runtime/vm/flow_graph_range_analysis.cc

// Copyright (c) 2014, the Dart project authors.  Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.

#include "vm/flow_graph_range_analysis.h"

#include "vm/bit_vector.h"
#include "vm/il_printer.h"

namespace dart {

DEFINE_FLAG(bool, array_bounds_check_elimination, true,
    "Eliminate redundant bounds checks.");
DEFINE_FLAG(bool, trace_range_analysis, false, "Trace range analysis progress");
DEFINE_FLAG(bool, trace_integer_ir_selection, false,
    "Print integer IR selection optimization pass.");
DECLARE_FLAG(bool, trace_constant_propagation);

// Quick access to the locally defined isolate() method.
#define I (isolate())

void RangeAnalysis::Analyze() {
  CollectValues();

  if (FLAG_trace_range_analysis) {
    FlowGraphPrinter::PrintGraph("Range Analysis (BBB)", flow_graph_);
  }

  InsertConstraints();
  InferRanges();
  EliminateRedundantBoundsChecks();
  MarkUnreachableBlocks();

  NarrowMintToInt32();

  IntegerInstructionSelector iis(flow_graph_);
  iis.Select();

  RemoveConstraints();
}


void RangeAnalysis::CollectValues() {
  const GrowableArray<Definition*>& initial =
      *flow_graph_->graph_entry()->initial_definitions();
  for (intptr_t i = 0; i < initial.length(); ++i) {
    Definition* current = initial[i];
    if (current->Type()->ToCid() == kSmiCid) {
      values_.Add(current);
    } else if (current->IsMintDefinition()) {
      values_.Add(current);
    } else if (current->IsInt32Definition()) {
      values_.Add(current);
    }
  }

  for (BlockIterator block_it = flow_graph_->reverse_postorder_iterator();
       !block_it.Done();
       block_it.Advance()) {
    BlockEntryInstr* block = block_it.Current();


    if (block->IsGraphEntry() || block->IsCatchBlockEntry()) {
      const GrowableArray<Definition*>& initial = block->IsGraphEntry()
          ? *block->AsGraphEntry()->initial_definitions()
          : *block->AsCatchBlockEntry()->initial_definitions();
      for (intptr_t i = 0; i < initial.length(); ++i) {
        Definition* current = initial[i];
        if (current->Type()->ToCid() == kSmiCid) {
          values_.Add(current);
        } else if (current->IsMintDefinition()) {
          values_.Add(current);
        } else if (current->IsInt32Definition()) {
          values_.Add(current);
        }
      }
    }

    JoinEntryInstr* join = block->AsJoinEntry();
    if (join != NULL) {
      for (PhiIterator phi_it(join); !phi_it.Done(); phi_it.Advance()) {
        PhiInstr* current = phi_it.Current();
        if (current->Type()->ToCid() == kSmiCid) {
          values_.Add(current);
        } else if (current->representation() == kUnboxedInt32) {
          values_.Add(current);
        }
      }
    }

    for (ForwardInstructionIterator instr_it(block);
         !instr_it.Done();
         instr_it.Advance()) {
      Instruction* current = instr_it.Current();
      Definition* defn = current->AsDefinition();
      if (defn != NULL) {
        if ((defn->Type()->ToCid() == kSmiCid) &&
            (defn->ssa_temp_index() != -1)) {
          values_.Add(defn);
        } else if ((defn->IsMintDefinition()) &&
                   (defn->ssa_temp_index() != -1)) {
          values_.Add(defn);
          if (defn->IsBinaryMintOp()) {
            binary_mint_ops_.Add(defn->AsBinaryMintOp());
          } else if (defn->IsShiftMintOp()) {
            shift_mint_ops_.Add(defn->AsShiftMintOp());
          }
        } else if (defn->IsInt32Definition()) {
          values_.Add(defn);
        }
      } else if (current->IsCheckArrayBound()) {
        bounds_checks_.Add(current->AsCheckArrayBound());
      }
    }
  }
}


// Returns true if use is dominated by the given instruction.
// Note: uses that occur at instruction itself are not dominated by it.
static bool IsDominatedUse(Instruction* dom, Value* use) {
  BlockEntryInstr* dom_block = dom->GetBlock();

  Instruction* instr = use->instruction();

  PhiInstr* phi = instr->AsPhi();
  if (phi != NULL) {
    return dom_block->Dominates(phi->block()->PredecessorAt(use->use_index()));
  }

  BlockEntryInstr* use_block = instr->GetBlock();
  if (use_block == dom_block) {
    // Fast path for the case of block entry.
    if (dom_block == dom) return true;

    for (Instruction* curr = dom->next(); curr != NULL; curr = curr->next()) {
      if (curr == instr) return true;
    }

    return false;
  }

  return dom_block->Dominates(use_block);
}


void RangeAnalysis::RenameDominatedUses(Definition* def,
                                        Instruction* dom,
                                        Definition* other) {
  for (Value::Iterator it(def->input_use_list());
       !it.Done();
       it.Advance()) {
    Value* use = it.Current();

    // Skip dead phis.
    PhiInstr* phi = use->instruction()->AsPhi();
    ASSERT((phi == NULL) || phi->is_alive());
    if (IsDominatedUse(dom, use)) {
      use->BindTo(other);
    }
  }
}


// For a comparison operation return an operation for the equivalent flipped
// comparison: a (op) b === b (op') a.
static Token::Kind FlipComparison(Token::Kind op) {
  switch (op) {
    case Token::kEQ: return Token::kEQ;
    case Token::kNE: return Token::kNE;
    case Token::kLT: return Token::kGT;
    case Token::kGT: return Token::kLT;
    case Token::kLTE: return Token::kGTE;
    case Token::kGTE: return Token::kLTE;
    default:
      UNREACHABLE();
      return Token::kILLEGAL;
  }
}


// Given a boundary (right operand) and a comparison operation return
// a symbolic range constraint for the left operand of the comparison assuming
// that it evaluated to true.
// For example for the comparison a < b symbol a is constrained with range
// [Smi::kMinValue, b - 1].
Range* RangeAnalysis::ConstraintSmiRange(Token::Kind op, Definition* boundary) {
  switch (op) {
    case Token::kEQ:
      return new(I) Range(RangeBoundary::FromDefinition(boundary),
                          RangeBoundary::FromDefinition(boundary));
    case Token::kNE:
      return new(I) Range(Range::Full(RangeBoundary::kRangeBoundarySmi));
    case Token::kLT:
      return new(I) Range(RangeBoundary::MinSmi(),
                          RangeBoundary::FromDefinition(boundary, -1));
    case Token::kGT:
      return new(I) Range(RangeBoundary::FromDefinition(boundary, 1),
                          RangeBoundary::MaxSmi());
    case Token::kLTE:
      return new(I) Range(RangeBoundary::MinSmi(),
                          RangeBoundary::FromDefinition(boundary));
    case Token::kGTE:
      return new(I) Range(RangeBoundary::FromDefinition(boundary),
                          RangeBoundary::MaxSmi());
    default:
      UNREACHABLE();
      return NULL;
  }
}


ConstraintInstr* RangeAnalysis::InsertConstraintFor(Value* use,
                                                    Definition* defn,
                                                    Range* constraint_range,
                                                    Instruction* after) {
  // No need to constrain constants.
  if (defn->IsConstant()) return NULL;

  // Check if the value is already constrained to avoid inserting duplicated
  // constraints.
  ConstraintInstr* constraint = after->next()->AsConstraint();
  while (constraint != NULL) {
    if ((constraint->value()->definition() == defn) &&
        constraint->constraint()->Equals(constraint_range)) {
      return NULL;
    }
    constraint = constraint->next()->AsConstraint();
  }

  constraint = new(I) ConstraintInstr(
      use->CopyWithType(), constraint_range);

  flow_graph_->InsertAfter(after, constraint, NULL, FlowGraph::kValue);
  RenameDominatedUses(defn, constraint, constraint);
  constraints_.Add(constraint);
  return constraint;
}


void RangeAnalysis::ConstrainValueAfterBranch(Value* use, Definition* defn) {
  BranchInstr* branch = use->instruction()->AsBranch();
  RelationalOpInstr* rel_op = branch->comparison()->AsRelationalOp();
  if ((rel_op != NULL) && (rel_op->operation_cid() == kSmiCid)) {
    // Found comparison of two smis. Constrain defn at true and false
    // successors using the other operand as a boundary.
    Definition* boundary;
    Token::Kind op_kind;
    if (use->use_index() == 0) {  // Left operand.
      boundary = rel_op->InputAt(1)->definition();
      op_kind = rel_op->kind();
    } else {
      ASSERT(use->use_index() == 1);  // Right operand.
      boundary = rel_op->InputAt(0)->definition();
      // InsertConstraintFor assumes that defn is left operand of a
      // comparison if it is right operand flip the comparison.
      op_kind = FlipComparison(rel_op->kind());
    }

    // Constrain definition at the true successor.
    ConstraintInstr* true_constraint =
        InsertConstraintFor(use,
                            defn,
                            ConstraintSmiRange(op_kind, boundary),
                            branch->true_successor());
    // Mark true_constraint an artificial use of boundary. This ensures
    // that constraint's range is recalculated if boundary's range changes.
    if (true_constraint != NULL) {
      true_constraint->AddDependency(boundary);
      true_constraint->set_target(branch->true_successor());
    }

