Refine expression typing, esp. by propagating range information.

src/compiler/typer.cc

Index: src/compiler/typer.cc
diff --git a/src/compiler/typer.cc b/src/compiler/typer.cc
index 8be542e48618a6e84e8c416c6dcb6a7573fc93d0..e13843363157faca843653369edc7eb2227a5572 100644
--- a/src/compiler/typer.cc
+++ b/src/compiler/typer.cc
@@ -17,6 +17,27 @@ namespace compiler {
 Typer::Typer(Zone* zone) : zone_(zone) {
   Factory* f = zone->isolate()->factory();
 
+  Handle<Object> zero = f->NewNumber(0);
+  Handle<Object> one = f->NewNumber(1);
+  Handle<Object> positive_infinity = f->NewNumber(+V8_INFINITY);
+  Handle<Object> negative_infinity = f->NewNumber(-V8_INFINITY);
+
+  negative_signed32 = Type::Union(
+      Type::SignedSmall(), Type::OtherSigned32(), zone);
+  non_negative_signed32 = Type::Union(
+      Type::UnsignedSmall(), Type::OtherUnsigned31(), zone);
+  undefined_or_null = Type::Union(Type::Undefined(), Type::Null(), zone);
+  singleton_false = Type::Constant(f->false_value(), zone);
+  singleton_true = Type::Constant(f->true_value(), zone);
+  singleton_zero = Type::Range(zero, zero, zone);
+  singleton_one = Type::Range(one, one, zone);
+  zero_or_one = Type::Union(singleton_zero, singleton_one, zone);
+  zeroish = Type::Union(
+      singleton_zero, Type::Union(Type::NaN(), Type::MinusZero(), zone), zone);
+  falsish = Type::Union(Type::Undetectable(),
+      Type::Union(zeroish, undefined_or_null, zone), zone);
+  integer = Type::Range(negative_infinity, positive_infinity, zone);
+
   Type* number = Type::Number();
   Type* signed32 = Type::Signed32();
   Type* unsigned32 = Type::Unsigned32();
@@ -24,8 +45,7 @@ Typer::Typer(Zone* zone) : zone_(zone) {
   Type* object = Type::Object();
   Type* undefined = Type::Undefined();
   Type* weakint = Type::Union(
-      Type::Range(f->NewNumber(-V8_INFINITY), f->NewNumber(+V8_INFINITY), zone),
-      Type::Union(Type::NaN(), Type::MinusZero(), zone), zone);
+      integer, Type::Union(Type::NaN(), Type::MinusZero(), zone), zone);
 
   number_fun0_ = Type::Function(number, zone);
   number_fun1_ = Type::Function(number, number, zone);
@@ -35,19 +55,27 @@ Typer::Typer(Zone* zone) : zone_(zone) {
   random_fun_ = Type::Function(Type::Union(
       Type::UnsignedSmall(), Type::OtherNumber(), zone), zone);
 
+  Type* int8 = Type::Intersect(
+      Type::Range(f->NewNumber(-0x7F), f->NewNumber(0x7F-1), zone),
+      Type::UntaggedInt8(), zone);
+  Type* int16 = Type::Intersect(
+      Type::Range(f->NewNumber(-0x7FFF), f->NewNumber(0x7FFF-1), zone),
+      Type::UntaggedInt16(), zone);
+  Type* uint8 = Type::Intersect(
+      Type::Range(zero, f->NewNumber(0xFF-1), zone),
+      Type::UntaggedInt8(), zone);
+  Type* uint16 = Type::Intersect(
+      Type::Range(zero, f->NewNumber(0xFFFF-1), zone),
+      Type::UntaggedInt16(), zone);
 
 #define NATIVE_TYPE(sem, rep) \
-  Type::Intersect(Type::sem(zone), Type::rep(zone), zone)
-  // TODO(rossberg): Use range types for more precision, once we have them.
-  Type* int8 = NATIVE_TYPE(SignedSmall, UntaggedInt8);
-  Type* int16 = NATIVE_TYPE(SignedSmall, UntaggedInt16);
+    Type::Intersect(Type::sem(), Type::rep(), zone)
   Type* int32 = NATIVE_TYPE(Signed32, UntaggedInt32);
-  Type* uint8 = NATIVE_TYPE(UnsignedSmall, UntaggedInt8);
-  Type* uint16 = NATIVE_TYPE(UnsignedSmall, UntaggedInt16);
   Type* uint32 = NATIVE_TYPE(Unsigned32, UntaggedInt32);
   Type* float32 = NATIVE_TYPE(Number, UntaggedFloat32);
   Type* float64 = NATIVE_TYPE(Number, UntaggedFloat64);
 #undef NATIVE_TYPE
+
   Type* buffer = Type::Buffer(zone);
   Type* int8_array = Type::Array(int8, zone);
   Type* int16_array = Type::Array(int16, zone);
@@ -79,9 +107,21 @@ class Typer::Visitor : public NullNodeVisitor {
 
   Bounds TypeNode(Node* node) {
     switch (node->opcode()) {
+#define DECLARE_CASE(x) \
+      case IrOpcode::k##x: return TypeBinaryOp(node, x##Typer);
+      JS_SIMPLE_BINOP_LIST(DECLARE_CASE)
+#undef DECLARE_CASE
+
 #define DECLARE_CASE(x) case IrOpcode::k##x: return Type##x(node);
       DECLARE_CASE(Start)
-      VALUE_OP_LIST(DECLARE_CASE)
+      // VALUE_OP_LIST without JS_SIMPLE_BINOP_LIST:
+      COMMON_OP_LIST(DECLARE_CASE)
+      SIMPLIFIED_OP_LIST(DECLARE_CASE)
+      MACHINE_OP_LIST(DECLARE_CASE)
+      JS_SIMPLE_UNOP_LIST(DECLARE_CASE)
+      JS_OBJECT_OP_LIST(DECLARE_CASE)
+      JS_CONTEXT_OP_LIST(DECLARE_CASE)
+      JS_OTHER_OP_LIST(DECLARE_CASE)
 #undef DECLARE_CASE
 
