Home | History | Annotate | Download | only in ast
      1 // Copyright 2014 the V8 project authors. All rights reserved.
      2 // Use of this source code is governed by a BSD-style license that can be
      3 // found in the LICENSE file.
      4 
      5 #ifndef V8_AST_AST_TYPES_H_
      6 #define V8_AST_AST_TYPES_H_
      7 
      8 #include "src/conversions.h"
      9 #include "src/handles.h"
     10 #include "src/objects.h"
     11 #include "src/ostreams.h"
     12 
     13 namespace v8 {
     14 namespace internal {
     15 
     16 // SUMMARY
     17 //
     18 // A simple type system for compiler-internal use. It is based entirely on
     19 // union types, and all subtyping hence amounts to set inclusion. Besides the
     20 // obvious primitive types and some predefined unions, the type language also
     21 // can express class types (a.k.a. specific maps) and singleton types (i.e.,
     22 // concrete constants).
     23 //
     24 // Types consist of two dimensions: semantic (value range) and representation.
     25 // Both are related through subtyping.
     26 //
     27 //
     28 // SEMANTIC DIMENSION
     29 //
     30 // The following equations and inequations hold for the semantic axis:
     31 //
     32 //   None <= T
     33 //   T <= Any
     34 //
     35 //   Number = Signed32 \/ Unsigned32 \/ Double
     36 //   Smi <= Signed32
     37 //   Name = String \/ Symbol
     38 //   UniqueName = InternalizedString \/ Symbol
     39 //   InternalizedString < String
     40 //
     41 //   Receiver = Object \/ Proxy
     42 //   Array < Object
     43 //   Function < Object
     44 //   RegExp < Object
     45 //   OtherUndetectable < Object
     46 //   DetectableReceiver = Receiver - OtherUndetectable
     47 //
     48 //   Class(map) < T   iff instance_type(map) < T
     49 //   Constant(x) < T  iff instance_type(map(x)) < T
     50 //   Array(T) < Array
     51 //   Function(R, S, T0, T1, ...) < Function
     52 //   Context(T) < Internal
     53 //
     54 // Both structural Array and Function types are invariant in all parameters;
     55 // relaxing this would make Union and Intersect operations more involved.
     56 // There is no subtyping relation between Array, Function, or Context types
     57 // and respective Constant types, since these types cannot be reconstructed
     58 // for arbitrary heap values.
     59 // Note also that Constant(x) < Class(map(x)) does _not_ hold, since x's map can
     60 // change! (Its instance type cannot, however.)
     61 // TODO(rossberg): the latter is not currently true for proxies, because of fix,
     62 // but will hold once we implement direct proxies.
     63 // However, we also define a 'temporal' variant of the subtyping relation that
     64 // considers the _current_ state only, i.e., Constant(x) <_now Class(map(x)).
     65 //
     66 //
     67 // REPRESENTATIONAL DIMENSION
     68 //
     69 // For the representation axis, the following holds:
     70 //
     71 //   None <= R
     72 //   R <= Any
     73 //
     74 //   UntaggedInt = UntaggedInt1 \/ UntaggedInt8 \/
     75 //                 UntaggedInt16 \/ UntaggedInt32
     76 //   UntaggedFloat = UntaggedFloat32 \/ UntaggedFloat64
     77 //   UntaggedNumber = UntaggedInt \/ UntaggedFloat
     78 //   Untagged = UntaggedNumber \/ UntaggedPtr
     79 //   Tagged = TaggedInt \/ TaggedPtr
     80 //
     81 // Subtyping relates the two dimensions, for example:
     82 //
     83 //   Number <= Tagged \/ UntaggedNumber
     84 //   Object <= TaggedPtr \/ UntaggedPtr
     85 //
     86 // That holds because the semantic type constructors defined by the API create
     87 // types that allow for all possible representations, and dually, the ones for
     88 // representation types initially include all semantic ranges. Representations
     89 // can then e.g. be narrowed for a given semantic type using intersection:
     90 //
     91 //   SignedSmall /\ TaggedInt       (a 'smi')
     92 //   Number /\ TaggedPtr            (a heap number)
     93 //
     94 //
     95 // RANGE TYPES
     96 //
     97 // A range type represents a continuous integer interval by its minimum and
     98 // maximum value.  Either value may be an infinity, in which case that infinity
     99 // itself is also included in the range.   A range never contains NaN or -0.