    // Constrain definition with a negated condition at the false successor.
    ConstraintInstr* false_constraint =
        InsertConstraintFor(
            use,
            defn,
            ConstraintSmiRange(Token::NegateComparison(op_kind), boundary),
            branch->false_successor());
    // Mark false_constraint an artificial use of boundary. This ensures
    // that constraint's range is recalculated if boundary's range changes.
    if (false_constraint != NULL) {
      false_constraint->AddDependency(boundary);
      false_constraint->set_target(branch->false_successor());
    }
  }
}


void RangeAnalysis::InsertConstraintsFor(Definition* defn) {
  for (Value* use = defn->input_use_list();
       use != NULL;
       use = use->next_use()) {
    if (use->instruction()->IsBranch()) {
      ConstrainValueAfterBranch(use, defn);
    } else if (use->instruction()->IsCheckArrayBound()) {
      ConstrainValueAfterCheckArrayBound(use, defn);
    }
  }
}


void RangeAnalysis::ConstrainValueAfterCheckArrayBound(
    Value* use,
    Definition* defn) {
  CheckArrayBoundInstr* check = use->instruction()->AsCheckArrayBound();
  intptr_t use_index = use->use_index();

  Range* constraint_range = NULL;
  if (use_index == CheckArrayBoundInstr::kIndexPos) {
    Definition* length = check->length()->definition();
    constraint_range = new(I) Range(
        RangeBoundary::FromConstant(0),
        RangeBoundary::FromDefinition(length, -1));
  } else {
    ASSERT(use_index == CheckArrayBoundInstr::kLengthPos);
    Definition* index = check->index()->definition();
    constraint_range = new(I) Range(
        RangeBoundary::FromDefinition(index, 1),
        RangeBoundary::MaxSmi());
  }
  InsertConstraintFor(use, defn, constraint_range, check);
}


void RangeAnalysis::InsertConstraints() {
  for (intptr_t i = 0; i < values_.length(); i++) {
    InsertConstraintsFor(values_[i]);
  }

  for (intptr_t i = 0; i < constraints_.length(); i++) {
    InsertConstraintsFor(constraints_[i]);
  }
}


const Range* RangeAnalysis::GetSmiRange(Value* value) const {
  Definition* defn = value->definition();
  const Range* range = defn->range();

  if ((range == NULL) && (defn->Type()->ToCid() != kSmiCid)) {
    // Type propagator determined that reaching type for this use is Smi.
    // However the definition itself is not a smi-definition and
    // thus it will never have range assigned to it. Just return the widest
    // range possible for this value.
    // We don't need to handle kMintCid here because all external mints
    // (e.g. results of loads or function call) can be used only after they
    // pass through UnboxIntegerInstr which is considered as mint-definition
    // and will have a range assigned to it.
    // Note: that we can't return NULL here because it is used as lattice's
    // bottom element to indicate that the range was not computed *yet*.
    return &smi_range_;
  }

  return range;
}


static Definition* UnwrapConstraint(Definition* defn) {
  while (defn->IsConstraint()) {
    defn = defn->AsConstraint()->value()->definition();
  }
  return defn;
}


static bool AreEqualDefinitions(Definition* a, Definition* b) {
  a = UnwrapConstraint(a);
  b = UnwrapConstraint(b);
  return (a == b) ||
      (a->AllowsCSE() &&
       a->Dependencies().IsNone() &&
       b->AllowsCSE() &&
       b->Dependencies().IsNone() &&
       a->Equals(b));
}


static bool DependOnSameSymbol(const RangeBoundary& a, const RangeBoundary& b) {
  return a.IsSymbol() && b.IsSymbol() &&
      AreEqualDefinitions(a.symbol(), b.symbol());
}


// Given the current range of a phi and a newly computed range check
// if it is growing towards negative infinity, if it does widen it to
// MinSmi.
static RangeBoundary WidenMin(const Range* range,
                              const Range* new_range,
                              RangeBoundary::RangeSize size) {
  RangeBoundary min = range->min();
  RangeBoundary new_min = new_range->min();

  if (min.IsSymbol()) {
    if (min.LowerBound().Overflowed(size)) {
      return RangeBoundary::MinConstant(size);
    } else if (DependOnSameSymbol(min, new_min)) {
      return min.offset() <= new_min.offset() ?
          min : RangeBoundary::MinConstant(size);
    } else if (min.UpperBound(size) <= new_min.LowerBound(size)) {
      return min;
    }
  }

  min = Range::ConstantMin(range, size);
  new_min = Range::ConstantMin(new_range, size);

  return (min.ConstantValue() <= new_min.ConstantValue()) ?
      min : RangeBoundary::MinConstant(size);
}

// Given the current range of a phi and a newly computed range check
// if it is growing towards positive infinity, if it does widen it to
// MaxSmi.
static RangeBoundary WidenMax(const Range* range,
                              const Range* new_range,
                              RangeBoundary::RangeSize size) {
  RangeBoundary max = range->max();
  RangeBoundary new_max = new_range->max();

  if (max.IsSymbol()) {
    if (max.UpperBound().Overflowed(size)) {
      return RangeBoundary::MaxConstant(size);
    } else if (DependOnSameSymbol(max, new_max)) {
      return max.offset() >= new_max.offset() ?
          max : RangeBoundary::MaxConstant(size);
    } else if (max.LowerBound(size) >= new_max.UpperBound(size)) {
      return max;
    }
  }

  max = Range::ConstantMax(range, size);
  new_max = Range::ConstantMax(new_range, size);

  return (max.ConstantValue() >= new_max.ConstantValue()) ?
      max : RangeBoundary::MaxConstant(size);
}


// Given the current range of a phi and a newly computed range check
// if we can perform narrowing: use newly computed minimum to improve precision
// of the computed range. We do it only if current minimum was widened and is
// equal to MinSmi.
// Newly computed minimum is expected to be greater of equal then old one as
// we are running after widening phase.
static RangeBoundary NarrowMin(const Range* range,
                               const Range* new_range,
                               RangeBoundary::RangeSize size) {
#ifdef DEBUG
  const RangeBoundary min = Range::ConstantMin(range, size);
  const RangeBoundary new_min = Range::ConstantMin(new_range, size);
  ASSERT(min.ConstantValue() <= new_min.ConstantValue());
#endif
  // TODO(vegorov): consider using negative infinity to indicate widened bound.
  return range->min().IsMinimumOrBelow(size) ? new_range->min() : range->min();
}


// Given the current range of a phi and a newly computed range check
// if we can perform narrowing: use newly computed maximum to improve precision
// of the computed range. We do it only if current maximum was widened and is
// equal to MaxSmi.
// Newly computed minimum is expected to be greater of equal then old one as
// we are running after widening phase.
static RangeBoundary NarrowMax(const Range* range,
                               const Range* new_range,
                               RangeBoundary::RangeSize size) {
#ifdef DEBUG
  const RangeBoundary max = Range::ConstantMax(range, size);
  const RangeBoundary new_max = Range::ConstantMax(new_range, size);
  ASSERT(max.ConstantValue() >= new_max.ConstantValue());
#endif
  // TODO(vegorov): consider using positive infinity to indicate widened bound.
  return range->max().IsMaximumOrAbove(size) ? new_range->max() : range->max();
}


char RangeAnalysis::OpPrefix(JoinOperator op) {
  switch (op) {
    case WIDEN: return 'W';
    case NARROW: return 'N';
    case NONE: return 'I';
  }
  UNREACHABLE();
  return ' ';
}


bool RangeAnalysis::InferRange(JoinOperator op,
                               Definition* defn,
                               intptr_t iteration) {
  Range range;
  defn->InferRange(this, &range);

  if (!Range::IsUnknown(&range)) {
    if (!Range::IsUnknown(defn->range()) && defn->IsPhi()) {
      // TODO(vegorov): we are currently supporting only smi/int32 phis.
      ASSERT((defn->Type()->ToCid() == kSmiCid) ||
             (defn->representation() == kUnboxedInt32));
      const RangeBoundary::RangeSize size = (defn->Type()->ToCid() == kSmiCid) ?
          RangeBoundary::kRangeBoundarySmi : RangeBoundary::kRangeBoundaryInt32;
      if (op == WIDEN) {
        range = Range(WidenMin(defn->range(), &range, size),
                      WidenMax(defn->range(), &range, size));
      } else if (op == NARROW) {
        range = Range(NarrowMin(defn->range(), &range, size),
                      NarrowMax(defn->range(), &range, size));
      }
    }

    if (!range.Equals(defn->range())) {
      if (FLAG_trace_range_analysis) {
        OS::Print("%c [%" Pd "] %s:  %s => %s\n",
                  OpPrefix(op),
                  iteration,
                  defn->ToCString(),
                  Range::ToCString(defn->range()),
                  Range::ToCString(&range));
      }
      defn->set_range(range);
      return true;
    }
  }

  return false;
}


void RangeAnalysis::CollectDefinitions(BlockEntryInstr* block, BitVector* set) {
  for (BlockIterator block_it = flow_graph_->reverse_postorder_iterator();
       !block_it.Done();
       block_it.Advance()) {
    BlockEntryInstr* block = block_it.Current();

