void ConnectedVNInfoEqClasses::Distribute(LiveInterval *LIV[], MachineRegisterInfo &MRI) { assert(LIV[0] && "LIV[0] must be set"); LiveInterval &LI = *LIV[0]; // Rewrite instructions. for (MachineRegisterInfo::reg_iterator RI = MRI.reg_begin(LI.reg), RE = MRI.reg_end(); RI != RE;) { MachineOperand &MO = RI.getOperand(); MachineInstr *MI = MO.getParent(); ++RI; // DBG_VALUE instructions don't have slot indexes, so get the index of the // instruction before them. // Normally, DBG_VALUE instructions are removed before this function is // called, but it is not a requirement. SlotIndex Idx; if (MI->isDebugValue()) Idx = LIS.getSlotIndexes()->getIndexBefore(MI); else Idx = LIS.getInstructionIndex(MI); LiveQueryResult LRQ = LI.Query(Idx); const VNInfo *VNI = MO.readsReg() ? LRQ.valueIn() : LRQ.valueDefined(); // In the case of an <undef> use that isn't tied to any def, VNI will be // NULL. If the use is tied to a def, VNI will be the defined value. if (!VNI) continue; MO.setReg(LIV[getEqClass(VNI)]->reg); } // Move runs to new intervals. LiveInterval::iterator J = LI.begin(), E = LI.end(); while (J != E && EqClass[J->valno->id] == 0) ++J; for (LiveInterval::iterator I = J; I != E; ++I) { if (unsigned eq = EqClass[I->valno->id]) { assert((LIV[eq]->empty() || LIV[eq]->expiredAt(I->start)) && "New intervals should be empty"); LIV[eq]->segments.push_back(*I); } else *J++ = *I; } LI.segments.erase(J, E); // Transfer VNInfos to their new owners and renumber them. unsigned j = 0, e = LI.getNumValNums(); while (j != e && EqClass[j] == 0) ++j; for (unsigned i = j; i != e; ++i) { VNInfo *VNI = LI.getValNumInfo(i); if (unsigned eq = EqClass[i]) { VNI->id = LIV[eq]->getNumValNums(); LIV[eq]->valnos.push_back(VNI); } else { VNI->id = j; LI.valnos[j++] = VNI; } } LI.valnos.resize(j); }
/// rewrite - after all the new live ranges have been created, rewrite /// instructions using curli to use the new intervals. void SplitEditor::rewrite() { assert(!openli_ && "Previous LI not closed before rewrite"); const LiveInterval *curli = sa_.getCurLI(); for (MachineRegisterInfo::reg_iterator RI = mri_.reg_begin(curli->reg), RE = mri_.reg_end(); RI != RE;) { MachineOperand &MO = RI.getOperand(); MachineInstr *MI = MO.getParent(); ++RI; if (MI->isDebugValue()) { DEBUG(dbgs() << "Zapping " << *MI); // FIXME: We can do much better with debug values. MO.setReg(0); continue; } SlotIndex Idx = lis_.getInstructionIndex(MI); Idx = MO.isUse() ? Idx.getUseIndex() : Idx.getDefIndex(); LiveInterval *LI = dupli_; for (unsigned i = firstInterval, e = intervals_.size(); i != e; ++i) { LiveInterval *testli = intervals_[i]; if (testli->liveAt(Idx)) { LI = testli; break; } } if (LI) { MO.setReg(LI->reg); sa_.removeUse(MI); DEBUG(dbgs() << " rewrite " << Idx << '\t' << *MI); } } // dupli_ goes in last, after rewriting. if (dupli_) { if (dupli_->empty()) { DEBUG(dbgs() << " dupli became empty?\n"); lis_.removeInterval(dupli_->reg); dupli_ = 0; } else { dupli_->RenumberValues(lis_); intervals_.push_back(dupli_); } } // Calculate spill weight and allocation hints for new intervals. VirtRegAuxInfo vrai(vrm_.getMachineFunction(), lis_, sa_.loops_); for (unsigned i = firstInterval, e = intervals_.size(); i != e; ++i) { LiveInterval &li = *intervals_[i]; vrai.CalculateRegClass(li.reg); vrai.CalculateWeightAndHint(li); DEBUG(dbgs() << " new interval " << mri_.getRegClass(li.reg)->getName() << ":" << li << '\n'); } }
