| /* |
| * Copyright (C) 2015 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 "induction_var_analysis.h" |
| #include "induction_var_range.h" |
| |
| namespace art { |
| |
| /** |
| * Returns true if instruction is invariant within the given loop. |
| */ |
| static bool IsLoopInvariant(HLoopInformation* loop, HInstruction* instruction) { |
| HLoopInformation* other_loop = instruction->GetBlock()->GetLoopInformation(); |
| if (other_loop != loop) { |
| // If instruction does not occur in same loop, it is invariant |
| // if it appears in an outer loop (including no loop at all). |
| return other_loop == nullptr || loop->IsIn(*other_loop); |
| } |
| return false; |
| } |
| |
| /** |
| * Since graph traversal may enter a SCC at any position, an initial representation may be rotated, |
| * along dependences, viz. any of (a, b, c, d), (d, a, b, c) (c, d, a, b), (b, c, d, a) assuming |
| * a chain of dependences (mutual independent items may occur in arbitrary order). For proper |
| * classification, the lexicographically first entry-phi is rotated to the front. |
| */ |
| static void RotateEntryPhiFirst(HLoopInformation* loop, |
| ArenaVector<HInstruction*>* scc, |
| ArenaVector<HInstruction*>* new_scc) { |
| // Find very first entry-phi. |
| const HInstructionList& phis = loop->GetHeader()->GetPhis(); |
| HInstruction* phi = nullptr; |
| size_t phi_pos = -1; |
| const size_t size = scc->size(); |
| for (size_t i = 0; i < size; i++) { |
| HInstruction* other = (*scc)[i]; |
| if (other->IsLoopHeaderPhi() && (phi == nullptr || phis.FoundBefore(other, phi))) { |
| phi = other; |
| phi_pos = i; |
| } |
| } |
| |
| // If found, bring that entry-phi to front. |
| if (phi != nullptr) { |
| new_scc->clear(); |
| for (size_t i = 0; i < size; i++) { |
| new_scc->push_back((*scc)[phi_pos]); |
| if (++phi_pos >= size) phi_pos = 0; |
| } |
| DCHECK_EQ(size, new_scc->size()); |
| scc->swap(*new_scc); |
| } |
| } |
| |
| // |
| // Class methods. |
| // |
| |
| HInductionVarAnalysis::HInductionVarAnalysis(HGraph* graph) |
| : HOptimization(graph, kInductionPassName), |
| global_depth_(0), |
| stack_(graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)), |
| scc_(graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)), |
| map_(std::less<HInstruction*>(), |
| graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)), |
| cycle_(std::less<HInstruction*>(), |
| graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)), |
| induction_(std::less<HLoopInformation*>(), |
| graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)) { |
| } |
| |
| void HInductionVarAnalysis::Run() { |
| // Detects sequence variables (generalized induction variables) during an inner-loop-first |
| // traversal of all loops using Gerlek's algorithm. The order is only relevant if outer |
| // loops would use induction information of inner loops (not currently done). |
| for (HPostOrderIterator it_graph(*graph_); !it_graph.Done(); it_graph.Advance()) { |
| HBasicBlock* graph_block = it_graph.Current(); |
| if (graph_block->IsLoopHeader()) { |
| VisitLoop(graph_block->GetLoopInformation()); |
| } |
| } |
| } |
| |
| void HInductionVarAnalysis::VisitLoop(HLoopInformation* loop) { |
| // Find strongly connected components (SSCs) in the SSA graph of this loop using Tarjan's |
| // algorithm. Due to the descendant-first nature, classification happens "on-demand". |
| global_depth_ = 0; |
| DCHECK(stack_.empty()); |
| map_.clear(); |
| |
| for (HBlocksInLoopIterator it_loop(*loop); !it_loop.Done(); it_loop.Advance()) { |
| HBasicBlock* loop_block = it_loop.Current(); |
| DCHECK(loop_block->IsInLoop()); |
| if (loop_block->GetLoopInformation() != loop) { |
| continue; // Inner loops already visited. |
| } |
| // Visit phi-operations and instructions. |
| for (HInstructionIterator it(loop_block->GetPhis()); !it.Done(); it.Advance()) { |
| HInstruction* instruction = it.Current(); |
| if (!IsVisitedNode(instruction)) { |
| VisitNode(loop, instruction); |
| } |
| } |
| for (HInstructionIterator it(loop_block->GetInstructions()); !it.Done(); it.Advance()) { |