 #define DECLARE_CASE(x) case IrOpcode::k##x:
@@ -102,11 +142,11 @@ class Typer::Visitor : public NullNodeVisitor {
   VALUE_OP_LIST(DECLARE_METHOD)
 #undef DECLARE_METHOD
 
-  Bounds OperandType(Node* node, int i) {
+  static Bounds OperandType(Node* node, int i) {
     return NodeProperties::GetBounds(NodeProperties::GetValueInput(node, i));
   }
 
-  Type* ContextType(Node* node) {
+  static Type* ContextType(Node* node) {
     Bounds result =
         NodeProperties::GetBounds(NodeProperties::GetContextInput(node));
     DCHECK(result.upper->Maybe(Type::Internal()));
@@ -122,6 +162,37 @@ class Typer::Visitor : public NullNodeVisitor {
  private:
   Typer* typer_;
   MaybeHandle<Context> context_;
+
+  typedef Type* (*UnaryTyperFun)(Type*, Typer* t);
+  typedef Type* (*BinaryTyperFun)(Type*, Type*, Typer* t);
+
+  Bounds TypeUnaryOp(Node* node, UnaryTyperFun);
+  Bounds TypeBinaryOp(Node* node, BinaryTyperFun);
+
+  static Type* Invert(Type*, Typer*);
+  static Type* FalsifyUndefined(Type*, Typer*);
+
+  static Type* ToPrimitive(Type*, Typer*);
+  static Type* ToBoolean(Type*, Typer*);
+  static Type* ToNumber(Type*, Typer*);
+  static Type* ToString(Type*, Typer*);
+  static Type* NumberToInt32(Type*, Typer*);
+  static Type* NumberToUint32(Type*, Typer*);
+
+  static Type* JSAddRanger(Type::RangeType*, Type::RangeType*, Typer*);
+  static Type* JSSubtractRanger(Type::RangeType*, Type::RangeType*, Typer*);
+  static Type* JSMultiplyRanger(Type::RangeType*, Type::RangeType*, Typer*);
+  static Type* JSDivideRanger(Type::RangeType*, Type::RangeType*, Typer*);
+
+  static Type* JSCompareTyper(Type*, Type*, Typer*);
+
+#define DECLARE_METHOD(x) static Type* x##Typer(Type*, Type*, Typer*);
+  JS_SIMPLE_BINOP_LIST(DECLARE_METHOD)
+#undef DECLARE_METHOD
+
+  static Type* JSUnaryNotTyper(Type*, Typer*);
+  static Type* JSLoadPropertyTyper(Type*, Type*, Typer*);
+  static Type* JSCallFunctionTyper(Type*, Typer*);
 };
 
 
@@ -238,48 +309,155 @@ void Typer::Init(Node* node) {
 // -----------------------------------------------------------------------------
 
 
+Bounds Typer::Visitor::TypeUnaryOp(Node* node, UnaryTyperFun f) {
+  Bounds input = OperandType(node, 0);
+  Type* upper = input.upper->Is(Type::None())
+      ? Type::None()
+      : f(input.upper, typer_);
+  Type* lower = input.lower->Is(Type::None())
+      ? Type::None()
+      : (input.lower == input.upper || upper->IsConstant())
+      ? upper  // TODO(neis): Extend this to Range(x,x), NaN, MinusZero, ...?
+      : f(input.lower, typer_);
+  // TODO(neis): Figure out what to do with lower bound.
+  return Bounds(lower, upper);
+}
+
+
+Bounds Typer::Visitor::TypeBinaryOp(Node* node, BinaryTyperFun f) {
+  Bounds left = OperandType(node, 0);
+  Bounds right = OperandType(node, 1);
+  Type* upper = left.upper->Is(Type::None()) || right.upper->Is(Type::None())
+      ? Type::None()
+      : f(left.upper, right.upper, typer_);
+  Type* lower = left.lower->Is(Type::None()) || right.lower->Is(Type::None())
+      ? Type::None()
+      : ((left.lower == left.upper && right.lower == right.upper) ||
+         upper->IsConstant())
+      ? upper
+      : f(left.lower, right.lower, typer_);
+  // TODO(neis): Figure out what to do with lower bound.
+  return Bounds(lower, upper);
+}
+
+
+Type* Typer::Visitor::Invert(Type* type, Typer* t) {
+  if (type->Is(t->singleton_false)) return t->singleton_true;
+  if (type->Is(t->singleton_true)) return t->singleton_false;
+  return type;
+}
+
+
+Type* Typer::Visitor::FalsifyUndefined(Type* type, Typer* t) {
+  if (type->Is(Type::Undefined())) return t->singleton_false;
+  return type;
+}
+
+
+// Type conversion.
+
+
+Type* Typer::Visitor::ToPrimitive(Type* type, Typer* t) {
+  if (type->Is(Type::Primitive()) && !type->Maybe(Type::Receiver())) {
+    return type;
+  }
+  return Type::Primitive();
+}
+
+
+Type* Typer::Visitor::ToBoolean(Type* type, Typer* t) {
+  if (type->Is(Type::Boolean())) return type;
+  if (type->Is(t->falsish)) return t->singleton_false;
+  if (type->Is(Type::DetectableReceiver())) return t->singleton_true;
+  if (type->Is(Type::OrderedNumber()) && (type->Max() < 0 || 0 < type->Min())) {
+    return t->singleton_true;  // Ruled out nan, -0 and +0.
+  }
+  return Type::Boolean();
+}
+
+
+Type* Typer::Visitor::ToNumber(Type* type, Typer* t) {
+  if (type->Is(Type::Number())) return type;
+  if (type->Is(Type::Undefined())) return Type::NaN();
+  if (type->Is(t->singleton_false)) return t->singleton_zero;
+  if (type->Is(t->singleton_true)) return t->singleton_one;
+  if (type->Is(Type::Boolean())) return t->zero_or_one;
+  return Type::Number();
+}
+
+
+Type* Typer::Visitor::ToString(Type* type, Typer* t) {
+  if (type->Is(Type::String())) return type;
+  return Type::String();
+}
+
+
+Type* Typer::Visitor::NumberToInt32(Type* type, Typer* t) {
+  DCHECK(type->Is(Type::Number()));
+  if (type->Is(Type::Signed32())) return type;
+  if (type->Is(t->zeroish)) return t->singleton_zero;
+  return Type::Signed32();
+}
+
+
+Type* Typer::Visitor::NumberToUint32(Type* type, Typer* t) {
+  DCHECK(type->Is(Type::Number()));
+  if (type->Is(Type::Unsigned32())) return type;
+  if (type->Is(t->zeroish)) return t->singleton_zero;
+  return Type::Unsigned32();
+}
+
+
+// -----------------------------------------------------------------------------
+
+
 // Control operators.
 