    100 //
    101 // If a value v happens to be an integer n, then Constant(v) is considered a
    102 // subtype of Range(n, n) (and therefore also a subtype of any larger range).
    103 // In order to avoid large unions, however, it is usually a good idea to use
    104 // Range rather than Constant.
    105 //
    106 //
    107 // PREDICATES
    108 //
    109 // There are two main functions for testing types:
    110 //
    111 //   T1->Is(T2)     -- tests whether T1 is included in T2 (i.e., T1 <= T2)
    112 //   T1->Maybe(T2)  -- tests whether T1 and T2 overlap (i.e., T1 /\ T2 =/= 0)
    113 //
    114 // Typically, the former is to be used to select representations (e.g., via
    115 // T->Is(SignedSmall())), and the latter to check whether a specific case needs
    116 // handling (e.g., via T->Maybe(Number())).
    117 //
    118 // There is no functionality to discover whether a type is a leaf in the
    119 // lattice. That is intentional. It should always be possible to refine the
    120 // lattice (e.g., splitting up number types further) without invalidating any
    121 // existing assumptions or tests.
    122 // Consequently, do not normally use Equals for type tests, always use Is!
    123 //
    124 // The NowIs operator implements state-sensitive subtying, as described above.
    125 // Any compilation decision based on such temporary properties requires runtime
    126 // guarding!
    127 //
    128 //
    129 // PROPERTIES
    130 //
    131 // Various formal properties hold for constructors, operators, and predicates
    132 // over types. For example, constructors are injective and subtyping is a
    133 // complete partial order.
    134 //
    135 // See test/cctest/test-types.cc for a comprehensive executable specification,
    136 // especially with respect to the properties of the more exotic 'temporal'
    137 // constructors and predicates (those prefixed 'Now').
    138 //
    139 //
    140 // IMPLEMENTATION
    141 //
    142 // Internally, all 'primitive' types, and their unions, are represented as
    143 // bitsets. Bit 0 is reserved for tagging. Class is a heap pointer to the
    144 // respective map. Only structured types require allocation.
    145 // Note that the bitset representation is closed under both Union and Intersect.
    146 
    147 // -----------------------------------------------------------------------------
    148 // Values for bitset types
    149 
    150 // clang-format off
    151 
    152 #define AST_MASK_BITSET_TYPE_LIST(V) \
    153   V(Representation, 0xffc00000u) \
    154   V(Semantic,       0x003ffffeu)
    155 
    156 #define AST_REPRESENTATION(k) ((k) & AstBitsetType::kRepresentation)
    157 #define AST_SEMANTIC(k)       ((k) & AstBitsetType::kSemantic)
    158 
    159 // Bits 21-22 are available.
