src/compiler/types.h

// Copyright 2014 the V8 project authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

#ifndef V8_COMPILER_TYPES_H_
#define V8_COMPILER_TYPES_H_

#include "src/base/compiler-specific.h"
#include "src/conversions.h"
#include "src/globals.h"
#include "src/handles.h"
#include "src/objects.h"
#include "src/ostreams.h"

namespace v8 {
namespace internal {
namespace compiler {

// SUMMARY
//
// A simple type system for compiler-internal use. It is based entirely on
// union types, and all subtyping hence amounts to set inclusion. Besides the
// obvious primitive types and some predefined unions, the type language also
// can express class types (a.k.a. specific maps) and singleton types (i.e.,
// concrete constants).
//
// The following equations and inequations hold:
//
//   None <= T
//   T <= Any
//
//   Number = Signed32 \/ Unsigned32 \/ Double
//   Smi <= Signed32
//   Name = String \/ Symbol
//   UniqueName = InternalizedString \/ Symbol
//   InternalizedString < String
//
//   Receiver = Object \/ Proxy
//   OtherUndetectable < Object
//   DetectableReceiver = Receiver - OtherUndetectable
//
//   Constant(x) < T  iff instance_type(map(x)) < T
//
//
// RANGE TYPES
//
// A range type represents a continuous integer interval by its minimum and
// maximum value.  Either value may be an infinity, in which case that infinity
// itself is also included in the range.   A range never contains NaN or -0.
//
// If a value v happens to be an integer n, then Constant(v) is considered a
// subtype of Range(n, n) (and therefore also a subtype of any larger range).
// In order to avoid large unions, however, it is usually a good idea to use
// Range rather than Constant.
//
//
// PREDICATES
//
// There are two main functions for testing types:
//
//   T1->Is(T2)     -- tests whether T1 is included in T2 (i.e., T1 <= T2)
//   T1->Maybe(T2)  -- tests whether T1 and T2 overlap (i.e., T1 /\ T2 =/= 0)
//
// Typically, the former is to be used to select representations (e.g., via
// T->Is(SignedSmall())), and the latter to check whether a specific case needs
// handling (e.g., via T->Maybe(Number())).
//
// There is no functionality to discover whether a type is a leaf in the
// lattice. That is intentional. It should always be possible to refine the
// lattice (e.g., splitting up number types further) without invalidating any
// existing assumptions or tests.
// Consequently, do not normally use Equals for type tests, always use Is!
//
// The NowIs operator implements state-sensitive subtying, as described above.
// Any compilation decision based on such temporary properties requires runtime
// guarding!
//
//
// PROPERTIES
//
// Various formal properties hold for constructors, operators, and predicates
// over types. For example, constructors are injective and subtyping is a
// complete partial order.
//
// See test/cctest/test-types.cc for a comprehensive executable specification,
// especially with respect to the properties of the more exotic 'temporal'
// constructors and predicates (those prefixed 'Now').
//
//
// IMPLEMENTATION
//
// Internally, all 'primitive' types, and their unions, are represented as
// bitsets. Bit 0 is reserved for tagging. Only structured types require
// allocation.

// -----------------------------------------------------------------------------
// Values for bitset types

// clang-format off

#define INTERNAL_BITSET_TYPE_LIST(V)                                      \
  V(OtherUnsigned31, 1u << 1)  \
  V(OtherUnsigned32, 1u << 2)  \
  V(OtherSigned32,   1u << 3)  \
  V(OtherNumber,     1u << 4)  \