+
 Bounds Typer::Visitor::TypeStart(Node* node) {
-  return Bounds(Type::Internal(zone()));
+  return Bounds(Type::Internal());
 }
 
 
 // Common operators.
 
+
 Bounds Typer::Visitor::TypeParameter(Node* node) {
   return Bounds::Unbounded(zone());
 }
 
 
 Bounds Typer::Visitor::TypeInt32Constant(Node* node) {
-  // TODO(titzer): only call Type::Of() if the type is not already known.
-  return Bounds(Type::Of(OpParameter<int32_t>(node), zone()));
+  Factory* f = zone()->isolate()->factory();
+  Handle<Object> number = f->NewNumber(OpParameter<int32_t>(node));
+  return Bounds(Type::Intersect(
+      Type::Range(number, number, zone()), Type::UntaggedInt32(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeInt64Constant(Node* node) {
-  // TODO(titzer): only call Type::Of() if the type is not already known.
-  return Bounds(
-      Type::Of(static_cast<double>(OpParameter<int64_t>(node)), zone()));
+  return Bounds(Type::Internal());  // TODO(rossberg): Add int64 bitset type?
 }
 
 
 Bounds Typer::Visitor::TypeFloat32Constant(Node* node) {
-  // TODO(titzer): only call Type::Of() if the type is not already known.
-  return Bounds(Type::Of(OpParameter<float>(node), zone()));
+  return Bounds(Type::Intersect(
+      Type::Of(OpParameter<float>(node), zone()),
+      Type::UntaggedFloat32(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeFloat64Constant(Node* node) {
-  // TODO(titzer): only call Type::Of() if the type is not already known.
-  return Bounds(Type::Of(OpParameter<double>(node), zone()));
+  return Bounds(Type::Intersect(
+      Type::Of(OpParameter<double>(node), zone()),
+      Type::UntaggedFloat64(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeNumberConstant(Node* node) {
-  // TODO(titzer): only call Type::Of() if the type is not already known.
-  return Bounds(Type::Of(OpParameter<double>(node), zone()));
+  Factory* f = zone()->isolate()->factory();
+  return Bounds(Type::Constant(
+      f->NewNumber(OpParameter<double>(node)), zone()));
 }
 
 
@@ -289,7 +467,7 @@ Bounds Typer::Visitor::TypeHeapConstant(Node* node) {
 
 
 Bounds Typer::Visitor::TypeExternalConstant(Node* node) {
-  return Bounds(Type::Internal(zone()));
+  return Bounds(Type::Internal());
 }
 
 
@@ -328,12 +506,12 @@ Bounds Typer::Visitor::TypeFinish(Node* node) {
 
 Bounds Typer::Visitor::TypeFrameState(Node* node) {
   // TODO(rossberg): Ideally FrameState wouldn't have a value output.
-  return Bounds(Type::Internal(zone()));
+  return Bounds(Type::Internal());
 }
 
 
 Bounds Typer::Visitor::TypeStateValues(Node* node) {
-  return Bounds(Type::Internal(zone()));
+  return Bounds(Type::Internal());
 }
 
 
@@ -350,159 +528,339 @@ Bounds Typer::Visitor::TypeProjection(Node* node) {
 
 // JS comparison operators.
 
