llvm-6502/lib/Transforms/InstCombine/InstCombineMulDivRem.cpp

623 lines
22 KiB
C++
Raw Normal View History

//===- InstCombineMulDivRem.cpp -------------------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file implements the visit functions for mul, fmul, sdiv, udiv, fdiv,
// srem, urem, frem.
//
//===----------------------------------------------------------------------===//
#include "InstCombine.h"
#include "llvm/IntrinsicInst.h"
#include "llvm/Analysis/InstructionSimplify.h"
#include "llvm/Support/PatternMatch.h"
using namespace llvm;
using namespace PatternMatch;
/// MultiplyOverflows - True if the multiply can not be expressed in an int
/// this size.
static bool MultiplyOverflows(ConstantInt *C1, ConstantInt *C2, bool sign) {
uint32_t W = C1->getBitWidth();
APInt LHSExt = C1->getValue(), RHSExt = C2->getValue();
if (sign) {
LHSExt = LHSExt.sext(W * 2);
RHSExt = RHSExt.sext(W * 2);
} else {
LHSExt = LHSExt.zext(W * 2);
RHSExt = RHSExt.zext(W * 2);
}
APInt MulExt = LHSExt * RHSExt;
if (!sign)
return MulExt.ugt(APInt::getLowBitsSet(W * 2, W));
APInt Min = APInt::getSignedMinValue(W).sext(W * 2);
APInt Max = APInt::getSignedMaxValue(W).sext(W * 2);
return MulExt.slt(Min) || MulExt.sgt(Max);
}
Instruction *InstCombiner::visitMul(BinaryOperator &I) {
bool Changed = SimplifyAssociativeOrCommutative(I);
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
if (Value *V = SimplifyMulInst(Op0, Op1, TD))
return ReplaceInstUsesWith(I, V);
if (Value *V = SimplifyUsingDistributiveLaws(I))
return ReplaceInstUsesWith(I, V);
if (match(Op1, m_AllOnes())) // X * -1 == 0 - X
return BinaryOperator::CreateNeg(Op0, I.getName());
if (ConstantInt *CI = dyn_cast<ConstantInt>(Op1)) {
// ((X << C1)*C2) == (X * (C2 << C1))
if (BinaryOperator *SI = dyn_cast<BinaryOperator>(Op0))
if (SI->getOpcode() == Instruction::Shl)
if (Constant *ShOp = dyn_cast<Constant>(SI->getOperand(1)))
return BinaryOperator::CreateMul(SI->getOperand(0),
ConstantExpr::getShl(CI, ShOp));
const APInt &Val = CI->getValue();
if (Val.isPowerOf2()) { // Replace X*(2^C) with X << C
Constant *NewCst = ConstantInt::get(Op0->getType(), Val.logBase2());
BinaryOperator *Shl = BinaryOperator::CreateShl(Op0, NewCst);
if (I.hasNoSignedWrap()) Shl->setHasNoSignedWrap();
if (I.hasNoUnsignedWrap()) Shl->setHasNoUnsignedWrap();
return Shl;
}
// Canonicalize (X+C1)*CI -> X*CI+C1*CI.
{ Value *X; ConstantInt *C1;
if (Op0->hasOneUse() &&
match(Op0, m_Add(m_Value(X), m_ConstantInt(C1)))) {
Value *Add = Builder->CreateMul(X, CI, "tmp");
return BinaryOperator::CreateAdd(Add, Builder->CreateMul(C1, CI));
}
}
}
// Simplify mul instructions with a constant RHS.
if (isa<Constant>(Op1)) {
// Try to fold constant mul into select arguments.