#define PROPER_BITSET_TYPE_LIST(V) \
  V(None,                0u)        \
  V(Negative31,          1u << 5)   \
  V(Null,                1u << 6)   \
  V(Undefined,           1u << 7)   \
  V(Boolean,             1u << 8)   \
  V(Unsigned30,          1u << 9)   \
  V(MinusZero,           1u << 10)  \
  V(NaN,                 1u << 11)  \
  V(Symbol,              1u << 12)  \
  V(InternalizedString,  1u << 13)  \
  V(OtherString,         1u << 14)  \
  V(Simd,                1u << 15)  \
  V(OtherObject,         1u << 17)  \
  V(OtherUndetectable,   1u << 16)  \
  V(Proxy,               1u << 18)  \
  V(Function,            1u << 19)  \
  V(Hole,                1u << 20)  \
  V(OtherInternal,       1u << 21)  \
  V(ExternalPointer,     1u << 22)  \
  \
  V(Signed31,                   kUnsigned30 | kNegative31) \
  V(Signed32,                   kSigned31 | kOtherUnsigned31 | kOtherSigned32) \
  V(Signed32OrMinusZero,        kSigned32 | kMinusZero) \
  V(Signed32OrMinusZeroOrNaN,   kSigned32 | kMinusZero | kNaN) \
  V(Negative32,                 kNegative31 | kOtherSigned32) \
  V(Unsigned31,                 kUnsigned30 | kOtherUnsigned31) \
  V(Unsigned32,                 kUnsigned30 | kOtherUnsigned31 | \
                                kOtherUnsigned32) \
  V(Unsigned32OrMinusZero,      kUnsigned32 | kMinusZero) \
  V(Unsigned32OrMinusZeroOrNaN, kUnsigned32 | kMinusZero | kNaN) \
  V(Integral32,                 kSigned32 | kUnsigned32) \
  V(PlainNumber,                kIntegral32 | kOtherNumber) \
  V(OrderedNumber,              kPlainNumber | kMinusZero) \
  V(MinusZeroOrNaN,             kMinusZero | kNaN) \
  V(Number,                     kOrderedNumber | kNaN) \
  V(String,                     kInternalizedString | kOtherString) \
  V(UniqueName,                 kSymbol | kInternalizedString) \
  V(Name,                       kSymbol | kString) \
  V(BooleanOrNumber,            kBoolean | kNumber) \
  V(BooleanOrNullOrNumber,      kBooleanOrNumber | kNull) \
  V(BooleanOrNullOrUndefined,   kBoolean | kNull | kUndefined) \
  V(NullOrNumber,               kNull | kNumber) \
  V(NullOrUndefined,            kNull | kUndefined) \
  V(Undetectable,               kNullOrUndefined | kOtherUndetectable) \
  V(NumberOrOddball,            kNumber | kNullOrUndefined | kBoolean | kHole) \
  V(NumberOrSimdOrString,       kNumber | kSimd | kString) \
  V(NumberOrString,             kNumber | kString) \
  V(NumberOrUndefined,          kNumber | kUndefined) \
  V(PlainPrimitive,             kNumberOrString | kBoolean | kNullOrUndefined) \
  V(Primitive,                  kSymbol | kSimd | kPlainPrimitive) \
  V(DetectableReceiver,         kFunction | kOtherObject | kProxy) \
  V(Object,                     kFunction | kOtherObject | kOtherUndetectable) \
  V(Receiver,                   kObject | kProxy) \
  V(ReceiverOrUndefined,        kReceiver | kUndefined) \
  V(StringOrReceiver,           kString | kReceiver) \
  V(Unique,                     kBoolean | kUniqueName | kNull | kUndefined | \
                                kReceiver) \
  V(Internal,                   kHole | kExternalPointer | kOtherInternal) \
  V(NonInternal,                kPrimitive | kReceiver) \
  V(NonNumber,                  kUnique | kString | kInternal) \
  V(Any,                        0xfffffffeu)

// clang-format on

/*
 * The following diagrams show how integers (in the mathematical sense) are
 * divided among the different atomic numerical types.
 *
 *   ON    OS32     N31     U30     OU31    OU32     ON
 * ______[_______[_______[_______[_______[_______[_______
 *     -2^31   -2^30     0      2^30    2^31    2^32
 *
 * E.g., OtherUnsigned32 (OU32) covers all integers from 2^31 to 2^32-1.
 *
 * Some of the atomic numerical bitsets are internal only (see
 * INTERNAL_BITSET_TYPE_LIST).  To a types user, they should only occur in
 * union with certain other bitsets.  For instance, OtherNumber should only
 * occur as part of PlainNumber.
 */

