compiler/optimizing/ssa_liveness_analysis.cc - LeafOS-Project/android_art - Gitiles

 /*
  * Copyright (C) 2014 The Android Open Source Project
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
  *
  *      http://www.apache.org/licenses/LICENSE-2.0
  *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  * See the License for the specific language governing permissions and
  * limitations under the License.
  */

 #include "ssa_liveness_analysis.h"

 #include "base/bit_vector-inl.h"
 #include "code_generator.h"
 #include "nodes.h"

 namespace art {

 void SsaLivenessAnalysis::Analyze() {
   LinearizeGraph();
   NumberInstructions();
   ComputeLiveness();
 }

 static bool IsLoop(HLoopInformation* info) {
   return info != nullptr;
 }

 static bool InSameLoop(HLoopInformation* first_loop, HLoopInformation* second_loop) {
   return first_loop == second_loop;
 }

 static bool IsInnerLoop(HLoopInformation* outer, HLoopInformation* inner) {
   return (inner != outer)
       && (inner != nullptr)
       && (outer != nullptr)
       && inner->IsIn(*outer);
 }

 static void AddToListForLinearization(ArenaVector<HBasicBlock*>* worklist, HBasicBlock* block) {
   HLoopInformation* block_loop = block->GetLoopInformation();
   auto insert_pos = worklist->rbegin();  // insert_pos.base() will be the actual position.
   for (auto end = worklist->rend(); insert_pos != end; ++insert_pos) {
     HBasicBlock* current = *insert_pos;
     HLoopInformation* current_loop = current->GetLoopInformation();
     if (InSameLoop(block_loop, current_loop)
         || !IsLoop(current_loop)
         || IsInnerLoop(current_loop, block_loop)) {
       // The block can be processed immediately.
       break;
     }
   }
   worklist->insert(insert_pos.base(), block);
 }

 void SsaLivenessAnalysis::LinearizeGraph() {
   // Create a reverse post ordering with the following properties:
   // - Blocks in a loop are consecutive,
   // - Back-edge is the last block before loop exits.

   // (1): Record the number of forward predecessors for each block. This is to
   //      ensure the resulting order is reverse post order. We could use the
   //      current reverse post order in the graph, but it would require making
   //      order queries to a GrowableArray, which is not the best data structure
   //      for it.
   ArenaVector<uint32_t> forward_predecessors(graph_->GetBlocks().size(),
                                              graph_->GetArena()->Adapter(kArenaAllocSsaLiveness));
   for (HReversePostOrderIterator it(*graph_); !it.Done(); it.Advance()) {
     HBasicBlock* block = it.Current();
     size_t number_of_forward_predecessors = block->GetPredecessors().size();
     if (block->IsLoopHeader()) {
       number_of_forward_predecessors -= block->GetLoopInformation()->NumberOfBackEdges();
     }
     forward_predecessors[block->GetBlockId()] = number_of_forward_predecessors;
   }

   // (2): Following a worklist approach, first start with the entry block, and
   //      iterate over the successors. When all non-back edge predecessors of a
   //      successor block are visited, the successor block is added in the worklist
   //      following an order that satisfies the requirements to build our linear graph.
   graph_->linear_order_.reserve(graph_->GetReversePostOrder().size());
   ArenaVector<HBasicBlock*> worklist(graph_->GetArena()->Adapter(kArenaAllocSsaLiveness));
   worklist.push_back(graph_->GetEntryBlock());
   do {
     HBasicBlock* current = worklist.back();
     worklist.pop_back();
     graph_->linear_order_.push_back(current);
     for (HBasicBlock* successor : current->GetSuccessors()) {
       int block_id = successor->GetBlockId();
       size_t number_of_remaining_predecessors = forward_predecessors[block_id];
       if (number_of_remaining_predecessors == 1) {
         AddToListForLinearization(&worklist, successor);
       }
       forward_predecessors[block_id] = number_of_remaining_predecessors - 1;
     }
   } while (!worklist.empty());
 }

 void SsaLivenessAnalysis::NumberInstructions() {
   int ssa_index = 0;
   size_t lifetime_position = 0;
   // Each instruction gets a lifetime position, and a block gets a lifetime
   // start and end position. Non-phi instructions have a distinct lifetime position than
   // the block they are in. Phi instructions have the lifetime start of their block as
   // lifetime position.
   //
   // Because the register allocator will insert moves in the graph, we need
   // to differentiate between the start and end of an instruction. Adding 2 to
   // the lifetime position for each instruction ensures the start of an
   // instruction is different than the end of the previous instruction.
   for (HLinearOrderIterator it(*graph_); !it.Done(); it.Advance()) {
     HBasicBlock* block = it.Current();
     block->SetLifetimeStart(lifetime_position);

     for (HInstructionIterator inst_it(block->GetPhis()); !inst_it.Done(); inst_it.Advance()) {
       HInstruction* current = inst_it.Current();
       codegen_->AllocateLocations(current);
       LocationSummary* locations = current->GetLocations();
       if (locations != nullptr && locations->Out().IsValid()) {
         instructions_from_ssa_index_.push_back(current);
         current->SetSsaIndex(ssa_index++);
         current->SetLiveInterval(
             LiveInterval::MakeInterval(graph_->GetArena(), current->GetType(), current));
       }
       current->SetLifetimePosition(lifetime_position);
     }
     lifetime_position += 2;