    JoinEntryInstr* join = block->AsJoinEntry();
    if (join != NULL) {
      for (PhiIterator it(join); !it.Done(); it.Advance()) {
        PhiInstr* phi = it.Current();
        if (set->Contains(phi->ssa_temp_index())) {
          definitions_.Add(phi);
        }
      }
    }

    for (ForwardInstructionIterator it(block); !it.Done(); it.Advance()) {
      Definition* defn = it.Current()->AsDefinition();
      if ((defn != NULL) &&
          (defn->ssa_temp_index() != -1) &&
          set->Contains(defn->ssa_temp_index())) {
        definitions_.Add(defn);
      }
    }
  }
}


void RangeAnalysis::Iterate(JoinOperator op, intptr_t max_iterations) {
  // TODO(vegorov): switch to worklist if this becomes performance bottleneck.
  intptr_t iteration = 0;
  bool changed;
  do {
    changed = false;
    for (intptr_t i = 0; i < definitions_.length(); i++) {
      Definition* defn = definitions_[i];
      if (InferRange(op, defn, iteration)) {
        changed = true;
      }
    }

    iteration++;
  } while (changed && (iteration < max_iterations));
}


void RangeAnalysis::InferRanges() {
  if (FLAG_trace_range_analysis) {
    FlowGraphPrinter::PrintGraph("Range Analysis (BEFORE)", flow_graph_);
  }

  // Initialize bitvector for quick filtering of int values.
  BitVector* set = new(I) BitVector(flow_graph_->current_ssa_temp_index());
  for (intptr_t i = 0; i < values_.length(); i++) {
    set->Add(values_[i]->ssa_temp_index());
  }
  for (intptr_t i = 0; i < constraints_.length(); i++) {
    set->Add(constraints_[i]->ssa_temp_index());
  }

  // Collect integer definitions (including constraints) in the reverse
  // postorder. This improves convergence speed compared to iterating
  // values_ and constraints_ array separately.
  const GrowableArray<Definition*>& initial =
      *flow_graph_->graph_entry()->initial_definitions();
  for (intptr_t i = 0; i < initial.length(); ++i) {
    Definition* definition = initial[i];
    if (set->Contains(definition->ssa_temp_index())) {
      definitions_.Add(definition);
    }
  }
  CollectDefinitions(flow_graph_->graph_entry(), set);

  // Perform an iteration of range inference just propagating ranges
  // through the graph as-is without applying widening or narrowing.
  // This helps to improve precision of initial bounds.
  Iterate(NONE, 1);

  // Perform fix-point iteration of range inference applying widening
  // operator to phis to ensure fast convergence.
  // Widening simply maps growing bounds to the respective range bound.
  Iterate(WIDEN, kMaxInt32);

  if (FLAG_trace_range_analysis) {
    FlowGraphPrinter::PrintGraph("Range Analysis (WIDEN)", flow_graph_);
  }

  // Perform fix-point iteration of range inference applying narrowing
  // to phis to compute more accurate range.
  // Narrowing only improves those boundaries that were widened up to
  // range boundary and leaves other boundaries intact.
  Iterate(NARROW, kMaxInt32);

  if (FLAG_trace_range_analysis) {
    FlowGraphPrinter::PrintGraph("Range Analysis (AFTER)", flow_graph_);
  }
}


void RangeAnalysis::EliminateRedundantBoundsChecks() {
  if (FLAG_array_bounds_check_elimination) {
    for (intptr_t i = 0; i < bounds_checks_.length(); i++) {
      CheckArrayBoundInstr* check = bounds_checks_[i];
      RangeBoundary array_length =
          RangeBoundary::FromDefinition(check->length()->definition());
      if (check->IsRedundant(array_length)) {
        check->RemoveFromGraph();
      }
    }
  }
}


void RangeAnalysis::MarkUnreachableBlocks() {
  for (intptr_t i = 0; i < constraints_.length(); i++) {
    if (Range::IsUnknown(constraints_[i]->range())) {
      TargetEntryInstr* target = constraints_[i]->target();
      if (target == NULL) {
        // TODO(vegorov): replace Constraint with an uncoditional
        // deoptimization and kill all dominated dead code.
        continue;
      }

      BranchInstr* branch =
          target->PredecessorAt(0)->last_instruction()->AsBranch();
      if (target == branch->true_successor()) {
        // True unreachable.
        if (FLAG_trace_constant_propagation) {
          OS::Print("Range analysis: True unreachable (B%" Pd ")\n",
                    branch->true_successor()->block_id());
        }
        branch->set_constant_target(branch->false_successor());
      } else {
        ASSERT(target == branch->false_successor());
        // False unreachable.
        if (FLAG_trace_constant_propagation) {
          OS::Print("Range analysis: False unreachable (B%" Pd ")\n",
                    branch->false_successor()->block_id());
        }
        branch->set_constant_target(branch->true_successor());
      }
    }
  }
}


void RangeAnalysis::RemoveConstraints() {
  for (intptr_t i = 0; i < constraints_.length(); i++) {
    Definition* def = constraints_[i]->value()->definition();
    // Some constraints might be constraining constraints. Unwind the chain of
    // constraints until we reach the actual definition.
    while (def->IsConstraint()) {
      def = def->AsConstraint()->value()->definition();
    }
    constraints_[i]->ReplaceUsesWith(def);
    constraints_[i]->RemoveFromGraph();
  }
}


static void NarrowBinaryMintOp(BinaryMintOpInstr* mint_op) {
  if (Range::Fits(mint_op->range(), RangeBoundary::kRangeBoundaryInt32) &&
      Range::Fits(mint_op->left()->definition()->range(),
                  RangeBoundary::kRangeBoundaryInt32) &&
      Range::Fits(mint_op->right()->definition()->range(),
                  RangeBoundary::kRangeBoundaryInt32) &&
      BinaryInt32OpInstr::IsSupported(mint_op->op_kind(),
                                      mint_op->left(),
                                      mint_op->right())) {
    BinaryInt32OpInstr* int32_op =
        new BinaryInt32OpInstr(mint_op->op_kind(),
                               mint_op->left()->CopyWithType(),
                               mint_op->right()->CopyWithType(),
                               mint_op->DeoptimizationTarget());
    int32_op->set_range(*mint_op->range());
    int32_op->set_overflow(false);
    mint_op->ReplaceWith(int32_op, NULL);
  }
}


static void NarrowShiftMintOp(ShiftMintOpInstr* mint_op) {
  if (Range::Fits(mint_op->range(), RangeBoundary::kRangeBoundaryInt32) &&
      Range::Fits(mint_op->left()->definition()->range(),
                  RangeBoundary::kRangeBoundaryInt32) &&
      Range::Fits(mint_op->right()->definition()->range(),
                  RangeBoundary::kRangeBoundaryInt32) &&
      BinaryInt32OpInstr::IsSupported(mint_op->op_kind(),
                                      mint_op->left(),
                                      mint_op->right())) {
    BinaryInt32OpInstr* int32_op =
        new BinaryInt32OpInstr(mint_op->op_kind(),
                               mint_op->left()->CopyWithType(),
                               mint_op->right()->CopyWithType(),
                               mint_op->DeoptimizationTarget());
    int32_op->set_range(*mint_op->range());
    int32_op->set_overflow(false);
    mint_op->ReplaceWith(int32_op, NULL);
  }
}


void RangeAnalysis::NarrowMintToInt32() {
  for (intptr_t i = 0; i < binary_mint_ops_.length(); i++) {
    NarrowBinaryMintOp(binary_mint_ops_[i]);
  }

  for (intptr_t i = 0; i < shift_mint_ops_.length(); i++) {
    NarrowShiftMintOp(shift_mint_ops_[i]);
  }
}


IntegerInstructionSelector::IntegerInstructionSelector(FlowGraph* flow_graph)
    : flow_graph_(flow_graph),
      isolate_(NULL) {
  ASSERT(flow_graph_ != NULL);
  isolate_ = flow_graph_->isolate();
  ASSERT(isolate_ != NULL);
  selected_uint32_defs_ =
      new(I) BitVector(flow_graph_->current_ssa_temp_index());
}


void IntegerInstructionSelector::Select() {
  if (FLAG_trace_integer_ir_selection) {
    OS::Print("---- starting integer ir selection -------\n");
  }
  FindPotentialUint32Definitions();
  FindUint32NarrowingDefinitions();
  Propagate();
  ReplaceInstructions();
  if (FLAG_trace_integer_ir_selection) {
    OS::Print("---- after integer ir selection -------\n");
    FlowGraphPrinter printer(*flow_graph_);
    printer.PrintBlocks();
  }
}


bool IntegerInstructionSelector::IsPotentialUint32Definition(Definition* def) {
  // TODO(johnmccutchan): Consider Smi operations, to avoid unnecessary tagging
  // & untagged of intermediate results.
  // TODO(johnmccutchan): Consider phis.
  return def->IsBoxInteger()   ||   // BoxMint.
         def->IsUnboxInteger() ||   // UnboxMint.
         def->IsBinaryMintOp() ||
         def->IsShiftMintOp()  ||
         def->IsUnaryMintOp();
}


void IntegerInstructionSelector::FindPotentialUint32Definitions() {
  if (FLAG_trace_integer_ir_selection) {
    OS::Print("++++ Finding potential Uint32 definitions:\n");
  }

  for (BlockIterator block_it = flow_graph_->reverse_postorder_iterator();
       !block_it.Done();
       block_it.Advance()) {
    BlockEntryInstr* block = block_it.Current();

    for (ForwardInstructionIterator instr_it(block);
         !instr_it.Done();
         instr_it.Advance()) {
      Instruction* current = instr_it.Current();
      Definition* defn = current->AsDefinition();
      if ((defn != NULL) && (defn->ssa_temp_index() != -1)) {
        if (IsPotentialUint32Definition(defn)) {
          if (FLAG_trace_integer_ir_selection) {
           OS::Print("Adding %s\n", current->ToCString());
          }
          potential_uint32_defs_.Add(defn);
        }
      }
    }
  }
}