#define BITSET_TYPE_LIST(V)    \
  INTERNAL_BITSET_TYPE_LIST(V) \
  PROPER_BITSET_TYPE_LIST(V)

class Type;

// -----------------------------------------------------------------------------
// Bitset types (internal).

class V8_EXPORT_PRIVATE BitsetType {
 public:
  typedef uint32_t bitset;  // Internal

  enum : uint32_t {
#define DECLARE_TYPE(type, value) k##type = (value),
    BITSET_TYPE_LIST(DECLARE_TYPE)
#undef DECLARE_TYPE
        kUnusedEOL = 0
  };

  static bitset SignedSmall();
  static bitset UnsignedSmall();

  bitset Bitset() {
    return static_cast<bitset>(reinterpret_cast<uintptr_t>(this) ^ 1u);
  }

  static bool IsInhabited(bitset bits) { return bits != kNone; }

  static bool Is(bitset bits1, bitset bits2) {
    return (bits1 | bits2) == bits2;
  }

  static double Min(bitset);
  static double Max(bitset);

  static bitset Glb(Type* type);  // greatest lower bound that's a bitset
  static bitset Glb(double min, double max);
  static bitset Lub(Type* type);  // least upper bound that's a bitset
  static bitset Lub(i::Map* map);
  static bitset Lub(i::Object* value);
  static bitset Lub(double value);
  static bitset Lub(double min, double max);
  static bitset ExpandInternals(bitset bits);

  static const char* Name(bitset);
  static void Print(std::ostream& os, bitset);  // NOLINT
#ifdef DEBUG
  static void Print(bitset);
#endif

  static bitset NumberBits(bitset bits);

  static bool IsBitset(Type* type) {
    return reinterpret_cast<uintptr_t>(type) & 1;
  }

  static Type* NewForTesting(bitset bits) { return New(bits); }

 private:
  friend class Type;

  static Type* New(bitset bits) {
    return reinterpret_cast<Type*>(static_cast<uintptr_t>(bits | 1u));
  }

  struct Boundary {
    bitset internal;
    bitset external;
    double min;
  };
  static const Boundary BoundariesArray[];
  static inline const Boundary* Boundaries();
  static inline size_t BoundariesSize();
};

// -----------------------------------------------------------------------------
// Superclass for non-bitset types (internal).
class TypeBase {
 protected:
  friend class Type;

  enum Kind { kHeapConstant, kOtherNumberConstant, kTuple, kUnion, kRange };

  Kind kind() const { return kind_; }
  explicit TypeBase(Kind kind) : kind_(kind) {}

  static bool IsKind(Type* type, Kind kind) {
    if (BitsetType::IsBitset(type)) return false;
    TypeBase* base = reinterpret_cast<TypeBase*>(type);
    return base->kind() == kind;
  }

  // The hacky conversion to/from Type*.
  static Type* AsType(TypeBase* type) { return reinterpret_cast<Type*>(type); }
  static TypeBase* FromType(Type* type) {
    return reinterpret_cast<TypeBase*>(type);
  }

 private:
  Kind kind_;
};

// -----------------------------------------------------------------------------
// Constant types.

class OtherNumberConstantType : public TypeBase {
 public:
  double Value() { return value_; }

  static bool IsOtherNumberConstant(double value);
  static bool IsOtherNumberConstant(Object* value);

 private:
  friend class Type;
  friend class BitsetType;

  static Type* New(double value, Zone* zone) {
    return AsType(new (zone->New(sizeof(OtherNumberConstantType)))
                      OtherNumberConstantType(value));  // NOLINT
  }

  static OtherNumberConstantType* cast(Type* type) {
    DCHECK(IsKind(type, kOtherNumberConstant));
    return static_cast<OtherNumberConstantType*>(FromType(type));
  }

  explicit OtherNumberConstantType(double value)
      : TypeBase(kOtherNumberConstant), value_(value) {
    CHECK(IsOtherNumberConstant(value));
  }