     // Add a null marker to notify we are starting a block.
     instructions_from_lifetime_position_.push_back(nullptr);

     for (HInstructionIterator inst_it(block->GetInstructions()); !inst_it.Done();
          inst_it.Advance()) {
       HInstruction* current = inst_it.Current();
       codegen_->AllocateLocations(current);
       LocationSummary* locations = current->GetLocations();
       if (locations != nullptr && locations->Out().IsValid()) {
         instructions_from_ssa_index_.push_back(current);
         current->SetSsaIndex(ssa_index++);
         current->SetLiveInterval(
             LiveInterval::MakeInterval(graph_->GetArena(), current->GetType(), current));
       }
       instructions_from_lifetime_position_.push_back(current);
       current->SetLifetimePosition(lifetime_position);
       lifetime_position += 2;
     }

     block->SetLifetimeEnd(lifetime_position);
   }
   number_of_ssa_values_ = ssa_index;
 }

 void SsaLivenessAnalysis::ComputeLiveness() {
   for (HLinearOrderIterator it(*graph_); !it.Done(); it.Advance()) {
     HBasicBlock* block = it.Current();
     DCHECK_LT(block->GetBlockId(), block_infos_.size());
     block_infos_[block->GetBlockId()] =
         new (graph_->GetArena()) BlockInfo(graph_->GetArena(), *block, number_of_ssa_values_);
   }

   // Compute the live ranges, as well as the initial live_in, live_out, and kill sets.
   // This method does not handle backward branches for the sets, therefore live_in
   // and live_out sets are not yet correct.
   ComputeLiveRanges();

   // Do a fixed point calculation to take into account backward branches,
   // that will update live_in of loop headers, and therefore live_out and live_in
   // of blocks in the loop.
   ComputeLiveInAndLiveOutSets();
 }

 void SsaLivenessAnalysis::ComputeLiveRanges() {
   // Do a post order visit, adding inputs of instructions live in the block where
   // that instruction is defined, and killing instructions that are being visited.
   for (HLinearPostOrderIterator it(*graph_); !it.Done(); it.Advance()) {
     HBasicBlock* block = it.Current();

     BitVector* kill = GetKillSet(*block);
     BitVector* live_in = GetLiveInSet(*block);

     // Set phi inputs of successors of this block corresponding to this block
     // as live_in.
     for (HBasicBlock* successor : block->GetSuccessors()) {
       live_in->Union(GetLiveInSet(*successor));
       if (successor->IsCatchBlock()) {
         // Inputs of catch phis will be kept alive through their environment
         // uses, allowing the runtime to copy their values to the corresponding
         // catch phi spill slots when an exception is thrown.
         // The only instructions which may not be recorded in the environments
         // are constants created by the SSA builder as typed equivalents of
         // untyped constants from the bytecode, or phis with only such constants
         // as inputs (verified by SSAChecker). Their raw binary value must
         // therefore be the same and we only need to keep alive one.
       } else {
         size_t phi_input_index = successor->GetPredecessorIndexOf(block);
         for (HInstructionIterator phi_it(successor->GetPhis()); !phi_it.Done(); phi_it.Advance()) {
           HInstruction* phi = phi_it.Current();
           HInstruction* input = phi->InputAt(phi_input_index);
           input->GetLiveInterval()->AddPhiUse(phi, phi_input_index, block);
           // A phi input whose last user is the phi dies at the end of the predecessor block,
           // and not at the phi's lifetime position.
           live_in->SetBit(input->GetSsaIndex());
         }
       }
     }

     // Add a range that covers this block to all instructions live_in because of successors.
     // Instructions defined in this block will have their start of the range adjusted.
     for (uint32_t idx : live_in->Indexes()) {
       HInstruction* current = GetInstructionFromSsaIndex(idx);
       current->GetLiveInterval()->AddRange(block->GetLifetimeStart(), block->GetLifetimeEnd());
     }

     for (HBackwardInstructionIterator back_it(block->GetInstructions()); !back_it.Done();
          back_it.Advance()) {
       HInstruction* current = back_it.Current();
       if (current->HasSsaIndex()) {
         // Kill the instruction and shorten its interval.
         kill->SetBit(current->GetSsaIndex());
         live_in->ClearBit(current->GetSsaIndex());
         current->GetLiveInterval()->SetFrom(current->GetLifetimePosition());
       }

       // Process the environment first, because we know their uses come after
       // or at the same liveness position of inputs.
       for (HEnvironment* environment = current->GetEnvironment();
            environment != nullptr;
            environment = environment->GetParent()) {
         // Handle environment uses. See statements (b) and (c) of the
         // SsaLivenessAnalysis.
         for (size_t i = 0, e = environment->Size(); i < e; ++i) {
           HInstruction* instruction = environment->GetInstructionAt(i);
           bool should_be_live = ShouldBeLiveForEnvironment(current, instruction);
           if (should_be_live) {
             DCHECK(instruction->HasSsaIndex());
             live_in->SetBit(instruction->GetSsaIndex());
           }
           if (instruction != nullptr) {
             instruction->GetLiveInterval()->AddUse(
                 current, environment, i, should_be_live);
           }
         }
       }