// BinaryMintOp masks and stores into unsigned typed arrays that truncate the
// value into a Uint32 range.
bool IntegerInstructionSelector::IsUint32NarrowingDefinition(Definition* def) {
  if (def->IsBinaryMintOp()) {
    BinaryMintOpInstr* op = def->AsBinaryMintOp();
    // Must be a mask operation.
    if (op->op_kind() != Token::kBIT_AND) {
      return false;
    }
    Range* range = op->range();
    if ((range == NULL) ||
        !range->IsWithin(0, static_cast<int64_t>(kMaxUint32))) {
      return false;
    }
    return true;
  }
  // TODO(johnmccutchan): Add typed array stores.
  return false;
}


void IntegerInstructionSelector::FindUint32NarrowingDefinitions() {
  ASSERT(selected_uint32_defs_ != NULL);
  if (FLAG_trace_integer_ir_selection) {
    OS::Print("++++ Selecting Uint32 definitions:\n");
    OS::Print("++++ Initial set:\n");
  }
  for (intptr_t i = 0; i < potential_uint32_defs_.length(); i++) {
    Definition* defn = potential_uint32_defs_[i];
    if (IsUint32NarrowingDefinition(defn)) {
      if (FLAG_trace_integer_ir_selection) {
        OS::Print("Adding %s\n", defn->ToCString());
      }
      selected_uint32_defs_->Add(defn->ssa_temp_index());
    }
  }
}


bool IntegerInstructionSelector::AllUsesAreUint32Narrowing(Value* list_head) {
  for (Value::Iterator it(list_head);
       !it.Done();
       it.Advance()) {
    Value* use = it.Current();
    Definition* defn = use->instruction()->AsDefinition();
    if ((defn == NULL) ||
        (defn->ssa_temp_index() == -1) ||
        !selected_uint32_defs_->Contains(defn->ssa_temp_index())) {
      return false;
    }
  }
  return true;
}


bool IntegerInstructionSelector::CanBecomeUint32(Definition* def) {
  ASSERT(IsPotentialUint32Definition(def));
  if (def->IsBoxInteger()) {
    // If a BoxInteger's input is a candidate, the box is a candidate.
    BoxIntegerInstr* box = def->AsBoxInteger();
    Definition* box_input = box->value()->definition();
    return selected_uint32_defs_->Contains(box_input->ssa_temp_index());
  }
  // A right shift with an input outside of Uint32 range cannot be converted
  // because we need the high bits.
  if (def->IsShiftMintOp()) {
    ShiftMintOpInstr* op = def->AsShiftMintOp();
    if (op->op_kind() == Token::kSHR) {
      Definition* shift_input = op->left()->definition();
      ASSERT(shift_input != NULL);
      Range* range = shift_input->range();
      if ((range == NULL) ||
          !range->IsWithin(0, static_cast<int64_t>(kMaxUint32))) {
        return false;
      }
    }
  }
  if (!def->HasUses()) {
    // No uses, skip.
    return false;
  }
  return AllUsesAreUint32Narrowing(def->input_use_list()) &&
         AllUsesAreUint32Narrowing(def->env_use_list());
}


void IntegerInstructionSelector::Propagate() {
  ASSERT(selected_uint32_defs_ != NULL);
  bool changed = true;
  intptr_t iteration = 0;
  while (changed) {
    if (FLAG_trace_integer_ir_selection) {
      OS::Print("+++ Iteration: %" Pd "\n", iteration++);
    }
    changed = false;
    for (intptr_t i = 0; i < potential_uint32_defs_.length(); i++) {
      Definition* defn = potential_uint32_defs_[i];
      if (selected_uint32_defs_->Contains(defn->ssa_temp_index())) {
        // Already marked as a candidate, skip.
        continue;
      }
      if (defn->IsConstant()) {
        // Skip constants.
        continue;
      }
      if (CanBecomeUint32(defn)) {
        if (FLAG_trace_integer_ir_selection) {
          OS::Print("Adding %s\n", defn->ToCString());
        }
        // Found a new candidate.
        selected_uint32_defs_->Add(defn->ssa_temp_index());
        // Haven't reached fixed point yet.
        changed = true;
      }
    }
  }
  if (FLAG_trace_integer_ir_selection) {
    OS::Print("Reached fixed point\n");
  }
}


Definition* IntegerInstructionSelector::ConstructReplacementFor(
    Definition* def) {
  // Should only see mint definitions.
  ASSERT(IsPotentialUint32Definition(def));
  // Should not see constant instructions.
  ASSERT(!def->IsConstant());
  if (def->IsBinaryMintOp()) {
    BinaryMintOpInstr* op = def->AsBinaryMintOp();
    Token::Kind op_kind = op->op_kind();
    Value* left = op->left()->CopyWithType();
    Value* right = op->right()->CopyWithType();
    intptr_t deopt_id = op->DeoptimizationTarget();
    return new(I) BinaryUint32OpInstr(op_kind, left, right, deopt_id);
  } else if (def->IsBoxInteger()) {
    BoxIntegerInstr* box = def->AsBoxInteger();
    Value* value = box->value()->CopyWithType();
    return new(I) BoxUint32Instr(value);
  } else if (def->IsUnboxInteger()) {
    UnboxIntegerInstr* unbox = def->AsUnboxInteger();
    Value* value = unbox->value()->CopyWithType();
    intptr_t deopt_id = unbox->deopt_id();
    return new(I) UnboxUint32Instr(value, deopt_id);
  } else if (def->IsUnaryMintOp()) {
    UnaryMintOpInstr* op = def->AsUnaryMintOp();
    Token::Kind op_kind = op->op_kind();
    Value* value = op->value()->CopyWithType();
    intptr_t deopt_id = op->DeoptimizationTarget();
    return new(I) UnaryUint32OpInstr(op_kind, value, deopt_id);
  } else if (def->IsShiftMintOp()) {
    ShiftMintOpInstr* op = def->AsShiftMintOp();
    Token::Kind op_kind = op->op_kind();
    Value* left = op->left()->CopyWithType();
    Value* right = op->right()->CopyWithType();
    intptr_t deopt_id = op->DeoptimizationTarget();
    return new(I) ShiftUint32OpInstr(op_kind, left, right, deopt_id);
  }
  UNREACHABLE();
  return NULL;
}


void IntegerInstructionSelector::ReplaceInstructions() {
  if (FLAG_trace_integer_ir_selection) {
    OS::Print("++++ Replacing instructions:\n");
  }
  for (intptr_t i = 0; i < potential_uint32_defs_.length(); i++) {
    Definition* defn = potential_uint32_defs_[i];
    if (!selected_uint32_defs_->Contains(defn->ssa_temp_index())) {
      // Not a candidate.
      continue;
    }
    Definition* replacement = ConstructReplacementFor(defn);
    ASSERT(replacement != NULL);
    if (FLAG_trace_integer_ir_selection) {
      OS::Print("Replacing %s with %s\n", defn->ToCString(),
                                          replacement->ToCString());
    }
    if (!Range::IsUnknown(defn->range())) {
      replacement->set_range(*defn->range());
    }
    defn->ReplaceWith(replacement, NULL);
    ASSERT(flow_graph_->VerifyUseLists());
  }
}


RangeBoundary RangeBoundary::FromDefinition(Definition* defn, int64_t offs) {
  if (defn->IsConstant() && defn->AsConstant()->value().IsSmi()) {
    return FromConstant(Smi::Cast(defn->AsConstant()->value()).Value() + offs);
  }
  return RangeBoundary(kSymbol, reinterpret_cast<intptr_t>(defn), offs);
}


RangeBoundary RangeBoundary::LowerBound() const {
  if (IsInfinity()) {
    return NegativeInfinity();
  }
  if (IsConstant()) return *this;
  return Add(Range::ConstantMinSmi(symbol()->range()),
             RangeBoundary::FromConstant(offset_),
             NegativeInfinity());
}


RangeBoundary RangeBoundary::UpperBound() const {
  if (IsInfinity()) {
    return PositiveInfinity();
  }
  if (IsConstant()) return *this;

  return Add(Range::ConstantMaxSmi(symbol()->range()),
             RangeBoundary::FromConstant(offset_),
             PositiveInfinity());
}


RangeBoundary RangeBoundary::Add(const RangeBoundary& a,
                                 const RangeBoundary& b,
                                 const RangeBoundary& overflow) {
  if (a.IsInfinity() || b.IsInfinity()) return overflow;

  ASSERT(a.IsConstant() && b.IsConstant());
  if (Utils::WillAddOverflow(a.ConstantValue(), b.ConstantValue())) {
    return overflow;
  }

  int64_t result = a.ConstantValue() + b.ConstantValue();

  return RangeBoundary::FromConstant(result);
}


RangeBoundary RangeBoundary::Sub(const RangeBoundary& a,
                                 const RangeBoundary& b,
                                 const RangeBoundary& overflow) {
  if (a.IsInfinity() || b.IsInfinity()) return overflow;
  ASSERT(a.IsConstant() && b.IsConstant());
  if (Utils::WillSubOverflow(a.ConstantValue(), b.ConstantValue())) {
    return overflow;
  }

  int64_t result = a.ConstantValue() - b.ConstantValue();

  return RangeBoundary::FromConstant(result);
}


bool RangeBoundary::SymbolicAdd(const RangeBoundary& a,
                                const RangeBoundary& b,
                                RangeBoundary* result) {
  if (a.IsSymbol() && b.IsConstant()) {
    if (Utils::WillAddOverflow(a.offset(), b.ConstantValue())) {
      return false;
    }

    const int64_t offset = a.offset() + b.ConstantValue();