if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
if (Instruction *R = FoldOpIntoSelect(I, SI))
return R;
if (isa<PHINode>(Op0))
if (Instruction *NV = FoldOpIntoPhi(I))
return NV;
}
if (Value *Op0v = dyn_castNegVal(Op0)) // -X * -Y = X*Y
if (Value *Op1v = dyn_castNegVal(Op1))
return BinaryOperator::CreateMul(Op0v, Op1v);
// (X / Y) * Y = X - (X % Y)
// (X / Y) * -Y = (X % Y) - X
{
Value *Op1C = Op1;
BinaryOperator *BO = dyn_cast<BinaryOperator>(Op0);
if (!BO ||
(BO->getOpcode() != Instruction::UDiv &&
BO->getOpcode() != Instruction::SDiv)) {
Op1C = Op0;
BO = dyn_cast<BinaryOperator>(Op1);
}
Value *Neg = dyn_castNegVal(Op1C);
if (BO && BO->hasOneUse() &&
(BO->getOperand(1) == Op1C || BO->getOperand(1) == Neg) &&
(BO->getOpcode() == Instruction::UDiv ||
BO->getOpcode() == Instruction::SDiv)) {
Value *Op0BO = BO->getOperand(0), *Op1BO = BO->getOperand(1);
// If the division is exact, X % Y is zero, so we end up with X or -X.
if (PossiblyExactOperator *SDiv = dyn_cast<PossiblyExactOperator>(BO))
if (SDiv->isExact()) {
if (Op1BO == Op1C)
return ReplaceInstUsesWith(I, Op0BO);
return BinaryOperator::CreateNeg(Op0BO);
}
Value *Rem;
if (BO->getOpcode() == Instruction::UDiv)
Rem = Builder->CreateURem(Op0BO, Op1BO);
else
Rem = Builder->CreateSRem(Op0BO, Op1BO);
Rem->takeName(BO);
if (Op1BO == Op1C)
return BinaryOperator::CreateSub(Op0BO, Rem);
return BinaryOperator::CreateSub(Rem, Op0BO);
}
}
/// i1 mul -> i1 and.
if (I.getType()->isIntegerTy(1))
return BinaryOperator::CreateAnd(Op0, Op1);
// X*(1 << Y) --> X << Y
// (1 << Y)*X --> X << Y
{
Value *Y;
if (match(Op0, m_Shl(m_One(), m_Value(Y))))
return BinaryOperator::CreateShl(Op1, Y);
if (match(Op1, m_Shl(m_One(), m_Value(Y))))
return BinaryOperator::CreateShl(Op0, Y);
}
// If one of the operands of the multiply is a cast from a boolean value, then
// we know the bool is either zero or one, so this is a 'masking' multiply.
// X * Y (where Y is 0 or 1) -> X & (0-Y)
if (!I.getType()->isVectorTy()) {
// -2 is "-1 << 1" so it is all bits set except the low one.
APInt Negative2(I.getType()->getPrimitiveSizeInBits(), (uint64_t)-2, true);
Value *BoolCast = 0, *OtherOp = 0;
if (MaskedValueIsZero(Op0, Negative2))
BoolCast = Op0, OtherOp = Op1;
else if (MaskedValueIsZero(Op1, Negative2))
BoolCast = Op1, OtherOp = Op0;
if (BoolCast) {
Value *V = Builder->CreateSub(Constant::getNullValue(I.getType()),
BoolCast, "tmp");
return BinaryOperator::CreateAnd(V, OtherOp);
}
}
return Changed ? &I : 0;
}
Instruction *InstCombiner::visitFMul(BinaryOperator &I) {
bool Changed = SimplifyAssociativeOrCommutative(I);
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
// Simplify mul instructions with a constant RHS...
if (Constant *Op1C = dyn_cast<Constant>(Op1)) {
if (ConstantFP *Op1F = dyn_cast<ConstantFP>(Op1C)) {
// "In IEEE floating point, x*1 is not equivalent to x for nans. However,
// ANSI says we can drop signals, so we can do this anyway." (from GCC)
if (Op1F->isExactlyValue(1.0))
return ReplaceInstUsesWith(I, Op0); // Eliminate 'fmul double %X, 1.0'
} else if (Op1C->getType()->isVectorTy()) {
if (ConstantVector *Op1V = dyn_cast<ConstantVector>(Op1C)) {
// As above, vector X*splat(1.0) -> X in all defined cases.
