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// 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(InternalizedNonSeqString, 1u << 13) \
V(InternalizedSeqString, 1u << 14) \
V(OtherNonSeqString, 1u << 15) \
V(OtherSeqString, 1u << 16) \
V(OtherCallable, 1u << 17) \
V(OtherObject, 1u << 18) \
V(OtherUndetectable, 1u << 19) \
V(CallableProxy, 1u << 20) \
V(OtherProxy, 1u << 21) \
V(Function, 1u << 22) \
V(BoundFunction, 1u << 23) \
V(Hole, 1u << 24) \
V(OtherInternal, 1u << 25) \
V(ExternalPointer, 1u << 26) \
V(Array, 1u << 27) \
V(BigInt, 1u << 28) \
\
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(Integral32OrMinusZero, kIntegral32 | kMinusZero) \
V(Integral32OrMinusZeroOrNaN, kIntegral32OrMinusZero | kNaN) \
V(PlainNumber, kIntegral32 | kOtherNumber) \
V(OrderedNumber, kPlainNumber | kMinusZero) \
V(MinusZeroOrNaN, kMinusZero | kNaN) \
V(Number, kOrderedNumber | kNaN) \
V(Numeric, kNumber | kBigInt) \
V(InternalizedString, kInternalizedNonSeqString | \
kInternalizedSeqString) \
V(OtherString, kOtherNonSeqString | kOtherSeqString) \
V(SeqString, kInternalizedSeqString | kOtherSeqString) \
V(NonSeqString, kInternalizedNonSeqString | \
kOtherNonSeqString) \
V(String, kInternalizedString | kOtherString) \
V(UniqueName, kSymbol | kInternalizedString) \
V(Name, kSymbol | kString) \
V(InternalizedStringOrNull, kInternalizedString | kNull) \
V(BooleanOrNumber, kBoolean | kNumber) \
V(BooleanOrNullOrNumber, kBooleanOrNumber | kNull) \
V(BooleanOrNullOrUndefined, kBoolean | kNull | kUndefined) \
V(Oddball, kBooleanOrNullOrUndefined | kHole) \
V(NullOrNumber, kNull | kNumber) \
V(NullOrUndefined, kNull | kUndefined) \
V(Undetectable, kNullOrUndefined | kOtherUndetectable) \
V(NumberOrHole, kNumber | kHole) \
V(NumberOrOddball, kNumber | kNullOrUndefined | kBoolean | \
kHole) \
V(NumericOrString, kNumeric | kString) \
V(NumberOrUndefined, kNumber | kUndefined) \
V(NumberOrUndefinedOrNullOrBoolean, \
kNumber | kNullOrUndefined | kBoolean) \
V(PlainPrimitive, kNumber | kString | kBoolean | \
kNullOrUndefined) \
V(Primitive, kSymbol | kBigInt | kPlainPrimitive) \
V(OtherUndetectableOrUndefined, kOtherUndetectable | kUndefined) \
V(Proxy, kCallableProxy | kOtherProxy) \
V(ArrayOrOtherObject, kArray | kOtherObject) \
V(ArrayOrProxy, kArray | kProxy) \
V(DetectableCallable, kFunction | kBoundFunction | \
kOtherCallable | kCallableProxy) \
V(Callable, kDetectableCallable | kOtherUndetectable) \
V(NonCallable, kArray | kOtherObject | kOtherProxy) \
V(NonCallableOrNull, kNonCallable | kNull) \
V(DetectableObject, kArray | kFunction | kBoundFunction | \
kOtherCallable | kOtherObject) \
V(DetectableReceiver, kDetectableObject | kProxy) \
V(DetectableReceiverOrNull, kDetectableReceiver | kNull) \
V(Object, kDetectableObject | kOtherUndetectable) \
V(Receiver, kObject | kProxy) \
V(ReceiverOrUndefined, kReceiver | kUndefined) \
V(ReceiverOrNullOrUndefined, kReceiver | kNull | kUndefined) \
V(SymbolOrReceiver, kSymbol | kReceiver) \
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 IsNone(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 IsNone() { return this == None(); }
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. NaN is ignored.
// Only call them on subtypes of Number whose intersection with OrderedNumber
// is not empty.
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, nullptr 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 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_