void ConnectedVNInfoEqClasses::Distribute(LiveInterval *LIV[], MachineRegisterInfo &MRI) { assert(LIV[0] && "LIV[0] must be set"); LiveInterval &LI = *LIV[0]; // Rewrite instructions. for (MachineRegisterInfo::reg_iterator RI = MRI.reg_begin(LI.reg), RE = MRI.reg_end(); RI != RE;) { MachineOperand &MO = RI.getOperand(); MachineInstr *MI = MO.getParent(); ++RI; if (MO.isUse() && MO.isUndef()) continue; // DBG_VALUE instructions should have been eliminated earlier. SlotIndex Idx = LIS.getInstructionIndex(MI); Idx = Idx.getRegSlot(MO.isUse()); const VNInfo *VNI = LI.getVNInfoAt(Idx); assert(VNI && "Interval not live at use."); MO.setReg(LIV[getEqClass(VNI)]->reg); } // Move runs to new intervals. LiveInterval::iterator J = LI.begin(), E = LI.end(); while (J != E && EqClass[J->valno->id] == 0) ++J; for (LiveInterval::iterator I = J; I != E; ++I) { if (unsigned eq = EqClass[I->valno->id]) { assert((LIV[eq]->empty() || LIV[eq]->expiredAt(I->start)) && "New intervals should be empty"); LIV[eq]->ranges.push_back(*I); } else *J++ = *I; } LI.ranges.erase(J, E); // Transfer VNInfos to their new owners and renumber them. unsigned j = 0, e = LI.getNumValNums(); while (j != e && EqClass[j] == 0) ++j; for (unsigned i = j; i != e; ++i) { VNInfo *VNI = LI.getValNumInfo(i); if (unsigned eq = EqClass[i]) { VNI->id = LIV[eq]->getNumValNums(); LIV[eq]->valnos.push_back(VNI); } else { VNI->id = j; LI.valnos[j++] = VNI; } } LI.valnos.resize(j); }
void ConnectedVNInfoEqClasses::Distribute(LiveInterval *LIV[], MachineRegisterInfo &MRI) { assert(LIV[0] && "LIV[0] must be set"); LiveInterval &LI = *LIV[0]; // Rewrite instructions. for (MachineRegisterInfo::reg_iterator RI = MRI.reg_begin(LI.reg), RE = MRI.reg_end(); RI != RE;) { MachineOperand &MO = RI.getOperand(); MachineInstr *MI = MO.getParent(); ++RI; // DBG_VALUE instructions should have been eliminated earlier. LiveRangeQuery LRQ(LI, LIS.getInstructionIndex(MI)); const VNInfo *VNI = MO.readsReg() ? LRQ.valueIn() : LRQ.valueDefined(); // In the case of an <undef> use that isn't tied to any def, VNI will be // NULL. If the use is tied to a def, VNI will be the defined value. if (!VNI) continue; MO.setReg(LIV[getEqClass(VNI)]->reg); } // Move runs to new intervals. LiveInterval::iterator J = LI.begin(), E = LI.end(); while (J != E && EqClass[J->valno->id] == 0) ++J; for (LiveInterval::iterator I = J; I != E; ++I) { if (unsigned eq = EqClass[I->valno->id]) { assert((LIV[eq]->empty() || LIV[eq]->expiredAt(I->start)) && "New intervals should be empty"); LIV[eq]->ranges.push_back(*I); } else *J++ = *I; } LI.ranges.erase(J, E); // Transfer VNInfos to their new owners and renumber them. unsigned j = 0, e = LI.getNumValNums(); while (j != e && EqClass[j] == 0) ++j; for (unsigned i = j; i != e; ++i) { VNInfo *VNI = LI.getValNumInfo(i); if (unsigned eq = EqClass[i]) { VNI->id = LIV[eq]->getNumValNums(); LIV[eq]->valnos.push_back(VNI); } else { VNI->id = j; LI.valnos[j++] = VNI; } } LI.valnos.resize(j); }
/// rewriteAssigned - Rewrite all uses of Edit->getReg(). void SplitEditor::rewriteAssigned(bool ExtendRanges) { for (MachineRegisterInfo::reg_iterator RI = MRI.reg_begin(Edit->getReg()), RE = MRI.reg_end(); RI != RE;) { MachineOperand &MO = RI.getOperand(); MachineInstr *MI = MO.getParent(); ++RI; // LiveDebugVariables should have handled all DBG_VALUE instructions. if (MI->isDebugValue()) { DEBUG(dbgs() << "Zapping " << *MI); MO.setReg(0); continue; } // <undef> operands don't really read the register, so it doesn't matter // which register we choose. When the use operand is tied to a def, we must // use the same register as the def, so just do that always. SlotIndex Idx = LIS.getInstructionIndex(MI); if (MO.isDef() || MO.isUndef()) Idx = MO.isEarlyClobber() ? Idx.getUseIndex() : Idx.getDefIndex(); // Rewrite to the mapped register at Idx. unsigned RegIdx = RegAssign.lookup(Idx); LiveInterval *LI = Edit->get(RegIdx); MO.setReg(LI->reg); DEBUG(dbgs() << " rewr BB#" << MI->getParent()->getNumber() << '\t' << Idx << ':' << RegIdx << '\t' << *MI); // Extend liveness to Idx if the instruction reads reg. if (!ExtendRanges || MO.isUndef()) continue; // Skip instructions that don't read Reg. if (MO.isDef()) { if (!MO.getSubReg() && !MO.isEarlyClobber()) continue; // We may wan't to extend a live range for a partial redef, or for a use // tied to an early clobber. Idx = Idx.getPrevSlot(); if (!Edit->getParent().liveAt(Idx)) continue; } else Idx = Idx.getUseIndex(); getLRCalc(RegIdx).extend(LI, Idx.getNextSlot(), LIS.getSlotIndexes(), &MDT, &LIS.getVNInfoAllocator()); } }
/// NoUseAfterLastDef - Return true if there are no intervening uses between the /// last instruction in the MBB that defines the specified register and the /// two-address instruction which is being processed. It also returns the last /// def location by reference bool TwoAddressInstructionPass::NoUseAfterLastDef(unsigned Reg, MachineBasicBlock *MBB, unsigned Dist, unsigned &LastDef) { LastDef = 0; unsigned LastUse = Dist; for (MachineRegisterInfo::reg_iterator I = MRI->reg_begin(Reg), E = MRI->reg_end(); I != E; ++I) { MachineOperand &MO = I.getOperand(); MachineInstr *MI = MO.getParent(); if (MI->getParent() != MBB) continue; DenseMap<MachineInstr*, unsigned>::iterator DI = DistanceMap.find(MI); if (DI == DistanceMap.end()) continue; if (MO.isUse() && DI->second < LastUse) LastUse = DI->second; if (MO.isDef() && DI->second > LastDef) LastDef = DI->second; } return !(LastUse > LastDef && LastUse < Dist); }
MachineInstr *TwoAddressInstructionPass::FindLastUseInMBB(unsigned Reg, MachineBasicBlock *MBB, unsigned Dist) { unsigned LastUseDist = 0; MachineInstr *LastUse = 0; for (MachineRegisterInfo::reg_iterator I = MRI->reg_begin(Reg), E = MRI->reg_end(); I != E; ++I) { MachineOperand &MO = I.getOperand(); MachineInstr *MI = MO.getParent(); if (MI->getParent() != MBB) continue; DenseMap<MachineInstr*, unsigned>::iterator DI = DistanceMap.find(MI); if (DI == DistanceMap.end()) continue; if (DI->second >= Dist) continue; if (MO.isUse() && DI->second > LastUseDist) { LastUse = DI->first; LastUseDist = DI->second; } } return LastUse; }
/// ComputeLocalLiveness - Computes liveness of registers within a basic /// block, setting the killed/dead flags as appropriate. void RALocal::ComputeLocalLiveness(MachineBasicBlock& MBB) { MachineRegisterInfo &MRI = MBB.getParent()->getRegInfo(); // Keep track of the most recently seen previous use or def of each reg, // so that we can update them with dead/kill markers. DenseMap<unsigned, std::pair<MachineInstr*, unsigned> > LastUseDef; for (MachineBasicBlock::iterator I = MBB.begin(), E = MBB.end(); I != E; ++I) { if (I->isDebugValue()) continue; for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { MachineOperand &MO = I->getOperand(i); // Uses don't trigger any flags, but we need to save // them for later. Also, we have to process these // _before_ processing the defs, since an instr // uses regs before it defs them. if (!MO.isReg() || !MO.getReg() || !MO.isUse()) continue; LastUseDef[MO.getReg()] = std::make_pair(I, i); if (TargetRegisterInfo::isVirtualRegister(MO.getReg())) continue; const unsigned *Aliases = TRI->getAliasSet(MO.getReg()); if (Aliases == 0) continue; while (*Aliases) { DenseMap<unsigned, std::pair<MachineInstr*, unsigned> >::iterator