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LeafOS / LeafOS-Project / android_art / 11c8959243751f7a8946bae40f4346bc8d00cea4 / . / compiler / optimizing / induction_var_analysis.cc
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/*
* 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 "base/scoped_arena_containers.h"
#include "induction_var_range.h"
namespace art HIDDEN {
/**
* Returns true if the from/to types denote a narrowing, integral conversion (precision loss).
*/
static bool IsNarrowingIntegralConversion(DataType::Type from, DataType::Type to) {
switch (from) {
case DataType::Type::kInt64:
return to == DataType::Type::kUint8 ||
to == DataType::Type::kInt8 ||
to == DataType::Type::kUint16 ||
to == DataType::Type::kInt16 ||
to == DataType::Type::kInt32;
case DataType::Type::kInt32:
return to == DataType::Type::kUint8 ||
to == DataType::Type::kInt8 ||
to == DataType::Type::kUint16 ||
to == DataType::Type::kInt16;
case DataType::Type::kUint16:
case DataType::Type::kInt16:
return to == DataType::Type::kUint8 || to == DataType::Type::kInt8;
default:
return false;
}
}
/**
* Returns result of implicit widening type conversion done in HIR.
*/
static DataType::Type ImplicitConversion(DataType::Type type) {
switch (type) {
case DataType::Type::kBool:
case DataType::Type::kUint8:
case DataType::Type::kInt8:
case DataType::Type::kUint16:
case DataType::Type::kInt16:
return DataType::Type::kInt32;
default:
return type;
}
}
/**
* Returns true if loop is guarded by "a cmp b" on entry.
*/
static bool IsGuardedBy(const HLoopInformation* loop,
IfCondition cmp,
HInstruction* a,
HInstruction* b) {
// Chase back through straightline code to the first potential
// block that has a control dependence.
// guard: if (x) bypass
// |
// entry: straightline code
// |
// preheader
// |
// header
HBasicBlock* guard = loop->GetPreHeader();
HBasicBlock* entry = loop->GetHeader();
while (guard->GetPredecessors().size() == 1 &&
guard->GetSuccessors().size() == 1) {
entry = guard;
guard = guard->GetSinglePredecessor();
}
// Find guard.
HInstruction* control = guard->GetLastInstruction();
if (!control->IsIf()) {
return false;
}
HIf* ifs = control->AsIf();
HInstruction* if_expr = ifs->InputAt(0);
if (if_expr->IsCondition()) {
IfCondition other_cmp = ifs->IfTrueSuccessor() == entry
? if_expr->AsCondition()->GetCondition()
: if_expr->AsCondition()->GetOppositeCondition();
if (if_expr->InputAt(0) == a && if_expr->InputAt(1) == b) {
return cmp == other_cmp;
} else if (if_expr->InputAt(1) == a && if_expr->InputAt(0) == b) {
switch (cmp) {
case kCondLT: return other_cmp == kCondGT;
case kCondLE: return other_cmp == kCondGE;
case kCondGT: return other_cmp == kCondLT;
case kCondGE: return other_cmp == kCondLE;
default: LOG(FATAL) << "unexpected cmp: " << cmp;
}
}
}
return false;
}
/* Finds first loop header phi use. */
HInstruction* FindFirstLoopHeaderPhiUse(const HLoopInformation* loop, HInstruction* instruction) {
for (const HUseListNode<HInstruction*>& use : instruction->GetUses()) {
if (use.GetUser()->GetBlock() == loop->GetHeader() &&
use.GetUser()->IsPhi() &&
use.GetUser()->InputAt(1) == instruction) {
return use.GetUser();
}
}
return nullptr;
}
/**
* Relinks the Phi structure after break-loop rewriting.
*/
static bool FixOutsideUse(const HLoopInformation* loop,
HInstruction* instruction,
HInstruction* replacement,
bool rewrite) {
// Deal with regular uses.
const HUseList<HInstruction*>& uses = instruction->GetUses();
for (auto it = uses.begin(), end = uses.end(); it != end; ) {
HInstruction* user = it->GetUser();
size_t index = it->GetIndex();
++it; // increment prior to potential removal
if (user->GetBlock()->GetLoopInformation() != loop) {
if (replacement == nullptr) {
return false;
} else if (rewrite) {
user->ReplaceInput(replacement, index);
}
}
}
// Deal with environment uses.
const HUseList<HEnvironment*>& env_uses = instruction->GetEnvUses();
for (auto it = env_uses.begin(), end = env_uses.end(); it != end;) {
HEnvironment* user = it->GetUser();
size_t index = it->GetIndex();
++it; // increment prior to potential removal
if (user->GetHolder()->GetBlock()->GetLoopInformation() != loop) {
if (replacement == nullptr) {
return false;
} else if (rewrite) {
user->ReplaceInput(replacement, index);
}
}
}
return true;
}
/**
* Test and rewrite the loop body of a break-loop. Returns true on success.
*/
static bool RewriteBreakLoopBody(const HLoopInformation* loop,
HBasicBlock* body,
HInstruction* cond,
HInstruction* index,
HInstruction* upper,
bool rewrite) {
// Deal with Phis. Outside use prohibited, except for index (which gets exit value).
for (HInstructionIterator it(loop->GetHeader()->GetPhis()); !it.Done(); it.Advance()) {
HInstruction* exit_value = it.Current() == index ? upper : nullptr;
if (!FixOutsideUse(loop, it.Current(), exit_value, rewrite)) {
return false;
}
}
// Deal with other statements in header.
for (HInstruction* m = cond->GetPrevious(); m && !m->IsSuspendCheck();) {
HInstruction* p = m->GetPrevious();
if (rewrite) {
m->MoveBefore(body->GetFirstInstruction(), false);
}
if (!FixOutsideUse(loop, m, FindFirstLoopHeaderPhiUse(loop, m), rewrite)) {
return false;
}
m = p;
}
return true;
}
//
// Class members.
//
struct HInductionVarAnalysis::NodeInfo {
explicit NodeInfo(uint32_t d) : depth(d), done(false) {}
uint32_t depth;
bool done;
};
struct HInductionVarAnalysis::StackEntry {
StackEntry(HInstruction* insn, NodeInfo* info, size_t link = std::numeric_limits<size_t>::max())
: instruction(insn),
node_info(info),
user_link(link),
num_visited_inputs(0u),
low_depth(info->depth) {}
HInstruction* instruction;
NodeInfo* node_info;
size_t user_link; // Stack index of the user that is visiting this input.
size_t num_visited_inputs;
size_t low_depth;
};
HInductionVarAnalysis::HInductionVarAnalysis(HGraph* graph,
OptimizingCompilerStats* stats,
const char* name)
: HOptimization(graph, name, stats),
induction_(std::less<const HLoopInformation*>(),
graph->GetAllocator()->Adapter(kArenaAllocInductionVarAnalysis)),
cycles_(std::less<HPhi*>(), graph->GetAllocator()->Adapter(kArenaAllocInductionVarAnalysis)) {
}
bool HInductionVarAnalysis::Run() {
// Detects sequence variables (generalized induction variables) during an outer to inner
// traversal of all loops using Gerlek's algorithm. The order is important to enable
// range analysis on outer loop while visiting inner loops.