       // All inputs of an instruction must be live.
       for (size_t i = 0, e = current->InputCount(); i < e; ++i) {
         HInstruction* input = current->InputAt(i);
         // Some instructions 'inline' their inputs, that is they do not need
         // to be materialized.
         if (input->HasSsaIndex() && current->GetLocations()->InAt(i).IsValid()) {
           live_in->SetBit(input->GetSsaIndex());
           input->GetLiveInterval()->AddUse(current, /* environment */ nullptr, i);
         }
       }
     }

     // Kill phis defined in this block.
     for (HInstructionIterator inst_it(block->GetPhis()); !inst_it.Done(); inst_it.Advance()) {
       HInstruction* current = inst_it.Current();
       if (current->HasSsaIndex()) {
         kill->SetBit(current->GetSsaIndex());
         live_in->ClearBit(current->GetSsaIndex());
         LiveInterval* interval = current->GetLiveInterval();
         DCHECK((interval->GetFirstRange() == nullptr)
                || (interval->GetStart() == current->GetLifetimePosition()));
         interval->SetFrom(current->GetLifetimePosition());
       }
     }

     if (block->IsLoopHeader()) {
       size_t last_position = block->GetLoopInformation()->GetLifetimeEnd();
       // For all live_in instructions at the loop header, we need to create a range
       // that covers the full loop.
       for (uint32_t idx : live_in->Indexes()) {
         HInstruction* current = GetInstructionFromSsaIndex(idx);
         current->GetLiveInterval()->AddLoopRange(block->GetLifetimeStart(), last_position);
       }
     }
   }
 }

 void SsaLivenessAnalysis::ComputeLiveInAndLiveOutSets() {
   bool changed;
   do {
     changed = false;

     for (HPostOrderIterator it(*graph_); !it.Done(); it.Advance()) {
       const HBasicBlock& block = *it.Current();

       // The live_in set depends on the kill set (which does not
       // change in this loop), and the live_out set.  If the live_out
       // set does not change, there is no need to update the live_in set.
       if (UpdateLiveOut(block) && UpdateLiveIn(block)) {
         changed = true;
       }
     }
   } while (changed);
 }

 bool SsaLivenessAnalysis::UpdateLiveOut(const HBasicBlock& block) {
   BitVector* live_out = GetLiveOutSet(block);
   bool changed = false;
   // The live_out set of a block is the union of live_in sets of its successors.
   for (HBasicBlock* successor : block.GetSuccessors()) {
     if (live_out->Union(GetLiveInSet(*successor))) {
       changed = true;
     }
   }
   return changed;
 }


 bool SsaLivenessAnalysis::UpdateLiveIn(const HBasicBlock& block) {
   BitVector* live_out = GetLiveOutSet(block);
   BitVector* kill = GetKillSet(block);
   BitVector* live_in = GetLiveInSet(block);
   // If live_out is updated (because of backward branches), we need to make
   // sure instructions in live_out are also in live_in, unless they are killed
   // by this block.
   return live_in->UnionIfNotIn(live_out, kill);
 }

 static int RegisterOrLowRegister(Location location) {
   return location.IsPair() ? location.low() : location.reg();
 }

 int LiveInterval::FindFirstRegisterHint(size_t* free_until,
                                         const SsaLivenessAnalysis& liveness) const {
   DCHECK(!IsHighInterval());
   if (IsTemp()) return kNoRegister;

   if (GetParent() == this && defined_by_ != nullptr) {
     // This is the first interval for the instruction. Try to find
     // a register based on its definition.
     DCHECK_EQ(defined_by_->GetLiveInterval(), this);
     int hint = FindHintAtDefinition();
     if (hint != kNoRegister && free_until[hint] > GetStart()) {
       return hint;
     }
   }

   if (IsSplit() && liveness.IsAtBlockBoundary(GetStart() / 2)) {
     // If the start of this interval is at a block boundary, we look at the
     // location of the interval in blocks preceding the block this interval
     // starts at. If one location is a register we return it as a hint. This
     // will avoid a move between the two blocks.
     HBasicBlock* block = liveness.GetBlockFromPosition(GetStart() / 2);
     size_t next_register_use = FirstRegisterUse();
     for (HBasicBlock* predecessor : block->GetPredecessors()) {
       size_t position = predecessor->GetLifetimeEnd() - 1;
       // We know positions above GetStart() do not have a location yet.
       if (position < GetStart()) {
         LiveInterval* existing = GetParent()->GetSiblingAt(position);
         if (existing != nullptr
             && existing->HasRegister()
             // It's worth using that register if it is available until
             // the next use.
             && (free_until[existing->GetRegister()] >= next_register_use)) {
           return existing->GetRegister();
         }
       }
     }
   }