    *result = RangeBoundary::FromDefinition(a.symbol(), offset);
    return true;
  } else if (b.IsSymbol() && a.IsConstant()) {
    return SymbolicAdd(b, a, result);
  }
  return false;
}


bool RangeBoundary::SymbolicSub(const RangeBoundary& a,
                                const RangeBoundary& b,
                                RangeBoundary* result) {
  if (a.IsSymbol() && b.IsConstant()) {
    if (Utils::WillSubOverflow(a.offset(), b.ConstantValue())) {
      return false;
    }

    const int64_t offset = a.offset() - b.ConstantValue();

    *result = RangeBoundary::FromDefinition(a.symbol(), offset);
    return true;
  }
  return false;
}


bool RangeBoundary::Equals(const RangeBoundary& other) const {
  if (IsConstant() && other.IsConstant()) {
    return ConstantValue() == other.ConstantValue();
  } else if (IsInfinity() && other.IsInfinity()) {
    return kind() == other.kind();
  } else if (IsSymbol() && other.IsSymbol()) {
    return (offset() == other.offset()) && DependOnSameSymbol(*this, other);
  } else if (IsUnknown() && other.IsUnknown()) {
    return true;
  }
  return false;
}


RangeBoundary RangeBoundary::Shl(const RangeBoundary& value_boundary,
                                 int64_t shift_count,
                                 const RangeBoundary& overflow) {
  ASSERT(value_boundary.IsConstant());
  ASSERT(shift_count >= 0);
  int64_t limit = 64 - shift_count;
  int64_t value = value_boundary.ConstantValue();

  if ((value == 0) ||
      (shift_count == 0) ||
      ((limit > 0) && Utils::IsInt(static_cast<int>(limit), value))) {
    // Result stays in 64 bit range.
    int64_t result = value << shift_count;
    return RangeBoundary(result);
  }

  return overflow;
}


static RangeBoundary CanonicalizeBoundary(const RangeBoundary& a,
                                          const RangeBoundary& overflow) {
  if (a.IsConstant() || a.IsInfinity()) {
    return a;
  }

  int64_t offset = a.offset();
  Definition* symbol = a.symbol();

  bool changed;
  do {
    changed = false;
    if (symbol->IsConstraint()) {
      symbol = symbol->AsConstraint()->value()->definition();
      changed = true;
    } else if (symbol->IsBinarySmiOp()) {
      BinarySmiOpInstr* op = symbol->AsBinarySmiOp();
      Definition* left = op->left()->definition();
      Definition* right = op->right()->definition();
      switch (op->op_kind()) {
        case Token::kADD:
          if (right->IsConstant()) {
            int64_t rhs = Smi::Cast(right->AsConstant()->value()).Value();
            if (Utils::WillAddOverflow(offset, rhs)) {
              return overflow;
            }
            offset += rhs;
            symbol = left;
            changed = true;
          } else if (left->IsConstant()) {
            int64_t rhs = Smi::Cast(left->AsConstant()->value()).Value();
            if (Utils::WillAddOverflow(offset, rhs)) {
              return overflow;
            }
            offset += rhs;
            symbol = right;
            changed = true;
          }
          break;

        case Token::kSUB:
          if (right->IsConstant()) {
            int64_t rhs = Smi::Cast(right->AsConstant()->value()).Value();
            if (Utils::WillSubOverflow(offset, rhs)) {
              return overflow;
            }
            offset -= rhs;
            symbol = left;
            changed = true;
          }
          break;

        default:
          break;
      }
    }
  } while (changed);

  return RangeBoundary::FromDefinition(symbol, offset);
}


static bool CanonicalizeMaxBoundary(RangeBoundary* a) {
  if (!a->IsSymbol()) return false;

  Range* range = a->symbol()->range();
  if ((range == NULL) || !range->max().IsSymbol()) return false;


  if (Utils::WillAddOverflow(range->max().offset(), a->offset())) {
    *a = RangeBoundary::PositiveInfinity();
    return true;
  }

  const int64_t offset = range->max().offset() + a->offset();


  *a = CanonicalizeBoundary(
      RangeBoundary::FromDefinition(range->max().symbol(), offset),
      RangeBoundary::PositiveInfinity());

  return true;
}


static bool CanonicalizeMinBoundary(RangeBoundary* a) {
  if (!a->IsSymbol()) return false;

  Range* range = a->symbol()->range();
  if ((range == NULL) || !range->min().IsSymbol()) return false;

  if (Utils::WillAddOverflow(range->min().offset(), a->offset())) {
    *a = RangeBoundary::NegativeInfinity();
    return true;
  }

  const int64_t offset = range->min().offset() + a->offset();

  *a = CanonicalizeBoundary(
      RangeBoundary::FromDefinition(range->min().symbol(), offset),
      RangeBoundary::NegativeInfinity());

  return true;
}

typedef bool (*BoundaryOp)(RangeBoundary*);

static bool CanonicalizeForComparison(RangeBoundary* a,
                                      RangeBoundary* b,
                                      BoundaryOp op,
                                      const RangeBoundary& overflow) {
  if (!a->IsSymbol() || !b->IsSymbol()) {
    return false;
  }

  if (DependOnSameSymbol(*a, *b)) {
    return true;
  }


  RangeBoundary canonical_a = CanonicalizeBoundary(*a, overflow);
  RangeBoundary canonical_b = CanonicalizeBoundary(*b, overflow);

  do {
    if (DependOnSameSymbol(canonical_a, canonical_b)) {
      *a = canonical_a;
      *b = canonical_b;
      return true;
    }
  } while (op(&canonical_a) || op(&canonical_b));

  return false;
}


RangeBoundary RangeBoundary::JoinMin(RangeBoundary a,
                                     RangeBoundary b,
                                     RangeBoundary::RangeSize size) {
  if (a.Equals(b)) {
    return b;
  }

  if (CanonicalizeForComparison(&a,
                                &b,
                                &CanonicalizeMinBoundary,
                                RangeBoundary::NegativeInfinity())) {
    return (a.offset() <= b.offset()) ? a : b;
  }

  const int64_t inf_a = a.LowerBound(size);
  const int64_t inf_b = b.LowerBound(size);
  const int64_t sup_a = a.UpperBound(size);
  const int64_t sup_b = b.UpperBound(size);

  if ((sup_a <= inf_b) && !a.LowerBound().Overflowed(size)) {
    return a;
  } else if ((sup_b <= inf_a) && !b.LowerBound().Overflowed(size)) {
    return b;
  } else {
    return RangeBoundary::FromConstant(Utils::Minimum(inf_a, inf_b));
  }
}


RangeBoundary RangeBoundary::JoinMax(RangeBoundary a,
                                     RangeBoundary b,
                                     RangeBoundary::RangeSize size) {
  if (a.Equals(b)) {
    return b;
  }

  if (CanonicalizeForComparison(&a,
                                &b,
                                &CanonicalizeMaxBoundary,
                                RangeBoundary::PositiveInfinity())) {
    return (a.offset() >= b.offset()) ? a : b;
  }

  const int64_t inf_a = a.LowerBound(size);
  const int64_t inf_b = b.LowerBound(size);
  const int64_t sup_a = a.UpperBound(size);
  const int64_t sup_b = b.UpperBound(size);

  if ((sup_a <= inf_b) && !b.UpperBound().Overflowed(size)) {
    return b;
  } else if ((sup_b <= inf_a) && !a.UpperBound().Overflowed(size)) {
    return a;
  } else {
    return RangeBoundary::FromConstant(Utils::Maximum(sup_a, sup_b));
  }
}


RangeBoundary RangeBoundary::IntersectionMin(RangeBoundary a, RangeBoundary b) {
  ASSERT(!a.IsPositiveInfinity() && !b.IsPositiveInfinity());
  ASSERT(!a.IsUnknown() && !b.IsUnknown());

  if (a.Equals(b)) {
    return a;
  }

  if (a.IsMinimumOrBelow(RangeBoundary::kRangeBoundarySmi)) {
    return b;
  } else if (b.IsMinimumOrBelow(RangeBoundary::kRangeBoundarySmi)) {
    return a;
  }

  if (CanonicalizeForComparison(&a,
                                &b,
                                &CanonicalizeMinBoundary,
                                RangeBoundary::NegativeInfinity())) {
    return (a.offset() >= b.offset()) ? a : b;
  }

  const int64_t inf_a = a.SmiLowerBound();
  const int64_t inf_b = b.SmiLowerBound();

  return (inf_a >= inf_b) ? a : b;
}


RangeBoundary RangeBoundary::IntersectionMax(RangeBoundary a, RangeBoundary b) {
  ASSERT(!a.IsNegativeInfinity() && !b.IsNegativeInfinity());
  ASSERT(!a.IsUnknown() && !b.IsUnknown());

  if (a.Equals(b)) {
    return a;
  }

  if (a.IsMaximumOrAbove(RangeBoundary::kRangeBoundarySmi)) {
    return b;
  } else if (b.IsMaximumOrAbove(RangeBoundary::kRangeBoundarySmi)) {
    return a;
  }

  if (CanonicalizeForComparison(&a,
                                &b,
                                &CanonicalizeMaxBoundary,
                                RangeBoundary::PositiveInfinity())) {
    return (a.offset() <= b.offset()) ? a : b;
  }

  const int64_t sup_a = a.SmiUpperBound();
  const int64_t sup_b = b.SmiUpperBound();

  return (sup_a <= sup_b) ? a : b;
}


int64_t RangeBoundary::ConstantValue() const {
  ASSERT(IsConstant());
  return value_;
}


bool Range::IsPositive() const {
  if (min().IsNegativeInfinity()) {
    return false;
  }
  if (min().LowerBound().ConstantValue() < 0) {
    return false;
  }
  if (max().IsPositiveInfinity()) {
    return true;
  }
  return max().UpperBound().ConstantValue() >= 0;
}


bool Range::OnlyLessThanOrEqualTo(int64_t val) const {
  if (max().IsPositiveInfinity()) {
    // Cannot be true.
    return false;
  }
  if (max().UpperBound().ConstantValue() > val) {
    // Not true.
    return false;
  }
  return true;
}


bool Range::OnlyGreaterThanOrEqualTo(int64_t val) const {
  if (min().IsNegativeInfinity()) {
    return false;
  }
  if (min().LowerBound().ConstantValue() < val) {
    return false;
  }
  return true;
}