| HInstruction* instruction = it.Current(); |
| if (!IsVisitedNode(instruction)) { |
| VisitNode(loop, instruction); |
| } |
| } |
| } |
| |
| DCHECK(stack_.empty()); |
| map_.clear(); |
| |
| // Determine the loop's trip count. |
| VisitControl(loop); |
| } |
| |
| void HInductionVarAnalysis::VisitNode(HLoopInformation* loop, HInstruction* instruction) { |
| const uint32_t d1 = ++global_depth_; |
| map_.Put(instruction, NodeInfo(d1)); |
| stack_.push_back(instruction); |
| |
| // Visit all descendants. |
| uint32_t low = d1; |
| for (size_t i = 0, count = instruction->InputCount(); i < count; ++i) { |
| low = std::min(low, VisitDescendant(loop, instruction->InputAt(i))); |
| } |
| |
| // Lower or found SCC? |
| if (low < d1) { |
| map_.find(instruction)->second.depth = low; |
| } else { |
| scc_.clear(); |
| cycle_.clear(); |
| |
| // Pop the stack to build the SCC for classification. |
| while (!stack_.empty()) { |
| HInstruction* x = stack_.back(); |
| scc_.push_back(x); |
| stack_.pop_back(); |
| map_.find(x)->second.done = true; |
| if (x == instruction) { |
| break; |
| } |
| } |
| |
| // Classify the SCC. |
| if (scc_.size() == 1 && !scc_[0]->IsLoopHeaderPhi()) { |
| ClassifyTrivial(loop, scc_[0]); |
| } else { |
| ClassifyNonTrivial(loop); |
| } |
| |
| scc_.clear(); |
| cycle_.clear(); |
| } |
| } |
| |
| uint32_t HInductionVarAnalysis::VisitDescendant(HLoopInformation* loop, HInstruction* instruction) { |
| // If the definition is either outside the loop (loop invariant entry value) |
| // or assigned in inner loop (inner exit value), the traversal stops. |
| HLoopInformation* otherLoop = instruction->GetBlock()->GetLoopInformation(); |
| if (otherLoop != loop) { |
| return global_depth_; |
| } |
| |
| // Inspect descendant node. |
| if (!IsVisitedNode(instruction)) { |
| VisitNode(loop, instruction); |
| return map_.find(instruction)->second.depth; |
| } else { |
| auto it = map_.find(instruction); |
| return it->second.done ? global_depth_ : it->second.depth; |
| } |
| } |
| |
| void HInductionVarAnalysis::ClassifyTrivial(HLoopInformation* loop, HInstruction* instruction) { |
| InductionInfo* info = nullptr; |
| if (instruction->IsPhi()) { |
| info = TransferPhi(loop, instruction, /* input_index */ 0); |
| } else if (instruction->IsAdd()) { |
| info = TransferAddSub(LookupInfo(loop, instruction->InputAt(0)), |
| LookupInfo(loop, instruction->InputAt(1)), kAdd); |
| } else if (instruction->IsSub()) { |
| info = TransferAddSub(LookupInfo(loop, instruction->InputAt(0)), |
| LookupInfo(loop, instruction->InputAt(1)), kSub); |
| } else if (instruction->IsMul()) { |
| info = TransferMul(LookupInfo(loop, instruction->InputAt(0)), |
| LookupInfo(loop, instruction->InputAt(1))); |
| } else if (instruction->IsShl()) { |
| info = TransferShl(LookupInfo(loop, instruction->InputAt(0)), |
| LookupInfo(loop, instruction->InputAt(1)), |
| instruction->InputAt(0)->GetType()); |
| } else if (instruction->IsNeg()) { |
| info = TransferNeg(LookupInfo(loop, instruction->InputAt(0))); |
| } else if (instruction->IsBoundsCheck()) { |
| info = LookupInfo(loop, instruction->InputAt(0)); // Pass-through. |
| } else if (instruction->IsTypeConversion()) { |
| HTypeConversion* conversion = instruction->AsTypeConversion(); |
| // TODO: accept different conversion scenarios. |
| if (conversion->GetResultType() == conversion->GetInputType()) { |
| info = LookupInfo(loop, conversion->GetInput()); |
| } |
| } |
| |
| // Successfully classified? |
| if (info != nullptr) { |
| AssignInfo(loop, instruction, info); |
| } |
| } |
| |
| void HInductionVarAnalysis::ClassifyNonTrivial(HLoopInformation* loop) { |
| const size_t size = scc_.size(); |
| DCHECK_GE(size, 1u); |
| |
| // Rotate proper entry-phi to front. |
| if (size > 1) { |
| ArenaVector<HInstruction*> other(graph_->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)); |
| RotateEntryPhiFirst(loop, &scc_, &other); |
| } |
| |
| // Analyze from entry-phi onwards. |
| HInstruction* phi = scc_[0]; |
| if (!phi->IsLoopHeaderPhi()) { |