if (Constant *Splat = Op1V->getSplatValue()) {
if (ConstantFP *F = dyn_cast<ConstantFP>(Splat))
if (F->isExactlyValue(1.0))
return ReplaceInstUsesWith(I, Op0);
}
}
}
// Try to fold constant mul into select arguments.
if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
if (Instruction *R = FoldOpIntoSelect(I, SI))
return R;
if (isa<PHINode>(Op0))
if (Instruction *NV = FoldOpIntoPhi(I))
return NV;
}
if (Value *Op0v = dyn_castFNegVal(Op0)) // -X * -Y = X*Y
if (Value *Op1v = dyn_castFNegVal(Op1))
return BinaryOperator::CreateFMul(Op0v, Op1v);
return Changed ? &I : 0;
}
/// SimplifyDivRemOfSelect - Try to fold a divide or remainder of a select
/// instruction.
bool InstCombiner::SimplifyDivRemOfSelect(BinaryOperator &I) {
SelectInst *SI = cast<SelectInst>(I.getOperand(1));
// div/rem X, (Cond ? 0 : Y) -> div/rem X, Y
int NonNullOperand = -1;
if (Constant *ST = dyn_cast<Constant>(SI->getOperand(1)))
if (ST->isNullValue())
NonNullOperand = 2;
// div/rem X, (Cond ? Y : 0) -> div/rem X, Y
if (Constant *ST = dyn_cast<Constant>(SI->getOperand(2)))
if (ST->isNullValue())
NonNullOperand = 1;
if (NonNullOperand == -1)
return false;
Value *SelectCond = SI->getOperand(0);
// Change the div/rem to use 'Y' instead of the select.
I.setOperand(1, SI->getOperand(NonNullOperand));
// Okay, we know we replace the operand of the div/rem with 'Y' with no
// problem. However, the select, or the condition of the select may have
// multiple uses. Based on our knowledge that the operand must be non-zero,
// propagate the known value for the select into other uses of it, and
// propagate a known value of the condition into its other users.
// If the select and condition only have a single use, don't bother with this,
// early exit.
if (SI->use_empty() && SelectCond->hasOneUse())
return true;
// Scan the current block backward, looking for other uses of SI.
BasicBlock::iterator BBI = &I, BBFront = I.getParent()->begin();
while (BBI != BBFront) {
--BBI;
// If we found a call to a function, we can't assume it will return, so
// information from below it cannot be propagated above it.
if (isa<CallInst>(BBI) && !isa<IntrinsicInst>(BBI))
break;
// Replace uses of the select or its condition with the known values.
for (Instruction::op_iterator I = BBI->op_begin(), E = BBI->op_end();
I != E; ++I) {
if (*I == SI) {
*I = SI->getOperand(NonNullOperand);
Worklist.Add(BBI);
} else if (*I == SelectCond) {
*I = NonNullOperand == 1 ? ConstantInt::getTrue(BBI->getContext()) :
ConstantInt::getFalse(BBI->getContext());
Worklist.Add(BBI);
}
}
// If we past the instruction, quit looking for it.
if (&*BBI == SI)
SI = 0;
if (&*BBI == SelectCond)
SelectCond = 0;
// If we ran out of things to eliminate, break out of the loop.
if (SelectCond == 0 && SI == 0)
break;
}
return true;
}
/// This function implements the transforms common to both integer division
/// instructions (udiv and sdiv). It is called by the visitors to those integer
/// division instructions.
/// @brief Common integer divide transforms
Instruction *InstCombiner::commonIDivTransforms(BinaryOperator &I) {
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
// Handle cases involving: [su]div X, (select Cond, Y, Z)
// This does not apply for fdiv.
