/*
* 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 {
/**
* 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.
*/
static void RotateEntryPhiFirst(HLoopInformation* loop,
ArenaVector<HInstruction*>* scc,
ArenaVector<HInstruction*>* new_scc) {
// Find very first loop-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 loop-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);
}
}
/**
* Returns true if the from/to types denote a narrowing, integral conversion (precision loss).
*/
static bool IsNarrowingIntegralConversion(Primitive::Type from, Primitive::Type to) {
switch (from) {
case Primitive::kPrimLong:
return to == Primitive::kPrimByte || to == Primitive::kPrimShort
|| to == Primitive::kPrimChar || to == Primitive::kPrimInt;
case Primitive::kPrimInt:
return to == Primitive::kPrimByte || to == Primitive::kPrimShort
|| to == Primitive::kPrimChar;
case Primitive::kPrimChar:
case Primitive::kPrimShort:
return to == Primitive::kPrimByte;
default:
return false;
}
}
/**
* Returns result of implicit widening type conversion done in HIR.
*/
static Primitive::Type ImplicitConversion(Primitive::Type type) {
switch (type) {
case Primitive::kPrimShort:
case Primitive::kPrimChar:
case Primitive::kPrimByte:
case Primitive::kPrimBoolean:
return Primitive::kPrimInt;
default:
return type;
}
}
//
// Class methods.
//
HInductionVarAnalysis::HInductionVarAnalysis(HGraph* graph)
: HOptimization(graph, kInductionPassName),
global_depth_(0),
stack_(graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)),
map_(std::less<HInstruction*>(),
graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)),
scc_(graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)),
cycle_(std::less<HInstruction*>(),
graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)),
type_(Primitive::kPrimVoid),
induction_(std::less<HLoopInformation*>(),
graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)),
cycles_(std::less<HPhi*>(),
graph->GetArena()->Adapter(kArenaAllocInductionVarAnalysis)) {
}
void 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.
for (HBasicBlock* graph_block : graph_->GetReversePostOrder()) {
// Don't analyze irreducible loops.
if (graph_block->IsLoopHeader() && !graph_block->GetLoopInformation()->IsIrreducible()) {
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 visited later.
}
// 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 (HInstruction* input : instruction->GetInputs()) {
low = std::min(low, VisitDescendant(loop, input));
}
// 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;
}
}
// Type of induction.
type_ = scc_[0]->GetType();
// 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, /*adjust_input_size*/ 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->IsNeg()) {
info = TransferNeg(LookupInfo(loop, instruction->InputAt(0)));
} else if (instruction->IsMul()) {
info = TransferMul(LookupInfo(loop, instruction->InputAt(0)),
LookupInfo(loop, instruction->InputAt(1)));
} else if (instruction->IsShl()) {
HInstruction* mulc = GetShiftConstant(loop, instruction, /*initial*/ nullptr);
if (mulc != nullptr) {
info = TransferMul(LookupInfo(loop, instruction->InputAt(0)),
LookupInfo(loop, mulc));
}
} 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(HLoopInformation* loop) {
const size_t size = scc_.size();
DCHECK_GE(size, 1u);
// Rotate proper loop-phi to front.
if (size > 1) {
ArenaVector<HInstruction*> other(graph_->GetArena()->Adapter(kArenaAllocInductionVarAnalysis));
RotateEntryPhiFirst(loop, &scc_, &other);
}
// 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());
}
}
// 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.