if (IsPathologicalCase()) {
MaybeRecordStat(stats_, MethodCompilationStat::kNotVarAnalyzedPathological);
return false;
}
for (HBasicBlock* graph_block : graph_->GetReversePostOrder()) {
// Don't analyze irreducible loops.
if (graph_block->IsLoopHeader() && !graph_block->GetLoopInformation()->IsIrreducible()) {
VisitLoop(graph_block->GetLoopInformation());
}
}
return !induction_.empty();
}
void HInductionVarAnalysis::VisitLoop(const HLoopInformation* loop) {
ScopedArenaAllocator local_allocator(graph_->GetArenaStack());
ScopedArenaSafeMap<HInstruction*, NodeInfo> visited_instructions(
std::less<HInstruction*>(), local_allocator.Adapter(kArenaAllocInductionVarAnalysis));
// 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".
size_t global_depth = 0;
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 visited later.
}
// Visit phi-operations and instructions.
for (HInstructionIterator it(loop_block->GetPhis()); !it.Done(); it.Advance()) {
global_depth = TryVisitNodes(loop, it.Current(), global_depth, &visited_instructions);
}
for (HInstructionIterator it(loop_block->GetInstructions()); !it.Done(); it.Advance()) {
global_depth = TryVisitNodes(loop, it.Current(), global_depth, &visited_instructions);
}
}
// Determine the loop's trip-count.
VisitControl(loop);
}
size_t HInductionVarAnalysis::TryVisitNodes(
const HLoopInformation* loop,
HInstruction* start_instruction,
size_t global_depth,
/*inout*/ ScopedArenaSafeMap<HInstruction*, NodeInfo>* visited_instructions) {
// This is recursion-free version of the SCC search algorithm. We have limited stack space,
// so recursion with the depth dependent on the input is undesirable as such depth is unlimited.
auto [it, inserted] =
visited_instructions->insert(std::make_pair(start_instruction, NodeInfo(global_depth + 1u)));
if (!inserted) {
return global_depth;
}
NodeInfo* start_info = &it->second;
++global_depth;
DCHECK_EQ(global_depth, start_info->depth);
ScopedArenaVector<StackEntry> stack(visited_instructions->get_allocator());
stack.push_back({start_instruction, start_info});
size_t current_entry = 0u;
while (!stack.empty()) {
StackEntry& entry = stack[current_entry];
// Look for unvisited inputs (also known as "descentants").
bool visit_input = false;
auto inputs = entry.instruction->GetInputs();
while (entry.num_visited_inputs != inputs.size()) {
HInstruction* input = inputs[entry.num_visited_inputs];
++entry.num_visited_inputs;
// If the definition is either outside the loop (loop invariant entry value)
// or assigned in inner loop (inner exit value), the input is not visited.
if (input->GetBlock()->GetLoopInformation() != loop) {
continue;
}
// Try visiting the input. If already visited, update `entry.low_depth`.
auto [input_it, input_inserted] =
visited_instructions->insert(std::make_pair(input, NodeInfo(global_depth + 1u)));
NodeInfo* input_info = &input_it->second;
if (input_inserted) {
// Push the input on the `stack` and visit it now.
++global_depth;
DCHECK_EQ(global_depth, input_info->depth);
stack.push_back({input, input_info, current_entry});
current_entry = stack.size() - 1u;
visit_input = true;
break;
} else if (!input_info->done && input_info->depth < entry.low_depth) {
entry.low_depth = input_it->second.depth;
}
continue;
}
if (visit_input) {
continue; // Process the new top of the stack.
}
// All inputs of the current node have been visited.
// Check if we have found an input below this entry on the stack.
DCHECK(!entry.node_info->done);
size_t previous_entry = entry.user_link;
if (entry.node_info->depth > entry.low_depth) {
DCHECK_LT(previous_entry, current_entry) << entry.node_info->depth << " " << entry.low_depth;
entry.node_info->depth = entry.low_depth;
if (stack[previous_entry].low_depth > entry.low_depth) {
stack[previous_entry].low_depth = entry.low_depth;
}
} else {
// Classify the SCC we have just found.
ArrayRef<StackEntry> stack_tail = ArrayRef<StackEntry>(stack).SubArray(current_entry);
for (StackEntry& tail_entry : stack_tail) {
tail_entry.node_info->done = true;
}
if (current_entry + 1u == stack.size() && !entry.instruction->IsLoopHeaderPhi()) {
ClassifyTrivial(loop, entry.instruction);
} else {
ClassifyNonTrivial(loop, ArrayRef<const StackEntry>(stack_tail));
}
stack.erase(stack.begin() + current_entry, stack.end());
}
current_entry = previous_entry;
}
return global_depth;
}
/**
* 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 loop-phi is rotated to the front. We do that
* as we extract the SCC instructions.
*/
void HInductionVarAnalysis::ExtractScc(ArrayRef<const StackEntry> stack_tail,
ScopedArenaVector<HInstruction*>* scc) {
// Find very first loop-phi.
HInstruction* phi = nullptr;
size_t split_pos = 0;
const size_t size = stack_tail.size();
for (size_t i = 0; i != size; ++i) {
const StackEntry& entry = stack_tail[i];
HInstruction* instruction = entry.instruction;
if (instruction->IsLoopHeaderPhi()) {
// All loop Phis in SCC come from the same loop header.
HBasicBlock* block = instruction->GetBlock();
DCHECK(block->GetLoopInformation()->GetHeader() == block);
DCHECK(phi == nullptr || phi->GetBlock() == block);
if (phi == nullptr || block->GetPhis().FoundBefore(instruction, phi)) {
phi = instruction;
split_pos = i + 1u;
}
}
}
// Extract SCC in two chunks.