    160 #define AST_REPRESENTATION_BITSET_TYPE_LIST(V)    \
    161   V(None,               0)                    \
    162   V(UntaggedBit,        1u << 23 | kSemantic) \
    163   V(UntaggedIntegral8,  1u << 24 | kSemantic) \
    164   V(UntaggedIntegral16, 1u << 25 | kSemantic) \
    165   V(UntaggedIntegral32, 1u << 26 | kSemantic) \
    166   V(UntaggedFloat32,    1u << 27 | kSemantic) \
    167   V(UntaggedFloat64,    1u << 28 | kSemantic) \
    168   V(UntaggedPointer,    1u << 29 | kSemantic) \
    169   V(TaggedSigned,       1u << 30 | kSemantic) \
    170   V(TaggedPointer,      1u << 31 | kSemantic) \
    171   \
    172   V(UntaggedIntegral,   kUntaggedBit | kUntaggedIntegral8 |        \
    173                         kUntaggedIntegral16 | kUntaggedIntegral32) \
    174   V(UntaggedFloat,      kUntaggedFloat32 | kUntaggedFloat64)       \
    175   V(UntaggedNumber,     kUntaggedIntegral | kUntaggedFloat)        \
    176   V(Untagged,           kUntaggedNumber | kUntaggedPointer)        \
    177   V(Tagged,             kTaggedSigned | kTaggedPointer)
    178 
    179 #define AST_INTERNAL_BITSET_TYPE_LIST(V)                                      \
    180   V(OtherUnsigned31, 1u << 1 | AST_REPRESENTATION(kTagged | kUntaggedNumber)) \
    181   V(OtherUnsigned32, 1u << 2 | AST_REPRESENTATION(kTagged | kUntaggedNumber)) \
    182   V(OtherSigned32,   1u << 3 | AST_REPRESENTATION(kTagged | kUntaggedNumber)) \
    183   V(OtherNumber,     1u << 4 | AST_REPRESENTATION(kTagged | kUntaggedNumber))
    184 
    185 #define AST_SEMANTIC_BITSET_TYPE_LIST(V)                                \
    186   V(Negative31,          1u << 5  |                                     \
    187                          AST_REPRESENTATION(kTagged | kUntaggedNumber)) \
    188   V(Null,                1u << 6  | AST_REPRESENTATION(kTaggedPointer)) \
    189   V(Undefined,           1u << 7  | AST_REPRESENTATION(kTaggedPointer)) \
    190   V(Boolean,             1u << 8  | AST_REPRESENTATION(kTaggedPointer)) \
    191   V(Unsigned30,          1u << 9  |                                     \
    192                          AST_REPRESENTATION(kTagged | kUntaggedNumber)) \
    193   V(MinusZero,           1u << 10 |                                     \
    194                          AST_REPRESENTATION(kTagged | kUntaggedNumber)) \
    195   V(NaN,                 1u << 11 |                                     \
    196                          AST_REPRESENTATION(kTagged | kUntaggedNumber)) \
    197   V(Symbol,              1u << 12 | AST_REPRESENTATION(kTaggedPointer)) \
    198   V(InternalizedString,  1u << 13 | AST_REPRESENTATION(kTaggedPointer)) \
    199   V(OtherString,         1u << 14 | AST_REPRESENTATION(kTaggedPointer)) \
    200   V(OtherObject,         1u << 15 | AST_REPRESENTATION(kTaggedPointer)) \
    201   V(OtherUndetectable,   1u << 16 | AST_REPRESENTATION(kTaggedPointer)) \
    202   V(Proxy,               1u << 17 | AST_REPRESENTATION(kTaggedPointer)) \
    203   V(Function,            1u << 18 | AST_REPRESENTATION(kTaggedPointer)) \
    204   V(Hole,                1u << 19 | AST_REPRESENTATION(kTaggedPointer)) \
    205   V(OtherInternal,       1u << 20 |                                     \
    206                          AST_REPRESENTATION(kTagged | kUntagged))       \
    207   \
    208   V(Signed31,                   kUnsigned30 | kNegative31) \
    209   V(Signed32,                   kSigned31 | kOtherUnsigned31 |          \
    210                                 kOtherSigned32)                         \
    211   V(Signed32OrMinusZero,        kSigned32 | kMinusZero) \
    212   V(Signed32OrMinusZeroOrNaN,   kSigned32 | kMinusZero | kNaN) \
    213   V(Negative32,                 kNegative31 | kOtherSigned32) \