if (isa<SelectInst>(Op1) && SimplifyDivRemOfSelect(I))
return &I;
if (ConstantInt *RHS = dyn_cast<ConstantInt>(Op1)) {
// (X / C1) / C2 -> X / (C1*C2)
if (Instruction *LHS = dyn_cast<Instruction>(Op0))
if (Instruction::BinaryOps(LHS->getOpcode()) == I.getOpcode())
if (ConstantInt *LHSRHS = dyn_cast<ConstantInt>(LHS->getOperand(1))) {
if (MultiplyOverflows(RHS, LHSRHS,
I.getOpcode()==Instruction::SDiv))
return ReplaceInstUsesWith(I, Constant::getNullValue(I.getType()));
return BinaryOperator::Create(I.getOpcode(), LHS->getOperand(0),
ConstantExpr::getMul(RHS, LHSRHS));
}
if (!RHS->isZero()) { // avoid X udiv 0
if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
if (Instruction *R = FoldOpIntoSelect(I, SI))
return R;
if (isa<PHINode>(Op0))
if (Instruction *NV = FoldOpIntoPhi(I))
return NV;
}
}
// (X - (X rem Y)) / Y -> X / Y; usually originates as ((X / Y) * Y) / Y
Value *X = 0, *Z = 0;
if (match(Op0, m_Sub(m_Value(X), m_Value(Z)))) { // (X - Z) / Y; Y = Op1
bool isSigned = I.getOpcode() == Instruction::SDiv;
if ((isSigned && match(Z, m_SRem(m_Specific(X), m_Specific(Op1)))) ||
(!isSigned && match(Z, m_URem(m_Specific(X), m_Specific(Op1)))))
return BinaryOperator::Create(I.getOpcode(), X, Op1);
}
return 0;
}
Instruction *InstCombiner::visitUDiv(BinaryOperator &I) {
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
if (Value *V = SimplifyUDivInst(Op0, Op1, TD))
return ReplaceInstUsesWith(I, V);
// Handle the integer div common cases
if (Instruction *Common = commonIDivTransforms(I))
return Common;
if (ConstantInt *C = dyn_cast<ConstantInt>(Op1)) {
// X udiv 2^C -> X >> C
// Check to see if this is an unsigned division with an exact power of 2,
// if so, convert to a right shift.
if (C->getValue().isPowerOf2()) { // 0 not included in isPowerOf2
BinaryOperator *LShr =
BinaryOperator::CreateLShr(Op0,
ConstantInt::get(Op0->getType(), C->getValue().logBase2()));
if (I.isExact()) LShr->setIsExact();
return LShr;
}
// X udiv C, where C >= signbit
if (C->getValue().isNegative()) {
Value *IC = Builder->CreateICmpULT(Op0, C);
return SelectInst::Create(IC, Constant::getNullValue(I.getType()),
ConstantInt::get(I.getType(), 1));
}
}
// X udiv (C1 << N), where C1 is "1<<C2" --> X >> (N+C2)
{ const APInt *CI; Value *N;
if (match(Op1, m_Shl(m_Power2(CI), m_Value(N)))) {
if (*CI != 1)
N = Builder->CreateAdd(N, ConstantInt::get(I.getType(), CI->logBase2()),
"tmp");
if (I.isExact())
return BinaryOperator::CreateExactLShr(Op0, N);
return BinaryOperator::CreateLShr(Op0, N);
}
}
// udiv X, (Select Cond, C1, C2) --> Select Cond, (shr X, C1), (shr X, C2)
// where C1&C2 are powers of two.
{ Value *Cond; const APInt *C1, *C2;
if (match(Op1, m_Select(m_Value(Cond), m_Power2(C1), m_Power2(C2)))) {
// Construct the "on true" case of the select
Value *TSI = Builder->CreateLShr(Op0, C1->logBase2(), Op1->getName()+".t",
I.isExact());
// Construct the "on false" case of the select
Value *FSI = Builder->CreateLShr(Op0, C2->logBase2(), Op1->getName()+".f",
I.isExact());
// construct the select instruction and return it.
return SelectInst::Create(Cond, TSI, FSI);
}
}
return 0;
}
Instruction *InstCombiner::visitSDiv(BinaryOperator &I) {
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
if (Value *V = SimplifySDivInst(Op0, Op1, TD))
return ReplaceInstUsesWith(I, V);
// Handle the integer div common cases
if (Instruction *Common = commonIDivTransforms(I))
return Common;
if (ConstantInt *RHS = dyn_cast<ConstantInt>(Op1)) {
// sdiv X, -1 == -X
if (RHS->isAllOnesValue())
return BinaryOperator::CreateNeg(Op0);
// sdiv X, C --> ashr exact X, log2(C)
if (I.isExact() && RHS->getValue().isNonNegative() &&
RHS->getValue().isPowerOf2()) {
Value *ShAmt = llvm::ConstantInt::get(RHS->getType(),
RHS->getValue().exactLogBase2());
return BinaryOperator::CreateExactAShr(Op0, ShAmt, I.getName());
}
// -X/C --> X/-C provided the negation doesn't overflow.