DCHECK(scc->empty());
scc->reserve(size);
for (const StackEntry& entry : ReverseRange(stack_tail.SubArray(/*pos=*/ 0u, split_pos))) {
scc->push_back(entry.instruction);
}
for (const StackEntry& entry : ReverseRange(stack_tail.SubArray(/*pos=*/ split_pos))) {
scc->push_back(entry.instruction);
}
DCHECK_EQ(scc->size(), stack_tail.size());
}
void HInductionVarAnalysis::ClassifyTrivial(const HLoopInformation* loop,
HInstruction* instruction) {
const HBasicBlock* context = instruction->GetBlock();
DataType::Type type = instruction->GetType();
InductionInfo* info = nullptr;
if (instruction->IsPhi()) {
info = TransferPhi(loop, instruction, /*input_index*/ 0, /*adjust_input_size*/ 0);
} else if (instruction->IsAdd()) {
info = TransferAddSub(context,
loop,
LookupInfo(loop, instruction->InputAt(0)),
LookupInfo(loop, instruction->InputAt(1)),
kAdd,
type);
} else if (instruction->IsSub()) {
info = TransferAddSub(context,
loop,
LookupInfo(loop, instruction->InputAt(0)),
LookupInfo(loop, instruction->InputAt(1)),
kSub,
type);
} else if (instruction->IsNeg()) {
info = TransferNeg(context, loop, LookupInfo(loop, instruction->InputAt(0)), type);
} else if (instruction->IsMul()) {
info = TransferMul(context,
loop,
LookupInfo(loop, instruction->InputAt(0)),
LookupInfo(loop, instruction->InputAt(1)),
type);
} else if (instruction->IsShl()) {
HInstruction* mulc = GetShiftConstant(loop, instruction, /*initial*/ nullptr);
if (mulc != nullptr) {
info = TransferMul(context,
loop,
LookupInfo(loop, instruction->InputAt(0)),
LookupInfo(loop, mulc),
type);
}
} else if (instruction->IsSelect()) {
info = TransferPhi(loop, instruction, /*input_index*/ 0, /*adjust_input_size*/ 1);
} else if (instruction->IsTypeConversion()) {
info = TransferConversion(LookupInfo(loop, instruction->InputAt(0)),
instruction->AsTypeConversion()->GetInputType(),
instruction->AsTypeConversion()->GetResultType());
} else if (instruction->IsBoundsCheck()) {
info = LookupInfo(loop, instruction->InputAt(0)); // Pass-through.
}
// Successfully classified?
if (info != nullptr) {
AssignInfo(loop, instruction, info);
}
}
void HInductionVarAnalysis::ClassifyNonTrivial(const HLoopInformation* loop,
ArrayRef<const StackEntry> stack_tail) {
const size_t size = stack_tail.size();
DCHECK_GE(size, 1u);
DataType::Type type = stack_tail.back().instruction->GetType();
ScopedArenaAllocator local_allocator(graph_->GetArenaStack());
ScopedArenaVector<HInstruction*> scc(local_allocator.Adapter(kArenaAllocInductionVarAnalysis));
ExtractScc(ArrayRef<const StackEntry>(stack_tail), &scc);
// Analyze from loop-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;
}
// Store interesting cycle in each loop phi.
for (size_t i = 0; i < size; i++) {
if (scc[i]->IsLoopHeaderPhi()) {
AssignCycle(scc[i]->AsPhi(), ArrayRef<HInstruction* const>(scc));
}
}
// Singleton is wrap-around induction if all internal links have the same meaning.
if (size == 1) {
InductionInfo* update = TransferPhi(loop, phi, /*input_index*/ 1, /*adjust_input_size*/ 0);
if (update != nullptr) {
AssignInfo(loop, phi, CreateInduction(kWrapAround,
kNop,
initial,
update,
/*fetch*/ nullptr,
type));
}
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.
ScopedArenaSafeMap<HInstruction*, InductionInfo*> cycle(
std::less<HInstruction*>(), local_allocator.Adapter(kArenaAllocInductionVarAnalysis));
for (size_t i = 1; i < size; i++) {
HInstruction* instruction = scc[i];
InductionInfo* update = nullptr;
if (instruction->IsPhi()) {
update = SolvePhiAllInputs(loop, phi, instruction, cycle, type);
} else if (instruction->IsAdd()) {
update = SolveAddSub(loop,
phi,
instruction,
instruction->InputAt(0),
instruction->InputAt(1),
kAdd,
cycle,
type);
} else if (instruction->IsSub()) {
update = SolveAddSub(loop,
phi,
instruction,
instruction->InputAt(0),
instruction->InputAt(1),
kSub,
cycle,
type);
} else if (instruction->IsMul()) {
update = SolveOp(
loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kMul, type);
} else if (instruction->IsDiv()) {
update = SolveOp(
loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kDiv, type);
} else if (instruction->IsRem()) {
update = SolveOp(
loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kRem, type);
} else if (instruction->IsShl()) {
HInstruction* mulc = GetShiftConstant(loop, instruction, /*initial*/ nullptr);
if (mulc != nullptr) {
update = SolveOp(loop, phi, instruction, instruction->InputAt(0), mulc, kMul, type);
}
} else if (instruction->IsShr() || instruction->IsUShr()) {
HInstruction* divc = GetShiftConstant(loop, instruction, initial);
if (divc != nullptr) {
update = SolveOp(loop, phi, instruction, instruction->InputAt(0), divc, kDiv, type);
}
} else if (instruction->IsXor()) {
update = SolveOp(
loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kXor, type);
} else if (instruction->IsEqual()) {
update = SolveTest(loop, phi, instruction, /*opposite_value=*/ 0, type);
} else if (instruction->IsNotEqual()) {
update = SolveTest(loop, phi, instruction, /*opposite_value=*/ 1, type);
} else if (instruction->IsSelect()) {
// Select acts like Phi.
update = SolvePhi(instruction, /*input_index=*/ 0, /*adjust_input_size=*/ 1, cycle);
} else if (instruction->IsTypeConversion()) {
update = SolveConversion(loop, phi, instruction->AsTypeConversion(), cycle, &type);
}
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, /*adjust_input_size=*/ 0, cycle);
if (induction != nullptr) {
switch (induction->induction_class) {
case kInvariant:
// Construct combined stride of the linear induction.
induction = CreateInduction(kLinear, kNop, induction, initial, /*fetch*/ nullptr, type);
FALLTHROUGH_INTENDED;
case kPolynomial:
case kGeometric:
case kWrapAround:
// Classify first phi and then the rest of the cycle "on-demand".
// Statements are scanned in order.
AssignInfo(loop, phi, induction);
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, type);
}
AssignInfo(loop, phi, induction);
break;
default:
break;
}
}
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::RotatePeriodicInduction(
InductionInfo* induction,
InductionInfo* last,
DataType::Type type) {
// 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,
kNop,
induction,
last,
/*fetch*/ nullptr,
type);
}
return CreateInduction(kPeriodic,
kNop,
induction->op_a,
RotatePeriodicInduction(induction->op_b, last, type),
/*fetch*/ nullptr,
type);
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferPhi(
const HLoopInformation* loop,
HInstruction* phi,
size_t input_index,
size_t adjust_input_size) {
// Match all phi inputs from input_index onwards exactly.
HInputsRef inputs = phi->GetInputs();
DCHECK_LT(input_index, inputs.size());
InductionInfo* a = LookupInfo(loop, inputs[input_index]);
for (size_t i = input_index + 1, n = inputs.size() - adjust_input_size; i < n; i++) {
InductionInfo* b = LookupInfo(loop, inputs[i]);
if (!InductionEqual(a, b)) {
return nullptr;
}
}
return a;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferAddSub(
const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* a,
InductionInfo* b,
InductionOp op,
DataType::Type type) {
// Transfer over an addition or subtraction: any invariant, linear, polynomial, geometric,
// wrap-around, or periodic can be combined with an invariant to yield a similar result.