-#define DEFINE_METHOD(x)                       \
-  Bounds Typer::Visitor::Type##x(Node* node) { \
-    return Bounds(Type::Boolean(zone()));      \
+
+Type* Typer::Visitor::JSEqualTyper(Type* lhs, Type* rhs, Typer* t) {
+  if (lhs->Is(Type::NaN()) || rhs->Is(Type::NaN())) return t->singleton_false;
+  if (lhs->Is(t->undefined_or_null) && rhs->Is(t->undefined_or_null)) {
+    return t->singleton_true;
   }
-JS_COMPARE_BINOP_LIST(DEFINE_METHOD)
-#undef DEFINE_METHOD
+  if (lhs->Is(Type::Number()) && rhs->Is(Type::Number()) &&
+      (lhs->Max() < rhs->Min() || lhs->Min() > rhs->Max())) {
+      return t->singleton_false;
+  }
+  if (lhs->IsConstant() && rhs->Is(lhs)) {
+    // Types are equal and are inhabited only by a single semantic value,
+    // which is not nan due to the earlier check.
+    // TODO(neis): Extend this to Range(x,x), MinusZero, ...?
+    return t->singleton_true;
+  }
+  return Type::Boolean();
+}
 
 
-// JS bitwise operators.
+Type* Typer::Visitor::JSNotEqualTyper(Type* lhs, Type* rhs, Typer* t) {
+  return Invert(JSEqualTyper(lhs, rhs, t), t);
+}
 
-Bounds Typer::Visitor::TypeJSBitwiseOr(Node* node) {
-  Bounds left = OperandType(node, 0);
-  Bounds right = OperandType(node, 1);
-  Type* upper = Type::Union(left.upper, right.upper, zone());
-  if (!upper->Is(Type::Signed32())) upper = Type::Signed32(zone());
-  Type* lower = Type::Intersect(Type::SignedSmall(zone()), upper, zone());
-  return Bounds(lower, upper);
+
+static Type* JSType(Type* type) {
+  if (type->Is(Type::Boolean())) return Type::Boolean();
+  if (type->Is(Type::String())) return Type::String();
+  if (type->Is(Type::Number())) return Type::Number();
+  if (type->Is(Type::Undefined())) return Type::Undefined();
+  if (type->Is(Type::Null())) return Type::Null();
+  if (type->Is(Type::Symbol())) return Type::Symbol();
+  if (type->Is(Type::Receiver())) return Type::Receiver();  // JS "Object"
+  return Type::Any();
 }
 
 
-Bounds Typer::Visitor::TypeJSBitwiseAnd(Node* node) {
-  Bounds left = OperandType(node, 0);
-  Bounds right = OperandType(node, 1);
-  Type* upper = Type::Union(left.upper, right.upper, zone());
-  if (!upper->Is(Type::Signed32())) upper = Type::Signed32(zone());
-  Type* lower = Type::Intersect(Type::SignedSmall(zone()), upper, zone());
-  return Bounds(lower, upper);
+Type* Typer::Visitor::JSStrictEqualTyper(Type* lhs, Type* rhs, Typer* t) {
+  if (!JSType(lhs)->Maybe(JSType(rhs))) return t->singleton_false;
+  if (lhs->Is(Type::NaN()) || rhs->Is(Type::NaN())) return t->singleton_false;
+  if (lhs->Is(Type::Number()) && rhs->Is(Type::Number()) &&
+      (lhs->Max() < rhs->Min() || lhs->Min() > rhs->Max())) {
+      return t->singleton_false;
+  }
+  if (lhs->IsConstant() && rhs->Is(lhs)) {
+    // Types are equal and are inhabited only by a single semantic value,
+    // which is not nan due to the earlier check.
+    return t->singleton_true;
+  }
+  return Type::Boolean();
+}
+
+
+Type* Typer::Visitor::JSStrictNotEqualTyper(Type* lhs, Type* rhs, Typer* t) {
+  return Invert(JSStrictEqualTyper(lhs, rhs, t), t);
+}
+
+
+// The EcmaScript specification defines the four relational comparison operators
+// (<, <=, >=, >) with the help of a single abstract one.  It behaves like <
+// but returns undefined when the inputs cannot be compared.
+// We implement the typing analogously.
+Type* Typer::Visitor::JSCompareTyper(Type* lhs, Type* rhs, Typer* t) {
+  lhs = ToPrimitive(lhs, t);
+  rhs = ToPrimitive(rhs, t);
+  if (lhs->Maybe(Type::String()) && rhs->Maybe(Type::String())) {
+    return Type::Boolean();
+  }
+  lhs = ToNumber(lhs, t);
+  rhs = ToNumber(rhs, t);
+  if (lhs->Is(Type::NaN()) || rhs->Is(Type::NaN())) return Type::Undefined();
+  if (lhs->IsConstant() && rhs->Is(lhs)) {
+    // Types are equal and are inhabited only by a single semantic value,
+    // which is not NaN due to the previous check.
+    return t->singleton_false;
+  }
+  if (lhs->Min() >= rhs->Max()) return t->singleton_false;
+  if (lhs->Max() < rhs->Min() &&
+      !lhs->Maybe(Type::NaN()) && !rhs->Maybe(Type::NaN())) {
+    return t->singleton_true;
+  }
+  return Type::Boolean();
+}
+
+
+Type* Typer::Visitor::JSLessThanTyper(Type* lhs, Type* rhs, Typer* t) {
+  return FalsifyUndefined(JSCompareTyper(lhs, rhs, t), t);
+}
+
+
+Type* Typer::Visitor::JSGreaterThanTyper(Type* lhs, Type* rhs, Typer* t) {
+  return FalsifyUndefined(JSCompareTyper(rhs, lhs, t), t);
+}
+
+
+Type* Typer::Visitor::JSLessThanOrEqualTyper(Type* lhs, Type* rhs, Typer* t) {
+  return FalsifyUndefined(Invert(JSCompareTyper(rhs, lhs, t), t), t);
 }
 
 
-Bounds Typer::Visitor::TypeJSBitwiseXor(Node* node) {
-  return Bounds(Type::SignedSmall(zone()), Type::Signed32(zone()));
+Type* Typer::Visitor::JSGreaterThanOrEqualTyper(
+    Type* lhs, Type* rhs, Typer* t) {
+  return FalsifyUndefined(Invert(JSCompareTyper(lhs, rhs, t), t), t);
 }
 