if (SubOperator *Sub = dyn_cast<SubOperator>(Op0))
if (match(Sub->getOperand(0), m_Zero()) && Sub->hasNoSignedWrap())
return BinaryOperator::CreateSDiv(Sub->getOperand(1),
ConstantExpr::getNeg(RHS));
}
// If the sign bits of both operands are zero (i.e. we can prove they are
// unsigned inputs), turn this into a udiv.
if (I.getType()->isIntegerTy()) {
APInt Mask(APInt::getSignBit(I.getType()->getPrimitiveSizeInBits()));
if (MaskedValueIsZero(Op0, Mask)) {
if (MaskedValueIsZero(Op1, Mask)) {
// X sdiv Y -> X udiv Y, iff X and Y don't have sign bit set
return BinaryOperator::CreateUDiv(Op0, Op1, I.getName());
}
if (match(Op1, m_Shl(m_Power2(), m_Value()))) {
// X sdiv (1 << Y) -> X udiv (1 << Y) ( -> X u>> Y)
// Safe because the only negative value (1 << Y) can take on is
// INT_MIN, and X sdiv INT_MIN == X udiv INT_MIN == 0 if X doesn't have
// the sign bit set.
return BinaryOperator::CreateUDiv(Op0, Op1, I.getName());
}
}
}
return 0;
}
Instruction *InstCombiner::visitFDiv(BinaryOperator &I) {
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
if (Value *V = SimplifyFDivInst(Op0, Op1, TD))
return ReplaceInstUsesWith(I, V);
return 0;
}
/// This function implements the transforms on rem instructions that work
/// regardless of the kind of rem instruction it is (urem, srem, or frem). It
/// is used by the visitors to those instructions.
/// @brief Transforms common to all three rem instructions
Instruction *InstCombiner::commonRemTransforms(BinaryOperator &I) {
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
if (isa<UndefValue>(Op0)) { // undef % X -> 0
if (I.getType()->isFPOrFPVectorTy())
return ReplaceInstUsesWith(I, Op0); // X % undef -> undef (could be SNaN)
return ReplaceInstUsesWith(I, Constant::getNullValue(I.getType()));
}
if (isa<UndefValue>(Op1))
return ReplaceInstUsesWith(I, Op1); // X % undef -> undef
// Handle cases involving: rem X, (select Cond, Y, Z)
if (isa<SelectInst>(Op1) && SimplifyDivRemOfSelect(I))
return &I;
return 0;
}
/// This function implements the transforms common to both integer remainder
/// instructions (urem and srem). It is called by the visitors to those integer
/// remainder instructions.
/// @brief Common integer remainder transforms
Instruction *InstCombiner::commonIRemTransforms(BinaryOperator &I) {
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
if (Instruction *common = commonRemTransforms(I))
return common;
// X % X == 0
if (Op0 == Op1)
return ReplaceInstUsesWith(I, Constant::getNullValue(I.getType()));
// 0 % X == 0 for integer, we don't need to preserve faults!
if (Constant *LHS = dyn_cast<Constant>(Op0))
if (LHS->isNullValue())
return ReplaceInstUsesWith(I, Constant::getNullValue(I.getType()));
if (ConstantInt *RHS = dyn_cast<ConstantInt>(Op1)) {
// X % 0 == undef, we don't need to preserve faults!