// Two linear or two polynomial inputs can be combined too. Other combinations fail.
if (a != nullptr && b != nullptr) {
if (IsNarrowingLinear(a) || IsNarrowingLinear(b)) {
return nullptr; // no transfer
} else if (a->induction_class == kInvariant && b->induction_class == kInvariant) {
return CreateInvariantOp(context, loop, op, a, b); // direct invariant
} else if ((a->induction_class == kLinear && b->induction_class == kLinear) ||
(a->induction_class == kPolynomial && b->induction_class == kPolynomial)) {
// Rule induc(a, b) + induc(a', b') -> induc(a + a', b + b').
InductionInfo* new_a = TransferAddSub(context, loop, a->op_a, b->op_a, op, type);
InductionInfo* new_b = TransferAddSub(context, loop, a->op_b, b->op_b, op, type);
if (new_a != nullptr && new_b != nullptr) {
return CreateInduction(a->induction_class, a->operation, new_a, new_b, a->fetch, type);
}
} else if (a->induction_class == kInvariant) {
// Rule a + induc(a', b') -> induc(a', a + b') or induc(a + a', a + b').
InductionInfo* new_a = b->op_a;
InductionInfo* new_b = TransferAddSub(context, loop, a, b->op_b, op, type);
if (b->induction_class == kWrapAround || b->induction_class == kPeriodic) {
new_a = TransferAddSub(context, loop, a, new_a, op, type);
} else if (op == kSub) { // Negation required.
new_a = TransferNeg(context, loop, new_a, type);
}
if (new_a != nullptr && new_b != nullptr) {
return CreateInduction(b->induction_class, b->operation, new_a, new_b, b->fetch, type);
}
} else if (b->induction_class == kInvariant) {
// Rule induc(a, b) + b' -> induc(a, b + b') or induc(a + b', b + b').
InductionInfo* new_a = a->op_a;
InductionInfo* new_b = TransferAddSub(context, loop, a->op_b, b, op, type);
if (a->induction_class == kWrapAround || a->induction_class == kPeriodic) {
new_a = TransferAddSub(context, loop, new_a, b, op, type);
}
if (new_a != nullptr && new_b != nullptr) {
return CreateInduction(a->induction_class, a->operation, new_a, new_b, a->fetch, type);
}
}
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferNeg(
const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* a,
DataType::Type type) {
// Transfer over a unary negation: an invariant, linear, polynomial, geometric (mul),
// wrap-around, or periodic input yields a similar but negated induction as result.
if (a != nullptr) {
if (IsNarrowingLinear(a)) {
return nullptr; // no transfer
} else if (a->induction_class == kInvariant) {
return CreateInvariantOp(context, loop, kNeg, nullptr, a); // direct invariant
} else if (a->induction_class != kGeometric || a->operation == kMul) {
// Rule - induc(a, b) -> induc(-a, -b).
InductionInfo* new_a = TransferNeg(context, loop, a->op_a, type);
InductionInfo* new_b = TransferNeg(context, loop, a->op_b, type);
if (new_a != nullptr && new_b != nullptr) {
return CreateInduction(a->induction_class, a->operation, new_a, new_b, a->fetch, type);
}
}
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferMul(
const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* a,
InductionInfo* b,
DataType::Type type) {
// Transfer over a multiplication: any invariant, linear, polynomial, geometric (mul),
// 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 (IsNarrowingLinear(a) || IsNarrowingLinear(b)) {
return nullptr; // no transfer
} else if (a->induction_class == kInvariant && b->induction_class == kInvariant) {
return CreateInvariantOp(context, loop, kMul, a, b); // direct invariant
} else if (a->induction_class == kInvariant && (b->induction_class != kGeometric ||
b->operation == kMul)) {
// Rule a * induc(a', b') -> induc(a * a', b * b').
InductionInfo* new_a = TransferMul(context, loop, a, b->op_a, type);
InductionInfo* new_b = TransferMul(context, loop, a, b->op_b, type);
if (new_a != nullptr && new_b != nullptr) {
return CreateInduction(b->induction_class, b->operation, new_a, new_b, b->fetch, type);
}
} else if (b->induction_class == kInvariant && (a->induction_class != kGeometric ||
a->operation == kMul)) {
// Rule induc(a, b) * b' -> induc(a * b', b * b').
InductionInfo* new_a = TransferMul(context, loop, a->op_a, b, type);
InductionInfo* new_b = TransferMul(context, loop, a->op_b, b, type);
if (new_a != nullptr && new_b != nullptr) {
return CreateInduction(a->induction_class, a->operation, new_a, new_b, a->fetch, type);
}
}
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferConversion(
InductionInfo* a,
DataType::Type from,
DataType::Type to) {
if (a != nullptr) {
// Allow narrowing conversion on linear induction in certain cases:
// induction is already at narrow type, or can be made narrower.
if (IsNarrowingIntegralConversion(from, to) &&
a->induction_class == kLinear &&
(a->type == to || IsNarrowingIntegralConversion(a->type, to))) {
return CreateInduction(kLinear, kNop, a->op_a, a->op_b, a->fetch, to);
}
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolvePhi(
HInstruction* phi,
size_t input_index,
size_t adjust_input_size,
const ScopedArenaSafeMap<HInstruction*, InductionInfo*>& cycle) {
// Match all phi inputs from input_index onwards exactly.
HInputsRef inputs = phi->GetInputs();
DCHECK_LT(input_index, inputs.size());
auto ita = cycle.find(inputs[input_index]);
if (ita != cycle.end()) {
for (size_t i = input_index + 1, n = inputs.size() - adjust_input_size; i < n; i++) {
auto itb = cycle.find(inputs[i]);
if (itb == cycle.end() ||
!HInductionVarAnalysis::InductionEqual(ita->second, itb->second)) {
return nullptr;
}
}
return ita->second;
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolvePhiAllInputs(
const HLoopInformation* loop,
HInstruction* entry_phi,
HInstruction* phi,
const ScopedArenaSafeMap<HInstruction*, InductionInfo*>& cycle,
DataType::Type type) {
// Match all phi inputs.
InductionInfo* match = SolvePhi(phi, /*input_index=*/ 0, /*adjust_input_size=*/ 0, cycle);
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, kNop, a, initial, /*fetch*/ nullptr, type);
}
InductionInfo* b = SolvePhi(phi, /*input_index=*/ 1, /*adjust_input_size=*/ 0, cycle);
if (b != nullptr && b->induction_class == kPeriodic) {
return CreateInduction(kPeriodic, kNop, a, b, /*fetch*/ nullptr, type);
}
}
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolveAddSub(
const HLoopInformation* loop,
HInstruction* entry_phi,
HInstruction* instruction,
HInstruction* x,
HInstruction* y,
InductionOp op,
const ScopedArenaSafeMap<HInstruction*, InductionInfo*>& cycle,
DataType::Type type) {
const HBasicBlock* context = instruction->GetBlock();
auto main_solve_add_sub = [&]() -> HInductionVarAnalysis::InductionInfo* {
// Solve within a cycle over an addition or subtraction.