 
-Bounds Typer::Visitor::TypeJSShiftLeft(Node* node) {
-  return Bounds(Type::SignedSmall(zone()), Type::Signed32(zone()));
+// JS bitwise operators.
+
+
+Type* Typer::Visitor::JSBitwiseOrTyper(Type* lhs, Type* rhs, Typer* t) {
+  Factory* f = t->zone()->isolate()->factory();
+  lhs = NumberToInt32(ToNumber(lhs, t), t);
+  rhs = NumberToInt32(ToNumber(rhs, t), t);
+  double lmin = lhs->Min();
+  double rmin = rhs->Min();
+  double lmax = lhs->Max();
+  double rmax = rhs->Max();
+  // Or-ing any two values results in a value no smaller than their minimum.
+  // Even no smaller than their maximum if both values are non-negative.
+  Handle<Object> min = f->NewNumber(
+      lmin >= 0 && rmin >= 0 ? std::max(lmin, rmin) : std::min(lmin, rmin));
+  if (lmax < 0 || rmax < 0) {
+    // Or-ing two values of which at least one is negative results in a negative
+    // value.
+    Handle<Object> max = f->NewNumber(-1);
+    return Type::Range(min, max, t->zone());
+  }
+  Handle<Object> max = f->NewNumber(Type::Signed32()->Max());
+  return Type::Range(min, max, t->zone());
+  // TODO(neis): Be precise for singleton inputs, here and elsewhere.
+}
+
+
+Type* Typer::Visitor::JSBitwiseAndTyper(Type* lhs, Type* rhs, Typer* t) {
+  Factory* f = t->zone()->isolate()->factory();
+  lhs = NumberToInt32(ToNumber(lhs, t), t);
+  rhs = NumberToInt32(ToNumber(rhs, t), t);
+  double lmin = lhs->Min();
+  double rmin = rhs->Min();
+  double lmax = lhs->Max();
+  double rmax = rhs->Max();
+  // And-ing any two values results in a value no larger than their maximum.
+  // Even no larger than their minimum if both values are non-negative.
+  Handle<Object> max = f->NewNumber(
+      lmin >= 0 && rmin >= 0 ? std::min(lmax, rmax) : std::max(lmax, rmax));
+  if (lmin >= 0 || rmin >= 0) {
+    // And-ing two values of which at least one is non-negative results in a
+    // non-negative value.
+    Handle<Object> min = f->NewNumber(0);
+    return Type::Range(min, max, t->zone());
+  }
+  Handle<Object> min = f->NewNumber(Type::Signed32()->Min());
+  return Type::Range(min, max, t->zone());
 }
 
 
-Bounds Typer::Visitor::TypeJSShiftRight(Node* node) {
-  return Bounds(Type::SignedSmall(zone()), Type::Signed32(zone()));
+Type* Typer::Visitor::JSBitwiseXorTyper(Type* lhs, Type* rhs, Typer* t) {
+  lhs = NumberToInt32(ToNumber(lhs, t), t);
+  rhs = NumberToInt32(ToNumber(rhs, t), t);
+  double lmin = lhs->Min();
+  double rmin = rhs->Min();
+  double lmax = lhs->Max();
+  double rmax = rhs->Max();
+  if ((lmin >= 0 && rmin >= 0) || (lmax < 0 && rmax < 0)) {
+    // Xor-ing negative or non-negative values results in a non-negative value.
+    return t->non_negative_signed32;
+  }
+  if ((lmax < 0 && rmin >= 0) || (lmin >= 0 && rmax < 0)) {
+    // Xor-ing a negative and a non-negative value results in a negative value.
+    return t->negative_signed32;
+  }
+  return Type::Signed32();
 }
 
 
-Bounds Typer::Visitor::TypeJSShiftRightLogical(Node* node) {
-  return Bounds(Type::UnsignedSmall(zone()), Type::Unsigned32(zone()));
+Type* Typer::Visitor::JSShiftLeftTyper(Type* lhs, Type* rhs, Typer* t) {
+  return Type::Signed32();
+}
+
+
+Type* Typer::Visitor::JSShiftRightTyper(Type* lhs, Type* rhs, Typer* t) {
+  lhs = NumberToInt32(ToNumber(lhs, t), t);
+  Factory* f = t->zone()->isolate()->factory();
+  if (lhs->Min() >= 0) {
+    // Right-shifting a non-negative value cannot make it negative, nor larger.
+    Handle<Object> min = f->NewNumber(0);
+    Handle<Object> max = f->NewNumber(lhs->Max());
+    return Type::Range(min, max, t->zone());
+  }
+  if (lhs->Max() < 0) {
+    // Right-shifting a negative value cannot make it non-negative, nor smaller.
+    Handle<Object> min = f->NewNumber(lhs->Min());
+    Handle<Object> max = f->NewNumber(-1);
+    return Type::Range(min, max, t->zone());
+  }
+  return Type::Signed32();
+}
+
+
+Type* Typer::Visitor::JSShiftRightLogicalTyper(Type* lhs, Type* rhs, Typer* t) {
+  lhs = NumberToUint32(ToNumber(lhs, t), t);
+  Factory* f = t->zone()->isolate()->factory();
+  // Logical right-shifting any value cannot make it larger.
+  Handle<Object> min = f->NewNumber(0);
+  Handle<Object> max = f->NewNumber(lhs->Max());
+  return Type::Range(min, max, t->zone());
 }
 
 
 // JS arithmetic operators.
 