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);
} else if (instruction->IsMul()) {
update = SolveOp(
loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kMul);
} else if (instruction->IsDiv()) {
update = SolveOp(
loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kDiv);
} else if (instruction->IsRem()) {
update = SolveOp(
loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kRem);
} else if (instruction->IsShl()) {
HInstruction* mulc = GetShiftConstant(loop, instruction, /*initial*/ nullptr);
if (mulc != nullptr) {
update = SolveOp(loop, phi, instruction, instruction->InputAt(0), mulc, kMul);
}
} 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);
}
} else if (instruction->IsXor()) {
update = SolveOp(
loop, phi, instruction, instruction->InputAt(0), instruction->InputAt(1), kXor);
} else if (instruction->IsEqual()) {
update = SolveTest(loop, phi, instruction, 0);
} else if (instruction->IsNotEqual()) {
update = SolveTest(loop, phi, instruction, 1);
} else if (instruction->IsSelect()) {
update = SolvePhi(instruction, /*input_index*/ 0, /*adjust_input_size*/ 1); // acts like Phi
} else if (instruction->IsTypeConversion()) {
update = SolveConversion(loop, phi, instruction->AsTypeConversion());
}
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);
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);
}
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,
kNop,
induction,
last,
/*fetch*/ nullptr,
type_);
}
return CreateInduction(kPeriodic,
kNop,
induction->op_a,
RotatePeriodicInduction(induction->op_b, last),
/*fetch*/ nullptr,
type_);
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::TransferPhi(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(InductionInfo* a,
InductionInfo* b,
InductionOp op) {
// 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(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(a->op_a, b->op_a, op);
InductionInfo* new_b = TransferAddSub(a->op_b, b->op_b, op);
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(a, b->op_b, op);
if (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);
}
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(a->op_b, b, op);
if (a->induction_class == kWrapAround || a->induction_class == kPeriodic) {
new_a = TransferAddSub(new_a, b, op);
}
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(InductionInfo* a) {
// 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(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(a->op_a);
InductionInfo* new_b = TransferNeg(a->op_b);
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(InductionInfo* a,
InductionInfo* b) {
// 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(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(a, b->op_a);
InductionInfo* new_b = TransferMul(a, b->op_b);
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(a->op_a, b);
InductionInfo* new_b = TransferMul(a->op_b, b);
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,
Primitive::Type from,
Primitive::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) {
// 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(
HLoopInformation* loop,
HInstruction* entry_phi,
HInstruction* phi) {
// Match all phi inputs.
InductionInfo* match = SolvePhi(phi, /*input_index*/ 0, /*adjust_input_size*/ 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, kNop, a, initial, /*fetch*/ nullptr, type_);
}
InductionInfo* b = SolvePhi(phi, /*input_index*/ 1, /*adjust_input_size*/ 0);
if (b != nullptr && b->induction_class == kPeriodic) {
return CreateInduction(kPeriodic, kNop, a, b, /*fetch*/ nullptr, type_);
}
}
}
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.
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(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);
}
}
} 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(b);
if (new_a != nullptr) {
return CreateInduction(kPolynomial, kNop, new_a, initial, /*fetch*/ nullptr, type_);
}
}
}
}
// 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,
kNop,
CreateInvariantOp(kSub, a, initial),
initial,
/*fetch*/ nullptr,
type_);
}
}
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolveOp(HLoopInformation* loop,
HInstruction* entry_phi,
HInstruction* instruction,
HInstruction* x,
HInstruction* y,
InductionOp op) {
// 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) {
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(kRem, initial, c),
/*fetch*/ nullptr,
type_);
case kXor:
// Idiomatic XOR periodic induction.
return CreateInduction(kPeriodic,
kNop,
CreateInvariantOp(kXor, initial, c),
initial,
/*fetch*/ nullptr,
type_);
default:
CHECK(false) << op;
break;
}
}
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolveTest(HLoopInformation* loop,
HInstruction* entry_phi,
HInstruction* instruction,
int64_t opposite_value) {
// Detect hidden XOR construction in x = (x == false) or x = (x != true).