| return; |
| } |
| |
| // External link should be loop invariant. |
| InductionInfo* initial = LookupInfo(loop, phi->InputAt(0)); |
| if (initial == nullptr || initial->induction_class != kInvariant) { |
| return; |
| } |
| |
| // Singleton is wrap-around induction if all internal links have the same meaning. |
| if (size == 1) { |
| InductionInfo* update = TransferPhi(loop, phi, /* input_index */ 1); |
| if (update != nullptr) { |
| AssignInfo(loop, phi, CreateInduction(kWrapAround, initial, update)); |
| } |
| return; |
| } |
| |
| // Inspect remainder of the cycle that resides in scc_. The cycle_ mapping assigns |
| // temporary meaning to its nodes, seeded from the phi instruction and back. |
| for (size_t i = 1; i < size; i++) { |
| HInstruction* instruction = scc_[i]; |
| InductionInfo* update = nullptr; |
| if (instruction->IsPhi()) { |
| update = SolvePhiAllInputs(loop, phi, instruction); |
| } else if (instruction->IsAdd()) { |
| update = SolveAddSub( |
| loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kAdd, true); |
| } else if (instruction->IsSub()) { |
| update = SolveAddSub( |
| loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kSub, true); |
| } |
| if (update == nullptr) { |
| return; |
| } |
| cycle_.Put(instruction, update); |
| } |
| |
| // Success if all internal links received the same temporary meaning. |
| InductionInfo* induction = SolvePhi(phi, /* input_index */ 1); |
| if (induction != nullptr) { |
| switch (induction->induction_class) { |
| case kInvariant: |
| // Classify first phi and then the rest of the cycle "on-demand". |
| // Statements are scanned in order. |
| AssignInfo(loop, phi, CreateInduction(kLinear, induction, initial)); |
| for (size_t i = 1; i < size; i++) { |
| ClassifyTrivial(loop, scc_[i]); |
| } |
| break; |
| case kPeriodic: |
| // Classify all elements in the cycle with the found periodic induction while |
| // rotating each first element to the end. Lastly, phi is classified. |
| // Statements are scanned in reverse order. |
| for (size_t i = size - 1; i >= 1; i--) { |
| AssignInfo(loop, scc_[i], induction); |
| induction = RotatePeriodicInduction(induction->op_b, induction->op_a); |
| } |
| AssignInfo(loop, phi, induction); |
| break; |
| default: |
| break; |
| } |
| } |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::RotatePeriodicInduction( |
| InductionInfo* induction, |
| InductionInfo* last) { |
| // Rotates a periodic induction of the form |
| // (a, b, c, d, e) |
| // into |
| // (b, c, d, e, a) |
| // in preparation of assigning this to the previous variable in the sequence. |
| if (induction->induction_class == kInvariant) { |
| return CreateInduction(kPeriodic, induction, last); |
| } |
| return CreateInduction(kPeriodic, induction->op_a, RotatePeriodicInduction(induction->op_b, last)); |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferPhi(HLoopInformation* loop, |
| HInstruction* phi, |
| size_t input_index) { |
| // Match all phi inputs from input_index onwards exactly. |
| const size_t count = phi->InputCount(); |
| DCHECK_LT(input_index, count); |
| InductionInfo* a = LookupInfo(loop, phi->InputAt(input_index)); |
| for (size_t i = input_index + 1; i < count; i++) { |
| InductionInfo* b = LookupInfo(loop, phi->InputAt(i)); |
| if (!InductionEqual(a, b)) { |
| return nullptr; |
| } |
| } |
| return a; |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferAddSub(InductionInfo* a, |
| InductionInfo* b, |
| InductionOp op) { |
| // Transfer over an addition or subtraction: any invariant, linear, wrap-around, or periodic |
| // can be combined with an invariant to yield a similar result. Even two linear inputs can |
| // be combined. All other combinations fail, however. |
| if (a != nullptr && b != nullptr) { |
| if (a->induction_class == kInvariant && b->induction_class == kInvariant) { |
| return CreateInvariantOp(op, a, b); |
| } else if (a->induction_class == kLinear && b->induction_class == kLinear) { |
| return CreateInduction( |
| kLinear, TransferAddSub(a->op_a, b->op_a, op), TransferAddSub(a->op_b, b->op_b, op)); |