InductionInfo* b = LookupInfo(loop, y);
if (b != nullptr) {
if (b->induction_class == kInvariant) {
// Adding or subtracting an invariant value, seeded from phi,
// keeps adding to the stride of the linear induction.
if (x == entry_phi) {
return (op == kAdd) ? b : CreateInvariantOp(context, loop, kNeg, nullptr, b);
}
auto it = cycle.find(x);
if (it != cycle.end()) {
InductionInfo* a = it->second;
if (a->induction_class == kInvariant) {
return CreateInvariantOp(context, loop, op, a, b);
}
}
} else if (b->induction_class == kLinear && b->type == type) {
// Solve within a tight cycle that adds a term that is already classified as a linear
// induction for a polynomial induction k = k + i (represented as sum over linear terms).
if (x == entry_phi &&
entry_phi->InputCount() == 2 &&
instruction == entry_phi->InputAt(1)) {
InductionInfo* initial = LookupInfo(loop, entry_phi->InputAt(0));
InductionInfo* new_a = op == kAdd ? b : TransferNeg(context, loop, b, type);
if (new_a != nullptr) {
return CreateInduction(kPolynomial, kNop, new_a, initial, /*fetch*/ nullptr, type);
}
}
}
}
return nullptr;
};
HInductionVarAnalysis::InductionInfo* result = main_solve_add_sub();
if (result == nullptr) {
// Try some alternatives before failing.
if (op == kAdd) {
// Try the other way around for an addition.
std::swap(x, y);
result = main_solve_add_sub();
} 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));
result = CreateInduction(kPeriodic,
kNop,
CreateInvariantOp(context, loop, kSub, a, initial),
initial,
/*fetch*/ nullptr,
type);
}
}
}
}
return result;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolveOp(const HLoopInformation* loop,
HInstruction* entry_phi,
HInstruction* instruction,
HInstruction* x,
HInstruction* y,
InductionOp op,
DataType::Type type) {
// Solve within a tight cycle for a binary operation k = k op c or, for some op, k = c op k.
if (entry_phi->InputCount() == 2 && instruction == entry_phi->InputAt(1)) {
InductionInfo* c = nullptr;
InductionInfo* b = LookupInfo(loop, y);
if (b != nullptr && b->induction_class == kInvariant && entry_phi == x) {
c = b;
} else if (op != kDiv && op != kRem) {
InductionInfo* a = LookupInfo(loop, x);
if (a != nullptr && a->induction_class == kInvariant && entry_phi == y) {
c = a;
}
}
// Found suitable operand left or right?
if (c != nullptr) {
const HBasicBlock* context = instruction->GetBlock();
InductionInfo* initial = LookupInfo(loop, entry_phi->InputAt(0));
switch (op) {
case kMul:
case kDiv:
// Restrict base of geometric induction to direct fetch.
if (c->operation == kFetch) {
return CreateInduction(kGeometric,
op,
initial,
CreateConstant(0, type),
c->fetch,
type);
}
break;
case kRem:
// Idiomatic MOD wrap-around induction.
return CreateInduction(kWrapAround,
kNop,
initial,
CreateInvariantOp(context, loop, kRem, initial, c),
/*fetch*/ nullptr,
type);
case kXor:
// Idiomatic XOR periodic induction.
return CreateInduction(kPeriodic,
kNop,
CreateInvariantOp(context, loop, kXor, initial, c),
initial,
/*fetch*/ nullptr,
type);
default:
LOG(FATAL) << op;
UNREACHABLE();
}
}
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolveTest(const HLoopInformation* loop,
HInstruction* entry_phi,
HInstruction* instruction,
int64_t opposite_value,
DataType::Type type) {
// Detect hidden XOR construction in x = (x == false) or x = (x != true).
const HBasicBlock* context = instruction->GetBlock();
HInstruction* x = instruction->InputAt(0);
HInstruction* y = instruction->InputAt(1);
int64_t value = -1;
if (IsExact(context, loop, LookupInfo(loop, x), &value) && value == opposite_value) {
return SolveOp(loop, entry_phi, instruction, graph_->GetIntConstant(1), y, kXor, type);
} else if (IsExact(context, loop, LookupInfo(loop, y), &value) && value == opposite_value) {
return SolveOp(loop, entry_phi, instruction, x, graph_->GetIntConstant(1), kXor, type);
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolveConversion(
const HLoopInformation* loop,
HInstruction* entry_phi,
HTypeConversion* conversion,
const ScopedArenaSafeMap<HInstruction*, InductionInfo*>& cycle,
/*inout*/ DataType::Type* type) {
DataType::Type from = conversion->GetInputType();
DataType::Type to = conversion->GetResultType();
// A narrowing conversion is allowed as *last* operation of the cycle of a linear induction
// with an initial value that fits the type, provided that the narrowest encountered type is
// recorded with the induction to account for the precision loss. The narrower induction does
// *not* transfer to any wider operations, however, since these may yield out-of-type values
if (entry_phi->InputCount() == 2 && conversion == entry_phi->InputAt(1)) {
int64_t min = DataType::MinValueOfIntegralType(to);
int64_t max = DataType::MaxValueOfIntegralType(to);
int64_t value = 0;
const HBasicBlock* context = conversion->GetBlock();
InductionInfo* initial = LookupInfo(loop, entry_phi->InputAt(0));
if (IsNarrowingIntegralConversion(from, to) &&
IsAtLeast(context, loop, initial, &value) && value >= min &&
IsAtMost(context, loop, initial, &value) && value <= max) {
auto it = cycle.find(conversion->GetInput());
if (it != cycle.end() && it->second->induction_class == kInvariant) {
*type = to;
return it->second;
}
}
}
return nullptr;
}
//
// Loop trip count analysis methods.
//
void HInductionVarAnalysis::VisitControl(const 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();
const HBasicBlock* context = condition->GetBlock();
InductionInfo* a = LookupInfo(loop, condition->InputAt(0));
InductionInfo* b = LookupInfo(loop, condition->InputAt(1));
DataType::Type type = ImplicitConversion(condition->InputAt(0)->GetType());
// Determine if the loop control uses a known sequence on an if-exit (X outside) or on
// an if-iterate (X inside), expressed as if-iterate when passed into VisitCondition().
if (a == nullptr || b == nullptr) {
return; // Loop control is not a sequence.