   UsePosition* use = first_use_;
   size_t start = GetStart();
   size_t end = GetEnd();
   while (use != nullptr && use->GetPosition() <= end) {
     size_t use_position = use->GetPosition();
     if (use_position >= start && !use->IsSynthesized()) {
       HInstruction* user = use->GetUser();
       size_t input_index = use->GetInputIndex();
       if (user->IsPhi()) {
         // If the phi has a register, try to use the same.
         Location phi_location = user->GetLiveInterval()->ToLocation();
         if (phi_location.IsRegisterKind()) {
           DCHECK(SameRegisterKind(phi_location));
           int reg = RegisterOrLowRegister(phi_location);
           if (free_until[reg] >= use_position) {
             return reg;
           }
         }
         // If the instruction dies at the phi assignment, we can try having the
         // same register.
         if (end == user->GetBlock()->GetPredecessor(input_index)->GetLifetimeEnd()) {
           for (size_t i = 0, e = user->InputCount(); i < e; ++i) {
             if (i == input_index) {
               continue;
             }
             HInstruction* input = user->InputAt(i);
             Location location = input->GetLiveInterval()->GetLocationAt(
                 user->GetBlock()->GetPredecessor(i)->GetLifetimeEnd() - 1);
             if (location.IsRegisterKind()) {
               int reg = RegisterOrLowRegister(location);
               if (free_until[reg] >= use_position) {
                 return reg;
               }
             }
           }
         }
       } else {
         // If the instruction is expected in a register, try to use it.
         LocationSummary* locations = user->GetLocations();
         Location expected = locations->InAt(use->GetInputIndex());
         // We use the user's lifetime position - 1 (and not `use_position`) because the
         // register is blocked at the beginning of the user.
         size_t position = user->GetLifetimePosition() - 1;
         if (expected.IsRegisterKind()) {
           DCHECK(SameRegisterKind(expected));
           int reg = RegisterOrLowRegister(expected);
           if (free_until[reg] >= position) {
             return reg;
           }
         }
       }
     }
     use = use->GetNext();
   }

   return kNoRegister;
 }

 int LiveInterval::FindHintAtDefinition() const {
   if (defined_by_->IsPhi()) {
     // Try to use the same register as one of the inputs.
     const ArenaVector<HBasicBlock*>& predecessors = defined_by_->GetBlock()->GetPredecessors();
     for (size_t i = 0, e = defined_by_->InputCount(); i < e; ++i) {
       HInstruction* input = defined_by_->InputAt(i);
       DCHECK_LT(i, predecessors.size());
       size_t end = predecessors[i]->GetLifetimeEnd();
       LiveInterval* input_interval = input->GetLiveInterval()->GetSiblingAt(end - 1);
       if (input_interval->GetEnd() == end) {
         // If the input dies at the end of the predecessor, we know its register can
         // be reused.
         Location input_location = input_interval->ToLocation();
         if (input_location.IsRegisterKind()) {
           DCHECK(SameRegisterKind(input_location));
           return RegisterOrLowRegister(input_location);
         }
       }
     }
   } else {
     LocationSummary* locations = GetDefinedBy()->GetLocations();
     Location out = locations->Out();
     if (out.IsUnallocated() && out.GetPolicy() == Location::kSameAsFirstInput) {
       // Try to use the same register as the first input.
       LiveInterval* input_interval =
           GetDefinedBy()->InputAt(0)->GetLiveInterval()->GetSiblingAt(GetStart() - 1);
       if (input_interval->GetEnd() == GetStart()) {
         // If the input dies at the start of this instruction, we know its register can
         // be reused.
         Location location = input_interval->ToLocation();
         if (location.IsRegisterKind()) {
           DCHECK(SameRegisterKind(location));
           return RegisterOrLowRegister(location);
         }
       }
     }
   }
   return kNoRegister;
 }

 bool LiveInterval::SameRegisterKind(Location other) const {
   if (IsFloatingPoint()) {
     if (IsLowInterval() || IsHighInterval()) {
       return other.IsFpuRegisterPair();
     } else {
       return other.IsFpuRegister();
     }
   } else {
     if (IsLowInterval() || IsHighInterval()) {
       return other.IsRegisterPair();
     } else {
       return other.IsRegister();
     }
   }
 }

 bool LiveInterval::NeedsTwoSpillSlots() const {
   return type_ == Primitive::kPrimLong || type_ == Primitive::kPrimDouble;
 }

 Location LiveInterval::ToLocation() const {
   DCHECK(!IsHighInterval());
   if (HasRegister()) {
     if (IsFloatingPoint()) {
       if (HasHighInterval()) {
         return Location::FpuRegisterPairLocation(GetRegister(), GetHighInterval()->GetRegister());
       } else {
         return Location::FpuRegisterLocation(GetRegister());
       }
     } else {
       if (HasHighInterval()) {
         return Location::RegisterPairLocation(GetRegister(), GetHighInterval()->GetRegister());
       } else {
         return Location::RegisterLocation(GetRegister());
       }
     }
   } else {
     HInstruction* defined_by = GetParent()->GetDefinedBy();
     if (defined_by->IsConstant()) {
       return defined_by->GetLocations()->Out();
     } else if (GetParent()->HasSpillSlot()) {
       if (NeedsTwoSpillSlots()) {
         return Location::DoubleStackSlot(GetParent()->GetSpillSlot());
       } else {
         return Location::StackSlot(GetParent()->GetSpillSlot());
       }
     } else {
       return Location();
     }
   }
 }

 Location LiveInterval::GetLocationAt(size_t position) {
   LiveInterval* sibling = GetSiblingAt(position);
   DCHECK(sibling != nullptr);
   return sibling->ToLocation();
 }

 LiveInterval* LiveInterval::GetSiblingAt(size_t position) {
   LiveInterval* current = this;
   while (current != nullptr && !current->IsDefinedAt(position)) {
     current = current->GetNextSibling();
   }
   return current;
 }