| } else if (a->induction_class == kInvariant) { |
| InductionInfo* new_a = b->op_a; |
| InductionInfo* new_b = TransferAddSub(a, b->op_b, op); |
| if (b->induction_class != kLinear) { |
| DCHECK(b->induction_class == kWrapAround || b->induction_class == kPeriodic); |
| new_a = TransferAddSub(a, new_a, op); |
| } else if (op == kSub) { // Negation required. |
| new_a = TransferNeg(new_a); |
| } |
| return CreateInduction(b->induction_class, new_a, new_b); |
| } else if (b->induction_class == kInvariant) { |
| InductionInfo* new_a = a->op_a; |
| InductionInfo* new_b = TransferAddSub(a->op_b, b, op); |
| if (a->induction_class != kLinear) { |
| DCHECK(a->induction_class == kWrapAround || a->induction_class == kPeriodic); |
| new_a = TransferAddSub(new_a, b, op); |
| } |
| return CreateInduction(a->induction_class, new_a, new_b); |
| } |
| } |
| return nullptr; |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferMul(InductionInfo* a, |
| InductionInfo* b) { |
| // Transfer over a multiplication: any invariant, linear, wrap-around, or periodic |
| // can be multiplied with an invariant to yield a similar but multiplied result. |
| // Two non-invariant inputs cannot be multiplied, however. |
| if (a != nullptr && b != nullptr) { |
| if (a->induction_class == kInvariant && b->induction_class == kInvariant) { |
| return CreateInvariantOp(kMul, a, b); |
| } else if (a->induction_class == kInvariant) { |
| return CreateInduction(b->induction_class, TransferMul(a, b->op_a), TransferMul(a, b->op_b)); |
| } else if (b->induction_class == kInvariant) { |
| return CreateInduction(a->induction_class, TransferMul(a->op_a, b), TransferMul(a->op_b, b)); |
| } |
| } |
| return nullptr; |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferShl(InductionInfo* a, |
| InductionInfo* b, |
| Primitive::Type type) { |
| // Transfer over a shift left: treat shift by restricted constant as equivalent multiplication. |
| int64_t value = -1; |
| if (a != nullptr && IsIntAndGet(b, &value)) { |
| // Obtain the constant needed for the multiplication. This yields an existing instruction |
| // if the constants is already there. Otherwise, this has a side effect on the HIR. |
| // The restriction on the shift factor avoids generating a negative constant |
| // (viz. 1 << 31 and 1L << 63 set the sign bit). The code assumes that generalization |
| // for shift factors outside [0,32) and [0,64) ranges is done by earlier simplification. |
| if ((type == Primitive::kPrimInt && 0 <= value && value < 31) || |
| (type == Primitive::kPrimLong && 0 <= value && value < 63)) { |
| return TransferMul(a, CreateConstant(1 << value, type)); |
| } |
| } |
| return nullptr; |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferNeg(InductionInfo* a) { |
| // Transfer over a unary negation: an invariant, linear, wrap-around, or periodic input |
| // yields a similar but negated induction as result. |
| if (a != nullptr) { |
| if (a->induction_class == kInvariant) { |
| return CreateInvariantOp(kNeg, nullptr, a); |
| } |
| return CreateInduction(a->induction_class, TransferNeg(a->op_a), TransferNeg(a->op_b)); |
| } |
| return nullptr; |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolvePhi(HInstruction* phi, |
| size_t input_index) { |
| // Match all phi inputs from input_index onwards exactly. |
| const size_t count = phi->InputCount(); |
| DCHECK_LT(input_index, count); |
| auto ita = cycle_.find(phi->InputAt(input_index)); |
| if (ita != cycle_.end()) { |
| for (size_t i = input_index + 1; i < count; i++) { |
| auto itb = cycle_.find(phi->InputAt(i)); |
| if (itb == cycle_.end() || |
| !HInductionVarAnalysis::InductionEqual(ita->second, itb->second)) { |
| return nullptr; |
| } |
| } |
| return ita->second; |
| } |
| return nullptr; |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolvePhiAllInputs( |
| HLoopInformation* loop, |
| HInstruction* entry_phi, |
| HInstruction* phi) { |
| // Match all phi inputs. |
| InductionInfo* match = SolvePhi(phi, /* input_index */ 0); |