    214   V(Unsigned31,                 kUnsigned30 | kOtherUnsigned31) \
    215   V(Unsigned32,                 kUnsigned30 | kOtherUnsigned31 | \
    216                                 kOtherUnsigned32) \
    217   V(Unsigned32OrMinusZero,      kUnsigned32 | kMinusZero) \
    218   V(Unsigned32OrMinusZeroOrNaN, kUnsigned32 | kMinusZero | kNaN) \
    219   V(Integral32,                 kSigned32 | kUnsigned32) \
    220   V(PlainNumber,                kIntegral32 | kOtherNumber) \
    221   V(OrderedNumber,              kPlainNumber | kMinusZero) \
    222   V(MinusZeroOrNaN,             kMinusZero | kNaN) \
    223   V(Number,                     kOrderedNumber | kNaN) \
    224   V(String,                     kInternalizedString | kOtherString) \
    225   V(UniqueName,                 kSymbol | kInternalizedString) \
    226   V(Name,                       kSymbol | kString) \
    227   V(BooleanOrNumber,            kBoolean | kNumber) \
    228   V(BooleanOrNullOrNumber,      kBooleanOrNumber | kNull) \
    229   V(BooleanOrNullOrUndefined,   kBoolean | kNull | kUndefined) \
    230   V(NullOrNumber,               kNull | kNumber) \
    231   V(NullOrUndefined,            kNull | kUndefined) \
    232   V(Undetectable,               kNullOrUndefined | kOtherUndetectable) \
    233   V(NumberOrOddball,            kNumber | kNullOrUndefined | kBoolean | kHole) \
    234   V(NumberOrString,             kNumber | kString) \
    235   V(NumberOrUndefined,          kNumber | kUndefined) \
    236   V(PlainPrimitive,             kNumberOrString | kBoolean | kNullOrUndefined) \
    237   V(Primitive,                  kSymbol | kPlainPrimitive) \
    238   V(DetectableReceiver,         kFunction | kOtherObject | kProxy) \
    239   V(Object,                     kFunction | kOtherObject | kOtherUndetectable) \
    240   V(Receiver,                   kObject | kProxy) \
    241   V(StringOrReceiver,           kString | kReceiver) \
    242   V(Unique,                     kBoolean | kUniqueName | kNull | kUndefined | \
    243                                 kReceiver) \
    244   V(Internal,                   kHole | kOtherInternal) \
    245   V(NonInternal,                kPrimitive | kReceiver) \
    246   V(NonNumber,                  kUnique | kString | kInternal) \
    247   V(Any,                        0xfffffffeu)
    248 
    249 // clang-format on
    250 
    251 /*
    252  * The following diagrams show how integers (in the mathematical sense) are
    253  * divided among the different atomic numerical types.
    254  *
    255  *   ON    OS32     N31     U30     OU31    OU32     ON
    256  * ______[_______[_______[_______[_______[_______[_______
    257  *     -2^31   -2^30     0      2^30    2^31    2^32
    258  *
    259  * E.g., OtherUnsigned32 (OU32) covers all integers from 2^31 to 2^32-1.
    260  *
    261  * Some of the atomic numerical bitsets are internal only (see
    262  * INTERNAL_BITSET_TYPE_LIST).  To a types user, they should only occur in
    263  * union with certain other bitsets.  For instance, OtherNumber should only
    264  * occur as part of PlainNumber.
    265  */
    266 
    267 #define AST_PROPER_BITSET_TYPE_LIST(V)   \
    268   AST_REPRESENTATION_BITSET_TYPE_LIST(V) \
    269   AST_SEMANTIC_BITSET_TYPE_LIST(V)
    270 
    271 #define AST_BITSET_TYPE_LIST(V)          \
    272   AST_MASK_BITSET_TYPE_LIST(V)           \
    273   AST_REPRESENTATION_BITSET_TYPE_LIST(V) \
    274   AST_INTERNAL_BITSET_TYPE_LIST(V)       \
    275   AST_SEMANTIC_BITSET_TYPE_LIST(V)
    276 
    277 class AstType;
    278 
    279 // -----------------------------------------------------------------------------
    280 // Bitset types (internal).