 }  // namespace art
	/*
	* Copyright (C) 2014 The Android Open Source Project
	*
	* Licensed under the Apache License, Version 2.0 (the "License");
	* you may not use this file except in compliance with the License.
	* You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing, software
	* distributed under the License is distributed on an "AS IS" BASIS,
	* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	* See the License for the specific language governing permissions and
	* limitations under the License.
	*/

	#include "ssa_liveness_analysis.h"

	#include "base/bit_vector-inl.h"
	#include "code_generator.h"
	#include "nodes.h"

	namespace art {

	void SsaLivenessAnalysis::Analyze() {
	LinearizeGraph();
	NumberInstructions();
	ComputeLiveness();
	}

	static bool IsLoop(HLoopInformation* info) {
	return info != nullptr;
	}

	static bool InSameLoop(HLoopInformation* first_loop, HLoopInformation* second_loop) {
	return first_loop == second_loop;
	}

	static bool IsInnerLoop(HLoopInformation* outer, HLoopInformation* inner) {
	return (inner != outer)
	&& (inner != nullptr)
	&& (outer != nullptr)
	&& inner->IsIn(*outer);
	}

	static void AddToListForLinearization(ArenaVector<HBasicBlock> worklist, HBasicBlock* block) {
	HLoopInformation* block_loop = block->GetLoopInformation();
	auto insert_pos = worklist->rbegin(); // insert_pos.base() will be the actual position.
	for (auto end = worklist->rend(); insert_pos != end; ++insert_pos) {
	HBasicBlock* current = *insert_pos;
	HLoopInformation* current_loop = current->GetLoopInformation();
	if (InSameLoop(block_loop, current_loop)
	\|\| !IsLoop(current_loop)
	\|\| IsInnerLoop(current_loop, block_loop)) {
	// The block can be processed immediately.
	break;
	}
	}
	worklist->insert(insert_pos.base(), block);
	}

	void SsaLivenessAnalysis::LinearizeGraph() {
	// Create a reverse post ordering with the following properties:
	// - Blocks in a loop are consecutive,
	// - Back-edge is the last block before loop exits.

	// (1): Record the number of forward predecessors for each block. This is to
	// ensure the resulting order is reverse post order. We could use the
	// current reverse post order in the graph, but it would require making
	// order queries to a GrowableArray, which is not the best data structure
	// for it.
	ArenaVector<uint32_t> forward_predecessors(graph_->GetBlocks().size(),
	graph_->GetArena()->Adapter(kArenaAllocSsaLiveness));
	for (HReversePostOrderIterator it(*graph_); !it.Done(); it.Advance()) {
	HBasicBlock* block = it.Current();
	size_t number_of_forward_predecessors = block->GetPredecessors().size();
	if (block->IsLoopHeader()) {
	number_of_forward_predecessors -= block->GetLoopInformation()->NumberOfBackEdges();
	}
	forward_predecessors[block->GetBlockId()] = number_of_forward_predecessors;
	}

	// (2): Following a worklist approach, first start with the entry block, and
	// iterate over the successors. When all non-back edge predecessors of a
	// successor block are visited, the successor block is added in the worklist
	// following an order that satisfies the requirements to build our linear graph.
	graph_->linear_order_.reserve(graph_->GetReversePostOrder().size());
	ArenaVector<HBasicBlock*> worklist(graph_->GetArena()->Adapter(kArenaAllocSsaLiveness));
	worklist.push_back(graph_->GetEntryBlock());
	do {
	HBasicBlock* current = worklist.back();
	worklist.pop_back();
	graph_->linear_order_.push_back(current);
	for (HBasicBlock* successor : current->GetSuccessors()) {
	int block_id = successor->GetBlockId();
	size_t number_of_remaining_predecessors = forward_predecessors[block_id];
	if (number_of_remaining_predecessors == 1) {
	AddToListForLinearization(&worklist, successor);
	}
	forward_predecessors[block_id] = number_of_remaining_predecessors - 1;
	}
	} while (!worklist.empty());
	}

	void SsaLivenessAnalysis::NumberInstructions() {
	int ssa_index = 0;
	size_t lifetime_position = 0;
	// Each instruction gets a lifetime position, and a block gets a lifetime
	// start and end position. Non-phi instructions have a distinct lifetime position than
	// the block they are in. Phi instructions have the lifetime start of their block as
	// lifetime position.
	//
	// Because the register allocator will insert moves in the graph, we need
	// to differentiate between the start and end of an instruction. Adding 2 to
	// the lifetime position for each instruction ensures the start of an
	// instruction is different than the end of the previous instruction.
	for (HLinearOrderIterator it(*graph_); !it.Done(); it.Advance()) {
	HBasicBlock* block = it.Current();
	block->SetLifetimeStart(lifetime_position);

	for (HInstructionIterator inst_it(block->GetPhis()); !inst_it.Done(); inst_it.Advance()) {
	HInstruction* current = inst_it.Current();
	codegen_->AllocateLocations(current);
	LocationSummary* locations = current->GetLocations();
	if (locations != nullptr && locations->Out().IsValid()) {
	instructions_from_ssa_index_.push_back(current);
	current->SetSsaIndex(ssa_index++);
	current->SetLiveInterval(
	LiveInterval::MakeInterval(graph_->GetArena(), current->GetType(), current));
	}
	current->SetLifetimePosition(lifetime_position);
	}
	lifetime_position += 2;