| if (match != nullptr) { |
| return match; |
| } |
| |
| // Otherwise, try to solve for a periodic seeded from phi onward. |
| // Only tight multi-statement cycles are considered in order to |
| // simplify rotating the periodic during the final classification. |
| if (phi->IsLoopHeaderPhi() && phi->InputCount() == 2) { |
| InductionInfo* a = LookupInfo(loop, phi->InputAt(0)); |
| if (a != nullptr && a->induction_class == kInvariant) { |
| if (phi->InputAt(1) == entry_phi) { |
| InductionInfo* initial = LookupInfo(loop, entry_phi->InputAt(0)); |
| return CreateInduction(kPeriodic, a, initial); |
| } |
| InductionInfo* b = SolvePhi(phi, /* input_index */ 1); |
| if (b != nullptr && b->induction_class == kPeriodic) { |
| return CreateInduction(kPeriodic, a, b); |
| } |
| } |
| } |
| return nullptr; |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolveAddSub(HLoopInformation* loop, |
| HInstruction* entry_phi, |
| HInstruction* instruction, |
| HInstruction* x, |
| HInstruction* y, |
| InductionOp op, |
| bool is_first_call) { |
| // Solve within a cycle over an addition or subtraction: adding or subtracting an |
| // invariant value, seeded from phi, keeps adding to the stride of the induction. |
| InductionInfo* b = LookupInfo(loop, y); |
| if (b != nullptr && b->induction_class == kInvariant) { |
| if (x == entry_phi) { |
| return (op == kAdd) ? b : CreateInvariantOp(kNeg, nullptr, b); |
| } |
| auto it = cycle_.find(x); |
| if (it != cycle_.end()) { |
| InductionInfo* a = it->second; |
| if (a->induction_class == kInvariant) { |
| return CreateInvariantOp(op, a, b); |
| } |
| } |
| } |
| |
| // Try some alternatives before failing. |
| if (op == kAdd) { |
| // Try the other way around for an addition if considered for first time. |
| if (is_first_call) { |
| return SolveAddSub(loop, entry_phi, instruction, y, x, op, false); |
| } |
| } else if (op == kSub) { |
| // Solve within a tight cycle that is formed by exactly two instructions, |
| // one phi and one update, for a periodic idiom of the form k = c - k; |
| if (y == entry_phi && entry_phi->InputCount() == 2 && instruction == entry_phi->InputAt(1)) { |
| InductionInfo* a = LookupInfo(loop, x); |
| if (a != nullptr && a->induction_class == kInvariant) { |
| InductionInfo* initial = LookupInfo(loop, entry_phi->InputAt(0)); |
| return CreateInduction(kPeriodic, CreateInvariantOp(kSub, a, initial), initial); |
| } |
| } |
| } |
| |
| return nullptr; |
| } |
| |
| void HInductionVarAnalysis::VisitControl(HLoopInformation* loop) { |
| HInstruction* control = loop->GetHeader()->GetLastInstruction(); |
| if (control->IsIf()) { |
| HIf* ifs = control->AsIf(); |
| HBasicBlock* if_true = ifs->IfTrueSuccessor(); |
| HBasicBlock* if_false = ifs->IfFalseSuccessor(); |
| HInstruction* if_expr = ifs->InputAt(0); |
| // Determine if loop has following structure in header. |
| // loop-header: .... |
| // if (condition) goto X |
| if (if_expr->IsCondition()) { |
| HCondition* condition = if_expr->AsCondition(); |
| InductionInfo* a = LookupInfo(loop, condition->InputAt(0)); |
| InductionInfo* b = LookupInfo(loop, condition->InputAt(1)); |
| Primitive::Type type = condition->InputAt(0)->GetType(); |
| // Determine if the loop control uses integral arithmetic and an if-exit (X outside) or an |
| // if-iterate (X inside), always expressed as if-iterate when passing into VisitCondition(). |
| if (type != Primitive::kPrimInt && type != Primitive::kPrimLong) { |
| // Loop control is not 32/64-bit integral. |
| } else if (a == nullptr || b == nullptr) { |
| // Loop control is not a sequence. |
| } else if (if_true->GetLoopInformation() != loop && if_false->GetLoopInformation() == loop) { |
| VisitCondition(loop, a, b, type, condition->GetOppositeCondition()); |
| } else if (if_true->GetLoopInformation() == loop && if_false->GetLoopInformation() != loop) { |
| VisitCondition(loop, a, b, type, condition->GetCondition()); |
| } |
| } |
| } |
| } |
| |
| void HInductionVarAnalysis::VisitCondition(HLoopInformation* loop, |
| InductionInfo* a, |
| InductionInfo* b, |