if (RHS->equalsInt(0))
return ReplaceInstUsesWith(I, UndefValue::get(I.getType()));
if (RHS->equalsInt(1)) // X % 1 == 0
return ReplaceInstUsesWith(I, Constant::getNullValue(I.getType()));
if (Instruction *Op0I = dyn_cast<Instruction>(Op0)) {
if (SelectInst *SI = dyn_cast<SelectInst>(Op0I)) {
if (Instruction *R = FoldOpIntoSelect(I, SI))
return R;
} else if (isa<PHINode>(Op0I)) {
if (Instruction *NV = FoldOpIntoPhi(I))
return NV;
}
// See if we can fold away this rem instruction.
if (SimplifyDemandedInstructionBits(I))
return &I;
}
}
return 0;
}
Instruction *InstCombiner::visitURem(BinaryOperator &I) {
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
if (Instruction *common = commonIRemTransforms(I))
return common;
// X urem C^2 -> X and C-1
{ const APInt *C;
if (match(Op1, m_Power2(C)))
return BinaryOperator::CreateAnd(Op0,
ConstantInt::get(I.getType(), *C-1));
}
// Turn A % (C << N), where C is 2^k, into A & ((C << N)-1)
if (match(Op1, m_Shl(m_Power2(), m_Value()))) {
Constant *N1 = Constant::getAllOnesValue(I.getType());
Value *Add = Builder->CreateAdd(Op1, N1, "tmp");
return BinaryOperator::CreateAnd(Op0, Add);
}
// urem X, (select Cond, 2^C1, 2^C2) -->
// select Cond, (and X, C1-1), (and X, C2-1)
// when C1&C2 are powers of two.
{ Value *Cond; const APInt *C1, *C2;
if (match(Op1, m_Select(m_Value(Cond), m_Power2(C1), m_Power2(C2)))) {
Value *TrueAnd = Builder->CreateAnd(Op0, *C1-1, Op1->getName()+".t");
Value *FalseAnd = Builder->CreateAnd(Op0, *C2-1, Op1->getName()+".f");
return SelectInst::Create(Cond, TrueAnd, FalseAnd);
}
}
return 0;
}
Instruction *InstCombiner::visitSRem(BinaryOperator &I) {
Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
// Handle the integer rem common cases
if (Instruction *Common = commonIRemTransforms(I))
return Common;
if (Value *RHSNeg = dyn_castNegVal(Op1))
if (!isa<Constant>(RHSNeg) ||
(isa<ConstantInt>(RHSNeg) &&
cast<ConstantInt>(RHSNeg)->getValue().isStrictlyPositive())) {
// X % -Y -> X % Y
Worklist.AddValue(I.getOperand(1));
I.setOperand(1, RHSNeg);
return &I;
}
// If the sign bits of both operands are zero (i.e. we can prove they are
// unsigned inputs), turn this into a urem.
if (I.getType()->isIntegerTy()) {
APInt Mask(APInt::getSignBit(I.getType()->getPrimitiveSizeInBits()));
if (MaskedValueIsZero(Op1, Mask) && MaskedValueIsZero(Op0, Mask)) {
// X srem Y -> X urem Y, iff X and Y don't have sign bit set
return BinaryOperator::CreateURem(Op0, Op1, I.getName());
}
}
// If it's a constant vector, flip any negative values positive.
if (ConstantVector *RHSV = dyn_cast<ConstantVector>(Op1)) {
unsigned VWidth = RHSV->getNumOperands();
bool hasNegative = false;
for (unsigned i = 0; !hasNegative && i != VWidth; ++i)
if (ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV->getOperand(i)))
if (RHS->getValue().isNegative())
hasNegative = true;
if (hasNegative) {
std::vector<Constant *> Elts(VWidth);
for (unsigned i = 0; i != VWidth; ++i) {
if (ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV->getOperand(i))) {
if (RHS->getValue().isNegative())
Elts[i] = cast<ConstantInt>(ConstantExpr::getNeg(RHS));
else
Elts[i] = RHS;
}
}
Constant *NewRHSV = ConstantVector::get(Elts);
if (NewRHSV != RHSV) {
Worklist.AddValue(I.getOperand(1));
I.setOperand(1, NewRHSV);
return &I;
}
}
}
return 0;
}
Instruction *InstCombiner::visitFRem(BinaryOperator &I) {
return commonRemTransforms(I);
}