alias = LastUseDef.find(*Aliases); if (alias != LastUseDef.end() && alias->second.first != I) LastUseDef[*Aliases] = std::make_pair(I, i); ++Aliases; } } for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { MachineOperand &MO = I->getOperand(i); // Defs others than 2-addr redefs _do_ trigger flag changes: // - A def followed by a def is dead // - A use followed by a def is a kill if (!MO.isReg() || !MO.getReg() || !MO.isDef()) continue; DenseMap<unsigned, std::pair<MachineInstr*, unsigned> >::iterator last = LastUseDef.find(MO.getReg()); if (last != LastUseDef.end()) { // Check if this is a two address instruction. If so, then // the def does not kill the use. if (last->second.first == I && I->isRegTiedToUseOperand(i)) continue; MachineOperand &lastUD = last->second.first->getOperand(last->second.second); if (lastUD.isDef()) lastUD.setIsDead(true); else lastUD.setIsKill(true); } LastUseDef[MO.getReg()] = std::make_pair(I, i); } } // Live-out (of the function) registers contain return values of the function, // so we need to make sure they are alive at return time. MachineBasicBlock::iterator Ret = MBB.getFirstTerminator(); bool BBEndsInReturn = (Ret != MBB.end() && Ret->getDesc().isReturn()); if (BBEndsInReturn) for (MachineRegisterInfo::liveout_iterator I = MF->getRegInfo().liveout_begin(), E = MF->getRegInfo().liveout_end(); I != E; ++I) if (!Ret->readsRegister(*I)) { Ret->addOperand(MachineOperand::CreateReg(*I, false, true)); LastUseDef[*I] = std::make_pair(Ret, Ret->getNumOperands()-1); } // Finally, loop over the final use/def of each reg // in the block and determine if it is dead. for (DenseMap<unsigned, std::pair<MachineInstr*, unsigned> >::iterator I = LastUseDef.begin(), E = LastUseDef.end(); I != E; ++I) { MachineInstr *MI = I->second.first; unsigned idx = I->second.second; MachineOperand &MO = MI->getOperand(idx); bool isPhysReg = TargetRegisterInfo::isPhysicalRegister(MO.getReg()); // A crude approximation of "live-out" calculation bool usedOutsideBlock = isPhysReg ? false : UsedInMultipleBlocks.test(MO.getReg() - TargetRegisterInfo::FirstVirtualRegister); // If the machine BB ends in a return instruction, then the value isn't used // outside of the BB. if (!isPhysReg && (!usedOutsideBlock || BBEndsInReturn)) { // DBG_VALUE complicates this: if the only refs of a register outside // this block are DBG_VALUE, we can't keep the reg live just for that, // as it will cause the reg to be spilled at the end of this block when // it wouldn't have been otherwise. Nullify the DBG_VALUEs when that // happens. bool UsedByDebugValueOnly = false; for (MachineRegisterInfo::reg_iterator UI = MRI.reg_begin(MO.getReg()), UE = MRI.reg_end(); UI != UE; ++UI) { // Two cases: // - used in another block // - used in the same block before it is defined (loop) if (UI->getParent() == &MBB && !(MO.isDef() && UI.getOperand().isUse() && precedes(&*UI, MI))) continue; if (UI->isDebugValue()) { UsedByDebugValueOnly = true; continue; } // A non-DBG_VALUE use means we can leave DBG_VALUE uses alone. UsedInMultipleBlocks.set(MO.getReg() - TargetRegisterInfo::FirstVirtualRegister); usedOutsideBlock = true; UsedByDebugValueOnly = false; break; } if (UsedByDebugValueOnly) for (MachineRegisterInfo::reg_iterator UI = MRI.reg_begin(MO.getReg()), UE = MRI.reg_end(); UI != UE; ++UI) if (UI->isDebugValue() && (UI->getParent() != &MBB || (MO.isDef() && precedes(&*UI, MI)))) UI.getOperand().setReg(0U); } // Physical registers and those that are not live-out of the block are // killed/dead at their last use/def within this block. if (isPhysReg || !usedOutsideBlock || BBEndsInReturn) { if (MO.isUse()) { // Don't mark uses that are tied to defs as kills. if (!MI->isRegTiedToDefOperand(idx)) MO.setIsKill(true); } else { MO.setIsDead(true); } } } }