  BitsetType::bitset Lub() { return BitsetType::kOtherNumber; }

  double value_;
};

class V8_EXPORT_PRIVATE HeapConstantType : public NON_EXPORTED_BASE(TypeBase) {
 public:
  i::Handle<i::HeapObject> Value() { return object_; }

 private:
  friend class Type;
  friend class BitsetType;

  static Type* New(i::Handle<i::HeapObject> value, Zone* zone) {
    BitsetType::bitset bitset = BitsetType::Lub(*value);
    return AsType(new (zone->New(sizeof(HeapConstantType)))
                      HeapConstantType(bitset, value));
  }

  static HeapConstantType* cast(Type* type) {
    DCHECK(IsKind(type, kHeapConstant));
    return static_cast<HeapConstantType*>(FromType(type));
  }

  HeapConstantType(BitsetType::bitset bitset, i::Handle<i::HeapObject> object);

  BitsetType::bitset Lub() { return bitset_; }

  BitsetType::bitset bitset_;
  Handle<i::HeapObject> object_;
};

// -----------------------------------------------------------------------------
// Range types.

class RangeType : public TypeBase {
 public:
  struct Limits {
    double min;
    double max;
    Limits(double min, double max) : min(min), max(max) {}
    explicit Limits(RangeType* range) : min(range->Min()), max(range->Max()) {}
    bool IsEmpty();
    static Limits Empty() { return Limits(1, 0); }
    static Limits Intersect(Limits lhs, Limits rhs);
    static Limits Union(Limits lhs, Limits rhs);
  };

  double Min() { return limits_.min; }
  double Max() { return limits_.max; }

 private:
  friend class Type;
  friend class BitsetType;
  friend class UnionType;

  static Type* New(double min, double max, Zone* zone) {
    return New(Limits(min, max), zone);
  }

  static bool IsInteger(double x) {
    return nearbyint(x) == x && !i::IsMinusZero(x);  // Allows for infinities.
  }

  static Type* New(Limits lim, Zone* zone) {
    DCHECK(IsInteger(lim.min) && IsInteger(lim.max));
    DCHECK(lim.min <= lim.max);
    BitsetType::bitset bits = BitsetType::Lub(lim.min, lim.max);

    return AsType(new (zone->New(sizeof(RangeType))) RangeType(bits, lim));
  }

  static RangeType* cast(Type* type) {
    DCHECK(IsKind(type, kRange));
    return static_cast<RangeType*>(FromType(type));
  }

  RangeType(BitsetType::bitset bitset, Limits limits)
      : TypeBase(kRange), bitset_(bitset), limits_(limits) {}

  BitsetType::bitset Lub() { return bitset_; }

  BitsetType::bitset bitset_;
  Limits limits_;
};

// -----------------------------------------------------------------------------
// Superclass for types with variable number of type fields.
class StructuralType : public TypeBase {
 public:
  int LengthForTesting() { return Length(); }

 protected:
  friend class Type;

  int Length() { return length_; }

  Type* Get(int i) {
    DCHECK(0 <= i && i < this->Length());
    return elements_[i];
  }

  void Set(int i, Type* type) {
    DCHECK(0 <= i && i < this->Length());
    elements_[i] = type;
  }

  void Shrink(int length) {
    DCHECK(2 <= length && length <= this->Length());
    length_ = length;
  }

  StructuralType(Kind kind, int length, i::Zone* zone)
      : TypeBase(kind), length_(length) {
    elements_ = reinterpret_cast<Type**>(zone->New(sizeof(Type*) * length));
  }

 private:
  int length_;
  Type** elements_;
};