	// Add a null marker to notify we are starting a block.
	instructions_from_lifetime_position_.push_back(nullptr);

	for (HInstructionIterator inst_it(block->GetInstructions()); !inst_it.Done();
	inst_it.Advance()) {
	HInstruction* current = inst_it.Current();
	codegen_->AllocateLocations(current);
	LocationSummary* locations = current->GetLocations();
	if (locations != nullptr && locations->Out().IsValid()) {
	instructions_from_ssa_index_.push_back(current);
	current->SetSsaIndex(ssa_index++);
	current->SetLiveInterval(
	LiveInterval::MakeInterval(graph_->GetArena(), current->GetType(), current));
	}
	instructions_from_lifetime_position_.push_back(current);
	current->SetLifetimePosition(lifetime_position);
	lifetime_position += 2;
	}

	block->SetLifetimeEnd(lifetime_position);
	}
	number_of_ssa_values_ = ssa_index;
	}

	void SsaLivenessAnalysis::ComputeLiveness() {
	for (HLinearOrderIterator it(*graph_); !it.Done(); it.Advance()) {
	HBasicBlock* block = it.Current();
	DCHECK_LT(block->GetBlockId(), block_infos_.size());
	block_infos_[block->GetBlockId()] =
	new (graph_->GetArena()) BlockInfo(graph_->GetArena(), *block, number_of_ssa_values_);
	}

	// Compute the live ranges, as well as the initial live_in, live_out, and kill sets.
	// This method does not handle backward branches for the sets, therefore live_in
	// and live_out sets are not yet correct.
	ComputeLiveRanges();

	// Do a fixed point calculation to take into account backward branches,
	// that will update live_in of loop headers, and therefore live_out and live_in
	// of blocks in the loop.
	ComputeLiveInAndLiveOutSets();
	}

	void SsaLivenessAnalysis::ComputeLiveRanges() {
	// Do a post order visit, adding inputs of instructions live in the block where
	// that instruction is defined, and killing instructions that are being visited.
	for (HLinearPostOrderIterator it(*graph_); !it.Done(); it.Advance()) {
	HBasicBlock* block = it.Current();

	BitVector* kill = GetKillSet(*block);
	BitVector* live_in = GetLiveInSet(*block);

	// Set phi inputs of successors of this block corresponding to this block
	// as live_in.
	for (HBasicBlock* successor : block->GetSuccessors()) {
	live_in->Union(GetLiveInSet(*successor));
	if (successor->IsCatchBlock()) {
	// Inputs of catch phis will be kept alive through their environment
	// uses, allowing the runtime to copy their values to the corresponding
	// catch phi spill slots when an exception is thrown.
	// The only instructions which may not be recorded in the environments
	// are constants created by the SSA builder as typed equivalents of
	// untyped constants from the bytecode, or phis with only such constants
	// as inputs (verified by SSAChecker). Their raw binary value must
	// therefore be the same and we only need to keep alive one.
	} else {
	size_t phi_input_index = successor->GetPredecessorIndexOf(block);
	for (HInstructionIterator phi_it(successor->GetPhis()); !phi_it.Done(); phi_it.Advance()) {
	HInstruction* phi = phi_it.Current();
	HInstruction* input = phi->InputAt(phi_input_index);
	input->GetLiveInterval()->AddPhiUse(phi, phi_input_index, block);
	// A phi input whose last user is the phi dies at the end of the predecessor block,
	// and not at the phi's lifetime position.
	live_in->SetBit(input->GetSsaIndex());
	}
	}
	}

	// Add a range that covers this block to all instructions live_in because of successors.
	// Instructions defined in this block will have their start of the range adjusted.
	for (uint32_t idx : live_in->Indexes()) {
	HInstruction* current = GetInstructionFromSsaIndex(idx);
	current->GetLiveInterval()->AddRange(block->GetLifetimeStart(), block->GetLifetimeEnd());
	}

	for (HBackwardInstructionIterator back_it(block->GetInstructions()); !back_it.Done();
	back_it.Advance()) {
	HInstruction* current = back_it.Current();
	if (current->HasSsaIndex()) {
	// Kill the instruction and shorten its interval.
	kill->SetBit(current->GetSsaIndex());
	live_in->ClearBit(current->GetSsaIndex());
	current->GetLiveInterval()->SetFrom(current->GetLifetimePosition());
	}

	// Process the environment first, because we know their uses come after
	// or at the same liveness position of inputs.
	for (HEnvironment* environment = current->GetEnvironment();
	environment != nullptr;
	environment = environment->GetParent()) {
	// Handle environment uses. See statements (b) and (c) of the
	// SsaLivenessAnalysis.
	for (size_t i = 0, e = environment->Size(); i < e; ++i) {
	HInstruction* instruction = environment->GetInstructionAt(i);
	bool should_be_live = ShouldBeLiveForEnvironment(current, instruction);
	if (should_be_live) {
	DCHECK(instruction->HasSsaIndex());
	live_in->SetBit(instruction->GetSsaIndex());
	}
	if (instruction != nullptr) {
	instruction->GetLiveInterval()->AddUse(
	current, environment, i, should_be_live);
	}
	}
	}