/// hasRegisterUseBelow - Return true if the specified register is used after /// the current instruction and before it's next definition. bool LiveVariables::hasRegisterUseBelow(unsigned Reg, MachineBasicBlock::iterator I, MachineBasicBlock *MBB) { if (I == MBB->end()) return false; // First find out if there are any uses / defs below. bool hasDistInfo = true; unsigned CurDist = DistanceMap[I]; SmallVector<MachineInstr*, 4> Uses; SmallVector<MachineInstr*, 4> Defs; for (MachineRegisterInfo::reg_iterator RI = MRI->reg_begin(Reg), RE = MRI->reg_end(); RI != RE; ++RI) { MachineOperand &UDO = RI.getOperand(); MachineInstr *UDMI = &*RI; if (UDMI->getParent() != MBB) continue; DenseMap<MachineInstr*, unsigned>::iterator DI = DistanceMap.find(UDMI); bool isBelow = false; if (DI == DistanceMap.end()) { // Must be below if it hasn't been assigned a distance yet. isBelow = true; hasDistInfo = false; } else if (DI->second > CurDist) isBelow = true; if (isBelow) { if (UDO.isUse()) Uses.push_back(UDMI); if (UDO.isDef()) Defs.push_back(UDMI); } } if (Uses.empty()) // No uses below. return false; else if (!Uses.empty() && Defs.empty()) // There are uses below but no defs below. return true; // There are both uses and defs below. We need to know which comes first. if (!hasDistInfo) { // Complete DistanceMap for this MBB. This information is computed only // once per MBB. ++I; ++CurDist; for (MachineBasicBlock::iterator E = MBB->end(); I != E; ++I, ++CurDist) DistanceMap.insert(std::make_pair(I, CurDist)); } unsigned EarliestUse = DistanceMap[Uses[0]]; for (unsigned i = 1, e = Uses.size(); i != e; ++i) { unsigned Dist = DistanceMap[Uses[i]]; if (Dist < EarliestUse) EarliestUse = Dist; } for (unsigned i = 0, e = Defs.size(); i != e; ++i) { unsigned Dist = DistanceMap[Defs[i]]; if (Dist < EarliestUse) // The register is defined before its first use below. return false; } return true; }
/// getTripCount - Return a loop-invariant LLVM value indicating the /// number of times the loop will be executed. The trip count can /// be either a register or a constant value. If the trip-count /// cannot be determined, this returns null. /// /// We find the trip count from the phi instruction that defines the /// induction variable. We follow the links to the CMP instruction /// to get the trip count. /// /// Based upon getTripCount in LoopInfo. /// CountValue *PPCCTRLoops::getTripCount(MachineLoop *L, SmallVector<MachineInstr *, 2> &OldInsts) const { MachineBasicBlock *LastMBB = L->getExitingBlock(); // Don't generate a CTR loop if the loop has more than one exit. if (LastMBB == 0) return 0; MachineBasicBlock::iterator LastI = LastMBB->getFirstTerminator(); if (LastI->getOpcode() != PPC::BCC) return 0; // We need to make sure that this compare is defining the condition // register actually used by the terminating branch. unsigned PredReg = LastI->getOperand(1).getReg(); DEBUG(dbgs() << "Examining loop with first terminator: " << *LastI); unsigned PredCond = LastI->getOperand(0).getImm(); if (PredCond != PPC::PRED_EQ && PredCond != PPC::PRED_NE) return 0; // Check that the loop has a induction variable. SmallVector<MachineInstr *, 4> IVars, IOps; getCanonicalInductionVariable(L, IVars, IOps); for (unsigned i = 0; i < IVars.size(); ++i) { MachineInstr *IOp = IOps[i]; MachineInstr *IV_Inst = IVars[i]; // Canonical loops will end with a 'cmpwi/cmpdi cr, IV, Imm', // if Imm is 0, get the count from the PHI opnd // if Imm is -M, than M is the count // Otherwise, Imm is the count MachineOperand *IV_Opnd; const MachineOperand *InitialValue; if (!L->contains(IV_Inst->getOperand(2).getMBB())) { InitialValue = &IV_Inst->getOperand(1); IV_Opnd = &IV_Inst->getOperand(3); } else { InitialValue = &IV_Inst->getOperand(3); IV_Opnd = &IV_Inst->getOperand(1); } DEBUG(dbgs() << "Considering:\n"); DEBUG(dbgs() << " induction operation: " << *IOp); DEBUG(dbgs() << " induction variable: " << *IV_Inst); DEBUG(dbgs() << " initial value: " << *InitialValue << "\n"); // Look for the cmp instruction to determine if we // can get a useful trip count. The trip count can // be either a register or an immediate. The location // of the value depends upon the type (reg or imm). for (MachineRegisterInfo::reg_iterator RI = MRI->reg_begin(IV_Opnd->getReg()), RE = MRI->reg_end(); RI != RE; ++RI) { IV_Opnd = &RI.getOperand(); bool SignedCmp, Int64Cmp; MachineInstr *MI = IV_Opnd->getParent(); if (L->contains(MI) && isCompareEqualsImm(MI, SignedCmp, Int64Cmp) && MI->getOperand(0).getReg() == PredReg) { OldInsts.push_back(MI); OldInsts.push_back(IOp); DEBUG(dbgs() << " compare: " << *MI); const MachineOperand &MO = MI->getOperand(2); assert(MO.isImm() && "IV Cmp Operand should be an immediate"); int64_t ImmVal; if (SignedCmp) ImmVal = (short) MO.getImm(); else ImmVal = MO.getImm(); const MachineInstr *IV_DefInstr = MRI->getVRegDef(IV_Opnd->getReg()); assert(L->contains(IV_DefInstr->getParent()) && "IV definition should occurs in loop"); int64_t iv_value = (short) IV_DefInstr->getOperand(2).getImm(); assert(InitialValue->isReg() && "Expecting register for init value"); unsigned InitialValueReg = InitialValue->getReg(); MachineInstr *DefInstr = MRI->getVRegDef(InitialValueReg); // Here we need to look for an immediate load (an li or lis/ori pair). if (DefInstr && (DefInstr->getOpcode() == PPC::ORI8 || DefInstr->getOpcode() == PPC::ORI)) { int64_t start = DefInstr->getOperand(2).getImm(); MachineInstr *DefInstr2 = MRI->getVRegDef(DefInstr->getOperand(1).getReg()); if (DefInstr2 && (DefInstr2->getOpcode() == PPC::LIS8 || DefInstr2->getOpcode() == PPC::LIS)) { DEBUG(dbgs() << " initial constant: " << *DefInstr); DEBUG(dbgs() << " initial constant: " << *DefInstr2); start |= int64_t(short(DefInstr2->getOperand(1).getImm())) << 16; int64_t count = ImmVal - start; if ((count % iv_value) != 0) { return 0; } OldInsts.push_back(DefInstr); OldInsts.push_back(DefInstr2); // count/iv_value, the trip count, should be positive here. If it // is negative, that indicates that the counter will wrap. if (Int64Cmp) return new CountValue(count/iv_value); else return new CountValue(uint32_t(count/iv_value)); } } else if (DefInstr && (DefInstr->getOpcode() == PPC::LI8 || DefInstr->getOpcode() == PPC::LI)) { DEBUG(dbgs() << " initial constant: " << *DefInstr); int64_t count = ImmVal - int64_t(short(DefInstr->getOperand(1).getImm())); if ((count % iv_value) != 0) { return 0; } OldInsts.push_back(DefInstr); if (Int64Cmp) return new CountValue(count/iv_value); else return new CountValue(uint32_t(count/iv_value)); } else if (iv_value == 1 || iv_value == -1) { // We can't determine a constant starting value. if (ImmVal == 0) { return new CountValue(InitialValueReg, iv_value > 0); } // FIXME: handle non-zero end value. } // FIXME: handle non-unit increments (we might not want to introduce // division but we can handle some 2^n cases with shifts). } } } return 0; }