBlock *ExitBlock = L->getExitBlock();
if (!ExitBlock) return;
BasicBlock *Preheader = L->getLoopPreheader();
if (!Preheader) return;
Instruction *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 landingpad instructions.
if (isa<LandingPadInst>(I))
// 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 (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
UI != UE; ++UI) {
User *U = *UI;
BasicBlock *UseBB = cast<Instruction>(U)->getParent();
if (PHINode *P = dyn_cast<PHINode>(U)) {
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;
if (Done) break;
InsertPt = ToMove;
// IndVarSimplify driver. Manage several subpasses of IV simplification.
bool PollyIndVarSimplify::runOnLoop(Loop *L, LPPassManager &LPM) {
// 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.
if (!L->isLoopSimplifyForm())
return false;
if (EnableIVRewrite)
IU = &getAnalysis<IVUsers>();
LI = &getAnalysis<LoopInfo>();
SE = &getAnalysis<ScalarEvolution>();
DT = &getAnalysis<DominatorTree>();
TD = getAnalysisIfAvailable<DataLayout>();
Changed = 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, "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.
if (!EnableIVRewrite) {
SimplifyAndExtend(L, Rewriter, LPM);
// 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 (!isa<SCEVCouldNotCompute>(BackedgeTakenCount))
RewriteLoopExitValues(L, Rewriter);
// Eliminate redundant IV users.
// FIXME: Disabled as the function was removed from LLVM trunk. We may get
// along with this, as Polly does not need a lot of simplifications,
// but just a canonical induction variable. In the near future, we
// should remove the need of canonical induction variables all
// together.
//if (EnableIVRewrite)
// Changed |= simplifyIVUsers(IU, SE, &LPM, DeadInsts);
// Eliminate redundant IV cycles.
if (!EnableIVRewrite)
NumElimIV += Rewriter.replaceCongruentIVs(L, DT, DeadInsts);
// Compute the type of the largest recurrence expression, and decide whether
// a canonical induction variable should be inserted.
Type *LargestType = 0;
bool NeedCannIV = false;
bool ExpandBECount = canExpandBackedgeTakenCount(L, SE);
if (EnableIVRewrite && ExpandBECount) {
// If we have a known trip count and a single exit block, we'll be
// rewriting the loop exit test condition below, which requires a
// canonical induction variable.
NeedCannIV = true;
Type *Ty = BackedgeTakenCount->getType();
if (!EnableIVRewrite) {
// In this mode, SimplifyIVUsers may have already widened the IV used by
// the backedge test and inserted a Trunc on the compare's operand. Get
// the wider type to avoid creating a redundant narrow IV only used by the
// loop test.
LargestType = getBackedgeIVType(L);
if (!LargestType ||
SE->getTypeSizeInBits(Ty) >
LargestType = SE->getEffectiveSCEVType(Ty);
if (EnableIVRewrite) {
for (IVUsers::const_iterator I = IU->begin(), E = IU->end(); I != E; ++I) {
NeedCannIV = true;
Type *Ty =
if (!LargestType ||
SE->getTypeSizeInBits(Ty) >
LargestType = Ty;
// Now that we know the largest of the induction variable expressions
// in this loop, insert a canonical induction variable of the largest size.
PHINode *IndVar = 0;
if (NeedCannIV) {
// Check to see if the loop already has any canonical-looking induction
// variables. If any are present and wider than the planned canonical
// induction variable, temporarily remove them, so that the Rewriter
// doesn't attempt to reuse them.
SmallVector<PHINode *, 2> OldCannIVs;
while (PHINode *OldCannIV = L->getCanonicalInductionVariable()) {
if (SE->getTypeSizeInBits(OldCannIV->getType()) >
IndVar = Rewriter.getOrInsertCanonicalInductionVariable(L, LargestType);
Changed = true;
DEBUG(dbgs() << "INDVARS: New CanIV: " << *IndVar << '\n');
// Now that the official induction variable is established, reinsert
// any old canonical-looking variables after it so that the IR remains
// consistent. They will be deleted as part of the dead-PHI deletion at
// the end of the pass.
while (!OldCannIVs.empty()) {
PHINode *OldCannIV = OldCannIVs.pop_back_val();
else if (!EnableIVRewrite && ExpandBECount && needsLFTR(L, DT)) {
IndVar = FindLoopCounter(L, BackedgeTakenCount, SE, DT, TD);
// 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.
Value *NewICmp = 0;
if (ExpandBECount && 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())
NewICmp =
LinearFunctionTestReplace(L, BackedgeTakenCount, IndVar, Rewriter);
// Rewrite IV-derived expressions.
if (EnableIVRewrite)
RewriteIVExpressions(L, Rewriter);
// 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 =
// 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.
// For completeness, inform IVUsers of the IV use in the newly-created
// loop exit test instruction.
if (IU && NewICmp) {
ICmpInst *NewICmpInst = dyn_cast<ICmpInst>(NewICmp);
if (NewICmpInst)
// Clean up dead instructions.
Changed |= DeleteDeadPHIs(L->getHeader());
// Check a post-condition.
assert(L->isLCSSAForm(*DT) &&
"Indvars did not leave the loop in lcssa form!");
// Verify that LFTR, and any other change have not interfered with SCEV's
// ability to compute trip count.
#ifndef NDEBUG
if (!EnableIVRewrite && 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;