int64_t value = -1;
HInstruction* x = instruction->InputAt(0);
HInstruction* y = instruction->InputAt(1);
if (IsExact(LookupInfo(loop, x), &value) && value == opposite_value) {
return SolveOp(loop, entry_phi, instruction, graph_->GetIntConstant(1), y, kXor);
} else if (IsExact(LookupInfo(loop, y), &value) && value == opposite_value) {
return SolveOp(loop, entry_phi, instruction, x, graph_->GetIntConstant(1), kXor);
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::SolveConversion(
HLoopInformation* loop,
HInstruction* entry_phi,
HTypeConversion* conversion) {
Primitive::Type from = conversion->GetInputType();
Primitive::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 = Primitive::MinValueOfIntegralType(to);
int64_t max = Primitive::MaxValueOfIntegralType(to);
int64_t value = 0;
InductionInfo* initial = LookupInfo(loop, entry_phi->InputAt(0));
if (IsNarrowingIntegralConversion(from, to) &&
IsAtLeast(initial, &value) && value >= min &&
IsAtMost(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;
}
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 = 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(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_expr = a->op_a;
// Constant stride?
int64_t stride_value = 0;
if (!IsExact(stride_expr, &stride_value)) {
return;
}
// 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(lower_expr, upper_expr, kCondLE)) ||
(stride_value == -1 && IsTaken(lower_expr, upper_expr, kCondGE)))) {
cmp = stride_value > 0 ? kCondLT : kCondGT;
}
// Only accept integral condition. 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 != Primitive::kPrimInt && type != Primitive::kPrimLong) {
return; // not integral
} else if (type != a->type &&
!FitsNarrowerControl(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(loop, lower_expr, upper_expr, stride_expr, stride_value, type, cmp);
}
}
}
void HInductionVarAnalysis::VisitTripCount(HLoopInformation* loop,
InductionInfo* lower_expr,
InductionInfo* upper_expr,
InductionInfo* stride_expr,
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 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(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) {
trip_count = CreateInvariantOp(kSub, trip_count, CreateConstant(1, type));
} else if (cmp == kCondGT) {
trip_count = CreateInvariantOp(kAdd, trip_count, CreateConstant(1, type));
}
// Compensate for stride.
trip_count = CreateInvariantOp(kAdd, trip_count, stride_expr);
}
trip_count = CreateInvariantOp(
kDiv, CreateInvariantOp(kSub, trip_count, lower_expr), 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(op, lower_expr, upper_expr);
DCHECK(control->IsIf());
AssignInfo(loop, control, CreateTripCount(tcKind, trip_count, taken_test, type));
}
bool HInductionVarAnalysis::IsTaken(InductionInfo* lower_expr,
InductionInfo* upper_expr,
IfCondition cmp) {
int64_t lower_value;
int64_t upper_value;
switch (cmp) {
case kCondLT:
return IsAtMost(lower_expr, &lower_value)
&& IsAtLeast(upper_expr, &upper_value)
&& lower_value < upper_value;
case kCondLE:
return IsAtMost(lower_expr, &lower_value)
&& IsAtLeast(upper_expr, &upper_value)
&& lower_value <= upper_value;
case kCondGT:
return IsAtLeast(lower_expr, &lower_value)
&& IsAtMost(upper_expr, &upper_value)
&& lower_value > upper_value;
case kCondGE:
return IsAtLeast(lower_expr, &lower_value)
&& IsAtMost(upper_expr, &upper_value)
&& lower_value >= upper_value;
default:
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) {
int64_t min = Primitive::MinValueOfIntegralType(type);
int64_t max = Primitive::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(upper_expr, &value) && value <= (max - stride_value + 1));
case kCondLE:
return (IsAtMost(upper_expr, &value) && value <= (max - stride_value));
case kCondGT:
return stride_value == -1 ||
(IsAtLeast(upper_expr, &value) && value >= (min - stride_value - 1));
case kCondGE:
return (IsAtLeast(upper_expr, &value) && value >= (min - stride_value));
default:
LOG(FATAL) << "CONDITION UNREACHABLE";
}
return false; // not certain, may be infinite
}
bool HInductionVarAnalysis::FitsNarrowerControl(InductionInfo* lower_expr,
InductionInfo* upper_expr,
int64_t stride_value,
Primitive::Type type,
IfCondition cmp) {
int64_t min = Primitive::MinValueOfIntegralType(type);
int64_t max = Primitive::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(lower_expr, &value) && value >= min &&
IsAtMost(lower_expr, &value) && value <= max &&
IsAtLeast(upper_expr, &value) && value >= min &&
IsAtMost(upper_expr, &value) && value <= max;
}
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 (loop->IsDefinedOutOfTheLoop(instruction)) {
InductionInfo* info = CreateInvariantFetch(instruction);
AssignInfo(loop, instruction, info);
return info;
}
return nullptr;
}
HInductionVarAnalysis::InductionInfo* HInductionVarAnalysis::CreateConstant(int64_t value,
Primitive::Type type) {
HInstruction* constant;
switch (type) {
case Primitive::kPrimDouble: constant = graph_->GetDoubleConstant(value); break;
case Primitive::kPrimFloat: constant = graph_->GetFloatConstant(value); break;
case Primitive::kPrimLong: constant = graph_->GetLongConstant(value); break;
default: constant = graph_->GetIntConstant(value); break;
}
return CreateInvariantFetch(constant);
}
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 (IsExact(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(kNeg, nullptr, b);
}
}
}
if (IsExact(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(kNeg, nullptr, a);
}
}
} else if (b->operation == kNeg) {
// Simplify a + (-b) = a - b, a - (-b) = a + b, -(-b) = b.