    281 
    282 class AstBitsetType {
    283  public:
    284   typedef uint32_t bitset;  // Internal
    285 
    286   enum : uint32_t {
    287 #define DECLARE_TYPE(type, value) k##type = (value),
    288     AST_BITSET_TYPE_LIST(DECLARE_TYPE)
    289 #undef DECLARE_TYPE
    290         kUnusedEOL = 0
    291   };
    292 
    293   static bitset SignedSmall();
    294   static bitset UnsignedSmall();
    295 
    296   bitset Bitset() {
    297     return static_cast<bitset>(reinterpret_cast<uintptr_t>(this) ^ 1u);
    298   }
    299 
    300   static bool IsInhabited(bitset bits) {
    301     return AST_SEMANTIC(bits) != kNone && AST_REPRESENTATION(bits) != kNone;
    302   }
    303 
    304   static bool SemanticIsInhabited(bitset bits) {
    305     return AST_SEMANTIC(bits) != kNone;
    306   }
    307 
    308   static bool Is(bitset bits1, bitset bits2) {
    309     return (bits1 | bits2) == bits2;
    310   }
    311 
    312   static double Min(bitset);
    313   static double Max(bitset);
    314 
    315   static bitset Glb(AstType* type);  // greatest lower bound that's a bitset
    316   static bitset Glb(double min, double max);
    317   static bitset Lub(AstType* type);  // least upper bound that's a bitset
    318   static bitset Lub(i::Map* map);
    319   static bitset Lub(i::Object* value);
    320   static bitset Lub(double value);
    321   static bitset Lub(double min, double max);
    322   static bitset ExpandInternals(bitset bits);
    323 
    324   static const char* Name(bitset);
    325   static void Print(std::ostream& os, bitset);  // NOLINT
    326 #ifdef DEBUG
    327   static void Print(bitset);
    328 #endif
    329 
    330   static bitset NumberBits(bitset bits);
    331 
    332   static bool IsBitset(AstType* type) {
    333     return reinterpret_cast<uintptr_t>(type) & 1;
    334   }
    335 
    336   static AstType* NewForTesting(bitset bits) { return New(bits); }
    337 
    338  private:
    339   friend class AstType;
    340 
    341   static AstType* New(bitset bits) {
    342     return reinterpret_cast<AstType*>(static_cast<uintptr_t>(bits | 1u));
    343   }
    344 
    345   struct Boundary {
    346     bitset internal;
    347     bitset external;
    348     double min;
    349   };
    350   static const Boundary BoundariesArray[];
    351   static inline const Boundary* Boundaries();
    352   static inline size_t BoundariesSize();
    353 };
    354 
    355 // -----------------------------------------------------------------------------
    356 // Superclass for non-bitset types (internal).
    357 class AstTypeBase {
    358  protected:
    359   friend class AstType;
    360 
    361   enum Kind {
    362     kClass,
    363     kConstant,
    364     kContext,
    365     kArray,
    366     kFunction,
    367     kTuple,
    368     kUnion,
    369     kRange
    370   };
    371 
    372   Kind kind() const { return kind_; }
    373   explicit AstTypeBase(Kind kind) : kind_(kind) {}
    374 
    375   static bool IsKind(AstType* type, Kind kind) {
    376     if (AstBitsetType::IsBitset(type)) return false;
    377     AstTypeBase* base = reinterpret_cast<AstTypeBase*>(type);
    378     return base->kind() == kind;
    379   }
    380 
    381   // The hacky conversion to/from AstType*.
    382   static AstType* AsType(AstTypeBase* type) {
    383     return reinterpret_cast<AstType*>(type);
    384   }
    385   static AstTypeBase* FromType(AstType* type) {
    386     return reinterpret_cast<AstTypeBase*>(type);
    387   }
    388 
    389  private:
    390   Kind kind_;
    391 };
    392 
    393 // -----------------------------------------------------------------------------
    394 // Class types.
    395 
    396 class AstClassType : public AstTypeBase {
    397  public:
    398   i::Handle<i::Map> Map() { return map_; }
    399 
    400  private:
    401   friend class AstType;
    402   friend class AstBitsetType;
    403 
    404   static AstType* New(i::Handle<i::Map> map, Zone* zone) {
    405     return AsType(new (zone->New(sizeof(AstClassType)))
    406                       AstClassType(AstBitsetType::Lub(*map), map));
    407   }
    408 
    409   static AstClassType* cast(AstType* type) {
    410     DCHECK(IsKind(type, kClass));
    411     return static_cast<AstClassType*>(FromType(type));
    412   }
    413 
    414   AstClassType(AstBitsetType::bitset bitset, i::Handle<i::Map> map)
    415       : AstTypeBase(kClass), bitset_(bitset), map_(map) {}
    416 
    417   AstBitsetType::bitset Lub() { return bitset_; }
    418 
    419   AstBitsetType::bitset bitset_;
    420   Handle<i::Map> map_;
    421 };
    422 
    423 // -----------------------------------------------------------------------------
    424 // Constant types.