| Primitive::Type type, |
| IfCondition cmp) { |
| if (a->induction_class == kInvariant && b->induction_class == kLinear) { |
| // Swap condition if induction is at right-hand-side (e.g. U > i is same as i < U). |
| switch (cmp) { |
| case kCondLT: VisitCondition(loop, b, a, type, kCondGT); break; |
| case kCondLE: VisitCondition(loop, b, a, type, kCondGE); break; |
| case kCondGT: VisitCondition(loop, b, a, type, kCondLT); break; |
| case kCondGE: VisitCondition(loop, b, a, type, kCondLE); break; |
| case kCondNE: VisitCondition(loop, b, a, type, kCondNE); break; |
| default: break; |
| } |
| } else if (a->induction_class == kLinear && b->induction_class == kInvariant) { |
| // Analyze condition with induction at left-hand-side (e.g. i < U). |
| InductionInfo* lower_expr = a->op_b; |
| InductionInfo* upper_expr = b; |
| InductionInfo* stride = a->op_a; |
| int64_t stride_value = 0; |
| if (!IsIntAndGet(stride, &stride_value)) { |
| return; |
| } |
| // Rewrite condition i != U into i < U or i > U if end condition is reached exactly. |
| if (cmp == kCondNE && ((stride_value == +1 && IsTaken(lower_expr, upper_expr, kCondLT)) || |
| (stride_value == -1 && IsTaken(lower_expr, upper_expr, kCondGT)))) { |
| cmp = stride_value > 0 ? kCondLT : kCondGT; |
| } |
| // Normalize a linear loop control with a nonzero stride: |
| // stride > 0, either i < U or i <= U |
| // stride < 0, either i > U or i >= U |
| if ((stride_value > 0 && (cmp == kCondLT || cmp == kCondLE)) || |
| (stride_value < 0 && (cmp == kCondGT || cmp == kCondGE))) { |
| VisitTripCount(loop, lower_expr, upper_expr, stride, stride_value, type, cmp); |
| } |
| } |
| } |
| |
| void HInductionVarAnalysis::VisitTripCount(HLoopInformation* loop, |
| InductionInfo* lower_expr, |
| InductionInfo* upper_expr, |
| InductionInfo* stride, |
| int64_t stride_value, |
| Primitive::Type type, |
| IfCondition cmp) { |
| // Any loop of the general form: |
| // |
| // for (i = L; i <= U; i += S) // S > 0 |
| // or for (i = L; i >= U; i += S) // S < 0 |
| // .. i .. |
| // |
| // can be normalized into: |
| // |
| // for (n = 0; n < TC; n++) // where TC = (U + S - L) / S |
| // .. L + S * n .. |
| // |
| // taking the following into consideration: |
| // |
| // (1) Using the same precision, the TC (trip-count) expression should be interpreted as |
| // an unsigned entity, for example, as in the following loop that uses the full range: |
| // for (int i = INT_MIN; i < INT_MAX; i++) // TC = UINT_MAX |
| // (2) The TC is only valid if the loop is taken, otherwise TC = 0, as in: |
| // for (int i = 12; i < U; i++) // TC = 0 when U >= 12 |
| // If this cannot be determined at compile-time, the TC is only valid within the |
| // loop-body proper, not the loop-header unless enforced with an explicit condition. |
| // (3) The TC is only valid if the loop is finite, otherwise TC has no value, as in: |
| // for (int i = 0; i <= U; i++) // TC = Inf when U = INT_MAX |
| // If this cannot be determined at compile-time, the TC is only valid when enforced |
| // with an explicit condition. |
| // (4) For loops which early-exits, the TC forms an upper bound, as in: |
| // for (int i = 0; i < 10 && ....; i++) // TC <= 10 |
| const bool is_taken = IsTaken(lower_expr, upper_expr, cmp); |
| const bool is_finite = IsFinite(upper_expr, stride_value, type, cmp); |
| const bool cancels = (cmp == kCondLT || cmp == kCondGT) && std::abs(stride_value) == 1; |
| if (!cancels) { |
| // Convert exclusive integral inequality into inclusive integral inequality, |
| // viz. condition i < U is i <= U - 1 and condition i > U is i >= U + 1. |
| if (cmp == kCondLT) { |
| upper_expr = CreateInvariantOp(kSub, upper_expr, CreateConstant(1, type)); |
| } else if (cmp == kCondGT) { |
| upper_expr = CreateInvariantOp(kAdd, upper_expr, CreateConstant(1, type)); |
| } |
| // Compensate for stride. |
| upper_expr = CreateInvariantOp(kAdd, upper_expr, stride); |
| } |
| InductionInfo* trip_count |
| = CreateInvariantOp(kDiv, CreateInvariantOp(kSub, upper_expr, lower_expr), stride); |