-Bounds Typer::Visitor::TypeJSAdd(Node* node) {
-  Bounds left = OperandType(node, 0);
-  Bounds right = OperandType(node, 1);
-  Type* lower =
-      left.lower->Is(Type::None()) || right.lower->Is(Type::None()) ?
-          Type::None(zone()) :
-      left.lower->Is(Type::Number()) && right.lower->Is(Type::Number()) ?
-          Type::SignedSmall(zone()) :
-      left.lower->Is(Type::String()) || right.lower->Is(Type::String()) ?
-          Type::String(zone()) : Type::None(zone());
-  Type* upper =
-      left.upper->Is(Type::None()) && right.upper->Is(Type::None()) ?
-          Type::None(zone()) :
-      left.upper->Is(Type::Number()) && right.upper->Is(Type::Number()) ?
-          Type::Number(zone()) :
-      left.upper->Is(Type::String()) || right.upper->Is(Type::String()) ?
-          Type::String(zone()) : Type::NumberOrString(zone());
-  return Bounds(lower, upper);
+
+Type* Typer::Visitor::JSAddTyper(Type* lhs, Type* rhs, Typer* t) {
+  lhs = ToPrimitive(lhs, t);
+  rhs = ToPrimitive(rhs, t);
+  if (lhs->Maybe(Type::String()) || rhs->Maybe(Type::String())) {
+    if (lhs->Is(Type::String()) || rhs->Is(Type::String())) {
+      return Type::String();
+    } else {
+      return Type::NumberOrString();
+    }
+  }
+  lhs = ToNumber(lhs, t);
+  rhs = ToNumber(rhs, t);
+  if (lhs->Is(Type::NaN()) || rhs->Is(Type::NaN())) return Type::NaN();
+  // TODO(neis): Do some analysis.
+  // TODO(neis): Deal with numeric bitsets here and elsewhere.
+  return Type::Number();
 }
 
 
-Bounds Typer::Visitor::TypeJSSubtract(Node* node) {
-  return Bounds(Type::SignedSmall(zone()), Type::Number(zone()));
+Type* Typer::Visitor::JSSubtractTyper(Type* lhs, Type* rhs, Typer* t) {
+  lhs = ToNumber(lhs, t);
+  rhs = ToNumber(rhs, t);
+  if (lhs->Is(Type::NaN()) || rhs->Is(Type::NaN())) return Type::NaN();
+  // TODO(neis): Do some analysis.
+  return Type::Number();
 }
 
 
-Bounds Typer::Visitor::TypeJSMultiply(Node* node) {
-  return Bounds(Type::SignedSmall(zone()), Type::Number(zone()));
+Type* Typer::Visitor::JSMultiplyTyper(Type* lhs, Type* rhs, Typer* t) {
+  lhs = ToNumber(lhs, t);
+  rhs = ToNumber(rhs, t);
+  if (lhs->Is(Type::NaN()) || rhs->Is(Type::NaN())) return Type::NaN();
+  // TODO(neis): Do some analysis.
+  return Type::Number();
 }
 
 
-Bounds Typer::Visitor::TypeJSDivide(Node* node) {
-  return Bounds(Type::SignedSmall(zone()), Type::Number(zone()));
+Type* Typer::Visitor::JSDivideTyper(Type* lhs, Type* rhs, Typer* t) {
+  lhs = ToNumber(lhs, t);
+  rhs = ToNumber(rhs, t);
+  if (lhs->Is(Type::NaN()) || rhs->Is(Type::NaN())) return Type::NaN();
+  // TODO(neis): Do some analysis.
+  return Type::Number();
 }
 
 
-Bounds Typer::Visitor::TypeJSModulus(Node* node) {
-  return Bounds(Type::SignedSmall(zone()), Type::Number(zone()));
+Type* Typer::Visitor::JSModulusTyper(Type* lhs, Type* rhs, Typer* t) {
+  lhs = ToNumber(lhs, t);
+  rhs = ToNumber(rhs, t);
+  if (lhs->Is(Type::NaN()) || rhs->Is(Type::NaN())) return Type::NaN();
+  // TODO(neis): Do some analysis.
+  return Type::Number();
 }
 
 
 // JS unary operators.
 
+
+Type* Typer::Visitor::JSUnaryNotTyper(Type* type, Typer* t) {
+  return Invert(ToBoolean(type, t), t);
+}
+
+
 Bounds Typer::Visitor::TypeJSUnaryNot(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return TypeUnaryOp(node, JSUnaryNotTyper);
 }
 
 
 Bounds Typer::Visitor::TypeJSTypeOf(Node* node) {
-  return Bounds(Type::InternalizedString(zone()));
+  return Bounds(Type::InternalizedString());
 }
 
 
 // JS conversion operators.
 
+
 Bounds Typer::Visitor::TypeJSToBoolean(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return TypeUnaryOp(node, ToBoolean);
 }
 
 
 Bounds Typer::Visitor::TypeJSToNumber(Node* node) {
-  return Bounds(Type::SignedSmall(zone()), Type::Number(zone()));
+  return TypeUnaryOp(node, ToNumber);
 }
 
 
 Bounds Typer::Visitor::TypeJSToString(Node* node) {
-  return Bounds(Type::None(zone()), Type::String(zone()));
+  return TypeUnaryOp(node, ToString);
 }
 
 
 Bounds Typer::Visitor::TypeJSToName(Node* node) {
-  return Bounds(Type::None(zone()), Type::Name(zone()));
+  return Bounds(Type::None(), Type::Name());
 }
 
 
 Bounds Typer::Visitor::TypeJSToObject(Node* node) {
-  return Bounds(Type::None(zone()), Type::Receiver(zone()));
+  return Bounds(Type::None(), Type::Receiver());
 }
 
 
 // JS object operators.
 