	// All inputs of an instruction must be live.
	for (size_t i = 0, e = current->InputCount(); i < e; ++i) {
	HInstruction* input = current->InputAt(i);
	// Some instructions 'inline' their inputs, that is they do not need
	// to be materialized.
	if (input->HasSsaIndex() && current->GetLocations()->InAt(i).IsValid()) {
	live_in->SetBit(input->GetSsaIndex());
	input->GetLiveInterval()->AddUse(current, /* environment */ nullptr, i);
	}
	}
	}

	// Kill phis defined in this block.
	for (HInstructionIterator inst_it(block->GetPhis()); !inst_it.Done(); inst_it.Advance()) {
	HInstruction* current = inst_it.Current();
	if (current->HasSsaIndex()) {
	kill->SetBit(current->GetSsaIndex());
	live_in->ClearBit(current->GetSsaIndex());
	LiveInterval* interval = current->GetLiveInterval();
	DCHECK((interval->GetFirstRange() == nullptr)
	\|\| (interval->GetStart() == current->GetLifetimePosition()));
	interval->SetFrom(current->GetLifetimePosition());
	}
	}

	if (block->IsLoopHeader()) {
	size_t last_position = block->GetLoopInformation()->GetLifetimeEnd();
	// For all live_in instructions at the loop header, we need to create a range
	// that covers the full loop.
	for (uint32_t idx : live_in->Indexes()) {
	HInstruction* current = GetInstructionFromSsaIndex(idx);
	current->GetLiveInterval()->AddLoopRange(block->GetLifetimeStart(), last_position);
	}
	}
	}
	}

	void SsaLivenessAnalysis::ComputeLiveInAndLiveOutSets() {
	bool changed;
	do {
	changed = false;

	for (HPostOrderIterator it(*graph_); !it.Done(); it.Advance()) {
	const HBasicBlock& block = *it.Current();

	// The live_in set depends on the kill set (which does not
	// change in this loop), and the live_out set. If the live_out
	// set does not change, there is no need to update the live_in set.
	if (UpdateLiveOut(block) && UpdateLiveIn(block)) {
	changed = true;
	}
	}
	} while (changed);
	}

	bool SsaLivenessAnalysis::UpdateLiveOut(const HBasicBlock& block) {
	BitVector* live_out = GetLiveOutSet(block);
	bool changed = false;
	// The live_out set of a block is the union of live_in sets of its successors.
	for (HBasicBlock* successor : block.GetSuccessors()) {
	if (live_out->Union(GetLiveInSet(*successor))) {
	changed = true;
	}
	}
	return changed;
	}


	bool SsaLivenessAnalysis::UpdateLiveIn(const HBasicBlock& block) {
	BitVector* live_out = GetLiveOutSet(block);
	BitVector* kill = GetKillSet(block);
	BitVector* live_in = GetLiveInSet(block);
	// If live_out is updated (because of backward branches), we need to make
	// sure instructions in live_out are also in live_in, unless they are killed
	// by this block.
	return live_in->UnionIfNotIn(live_out, kill);
	}

	static int RegisterOrLowRegister(Location location) {
	return location.IsPair() ? location.low() : location.reg();
	}

	int LiveInterval::FindFirstRegisterHint(size_t* free_until,
	const SsaLivenessAnalysis& liveness) const {
	DCHECK(!IsHighInterval());
	if (IsTemp()) return kNoRegister;

	if (GetParent() == this && defined_by_ != nullptr) {
	// This is the first interval for the instruction. Try to find
	// a register based on its definition.
	DCHECK_EQ(defined_by_->GetLiveInterval(), this);
	int hint = FindHintAtDefinition();
	if (hint != kNoRegister && free_until[hint] > GetStart()) {
	return hint;
	}
	}

	if (IsSplit() && liveness.IsAtBlockBoundary(GetStart() / 2)) {
	// If the start of this interval is at a block boundary, we look at the
	// location of the interval in blocks preceding the block this interval
	// starts at. If one location is a register we return it as a hint. This
	// will avoid a move between the two blocks.
	HBasicBlock* block = liveness.GetBlockFromPosition(GetStart() / 2);
	size_t next_register_use = FirstRegisterUse();
	for (HBasicBlock* predecessor : block->GetPredecessors()) {
	size_t position = predecessor->GetLifetimeEnd() - 1;
	// We know positions above GetStart() do not have a location yet.
	if (position < GetStart()) {
	LiveInterval* existing = GetParent()->GetSiblingAt(position);
	if (existing != nullptr
	&& existing->HasRegister()
	// It's worth using that register if it is available until
	// the next use.
	&& (free_until[existing->GetRegister()] >= next_register_use)) {
	return existing->GetRegister();
	}
	}
	}
	}