} else if (if_true->GetLoopInformation() != loop && if_false->GetLoopInformation() == loop) {
VisitCondition(context, loop, if_false, a, b, type, condition->GetOppositeCondition());
} else if (if_true->GetLoopInformation() == loop && if_false->GetLoopInformation() != loop) {
VisitCondition(context, loop, if_true, a, b, type, condition->GetCondition());
}
}
}
}
void HInductionVarAnalysis::VisitCondition(const HBasicBlock* context,
const HLoopInformation* loop,
HBasicBlock* body,
InductionInfo* a,
InductionInfo* b,
DataType::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(context, loop, body, b, a, type, kCondGT); break;
case kCondLE: VisitCondition(context, loop, body, b, a, type, kCondGE); break;
case kCondGT: VisitCondition(context, loop, body, b, a, type, kCondLT); break;
case kCondGE: VisitCondition(context, loop, body, b, a, type, kCondLE); break;
case kCondNE: VisitCondition(context, loop, body, 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_expr = a->op_a;
// Test for constant stride and integral condition.
int64_t stride_value = 0;
if (!IsExact(context, loop, stride_expr, &stride_value)) {
return; // unknown stride
} else if (type != DataType::Type::kInt32 && type != DataType::Type::kInt64) {
return; // not integral
}
// Since loops with a i != U condition will not be normalized by the method below, first
// try to rewrite a break-loop with terminating condition i != U into an equivalent loop
// with non-strict end condition i <= U or i >= U if such a rewriting is possible and safe.
if (cmp == kCondNE && RewriteBreakLoop(context, loop, body, stride_value, type)) {
cmp = stride_value > 0 ? kCondLE : kCondGE;
}
// If this rewriting failed, try to rewrite condition i != U into strict end condition i < U
// or i > U if this end condition is reached exactly (tested by verifying if the loop has a
// unit stride and the non-strict condition would be always taken).
if (cmp == kCondNE &&
((stride_value == +1 && IsTaken(context, loop, lower_expr, upper_expr, kCondLE)) ||
(stride_value == -1 && IsTaken(context, loop, lower_expr, upper_expr, kCondGE)))) {
cmp = stride_value > 0 ? kCondLT : kCondGT;
}
// A mismatch between the type of condition and the induction is only allowed if the,
// necessarily narrower, induction range fits the narrower control.
if (type != a->type &&
!FitsNarrowerControl(context, loop, lower_expr, upper_expr, stride_value, a->type, cmp)) {
return; // mismatched type
}
// 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(context, loop, lower_expr, upper_expr, stride_expr, stride_value, type, cmp);
}
}
}
void HInductionVarAnalysis::VisitTripCount(const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* lower_expr,
InductionInfo* upper_expr,
InductionInfo* stride_expr,
int64_t stride_value,
DataType::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 taken-test.
// (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 finite-test.
// (4) For loops which early-exits, the TC forms an upper bound, as in:
// for (int i = 0; i < 10 && ....; i++) // TC <= 10
InductionInfo* trip_count = upper_expr;
const bool is_taken = IsTaken(context, loop, lower_expr, upper_expr, cmp);
const bool is_finite = IsFinite(context, loop, 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) {
trip_count = CreateInvariantOp(context, loop, kSub, trip_count, CreateConstant(1, type));
} else if (cmp == kCondGT) {
trip_count = CreateInvariantOp(context, loop, kAdd, trip_count, CreateConstant(1, type));
}
// Compensate for stride.
trip_count = CreateInvariantOp(context, loop, kAdd, trip_count, stride_expr);
}
trip_count = CreateInvariantOp(context, loop, kSub, trip_count, lower_expr);
trip_count = CreateInvariantOp(context, loop, kDiv, trip_count, stride_expr);
// 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; // needs both tests
if (is_taken && is_finite) {
tcKind = kTripCountInLoop; // needs neither test
} else if (is_finite) {
tcKind = kTripCountInBody; // needs taken-test
} else if (is_taken) {
tcKind = kTripCountInLoopUnsafe; // needs finite-test
}
InductionOp op = kNop;
switch (cmp) {
case kCondLT: op = kLT; break;
case kCondLE: op = kLE; break;
case kCondGT: op = kGT; break;
case kCondGE: op = kGE; break;
default: LOG(FATAL) << "CONDITION UNREACHABLE";
}
// Associate trip count with control instruction, rather than the condition (even
// though it's its use) since former provides a convenient use-free placeholder.
HInstruction* control = loop->GetHeader()->GetLastInstruction();
InductionInfo* taken_test = CreateInvariantOp(context, loop, op, lower_expr, upper_expr);
DCHECK(control->IsIf());
AssignInfo(loop, control, CreateTripCount(tcKind, trip_count, taken_test, type));
}
bool HInductionVarAnalysis::IsTaken(const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* lower_expr,
InductionInfo* upper_expr,
IfCondition cmp) {
int64_t lower_value;
int64_t upper_value;
switch (cmp) {
case kCondLT:
return IsAtMost(context, loop, lower_expr, &lower_value)
&& IsAtLeast(context, loop, upper_expr, &upper_value)
&& lower_value < upper_value;
case kCondLE:
return IsAtMost(context, loop, lower_expr, &lower_value)
&& IsAtLeast(context, loop, upper_expr, &upper_value)
&& lower_value <= upper_value;
case kCondGT:
return IsAtLeast(context, loop, lower_expr, &lower_value)
&& IsAtMost(context, loop, upper_expr, &upper_value)
&& lower_value > upper_value;
case kCondGE:
return IsAtLeast(context, loop, lower_expr, &lower_value)
&& IsAtMost(context, loop, upper_expr, &upper_value)
&& lower_value >= upper_value;
default:
LOG(FATAL) << "CONDITION UNREACHABLE";
UNREACHABLE();
}
}
bool HInductionVarAnalysis::IsFinite(const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* upper_expr,
int64_t stride_value,
DataType::Type type,
IfCondition cmp) {
int64_t min = DataType::MinValueOfIntegralType(type);
int64_t max = DataType::MaxValueOfIntegralType(type);
// 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 ||
(IsAtMost(context, loop, upper_expr, &value) && value <= (max - stride_value + 1));
case kCondLE:
return (IsAtMost(context, loop, upper_expr, &value) && value <= (max - stride_value));
case kCondGT:
return stride_value == -1 ||
(IsAtLeast(context, loop, upper_expr, &value) && value >= (min - stride_value - 1));
case kCondGE:
return (IsAtLeast(context, loop, upper_expr, &value) && value >= (min - stride_value));
default:
LOG(FATAL) << "CONDITION UNREACHABLE";
UNREACHABLE();
}
}
bool HInductionVarAnalysis::FitsNarrowerControl(const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* lower_expr,
InductionInfo* upper_expr,
int64_t stride_value,
DataType::Type type,
IfCondition cmp) {
int64_t min = DataType::MinValueOfIntegralType(type);
int64_t max = DataType::MaxValueOfIntegralType(type);
// Inclusive test need one extra.
if (stride_value != 1 && stride_value != -1) {
return false; // non-unit stride
} else if (cmp == kCondLE) {
max--;
} else if (cmp == kCondGE) {
min++;
}
// Do both bounds fit the range?
int64_t value = 0;
return IsAtLeast(context, loop, lower_expr, &value) && value >= min &&
IsAtMost(context, loop, lower_expr, &value) && value <= max &&
IsAtLeast(context, loop, upper_expr, &value) && value >= min &&
IsAtMost(context, loop, upper_expr, &value) && value <= max;
}
bool HInductionVarAnalysis::RewriteBreakLoop(const HBasicBlock* context,
const HLoopInformation* loop,
HBasicBlock* body,
int64_t stride_value,
DataType::Type type) {
// Only accept unit stride.
if (std::abs(stride_value) != 1) {
return false;
}
// Simple terminating i != U condition, used nowhere else.