// Inclusive.
bool Range::IsWithin(int64_t min_int, int64_t max_int) const {
  RangeBoundary lower_min = min().LowerBound();
  if (lower_min.IsNegativeInfinity() || (lower_min.ConstantValue() < min_int)) {
    return false;
  }
  RangeBoundary upper_max = max().UpperBound();
  if (upper_max.IsPositiveInfinity() || (upper_max.ConstantValue() > max_int)) {
    return false;
  }
  return true;
}


bool Range::Overlaps(int64_t min_int, int64_t max_int) const {
  RangeBoundary lower = min().LowerBound();
  RangeBoundary upper = max().UpperBound();
  const int64_t this_min = lower.IsNegativeInfinity() ?
      RangeBoundary::kMin : lower.ConstantValue();
  const int64_t this_max = upper.IsPositiveInfinity() ?
      RangeBoundary::kMax : upper.ConstantValue();
  if ((this_min <= min_int) && (min_int <= this_max)) return true;
  if ((this_min <= max_int) && (max_int <= this_max)) return true;
  if ((min_int < this_min) && (max_int > this_max)) return true;
  return false;
}


bool Range::IsUnsatisfiable() const {
  // Infinity case: [+inf, ...] || [..., -inf]
  if (min().IsPositiveInfinity() || max().IsNegativeInfinity()) {
    return true;
  }
  // Constant case: For example [0, -1].
  if (Range::ConstantMin(this).ConstantValue() >
      Range::ConstantMax(this).ConstantValue()) {
    return true;
  }
  // Symbol case: For example [v+1, v].
  if (DependOnSameSymbol(min(), max()) && min().offset() > max().offset()) {
    return true;
  }
  return false;
}


void Range::Clamp(RangeBoundary::RangeSize size) {
  min_ = min_.Clamp(size);
  max_ = max_.Clamp(size);
}


void Range::Shl(const Range* left,
                const Range* right,
                RangeBoundary* result_min,
                RangeBoundary* result_max) {
  ASSERT(left != NULL);
  ASSERT(right != NULL);
  ASSERT(result_min != NULL);
  ASSERT(result_max != NULL);
  RangeBoundary left_max = Range::ConstantMax(left);
  RangeBoundary left_min = Range::ConstantMin(left);
  // A negative shift count always deoptimizes (and throws), so the minimum
  // shift count is zero.
  int64_t right_max = Utils::Maximum(Range::ConstantMax(right).ConstantValue(),
                                     static_cast<int64_t>(0));
  int64_t right_min = Utils::Maximum(Range::ConstantMin(right).ConstantValue(),
                                     static_cast<int64_t>(0));

  *result_min = RangeBoundary::Shl(
      left_min,
      left_min.ConstantValue() > 0 ? right_min : right_max,
      left_min.ConstantValue() > 0
          ? RangeBoundary::PositiveInfinity()
          : RangeBoundary::NegativeInfinity());

  *result_max = RangeBoundary::Shl(
      left_max,
      left_max.ConstantValue() > 0 ? right_max : right_min,
      left_max.ConstantValue() > 0
          ? RangeBoundary::PositiveInfinity()
          : RangeBoundary::NegativeInfinity());
}


void Range::Shr(const Range* left,
                const Range* right,
                RangeBoundary* result_min,
                RangeBoundary* result_max) {
  RangeBoundary left_max = Range::ConstantMax(left);
  RangeBoundary left_min = Range::ConstantMin(left);
  // A negative shift count always deoptimizes (and throws), so the minimum
  // shift count is zero.
  int64_t right_max = Utils::Maximum(Range::ConstantMax(right).ConstantValue(),
                                     static_cast<int64_t>(0));
  int64_t right_min = Utils::Maximum(Range::ConstantMin(right).ConstantValue(),
                                     static_cast<int64_t>(0));

  *result_min = RangeBoundary::Shr(
      left_min,
      left_min.ConstantValue() > 0 ? right_max : right_min);

  *result_max = RangeBoundary::Shr(
      left_max,
      left_max.ConstantValue() > 0 ? right_min : right_max);
}


bool Range::And(const Range* left_range,
                const Range* right_range,
                RangeBoundary* result_min,
                RangeBoundary* result_max) {
  ASSERT(left_range != NULL);
  ASSERT(right_range != NULL);
  ASSERT(result_min != NULL);
  ASSERT(result_max != NULL);

  if (Range::ConstantMin(right_range).ConstantValue() >= 0) {
    *result_min = RangeBoundary::FromConstant(0);
    *result_max = Range::ConstantMax(right_range);
    return true;
  }

  if (Range::ConstantMin(left_range).ConstantValue() >= 0) {
    *result_min = RangeBoundary::FromConstant(0);
    *result_max = Range::ConstantMax(left_range);
    return true;
  }

  return false;
}


static bool IsArrayLength(Definition* defn) {
  if (defn == NULL) {
    return false;
  }
  LoadFieldInstr* load = UnwrapConstraint(defn)->AsLoadField();
  return (load != NULL) && load->IsImmutableLengthLoad();
}


void Range::Add(const Range* left_range,
                const Range* right_range,
                RangeBoundary* result_min,
                RangeBoundary* result_max,
                Definition* left_defn) {
  ASSERT(left_range != NULL);
  ASSERT(right_range != NULL);
  ASSERT(result_min != NULL);
  ASSERT(result_max != NULL);

  RangeBoundary left_min =
    IsArrayLength(left_defn) ?
        RangeBoundary::FromDefinition(left_defn) : left_range->min();

  RangeBoundary left_max =
    IsArrayLength(left_defn) ?
        RangeBoundary::FromDefinition(left_defn) : left_range->max();

  if (!RangeBoundary::SymbolicAdd(left_min, right_range->min(), result_min)) {
    *result_min = RangeBoundary::Add(left_range->min().LowerBound(),
                                     right_range->min().LowerBound(),
                                     RangeBoundary::NegativeInfinity());
  }
  if (!RangeBoundary::SymbolicAdd(left_max, right_range->max(), result_max)) {
    *result_max = RangeBoundary::Add(right_range->max().UpperBound(),
                                     left_range->max().UpperBound(),
                                     RangeBoundary::PositiveInfinity());
  }
}


void Range::Sub(const Range* left_range,
                const Range* right_range,
                RangeBoundary* result_min,
                RangeBoundary* result_max,
                Definition* left_defn) {
  ASSERT(left_range != NULL);
  ASSERT(right_range != NULL);
  ASSERT(result_min != NULL);
  ASSERT(result_max != NULL);

  RangeBoundary left_min =
    IsArrayLength(left_defn) ?
        RangeBoundary::FromDefinition(left_defn) : left_range->min();

  RangeBoundary left_max =
    IsArrayLength(left_defn) ?
        RangeBoundary::FromDefinition(left_defn) : left_range->max();

  if (!RangeBoundary::SymbolicSub(left_min, right_range->max(), result_min)) {
    *result_min = RangeBoundary::Sub(left_range->min().LowerBound(),
                              right_range->max().UpperBound(),
                              RangeBoundary::NegativeInfinity());
  }
  if (!RangeBoundary::SymbolicSub(left_max, right_range->min(), result_max)) {
    *result_max = RangeBoundary::Sub(left_range->max().UpperBound(),
                                     right_range->min().LowerBound(),
                                     RangeBoundary::PositiveInfinity());
  }
}


bool Range::Mul(const Range* left_range,
                const Range* right_range,
                RangeBoundary* result_min,
                RangeBoundary* result_max) {
  ASSERT(left_range != NULL);
  ASSERT(right_range != NULL);
  ASSERT(result_min != NULL);
  ASSERT(result_max != NULL);

  const int64_t left_max = ConstantAbsMax(left_range);
  const int64_t right_max = ConstantAbsMax(right_range);
  if ((left_max <= -kSmiMin) && (right_max <= -kSmiMin) &&
      ((left_max == 0) || (right_max <= kMaxInt64 / left_max))) {
    // Product of left and right max values stays in 64 bit range.
    const int64_t mul_max = left_max * right_max;
    const int64_t r_min =
        OnlyPositiveOrZero(*left_range, *right_range) ? 0 : -mul_max;
    *result_min = RangeBoundary::FromConstant(r_min);
    const int64_t r_max =
        OnlyNegativeOrZero(*left_range, *right_range) ? 0 : mul_max;
    *result_max = RangeBoundary::FromConstant(r_max);
    return true;
  }