| // Assign the trip-count expression to the loop control. Clients that use the information |
| // should be aware that the expression is only valid under the conditions listed above. |
| InductionOp tcKind = kTripCountInBodyUnsafe; |
| if (is_taken && is_finite) { |
| tcKind = kTripCountInLoop; |
| } else if (is_finite) { |
| tcKind = kTripCountInBody; |
| } else if (is_taken) { |
| tcKind = kTripCountInLoopUnsafe; |
| } |
| AssignInfo(loop, loop->GetHeader()->GetLastInstruction(), CreateTripCount(tcKind, trip_count)); |
| } |
| |
| bool HInductionVarAnalysis::IsTaken(InductionInfo* lower_expr, |
| InductionInfo* upper_expr, |
| IfCondition cmp) { |
| int64_t lower_value; |
| int64_t upper_value; |
| if (IsIntAndGet(lower_expr, &lower_value) && IsIntAndGet(upper_expr, &upper_value)) { |
| switch (cmp) { |
| case kCondLT: return lower_value < upper_value; |
| case kCondLE: return lower_value <= upper_value; |
| case kCondGT: return lower_value > upper_value; |
| case kCondGE: return lower_value >= upper_value; |
| case kCondEQ: |
| case kCondNE: LOG(FATAL) << "CONDITION UNREACHABLE"; |
| } |
| } |
| return false; // not certain, may be untaken |
| } |
| |
| bool HInductionVarAnalysis::IsFinite(InductionInfo* upper_expr, |
| int64_t stride_value, |
| Primitive::Type type, |
| IfCondition cmp) { |
| const int64_t min = type == Primitive::kPrimInt |
| ? std::numeric_limits<int32_t>::min() |
| : std::numeric_limits<int64_t>::min(); |
| const int64_t max = type == Primitive::kPrimInt |
| ? std::numeric_limits<int32_t>::max() |
| : std::numeric_limits<int64_t>::max(); |
| // Some rules under which it is certain at compile-time that the loop is finite. |
| int64_t value; |
| switch (cmp) { |
| case kCondLT: |
| return stride_value == 1 || |
| (IsIntAndGet(upper_expr, &value) && value <= (max - stride_value + 1)); |
| case kCondLE: |
| return (IsIntAndGet(upper_expr, &value) && value <= (max - stride_value)); |
| case kCondGT: |
| return stride_value == -1 || |
| (IsIntAndGet(upper_expr, &value) && value >= (min - stride_value - 1)); |
| case kCondGE: |
| return (IsIntAndGet(upper_expr, &value) && value >= (min - stride_value)); |
| case kCondEQ: |
| case kCondNE: LOG(FATAL) << "CONDITION UNREACHABLE"; |
| } |
| return false; // not certain, may be infinite |
| } |
| |
| void HInductionVarAnalysis::AssignInfo(HLoopInformation* loop, |
| HInstruction* instruction, |
| InductionInfo* info) { |
| auto it = induction_.find(loop); |
| if (it == induction_.end()) { |
| it = induction_.Put(loop, |
| ArenaSafeMap<HInstruction*, InductionInfo*>( |
| std::less<HInstruction*>(), |
| graph_->GetArena()->Adapter(kArenaAllocInductionVarAnalysis))); |
| } |
| it->second.Put(instruction, info); |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::LookupInfo(HLoopInformation* loop, |
| HInstruction* instruction) { |
| auto it = induction_.find(loop); |
| if (it != induction_.end()) { |
| auto loop_it = it->second.find(instruction); |
| if (loop_it != it->second.end()) { |
| return loop_it->second; |
| } |
| } |
| if (IsLoopInvariant(loop, instruction)) { |
| InductionInfo* info = CreateInvariantFetch(instruction); |
| AssignInfo(loop, instruction, info); |
| return info; |
| } |
| return nullptr; |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::CreateConstant(int64_t value, |
| Primitive::Type type) { |
| if (type == Primitive::kPrimInt) { |
| return CreateInvariantFetch(graph_->GetIntConstant(value)); |
| } |
| DCHECK_EQ(type, Primitive::kPrimLong); |
| return CreateInvariantFetch(graph_->GetLongConstant(value)); |
| } |
| |
| HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::CreateSimplifiedInvariant( |
| InductionOp op, |
| InductionInfo* a, |
| InductionInfo* b) { |
| // Perform some light-weight simplifications during construction of a new invariant. |
| // This often safes memory and yields a more concise representation of the induction. |
| // More exhaustive simplifications are done by later phases once induction nodes are |
| // translated back into HIR code (e.g. by loop optimizations or BCE). |