HIf* ifs = loop->GetHeader()->GetLastInstruction()->AsIf();
HInstruction* cond = ifs->InputAt(0);
if (ifs->GetPrevious() != cond || !cond->HasOnlyOneNonEnvironmentUse()) {
return false;
}
int c = LookupInfo(loop, cond->InputAt(0))->induction_class == kLinear ? 0 : 1;
HInstruction* index = cond->InputAt(c);
HInstruction* upper = cond->InputAt(1 - c);
// Safe to rewrite into i <= U?
IfCondition cmp = stride_value > 0 ? kCondLE : kCondGE;
if (!index->IsPhi() ||
!IsFinite(context, loop, LookupInfo(loop, upper), stride_value, type, cmp)) {
return false;
}
// Body consists of update to index i only, used nowhere else.
if (body->GetSuccessors().size() != 1 ||
body->GetSingleSuccessor() != loop->GetHeader() ||
!body->GetPhis().IsEmpty() ||
body->GetInstructions().IsEmpty() ||
body->GetFirstInstruction() != index->InputAt(1) ||
!body->GetFirstInstruction()->HasOnlyOneNonEnvironmentUse() ||
!body->GetFirstInstruction()->GetNext()->IsGoto()) {
return false;
}
// Always taken or guarded by enclosing condition.
if (!IsTaken(context, loop, LookupInfo(loop, index)->op_b, LookupInfo(loop, upper), cmp) &&
!IsGuardedBy(loop, cmp, index->InputAt(0), upper)) {
return false;
}
// Test if break-loop body can be written, and do so on success.
if (RewriteBreakLoopBody(loop, body, cond, index, upper, /*rewrite*/ false)) {
RewriteBreakLoopBody(loop, body, cond, index, upper, /*rewrite*/ true);
} else {
return false;
}
// Rewrite condition in HIR.
if (ifs->IfTrueSuccessor() != body) {
cmp = (cmp == kCondLE) ? kCondGT : kCondLT;
}
HInstruction* rep = nullptr;
switch (cmp) {
case kCondLT: rep = new (graph_->GetAllocator()) HLessThan(index, upper); break;
case kCondGT: rep = new (graph_->GetAllocator()) HGreaterThan(index, upper); break;
case kCondLE: rep = new (graph_->GetAllocator()) HLessThanOrEqual(index, upper); break;
case kCondGE: rep = new (graph_->GetAllocator()) HGreaterThanOrEqual(index, upper); break;
default: LOG(FATAL) << cmp; UNREACHABLE();
}
loop->GetHeader()->ReplaceAndRemoveInstructionWith(cond, rep);
return true;
}
//
// Helper methods.
//
void HInductionVarAnalysis::AssignInfo(const 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_->GetAllocator()->Adapter(kArenaAllocInductionVarAnalysis)));
}
it->second.Put(instruction, info);
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::LookupInfo(
const 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 (loop->IsDefinedOutOfTheLoop(instruction)) {
InductionInfo* info = CreateInvariantFetch(instruction);
AssignInfo(loop, instruction, info);
return info;
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::CreateConstant(int64_t value,
DataType::Type type) {
HInstruction* constant;
switch (type) {
case DataType::Type::kFloat64: constant = graph_->GetDoubleConstant(value); break;
case DataType::Type::kFloat32: constant = graph_->GetFloatConstant(value); break;
case DataType::Type::kInt64: constant = graph_->GetLongConstant(value); break;
default: constant = graph_->GetIntConstant(value); break;
}
return CreateInvariantFetch(constant);
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::CreateSimplifiedInvariant(
const HBasicBlock* context,
const HLoopInformation* loop,
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 (IsExact(context, loop, a, &value)) {
if (value == 0) {
// Simplify 0 + b = b, 0 ^ b = b, 0 * b = 0.
if (op == kAdd || op == kXor) {
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) {
return CreateSimplifiedInvariant(context, loop, kNeg, nullptr, b);
}
}
}
if (IsExact(context, loop, b, &value)) {
if (value == 0) {
// Simplify a + 0 = a, a - 0 = a, a ^ 0 = a, a * 0 = 0, -0 = 0.
if (op == kAdd || op == kSub || op == kXor) {
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) {
return CreateSimplifiedInvariant(context, loop, kNeg, nullptr, a);
}
}
} else if (b->operation == kNeg) {
// Simplify a + (-b) = a - b, a - (-b) = a + b, -(-b) = b.
if (op == kAdd) {
return CreateSimplifiedInvariant(context, loop, kSub, a, b->op_b);
} else if (op == kSub) {
return CreateSimplifiedInvariant(context, loop, kAdd, a, b->op_b);
} else if (op == kNeg) {
return b->op_b;
}
} else if (b->operation == kSub) {
// Simplify - (a - b) = b - a.
if (op == kNeg) {
return CreateSimplifiedInvariant(context, loop, kSub, b->op_b, b->op_a);
}
}
return new (graph_->GetAllocator()) InductionInfo(
kInvariant, op, a, b, nullptr, ImplicitConversion(b->type));
}
HInstruction* HInductionVarAnalysis::GetShiftConstant(const HLoopInformation* loop,
HInstruction* instruction,
InductionInfo* initial) {
DCHECK(instruction->IsShl() || instruction->IsShr() || instruction->IsUShr());
const HBasicBlock* context = instruction->GetBlock();
// Shift-rights are only the same as division for non-negative initial inputs.
// Otherwise we would round incorrectly.
if (initial != nullptr) {
int64_t value = -1;
if (!IsAtLeast(context, loop, initial, &value) || value < 0) {
return nullptr;
}
}
// Obtain the constant needed to treat shift as equivalent multiplication or division.
// This yields an existing instruction if the constant 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 earlier.