  // TODO(vegorov): handle mixed sign case that leads to (-Infinity, 0] range.
  if (OnlyPositiveOrZero(*left_range, *right_range) ||
      OnlyNegativeOrZero(*left_range, *right_range)) {
    *result_min = RangeBoundary::FromConstant(0);
    *result_max = RangeBoundary::PositiveInfinity();
    return true;
  }

  return false;
}


// Both the a and b ranges are >= 0.
bool Range::OnlyPositiveOrZero(const Range& a, const Range& b) {
  return a.OnlyGreaterThanOrEqualTo(0) && b.OnlyGreaterThanOrEqualTo(0);
}


// Both the a and b ranges are <= 0.
bool Range::OnlyNegativeOrZero(const Range& a, const Range& b) {
  return a.OnlyLessThanOrEqualTo(0) && b.OnlyLessThanOrEqualTo(0);
}


// Return the maximum absolute value included in range.
int64_t Range::ConstantAbsMax(const Range* range) {
  if (range == NULL) {
    return RangeBoundary::kMax;
  }
  const int64_t abs_min = Utils::Abs(Range::ConstantMin(range).ConstantValue());
  const int64_t abs_max = Utils::Abs(Range::ConstantMax(range).ConstantValue());
  return Utils::Maximum(abs_min, abs_max);
}


void Range::BinaryOp(const Token::Kind op,
                     const Range* left_range,
                     const Range* right_range,
                     Definition* left_defn,
                     Range* result) {
  ASSERT(left_range != NULL);
  ASSERT(right_range != NULL);

  // Both left and right ranges are finite.
  ASSERT(left_range->IsFinite());
  ASSERT(right_range->IsFinite());

  RangeBoundary min;
  RangeBoundary max;
  ASSERT(min.IsUnknown() && max.IsUnknown());

  switch (op) {
    case Token::kADD:
      Range::Add(left_range, right_range, &min, &max, left_defn);
      break;
    case Token::kSUB:
      Range::Sub(left_range, right_range, &min, &max, left_defn);
      break;
    case Token::kMUL: {
      if (!Range::Mul(left_range, right_range, &min, &max)) {
        *result = Range::Full(RangeBoundary::kRangeBoundaryInt64);
        return;
      }
      break;
    }
    case Token::kSHL: {
      Range::Shl(left_range, right_range, &min, &max);
      break;
    }
    case Token::kSHR: {
      Range::Shr(left_range, right_range, &min, &max);
      break;
    }
    case Token::kBIT_AND:
      if (!Range::And(left_range, right_range, &min, &max)) {
        *result = Range::Full(RangeBoundary::kRangeBoundaryInt64);
        return;
      }
      break;
    default:
      *result = Range::Full(RangeBoundary::kRangeBoundaryInt64);
      return;
  }

  ASSERT(!min.IsUnknown() && !max.IsUnknown());

  *result = Range(min, max);
}


void Definition::set_range(const Range& range) {
  if (range_ == NULL) {
    range_ = new Range();
  }
  *range_ = range;
}


void Definition::InferRange(RangeAnalysis* analysis, Range* range) {
  if (Type()->ToCid() == kSmiCid) {
    *range = Range::Full(RangeBoundary::kRangeBoundarySmi);
  } else if (IsMintDefinition()) {
    *range = Range::Full(RangeBoundary::kRangeBoundaryInt64);
  } else if (IsInt32Definition()) {
    *range = Range::Full(RangeBoundary::kRangeBoundaryInt32);
  } else {
    // Only Smi and Mint supported.
    UNREACHABLE();
  }
}


static bool DependsOnSymbol(const RangeBoundary& a, Definition* symbol) {
  return a.IsSymbol() && (UnwrapConstraint(a.symbol()) == symbol);
}


// Given the range and definition update the range so that
// it covers both original range and defintions range.
//
// The following should also hold:
//
//     [_|_, _|_] U a = a U [_|_, _|_] = a
//
static void Join(Range* range,
                 Definition* defn,
                 const Range* defn_range,
                 RangeBoundary::RangeSize size) {
  if (Range::IsUnknown(defn_range)) {
    return;
  }

  if (Range::IsUnknown(range)) {
    *range = *defn_range;
    return;
  }

  Range other = *defn_range;

  // Handle patterns where range already depends on defn as a symbol:
  //
  //    (..., S+o] U range(S) and [S+o, ...) U range(S)
  //
  // To improve precision of the computed join use [S, S] instead of
  // using range(S). It will be canonicalized away by JoinMin/JoinMax
  // functions.
  Definition* unwrapped = UnwrapConstraint(defn);
  if (DependsOnSymbol(range->min(), unwrapped) ||
      DependsOnSymbol(range->max(), unwrapped)) {
    other = Range(RangeBoundary::FromDefinition(defn, 0),
                  RangeBoundary::FromDefinition(defn, 0));
  }

  // First try to compare ranges based on their upper and lower bounds.
  const int64_t inf_range = range->min().LowerBound(size);
  const int64_t inf_other = other.min().LowerBound(size);
  const int64_t sup_range = range->max().UpperBound(size);
  const int64_t sup_other = other.max().UpperBound(size);

  if (sup_range <= inf_other) {
    // The range is fully below defn's range. Keep the minimum and
    // expand the maximum.
    range->set_max(other.max());
  } else if (sup_other <= inf_range) {
    // The range is fully above defn's range. Keep the maximum and
    // expand the minimum.
    range->set_min(other.min());
  } else {
    // Can't compare ranges as whole. Join minimum and maximum separately.
    *range = Range(RangeBoundary::JoinMin(range->min(), other.min(), size),
                   RangeBoundary::JoinMax(range->max(), other.max(), size));
  }
}


// When assigning range to a phi we must take care to avoid self-reference
// cycles when phi's range depends on the phi itself.
// To prevent such cases we impose additional restriction on symbols that
// can be used as boundaries for phi's range: they must dominate
// phi's definition.
static RangeBoundary EnsureAcyclicSymbol(BlockEntryInstr* phi_block,
                                         const RangeBoundary& a,
                                         const RangeBoundary& limit) {
  if (!a.IsSymbol() || a.symbol()->GetBlock()->Dominates(phi_block)) {
    return a;
  }

  // Symbol does not dominate phi. Try unwrapping constraint and check again.
  Definition* unwrapped = UnwrapConstraint(a.symbol());
  if ((unwrapped != a.symbol()) &&
      unwrapped->GetBlock()->Dominates(phi_block)) {
    return RangeBoundary::FromDefinition(unwrapped, a.offset());
  }

  return limit;
}


void PhiInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  ASSERT((Type()->ToCid() == kSmiCid) || (representation() == kUnboxedInt32));
  const RangeBoundary::RangeSize size = (Type()->ToCid() == kSmiCid) ?
      RangeBoundary::kRangeBoundarySmi : RangeBoundary::kRangeBoundaryInt32;
  for (intptr_t i = 0; i < InputCount(); i++) {
    Value* input = InputAt(i);
    const Range* input_range = (size == RangeBoundary::kRangeBoundarySmi) ?
        analysis->GetSmiRange(input) : input->definition()->range();
    Join(range,
         input->definition(), input_range, size);
  }

  BlockEntryInstr* phi_block = GetBlock();
  range->set_min(EnsureAcyclicSymbol(
      phi_block, range->min(), RangeBoundary::MinSmi()));
  range->set_max(EnsureAcyclicSymbol(
      phi_block, range->max(), RangeBoundary::MaxSmi()));
}


void ConstantInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  if (value_.IsSmi()) {
    int64_t value = Smi::Cast(value_).Value();
    *range = Range(RangeBoundary::FromConstant(value),
                   RangeBoundary::FromConstant(value));
  } else if (value_.IsMint()) {
    int64_t value = Mint::Cast(value_).value();
    *range = Range(RangeBoundary::FromConstant(value),
                   RangeBoundary::FromConstant(value));
  } else {
    // Only Smi and Mint supported.
    UNREACHABLE();
  }
}


void ConstraintInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  const Range* value_range = analysis->GetSmiRange(value());
  if (Range::IsUnknown(value_range)) {
    return;
  }