if (op == kAdd) {
return CreateSimplifiedInvariant(kSub, a, b->op_b);
} else if (op == kSub) {
return CreateSimplifiedInvariant(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(kSub, b->op_b, b->op_a);
}
}
return new (graph_->GetArena()) InductionInfo(
kInvariant, op, a, b, nullptr, ImplicitConversion(b->type));
}
HInstruction* HInductionVarAnalysis::GetShiftConstant(HLoopInformation* loop,
HInstruction* instruction,
InductionInfo* initial) {
DCHECK(instruction->IsShl() || instruction->IsShr() || instruction->IsUShr());
// 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(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(b, &value)) {
Primitive::Type type = instruction->InputAt(0)->GetType();
if (type == Primitive::kPrimInt && 0 <= value && value < 31) {
return graph_->GetIntConstant(1 << value);
}
if (type == Primitive::kPrimLong && 0 <= value && value < 63) {
return graph_->GetLongConstant(1L << value);
}
}
return nullptr;
}
void HInductionVarAnalysis::AssignCycle(HPhi* phi) {
ArenaSet<HInstruction*>* set = &cycles_.Put(phi, ArenaSet<HInstruction*>(
graph_->GetArena()->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(InductionInfo* info, int64_t* value) {
return InductionVarRange(this).IsConstant(info, InductionVarRange::kExact, value);
}
bool HInductionVarAnalysis::IsAtMost(InductionInfo* info, int64_t* value) {
return InductionVarRange(this).IsConstant(info, InductionVarRange::kAtMost, value);
}
bool HInductionVarAnalysis::IsAtLeast(InductionInfo* info, int64_t* value) {
return InductionVarRange(this).IsConstant(info, InductionVarRange::kAtLeast, value);
}
bool HInductionVarAnalysis::IsNarrowingLinear(InductionInfo* info) {
return info != nullptr &&
info->induction_class == kLinear &&
(info->type == Primitive::kPrimByte ||
info->type == Primitive::kPrimShort ||
info->type == Primitive::kPrimChar ||
(info->type == Primitive::kPrimInt && (info->op_a->type == Primitive::kPrimLong ||
info->op_b->type == Primitive::kPrimLong)));
}
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) + "):" +
Primitive::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) + "):" +
Primitive::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) + "):" +
Primitive::PrettyDescriptor(info->type);
} else if (info->induction_class == kWrapAround) {
DCHECK(info->operation == kNop);
return "wrap(" + InductionToString(info->op_a) + ", " +
InductionToString(info->op_b) + "):" +
Primitive::PrettyDescriptor(info->type);
} else if (info->induction_class == kPeriodic) {
DCHECK(info->operation == kNop);
return "periodic(" + InductionToString(info->op_a) + ", " +
InductionToString(info->op_b) + "):" +
Primitive::PrettyDescriptor(info->type);
}
}
}
return "";
}
} // namespace art