InductionInfo* b = LookupInfo(loop, instruction->InputAt(1));
int64_t value = -1;
if (IsExact(context, loop, b, &value)) {
DataType::Type type = instruction->InputAt(0)->GetType();
if (type == DataType::Type::kInt32 && 0 <= value && value < 31) {
return graph_->GetIntConstant(1 << value);
}
if (type == DataType::Type::kInt64 && 0 <= value && value < 63) {
return graph_->GetLongConstant(1L << value);
}
}
return nullptr;
}
void HInductionVarAnalysis::AssignCycle(HPhi* phi, ArrayRef<HInstruction* const> scc) {
ArenaSet<HInstruction*>* set = &cycles_.Put(phi, ArenaSet<HInstruction*>(
graph_->GetAllocator()->Adapter(kArenaAllocInductionVarAnalysis)))->second;
for (HInstruction* i : scc) {
set->insert(i);
}
}
ArenaSet<HInstruction*>* HInductionVarAnalysis::LookupCycle(HPhi* phi) {
auto it = cycles_.find(phi);
if (it != cycles_.end()) {
return &it->second;
}
return nullptr;
}
bool HInductionVarAnalysis::IsExact(const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* info,
/*out*/int64_t* value) {
InductionVarRange range(this);
return range.IsConstant(context, loop, info, InductionVarRange::kExact, value);
}
bool HInductionVarAnalysis::IsAtMost(const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* info,
/*out*/int64_t* value) {
InductionVarRange range(this);
return range.IsConstant(context, loop, info, InductionVarRange::kAtMost, value);
}
bool HInductionVarAnalysis::IsAtLeast(const HBasicBlock* context,
const HLoopInformation* loop,
InductionInfo* info,
/*out*/int64_t* value) {
InductionVarRange range(this);
return range.IsConstant(context, loop, info, InductionVarRange::kAtLeast, value);
}
bool HInductionVarAnalysis::IsNarrowingLinear(InductionInfo* info) {
return info != nullptr &&
info->induction_class == kLinear &&
(info->type == DataType::Type::kUint8 ||
info->type == DataType::Type::kInt8 ||
info->type == DataType::Type::kUint16 ||
info->type == DataType::Type::kInt16 ||
(info->type == DataType::Type::kInt32 && (info->op_a->type == DataType::Type::kInt64 ||
info->op_b->type == DataType::Type::kInt64)));
}
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 &&
info1->type == info2->type &&
InductionEqual(info1->op_a, info2->op_a) &&
InductionEqual(info1->op_b, info2->op_b);
}
// Otherwise only two nullptrs are considered equal.
return info1 == info2;
}
std::string HInductionVarAnalysis::FetchToString(HInstruction* fetch) {
DCHECK(fetch != nullptr);
if (fetch->IsIntConstant()) {
return std::to_string(fetch->AsIntConstant()->GetValue());
} else if (fetch->IsLongConstant()) {
return std::to_string(fetch->AsLongConstant()->GetValue());
}
return std::to_string(fetch->GetId()) + ":" + fetch->DebugName();
}
std::string HInductionVarAnalysis::InductionToString(InductionInfo* info) {
if (info != nullptr) {
if (info->induction_class == kInvariant) {
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 kRem: inv += " % "; break;
case kXor: inv += " ^ "; break;
case kLT: inv += " < "; break;
case kLE: inv += " <= "; break;
case kGT: inv += " > "; break;
case kGE: inv += " >= "; break;
case kFetch: inv += FetchToString(info->fetch); 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);
inv += ")";
return inv;
} else {
if (info->induction_class == kLinear) {
DCHECK(info->operation == kNop);
return "(" + InductionToString(info->op_a) + " * i + " +
InductionToString(info->op_b) + "):" +
DataType::PrettyDescriptor(info->type);
} else if (info->induction_class == kPolynomial) {
DCHECK(info->operation == kNop);
return "poly(sum_lt(" + InductionToString(info->op_a) + ") + " +
InductionToString(info->op_b) + "):" +
DataType::PrettyDescriptor(info->type);
} else if (info->induction_class == kGeometric) {
DCHECK(info->operation == kMul || info->operation == kDiv);
DCHECK(info->fetch != nullptr);
return "geo(" + InductionToString(info->op_a) + " * " +
FetchToString(info->fetch) +
(info->operation == kMul ? " ^ i + " : " ^ -i + ") +
InductionToString(info->op_b) + "):" +
DataType::PrettyDescriptor(info->type);
} else if (info->induction_class == kWrapAround) {
DCHECK(info->operation == kNop);
return "wrap(" + InductionToString(info->op_a) + ", " +
InductionToString(info->op_b) + "):" +
DataType::PrettyDescriptor(info->type);
} else if (info->induction_class == kPeriodic) {
DCHECK(info->operation == kNop);
return "periodic(" + InductionToString(info->op_a) + ", " +
InductionToString(info->op_b) + "):" +
DataType::PrettyDescriptor(info->type);
}
}
}
return "";
}
void HInductionVarAnalysis::CalculateLoopHeaderPhisInARow(
HPhi* initial_phi,
ScopedArenaSafeMap<HPhi*, int>& cached_values,
ScopedArenaAllocator& allocator) {
DCHECK(initial_phi->IsLoopHeaderPhi());
ScopedArenaQueue<HPhi*> worklist(allocator.Adapter(kArenaAllocInductionVarAnalysis));
worklist.push(initial_phi);
// Used to check which phis are in the current chain we are checking.
ScopedArenaSet<HPhi*> phis_in_chain(allocator.Adapter(kArenaAllocInductionVarAnalysis));
while (!worklist.empty()) {
HPhi* current_phi = worklist.front();
DCHECK(current_phi->IsLoopHeaderPhi());
if (cached_values.find(current_phi) != cached_values.end()) {
// Already processed.
worklist.pop();
continue;
}
phis_in_chain.insert(current_phi);
int max_value = 0;
bool pushed_other_phis = false;
for (size_t index = 0; index < current_phi->InputCount(); index++) {
// If the input is not a loop header phi, we only have 1 (current_phi).
int current_value = 1;
if (current_phi->InputAt(index)->IsLoopHeaderPhi()) {
HPhi* loop_header_phi = current_phi->InputAt(index)->AsPhi();
auto it = cached_values.find(loop_header_phi);
if (it != cached_values.end()) {
current_value += it->second;
} else if (phis_in_chain.find(current_phi) == phis_in_chain.end()) {
// Push phis which aren't in the chain already to be processed.
pushed_other_phis = true;
worklist.push(loop_header_phi);
}
// Phis in the chain will get processed later. We keep `current_value` as 1 to avoid
// double counting `loop_header_phi`.
}
max_value = std::max(max_value, current_value);
}
if (!pushed_other_phis) {
// Only finish processing after all inputs were processed.
worklist.pop();
phis_in_chain.erase(current_phi);
cached_values.FindOrAdd(current_phi, max_value);
}
}
}
bool HInductionVarAnalysis::IsPathologicalCase() {
ScopedArenaAllocator local_allocator(graph_->GetArenaStack());
ScopedArenaSafeMap<HPhi*, int> cached_values(
std::less<HPhi*>(), local_allocator.Adapter(kArenaAllocInductionVarAnalysis));
// Due to how our induction passes work, we will take a lot of time compiling if we have several
// loop header phis in a row. If we have more than 15 different loop header phis in a row, we
// don't perform the analysis.
constexpr int kMaximumLoopHeaderPhisInARow = 15;
for (HBasicBlock* block : graph_->GetReversePostOrder()) {
if (!block->IsLoopHeader()) {
continue;
}
for (HInstructionIterator it(block->GetPhis()); !it.Done(); it.Advance()) {
DCHECK(it.Current()->IsLoopHeaderPhi());
HPhi* phi = it.Current()->AsPhi();
CalculateLoopHeaderPhisInARow(phi, cached_values, local_allocator);
DCHECK(cached_values.find(phi) != cached_values.end())
<< " we should have a value for Phi " << phi->GetId()
<< " in block " << phi->GetBlock()->GetBlockId();
if (cached_values.find(phi)->second > kMaximumLoopHeaderPhisInARow) {
return true;
}
}
}
return false;
}
} // namespace art