// -----------------------------------------------------------------------------
// Tuple types.

class TupleType : public StructuralType {
 public:
  int Arity() { return this->Length(); }
  Type* Element(int i) { return this->Get(i); }

  void InitElement(int i, Type* type) { this->Set(i, type); }

 private:
  friend class Type;

  TupleType(int length, Zone* zone) : StructuralType(kTuple, length, zone) {}

  static Type* New(int length, Zone* zone) {
    return AsType(new (zone->New(sizeof(TupleType))) TupleType(length, zone));
  }

  static TupleType* cast(Type* type) {
    DCHECK(IsKind(type, kTuple));
    return static_cast<TupleType*>(FromType(type));
  }
};

// -----------------------------------------------------------------------------
// Union types (internal).
// A union is a structured type with the following invariants:
// - its length is at least 2
// - at most one field is a bitset, and it must go into index 0
// - no field is a union
// - no field is a subtype of any other field
class UnionType : public StructuralType {
 private:
  friend Type;
  friend BitsetType;

  UnionType(int length, Zone* zone) : StructuralType(kUnion, length, zone) {}

  static Type* New(int length, Zone* zone) {
    return AsType(new (zone->New(sizeof(UnionType))) UnionType(length, zone));
  }

  static UnionType* cast(Type* type) {
    DCHECK(IsKind(type, kUnion));
    return static_cast<UnionType*>(FromType(type));
  }

  bool Wellformed();
};

class V8_EXPORT_PRIVATE Type {
 public:
  typedef BitsetType::bitset bitset;  // Internal

// Constructors.
#define DEFINE_TYPE_CONSTRUCTOR(type, value) \
  static Type* type() { return BitsetType::New(BitsetType::k##type); }
  PROPER_BITSET_TYPE_LIST(DEFINE_TYPE_CONSTRUCTOR)
#undef DEFINE_TYPE_CONSTRUCTOR

  static Type* SignedSmall() {
    return BitsetType::New(BitsetType::SignedSmall());
  }
  static Type* UnsignedSmall() {
    return BitsetType::New(BitsetType::UnsignedSmall());
  }

  static Type* OtherNumberConstant(double value, Zone* zone) {
    return OtherNumberConstantType::New(value, zone);
  }
  static Type* HeapConstant(i::Handle<i::HeapObject> value, Zone* zone) {
    return HeapConstantType::New(value, zone);
  }
  static Type* Range(double min, double max, Zone* zone) {
    return RangeType::New(min, max, zone);
  }
  static Type* Tuple(Type* first, Type* second, Type* third, Zone* zone) {
    Type* tuple = TupleType::New(3, zone);
    tuple->AsTuple()->InitElement(0, first);
    tuple->AsTuple()->InitElement(1, second);
    tuple->AsTuple()->InitElement(2, third);
    return tuple;
  }

  // NewConstant is a factory that returns Constant, Range or Number.
  static Type* NewConstant(i::Handle<i::Object> value, Zone* zone);
  static Type* NewConstant(double value, Zone* zone);

  static Type* Union(Type* type1, Type* type2, Zone* zone);
  static Type* Intersect(Type* type1, Type* type2, Zone* zone);

  static Type* Of(double value, Zone* zone) {
    return BitsetType::New(BitsetType::ExpandInternals(BitsetType::Lub(value)));
  }
  static Type* Of(i::Object* value, Zone* zone) {
    return BitsetType::New(BitsetType::ExpandInternals(BitsetType::Lub(value)));
  }
  static Type* Of(i::Handle<i::Object> value, Zone* zone) {
    return Of(*value, zone);
  }

  static Type* For(i::Map* map) {
    return BitsetType::New(BitsetType::ExpandInternals(BitsetType::Lub(map)));
  }
  static Type* For(i::Handle<i::Map> map) { return For(*map); }