+
 Bounds Typer::Visitor::TypeJSCreate(Node* node) {
-  return Bounds(Type::None(zone()), Type::Object(zone()));
+  return Bounds(Type::None(), Type::Object());
 }
 
 
-Bounds Typer::Visitor::TypeJSLoadProperty(Node* node) {
-  Bounds object = OperandType(node, 0);
-  Bounds name = OperandType(node, 1);
-  Bounds result = Bounds::Unbounded(zone());
+Type* Typer::Visitor::JSLoadPropertyTyper(Type* object, Type* name, Typer* t) {
   // TODO(rossberg): Use range types and sized array types to filter undefined.
-  if (object.lower->IsArray() && name.lower->Is(Type::Integral32())) {
-    result.lower = Type::Union(
-        object.lower->AsArray()->Element(), Type::Undefined(zone()), zone());
-  }
-  if (object.upper->IsArray() && name.upper->Is(Type::Integral32())) {
-    result.upper = Type::Union(
-        object.upper->AsArray()->Element(),  Type::Undefined(zone()), zone());
+  if (object->IsArray() && name->Is(Type::Integral32())) {
+    return Type::Union(
+        object->AsArray()->Element(), Type::Undefined(), t->zone());
   }
-  return result;
+  return Type::Any();
+}
+
+
+Bounds Typer::Visitor::TypeJSLoadProperty(Node* node) {
+  return TypeBinaryOp(node, JSLoadPropertyTyper);
 }
 
 
@@ -524,22 +882,23 @@ Bounds Typer::Visitor::TypeJSStoreNamed(Node* node) {
 
 
 Bounds Typer::Visitor::TypeJSDeleteProperty(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeJSHasProperty(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeJSInstanceOf(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 // JS context operators.
 
+
 Bounds Typer::Visitor::TypeJSLoadContext(Node* node) {
   Bounds outer = OperandType(node, 0);
   DCHECK(outer.upper->Maybe(Type::Internal()));
@@ -574,7 +933,7 @@ Bounds Typer::Visitor::TypeJSLoadContext(Node* node) {
         handle(context.ToHandleChecked()->get(static_cast<int>(access.index())),
                isolate());
     Type* lower = TypeConstant(value);
-    return Bounds(lower, Type::Any(zone()));
+    return Bounds(lower, Type::Any());
   }
 }
 
@@ -624,23 +983,24 @@ Bounds Typer::Visitor::TypeJSCreateGlobalContext(Node* node) {
 
 // JS other operators.
 
+
 Bounds Typer::Visitor::TypeJSYield(Node* node) {
   return Bounds::Unbounded(zone());
 }
 
 
 Bounds Typer::Visitor::TypeJSCallConstruct(Node* node) {
-  return Bounds(Type::None(zone()), Type::Receiver(zone()));
+  return Bounds(Type::None(), Type::Receiver());
+}
+
+
+Type* Typer::Visitor::JSCallFunctionTyper(Type* fun, Typer* t) {
+  return fun->IsFunction() ? fun->AsFunction()->Result() : Type::Any();
 }
 
 
 Bounds Typer::Visitor::TypeJSCallFunction(Node* node) {
-  Bounds fun = OperandType(node, 0);
-  Type* lower = fun.lower->IsFunction()
-      ? fun.lower->AsFunction()->Result() : Type::None(zone());
-  Type* upper = fun.upper->IsFunction()
-      ? fun.upper->AsFunction()->Result() : Type::Any(zone());
-  return Bounds(lower, upper);
+  return TypeUnaryOp(node, JSCallFunctionTyper);  // We ignore argument types.
 }
 
 
@@ -656,143 +1016,173 @@ Bounds Typer::Visitor::TypeJSDebugger(Node* node) {
 
 // Simplified operators.
 
+
 Bounds Typer::Visitor::TypeBooleanNot(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeBooleanToNumber(Node* node) {
-  return Bounds(Type::Number(zone()));
+  return Bounds(Type::Number());
 }
 
 
 Bounds Typer::Visitor::TypeNumberEqual(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeNumberLessThan(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeNumberLessThanOrEqual(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeNumberAdd(Node* node) {
-  return Bounds(Type::Number(zone()));
+  return Bounds(Type::Number());
 }
 
 
 Bounds Typer::Visitor::TypeNumberSubtract(Node* node) {
-  return Bounds(Type::Number(zone()));
+  return Bounds(Type::Number());
 }
 
 
 Bounds Typer::Visitor::TypeNumberMultiply(Node* node) {
-  return Bounds(Type::Number(zone()));
+  return Bounds(Type::Number());
 }
 
 
 Bounds Typer::Visitor::TypeNumberDivide(Node* node) {
-  return Bounds(Type::Number(zone()));
+  return Bounds(Type::Number());
 }
 
 
 Bounds Typer::Visitor::TypeNumberModulus(Node* node) {
-  return Bounds(Type::Number(zone()));
+  return Bounds(Type::Number());
 }
 
 
 Bounds Typer::Visitor::TypeNumberToInt32(Node* node) {
-  Bounds arg = OperandType(node, 0);
-  Type* s32 = Type::Signed32(zone());
-  Type* lower = arg.lower->Is(s32) ? arg.lower : s32;
-  Type* upper = arg.upper->Is(s32) ? arg.upper : s32;
-  return Bounds(lower, upper);
+  return TypeUnaryOp(node, NumberToInt32);
 }
 