  // TODO(vegorov) check if precision of the analysis can be improved by
  // recognizing intersections of the form:
  //
  //       (..., S+x] ^ [S+x, ...) = [S+x, S+x]
  //
  Range result = value_range->Intersect(constraint());

  if (result.IsUnsatisfiable()) {
    return;
  }

  *range = result;
}


void LoadFieldInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  switch (recognized_kind()) {
    case MethodRecognizer::kObjectArrayLength:
    case MethodRecognizer::kImmutableArrayLength:
      *range = Range(RangeBoundary::FromConstant(0),
                     RangeBoundary::FromConstant(Array::kMaxElements));
      break;

    case MethodRecognizer::kTypedDataLength:
      *range = Range(RangeBoundary::FromConstant(0), RangeBoundary::MaxSmi());
      break;

    case MethodRecognizer::kStringBaseLength:
      *range = Range(RangeBoundary::FromConstant(0),
                     RangeBoundary::FromConstant(String::kMaxElements));
      break;

    default:
      Definition::InferRange(analysis, range);
  }
}



void LoadIndexedInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  switch (class_id()) {
    case kTypedDataInt8ArrayCid:
      *range = Range(RangeBoundary::FromConstant(-128),
                     RangeBoundary::FromConstant(127));
      break;
    case kTypedDataUint8ArrayCid:
    case kTypedDataUint8ClampedArrayCid:
    case kExternalTypedDataUint8ArrayCid:
    case kExternalTypedDataUint8ClampedArrayCid:
      *range = Range(RangeBoundary::FromConstant(0),
                     RangeBoundary::FromConstant(255));
      break;
    case kTypedDataInt16ArrayCid:
      *range = Range(RangeBoundary::FromConstant(-32768),
                     RangeBoundary::FromConstant(32767));
      break;
    case kTypedDataUint16ArrayCid:
      *range = Range(RangeBoundary::FromConstant(0),
                     RangeBoundary::FromConstant(65535));
      break;
    case kTypedDataInt32ArrayCid:
      if (Typed32BitIsSmi()) {
        *range = Range::Full(RangeBoundary::kRangeBoundarySmi);
      } else {
        *range = Range(RangeBoundary::FromConstant(kMinInt32),
                       RangeBoundary::FromConstant(kMaxInt32));
      }
      break;
    case kTypedDataUint32ArrayCid:
      if (Typed32BitIsSmi()) {
        *range = Range::Full(RangeBoundary::kRangeBoundarySmi);
      } else {
        *range = Range(RangeBoundary::FromConstant(0),
                       RangeBoundary::FromConstant(kMaxUint32));
      }
      break;
    case kOneByteStringCid:
      *range = Range(RangeBoundary::FromConstant(0),
                     RangeBoundary::FromConstant(0xFF));
      break;
    case kTwoByteStringCid:
      *range = Range(RangeBoundary::FromConstant(0),
                     RangeBoundary::FromConstant(0xFFFF));
      break;
    default:
      Definition::InferRange(analysis, range);
      break;
  }
}


void IfThenElseInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  const intptr_t min = Utils::Minimum(if_true_, if_false_);
  const intptr_t max = Utils::Maximum(if_true_, if_false_);
  *range = Range(RangeBoundary::FromConstant(min),
                 RangeBoundary::FromConstant(max));
}


void BinarySmiOpInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  // TODO(vegorov): canonicalize BinarySmiOp to always have constant on the
  // right and a non-constant on the left.
  Definition* left_defn = left()->definition();

  const Range* left_range = analysis->GetSmiRange(left());
  const Range* right_range = analysis->GetSmiRange(right());

  if (Range::IsUnknown(left_range) || Range::IsUnknown(right_range)) {
    return;
  }

  Range::BinaryOp(op_kind(),
                  left_range,
                  right_range,
                  left_defn,
                  range);
  ASSERT(!Range::IsUnknown(range));

  // Calculate overflowed status before clamping.
  const bool overflowed = range->min().LowerBound().OverflowedSmi() ||
                          range->max().UpperBound().OverflowedSmi();
  set_overflow(overflowed);

  // Clamp value to be within smi range.
  range->Clamp(RangeBoundary::kRangeBoundarySmi);
}


void BoxInt32Instr::InferRange(RangeAnalysis* analysis, Range* range) {
  const Range* value_range = value()->definition()->range();
  if (!Range::IsUnknown(value_range)) {
    *range = *value_range;
  }
}


void UnboxInt32Instr::InferRange(RangeAnalysis* analysis, Range* range) {
  if (value()->definition()->Type()->ToCid() == kSmiCid) {
    const Range* value_range = analysis->GetSmiRange(value());
    if (!Range::IsUnknown(value_range)) {
      *range = *value_range;
    }
  } else if (value()->definition()->IsMintDefinition() ||
             value()->definition()->IsInt32Definition()) {
    const Range* value_range = value()->definition()->range();
    if (!Range::IsUnknown(value_range)) {
      *range = *value_range;
    }
  } else if (value()->Type()->ToCid() == kSmiCid) {
    *range = Range::Full(RangeBoundary::kRangeBoundarySmi);
  } else {
    *range = Range::Full(RangeBoundary::kRangeBoundaryInt32);
  }
}


void UnboxedIntConverterInstr::InferRange(RangeAnalysis* analysis,
                                          Range* range) {
  ASSERT((from() == kUnboxedInt32) ||
         (from() == kUnboxedMint) ||
         (from() == kUnboxedUint32));
  ASSERT((to() == kUnboxedInt32) ||
         (to() == kUnboxedMint) ||
         (to() == kUnboxedUint32));
  const Range* value_range = value()->definition()->range();
  if (Range::IsUnknown(value_range)) {
    return;
  }

  if (to() == kUnboxedUint32) {
    // TODO(vegorov): improve range information for unboxing to Uint32.
    *range = Range(
        RangeBoundary::FromConstant(0),
        RangeBoundary::FromConstant(static_cast<int64_t>(kMaxUint32)));
  } else {
    *range = *value_range;
    if (to() == kUnboxedInt32) {
      range->Clamp(RangeBoundary::kRangeBoundaryInt32);
    }
  }
}


void BinaryInt32OpInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  // TODO(vegorov): canonicalize BinarySmiOp to always have constant on the
  // right and a non-constant on the left.
  Definition* left_defn = left()->definition();

  const Range* left_range = analysis->GetSmiRange(left());
  const Range* right_range = analysis->GetSmiRange(right());

  if (Range::IsUnknown(left_range) || Range::IsUnknown(right_range)) {
    return;
  }

  Range::BinaryOp(op_kind(),
                  left_range,
                  right_range,
                  left_defn,
                  range);
  ASSERT(!Range::IsUnknown(range));

  // Calculate overflowed status before clamping.
  set_overflow(!range->Fits(RangeBoundary::kRangeBoundaryInt32));

  // Clamp value to be within smi range.
  range->Clamp(RangeBoundary::kRangeBoundaryInt32);
}

void BinaryMintOpInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  // TODO(vegorov): canonicalize BinaryMintOpInstr to always have constant on
  // the right and a non-constant on the left.
  Definition* left_defn = left()->definition();

  const Range* left_range = left_defn->range();
  const Range* right_range = right()->definition()->range();

  if (Range::IsUnknown(left_range) || Range::IsUnknown(right_range)) {
    return;
  }

  Range::BinaryOp(op_kind(),
                  left_range,
                  right_range,
                  left_defn,
                  range);
  ASSERT(!Range::IsUnknown(range));

  // Calculate overflowed status before clamping.
  set_can_overflow(!range->Fits(RangeBoundary::kRangeBoundaryInt64));

  // Clamp value to be within mint range.
  range->Clamp(RangeBoundary::kRangeBoundaryInt64);
}


void ShiftMintOpInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  Definition* left_defn = left()->definition();

  const Range* left_range = left_defn->range();
  const Range* right_range = right()->definition()->range();

  if (Range::IsUnknown(left_range) || Range::IsUnknown(right_range)) {
    return;
  }

  Range::BinaryOp(op_kind(),
                  left_range,
                  right_range,
                  left_defn,
                  range);
  ASSERT(!Range::IsUnknown(range));

  // Calculate overflowed status before clamping.
  const bool overflowed = range->min().LowerBound().OverflowedMint() ||
                          range->max().UpperBound().OverflowedMint();
  set_can_overflow(overflowed);

  // Clamp value to be within mint range.
  range->Clamp(RangeBoundary::kRangeBoundaryInt64);
}


void BoxIntegerInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  const Range* input_range = value()->definition()->range();
  if (input_range != NULL) {
    bool is_smi = input_range->Fits(RangeBoundary::kRangeBoundarySmi);
    set_is_smi(is_smi);
    // The output range is the same as the input range.
    *range = *input_range;
  }
}


void UnboxIntegerInstr::InferRange(RangeAnalysis* analysis, Range* range) {
  const Range* value_range = value()->definition()->range();
  if (value_range != NULL) {
    *range = *value_range;
  } else if (!value()->definition()->IsMintDefinition() &&
             (value()->definition()->Type()->ToCid() != kSmiCid)) {
    *range = Range::Full(RangeBoundary::kRangeBoundaryInt64);
  }
}


bool CheckArrayBoundInstr::IsRedundant(const RangeBoundary& length) {
  Range* index_range = index()->definition()->range();

  // Range of the index is unknown can't decide if the check is redundant.
  if (index_range == NULL) {
    return false;
  }

  // Range of the index is not positive. Check can't be redundant.
  if (Range::ConstantMinSmi(index_range).ConstantValue() < 0) {
    return false;
  }

  RangeBoundary max = CanonicalizeBoundary(index_range->max(),
                                           RangeBoundary::PositiveInfinity());

  if (max.OverflowedSmi()) {
    return false;
  }


  RangeBoundary max_upper = max.UpperBound();
  RangeBoundary length_lower = length.LowerBound();

  if (max_upper.OverflowedSmi() || length_lower.OverflowedSmi()) {
    return false;
  }

  // Try to compare constant boundaries.
  if (max_upper.ConstantValue() < length_lower.ConstantValue()) {
    return true;
  }

  RangeBoundary canonical_length =
      CanonicalizeBoundary(length, RangeBoundary::PositiveInfinity());
  if (canonical_length.OverflowedSmi()) {
    return false;
  }

  // Try symbolic comparison.
  do {
    if (DependOnSameSymbol(max, canonical_length)) {
      return max.offset() < canonical_length.offset();
    }
  } while (CanonicalizeMaxBoundary(&max) ||
           CanonicalizeMinBoundary(&canonical_length));

  // Failed to prove that maximum is bounded with array length.
  return false;
}


}  // namespace dart