  // Predicates.
  bool IsInhabited() { return BitsetType::IsInhabited(this->BitsetLub()); }

  bool Is(Type* that) { return this == that || this->SlowIs(that); }
  bool Maybe(Type* that);
  bool Equals(Type* that) { return this->Is(that) && that->Is(this); }

  // Inspection.
  bool IsRange() { return IsKind(TypeBase::kRange); }
  bool IsHeapConstant() { return IsKind(TypeBase::kHeapConstant); }
  bool IsOtherNumberConstant() {
    return IsKind(TypeBase::kOtherNumberConstant);
  }
  bool IsTuple() { return IsKind(TypeBase::kTuple); }

  HeapConstantType* AsHeapConstant() { return HeapConstantType::cast(this); }
  OtherNumberConstantType* AsOtherNumberConstant() {
    return OtherNumberConstantType::cast(this);
  }
  RangeType* AsRange() { return RangeType::cast(this); }
  TupleType* AsTuple() { return TupleType::cast(this); }

  // Minimum and maximum of a numeric type.
  // These functions do not distinguish between -0 and +0.  If the type equals
  // kNaN, they return NaN; otherwise kNaN is ignored.  Only call these
  // functions on subtypes of Number.
  double Min();
  double Max();

  // Extracts a range from the type: if the type is a range or a union
  // containing a range, that range is returned; otherwise, NULL is returned.
  Type* GetRange();

  static bool IsInteger(i::Object* x);
  static bool IsInteger(double x) {
    return nearbyint(x) == x && !i::IsMinusZero(x);  // Allows for infinities.
  }

  int NumConstants();

  // Printing.

  void PrintTo(std::ostream& os);

#ifdef DEBUG
  void Print();
#endif

  // Helpers for testing.
  bool IsBitsetForTesting() { return IsBitset(); }
  bool IsUnionForTesting() { return IsUnion(); }
  bitset AsBitsetForTesting() { return AsBitset(); }
  UnionType* AsUnionForTesting() { return AsUnion(); }

 private:
  // Friends.
  template <class>
  friend class Iterator;
  friend BitsetType;
  friend UnionType;

  // Internal inspection.
  bool IsKind(TypeBase::Kind kind) { return TypeBase::IsKind(this, kind); }

  bool IsNone() { return this == None(); }
  bool IsAny() { return this == Any(); }
  bool IsBitset() { return BitsetType::IsBitset(this); }
  bool IsUnion() { return IsKind(TypeBase::kUnion); }

  bitset AsBitset() {
    DCHECK(this->IsBitset());
    return reinterpret_cast<BitsetType*>(this)->Bitset();
  }
  UnionType* AsUnion() { return UnionType::cast(this); }

  bitset BitsetGlb() { return BitsetType::Glb(this); }
  bitset BitsetLub() { return BitsetType::Lub(this); }

  bool SlowIs(Type* that);

  static bool Overlap(RangeType* lhs, RangeType* rhs);
  static bool Contains(RangeType* lhs, RangeType* rhs);
  static bool Contains(RangeType* range, i::Object* val);

  static int UpdateRange(Type* type, UnionType* result, int size, Zone* zone);

  static RangeType::Limits IntersectRangeAndBitset(Type* range, Type* bits,
                                                   Zone* zone);
  static RangeType::Limits ToLimits(bitset bits, Zone* zone);

  bool SimplyEquals(Type* that);

  static int AddToUnion(Type* type, UnionType* result, int size, Zone* zone);
  static int IntersectAux(Type* type, Type* other, UnionType* result, int size,
                          RangeType::Limits* limits, Zone* zone);
  static Type* NormalizeUnion(Type* unioned, int size, Zone* zone);
  static Type* NormalizeRangeAndBitset(Type* range, bitset* bits, Zone* zone);
};

}  // namespace compiler
}  // namespace internal
}  // namespace v8

#endif  // V8_COMPILER_TYPES_H_