| int64_t value = -1; |
| if (IsIntAndGet(a, &value)) { |
| if (value == 0) { |
| // Simplify 0 + b = b, 0 * b = 0. |
| if (op == kAdd) { |
| return b; |
| } else if (op == kMul) { |
| return a; |
| } |
| } else if (op == kMul) { |
| // Simplify 1 * b = b, -1 * b = -b |
| if (value == 1) { |
| return b; |
| } else if (value == -1) { |
| op = kNeg; |
| a = nullptr; |
| } |
| } |
| } |
| if (IsIntAndGet(b, &value)) { |
| if (value == 0) { |
| // Simplify a + 0 = a, a - 0 = a, a * 0 = 0, -0 = 0. |
| if (op == kAdd || op == kSub) { |
| return a; |
| } else if (op == kMul || op == kNeg) { |
| return b; |
| } |
| } else if (op == kMul || op == kDiv) { |
| // Simplify a * 1 = a, a / 1 = a, a * -1 = -a, a / -1 = -a |
| if (value == 1) { |
| return a; |
| } else if (value == -1) { |
| op = kNeg; |
| b = a; |
| a = nullptr; |
| } |
| } |
| } else if (b->operation == kNeg) { |
| // Simplify a + (-b) = a - b, a - (-b) = a + b, -(-b) = b. |
| if (op == kAdd) { |
| op = kSub; |
| b = b->op_b; |
| } else if (op == kSub) { |
| op = kAdd; |
| b = b->op_b; |
| } else if (op == kNeg) { |
| return b->op_b; |
| } |
| } |
| return new (graph_->GetArena()) InductionInfo(kInvariant, op, a, b, nullptr); |
| } |
| |
| bool HInductionVarAnalysis::InductionEqual(InductionInfo* info1, |
| InductionInfo* info2) { |
| // Test structural equality only, without accounting for simplifications. |
| if (info1 != nullptr && info2 != nullptr) { |
| return |
| info1->induction_class == info2->induction_class && |
| info1->operation == info2->operation && |
| info1->fetch == info2->fetch && |
| InductionEqual(info1->op_a, info2->op_a) && |
| InductionEqual(info1->op_b, info2->op_b); |
| } |
| // Otherwise only two nullptrs are considered equal. |
| return info1 == info2; |
| } |
| |
| bool HInductionVarAnalysis::IsIntAndGet(InductionInfo* info, int64_t* value) { |
| if (info != nullptr && info->induction_class == kInvariant) { |
| // A direct constant fetch. |
| if (info->operation == kFetch) { |
| DCHECK(info->fetch); |
| if (info->fetch->IsIntConstant()) { |
| *value = info->fetch->AsIntConstant()->GetValue(); |
| return true; |
| } else if (info->fetch->IsLongConstant()) { |
| *value = info->fetch->AsLongConstant()->GetValue(); |
| return true; |
| } |
| } |
| // Use range analysis to resolve compound values. |
| int32_t range_value; |
| if (InductionVarRange::GetConstant(info, &range_value)) { |
| *value = range_value; |
| return true; |
| } |
| } |
| return false; |
| } |
| |
| std::string HInductionVarAnalysis::InductionToString(InductionInfo* info) { |
| if (info != nullptr) { |
| if (info->induction_class == kInvariant) { |
| int64_t value = -1; |
| std::string inv = "("; |
| inv += InductionToString(info->op_a); |
| switch (info->operation) { |
| case kNop: inv += " @ "; break; |
| case kAdd: inv += " + "; break; |
| case kSub: |
| case kNeg: inv += " - "; break; |
| case kMul: inv += " * "; break; |
| case kDiv: inv += " / "; break; |
| case kFetch: |
| DCHECK(info->fetch); |
| if (IsIntAndGet(info, &value)) { |
| inv += std::to_string(value); |
| } else { |
| inv += std::to_string(info->fetch->GetId()) + ":" + info->fetch->DebugName(); |
| } |
| break; |
| case kTripCountInLoop: inv += "TC-loop:"; break; |
| case kTripCountInBody: inv += "TC-body:"; break; |
| case kTripCountInLoopUnsafe: inv += "TC-loop-unsafe:"; break; |
| case kTripCountInBodyUnsafe: inv += "TC-body-unsafe:"; break; |
| } |
| inv += InductionToString(info->op_b); |
| return inv + ")"; |
| } else { |
| DCHECK(info->operation == kNop); |
| if (info->induction_class == kLinear) { |
| return "(" + InductionToString(info->op_a) + " * i + " + |
| InductionToString(info->op_b) + ")"; |
| } else if (info->induction_class == kWrapAround) { |
| return "wrap(" + InductionToString(info->op_a) + ", " + |
| InductionToString(info->op_b) + ")"; |
| } else if (info->induction_class == kPeriodic) { |
| return "periodic(" + InductionToString(info->op_a) + ", " + |
| InductionToString(info->op_b) + ")"; |
| } |
| } |
| } |
| return ""; |
| } |
| |
| } // namespace art |