 
 Bounds Typer::Visitor::TypeNumberToUint32(Node* node) {
-  Bounds arg = OperandType(node, 0);
-  Type* u32 = Type::Unsigned32(zone());
-  Type* lower = arg.lower->Is(u32) ? arg.lower : u32;
-  Type* upper = arg.upper->Is(u32) ? arg.upper : u32;
-  return Bounds(lower, upper);
+  return TypeUnaryOp(node, NumberToUint32);
 }
 
 
 Bounds Typer::Visitor::TypeReferenceEqual(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeStringEqual(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeStringLessThan(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeStringLessThanOrEqual(Node* node) {
-  return Bounds(Type::Boolean(zone()));
+  return Bounds(Type::Boolean());
 }
 
 
 Bounds Typer::Visitor::TypeStringAdd(Node* node) {
-  return Bounds(Type::String(zone()));
+  return Bounds(Type::String());
+}
+
+
+static Type* ChangeRepresentation(Type* type, Type* rep, Zone* zone) {
+  // TODO(neis): Enable when expressible.
+  /*
+  return Type::Union(
+      Type::Intersect(type, Type::Semantic(), zone),
+      Type::Intersect(rep, Type::Representation(), zone), zone);
+  */
+  return type;
 }
 
 
 Bounds Typer::Visitor::TypeChangeTaggedToInt32(Node* node) {
-  // TODO(titzer): type is type of input, representation is Word32.
-  return Bounds(Type::Integral32());
+  Bounds arg = OperandType(node, 0);
+  DCHECK(arg.upper->Is(Type::Signed32()));
+  return Bounds(
+      ChangeRepresentation(arg.lower, Type::UntaggedInt32(), zone()),
+      ChangeRepresentation(arg.upper, Type::UntaggedInt32(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeChangeTaggedToUint32(Node* node) {
-  return Bounds(Type::Integral32());  // TODO(titzer): add appropriate rep
+  Bounds arg = OperandType(node, 0);
+  DCHECK(arg.upper->Is(Type::Unsigned32()));
+  return Bounds(
+      ChangeRepresentation(arg.lower, Type::UntaggedInt32(), zone()),
+      ChangeRepresentation(arg.upper, Type::UntaggedInt32(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeChangeTaggedToFloat64(Node* node) {
-  // TODO(titzer): type is type of input, representation is Float64.
-  return Bounds(Type::Number());
+  Bounds arg = OperandType(node, 0);
+  DCHECK(arg.upper->Is(Type::Number()));
+  return Bounds(
+      ChangeRepresentation(arg.lower, Type::UntaggedFloat64(), zone()),
+      ChangeRepresentation(arg.upper, Type::UntaggedFloat64(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeChangeInt32ToTagged(Node* node) {
-  // TODO(titzer): type is type of input, representation is Tagged.
-  return Bounds(Type::Integral32());
+  Bounds arg = OperandType(node, 0);
+  DCHECK(arg.upper->Is(Type::Signed32()));
+  return Bounds(
+      ChangeRepresentation(arg.lower, Type::Tagged(), zone()),
+      ChangeRepresentation(arg.upper, Type::Tagged(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeChangeUint32ToTagged(Node* node) {
-  // TODO(titzer): type is type of input, representation is Tagged.
-  return Bounds(Type::Unsigned32());
+  Bounds arg = OperandType(node, 0);
+  DCHECK(arg.upper->Is(Type::Unsigned32()));
+  return Bounds(
+      ChangeRepresentation(arg.lower, Type::Tagged(), zone()),
+      ChangeRepresentation(arg.upper, Type::Tagged(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeChangeFloat64ToTagged(Node* node) {
-  // TODO(titzer): type is type of input, representation is Tagged.
-  return Bounds(Type::Number());
+  Bounds arg = OperandType(node, 0);
+  // CHECK(arg.upper->Is(Type::Number()));
+  // TODO(neis): This check currently fails due to inconsistent typing.
+  return Bounds(
+      ChangeRepresentation(arg.lower, Type::Tagged(), zone()),
+      ChangeRepresentation(arg.upper, Type::Tagged(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeChangeBoolToBit(Node* node) {
-  // TODO(titzer): type is type of input, representation is Bit.
-  return Bounds(Type::Boolean());
+  Bounds arg = OperandType(node, 0);
+  DCHECK(arg.upper->Is(Type::Boolean()));
+  return Bounds(
+      ChangeRepresentation(arg.lower, Type::UntaggedInt1(), zone()),
+      ChangeRepresentation(arg.upper, Type::UntaggedInt1(), zone()));
 }
 
 
 Bounds Typer::Visitor::TypeChangeBitToBool(Node* node) {
-  // TODO(titzer): type is type of input, representation is Tagged.
-  return Bounds(Type::Boolean());
+  Bounds arg = OperandType(node, 0);
+  DCHECK(arg.upper->Is(Type::Boolean()));
+  return Bounds(
+      ChangeRepresentation(arg.lower, Type::TaggedPtr(), zone()),
+      ChangeRepresentation(arg.upper, Type::TaggedPtr(), zone()));
 }
 
 
@@ -820,9 +1210,12 @@ Bounds Typer::Visitor::TypeStoreElement(Node* node) {
 
 // Machine operators.
 
+
 // TODO(rossberg): implement
 #define DEFINE_METHOD(x) \
-    Bounds Typer::Visitor::Type##x(Node* node) { return Bounds(Type::None()); }
+  Bounds Typer::Visitor::Type##x(Node* node) { \
+    return Bounds::Unbounded(zone()); \
+  }
 MACHINE_OP_LIST(DEFINE_METHOD)
 #undef DEFINE_METHOD