	UsePosition* use = first_use_;
	size_t start = GetStart();
	size_t end = GetEnd();
	while (use != nullptr && use->GetPosition() <= end) {
	size_t use_position = use->GetPosition();
	if (use_position >= start && !use->IsSynthesized()) {
	HInstruction* user = use->GetUser();
	size_t input_index = use->GetInputIndex();
	if (user->IsPhi()) {
	// If the phi has a register, try to use the same.
	Location phi_location = user->GetLiveInterval()->ToLocation();
	if (phi_location.IsRegisterKind()) {
	DCHECK(SameRegisterKind(phi_location));
	int reg = RegisterOrLowRegister(phi_location);
	if (free_until[reg] >= use_position) {
	return reg;
	}
	}
	// If the instruction dies at the phi assignment, we can try having the
	// same register.
	if (end == user->GetBlock()->GetPredecessor(input_index)->GetLifetimeEnd()) {
	for (size_t i = 0, e = user->InputCount(); i < e; ++i) {
	if (i == input_index) {
	continue;
	}
	HInstruction* input = user->InputAt(i);
	Location location = input->GetLiveInterval()->GetLocationAt(
	user->GetBlock()->GetPredecessor(i)->GetLifetimeEnd() - 1);
	if (location.IsRegisterKind()) {
	int reg = RegisterOrLowRegister(location);
	if (free_until[reg] >= use_position) {
	return reg;
	}
	}
	}
	}
	} else {
	// If the instruction is expected in a register, try to use it.
	LocationSummary* locations = user->GetLocations();
	Location expected = locations->InAt(use->GetInputIndex());
	// We use the user's lifetime position - 1 (and not `use_position`) because the
	// register is blocked at the beginning of the user.
	size_t position = user->GetLifetimePosition() - 1;
	if (expected.IsRegisterKind()) {
	DCHECK(SameRegisterKind(expected));
	int reg = RegisterOrLowRegister(expected);
	if (free_until[reg] >= position) {
	return reg;
	}
	}
	}
	}
	use = use->GetNext();
	}

	return kNoRegister;
	}

	int LiveInterval::FindHintAtDefinition() const {
	if (defined_by_->IsPhi()) {
	// Try to use the same register as one of the inputs.
	const ArenaVector<HBasicBlock*>& predecessors = defined_by_->GetBlock()->GetPredecessors();
	for (size_t i = 0, e = defined_by_->InputCount(); i < e; ++i) {
	HInstruction* input = defined_by_->InputAt(i);
	DCHECK_LT(i, predecessors.size());
	size_t end = predecessors[i]->GetLifetimeEnd();
	LiveInterval* input_interval = input->GetLiveInterval()->GetSiblingAt(end - 1);
	if (input_interval->GetEnd() == end) {
	// If the input dies at the end of the predecessor, we know its register can
	// be reused.
	Location input_location = input_interval->ToLocation();
	if (input_location.IsRegisterKind()) {
	DCHECK(SameRegisterKind(input_location));
	return RegisterOrLowRegister(input_location);
	}
	}
	}
	} else {
	LocationSummary* locations = GetDefinedBy()->GetLocations();
	Location out = locations->Out();
	if (out.IsUnallocated() && out.GetPolicy() == Location::kSameAsFirstInput) {
	// Try to use the same register as the first input.
	LiveInterval* input_interval =
	GetDefinedBy()->InputAt(0)->GetLiveInterval()->GetSiblingAt(GetStart() - 1);
	if (input_interval->GetEnd() == GetStart()) {
	// If the input dies at the start of this instruction, we know its register can
	// be reused.
	Location location = input_interval->ToLocation();
	if (location.IsRegisterKind()) {
	DCHECK(SameRegisterKind(location));
	return RegisterOrLowRegister(location);
	}
	}
	}
	}
	return kNoRegister;
	}

	bool LiveInterval::SameRegisterKind(Location other) const {
	if (IsFloatingPoint()) {
	if (IsLowInterval() \|\| IsHighInterval()) {
	return other.IsFpuRegisterPair();
	} else {
	return other.IsFpuRegister();
	}
	} else {
	if (IsLowInterval() \|\| IsHighInterval()) {
	return other.IsRegisterPair();
	} else {
	return other.IsRegister();
	}
	}
	}

	bool LiveInterval::NeedsTwoSpillSlots() const {
	return type_ == Primitive::kPrimLong \|\| type_ == Primitive::kPrimDouble;
	}

	Location LiveInterval::ToLocation() const {
	DCHECK(!IsHighInterval());
	if (HasRegister()) {
	if (IsFloatingPoint()) {
	if (HasHighInterval()) {
	return Location::FpuRegisterPairLocation(GetRegister(), GetHighInterval()->GetRegister());
	} else {
	return Location::FpuRegisterLocation(GetRegister());
	}
	} else {
	if (HasHighInterval()) {
	return Location::RegisterPairLocation(GetRegister(), GetHighInterval()->GetRegister());
	} else {
	return Location::RegisterLocation(GetRegister());
	}
	}
	} else {
	HInstruction* defined_by = GetParent()->GetDefinedBy();
	if (defined_by->IsConstant()) {
	return defined_by->GetLocations()->Out();
	} else if (GetParent()->HasSpillSlot()) {
	if (NeedsTwoSpillSlots()) {
	return Location::DoubleStackSlot(GetParent()->GetSpillSlot());
	} else {
	return Location::StackSlot(GetParent()->GetSpillSlot());
	}
	} else {
	return Location();
	}
	}
	}

	Location LiveInterval::GetLocationAt(size_t position) {
	LiveInterval* sibling = GetSiblingAt(position);
	DCHECK(sibling != nullptr);
	return sibling->ToLocation();
	}

	LiveInterval* LiveInterval::GetSiblingAt(size_t position) {
	LiveInterval* current = this;
	while (current != nullptr && !current->IsDefinedAt(position)) {
	current = current->GetNextSibling();
	}
	return current;
	}

	} // namespace art