    425 
    426 class AstConstantType : public AstTypeBase {
    427  public:
    428   i::Handle<i::Object> Value() { return object_; }
    429 
    430  private:
    431   friend class AstType;
    432   friend class AstBitsetType;
    433 
    434   static AstType* New(i::Handle<i::Object> value, Zone* zone) {
    435     AstBitsetType::bitset bitset = AstBitsetType::Lub(*value);
    436     return AsType(new (zone->New(sizeof(AstConstantType)))
    437                       AstConstantType(bitset, value));
    438   }
    439 
    440   static AstConstantType* cast(AstType* type) {
    441     DCHECK(IsKind(type, kConstant));
    442     return static_cast<AstConstantType*>(FromType(type));
    443   }
    444 
    445   AstConstantType(AstBitsetType::bitset bitset, i::Handle<i::Object> object)
    446       : AstTypeBase(kConstant), bitset_(bitset), object_(object) {}
    447 
    448   AstBitsetType::bitset Lub() { return bitset_; }
    449 
    450   AstBitsetType::bitset bitset_;
    451   Handle<i::Object> object_;
    452 };
    453 // TODO(neis): Also cache value if numerical.
    454 // TODO(neis): Allow restricting the representation.
    455 
    456 // -----------------------------------------------------------------------------
    457 // Range types.
    458 
    459 class AstRangeType : public AstTypeBase {
    460  public:
    461   struct Limits {
    462     double min;
    463     double max;
    464     Limits(double min, double max) : min(min), max(max) {}
    465     explicit Limits(AstRangeType* range)
    466         : min(range->Min()), max(range->Max()) {}
    467     bool IsEmpty();
    468     static Limits Empty() { return Limits(1, 0); }
    469     static Limits Intersect(Limits lhs, Limits rhs);
    470     static Limits Union(Limits lhs, Limits rhs);
    471   };
    472 
    473   double Min() { return limits_.min; }
    474   double Max() { return limits_.max; }
    475 
    476  private:
    477   friend class AstType;
    478   friend class AstBitsetType;
    479   friend class AstUnionType;
    480 
    481   static AstType* New(double min, double max,
    482                       AstBitsetType::bitset representation, Zone* zone) {
    483     return New(Limits(min, max), representation, zone);
    484   }
    485 
    486   static bool IsInteger(double x) {
    487     return nearbyint(x) == x && !i::IsMinusZero(x);  // Allows for infinities.
    488   }
    489 
    490   static AstType* New(Limits lim, AstBitsetType::bitset representation,
    491                       Zone* zone) {
    492     DCHECK(IsInteger(lim.min) && IsInteger(lim.max));
    493     DCHECK(lim.min <= lim.max);
    494     DCHECK(AST_REPRESENTATION(representation) == representation);
    495     AstBitsetType::bitset bits =
    496         AST_SEMANTIC(AstBitsetType::Lub(lim.min, lim.max)) | representation;
    497 
    498     return AsType(new (zone->New(sizeof(AstRangeType)))
    499                       AstRangeType(bits, lim));
    500   }
    501 
    502   static AstRangeType* cast(AstType* type) {
    503     DCHECK(IsKind(type, kRange));
    504     return static_cast<AstRangeType*>(FromType(type));
    505   }
    506 
    507   AstRangeType(AstBitsetType::bitset bitset, Limits limits)
    508       : AstTypeBase(kRange), bitset_(bitset), limits_(limits) {}
    509 
    510   AstBitsetType::bitset Lub() { return bitset_; }
    511 
    512   AstBitsetType::bitset bitset_;
    513   Limits limits_;
    514 };
    515 
    516 // -----------------------------------------------------------------------------
    517 // Context types.
    518 
    519 class AstContextType : public AstTypeBase {
    520  public:
    521   AstType* Outer() { return outer_; }
    522 
    523  private:
    524   friend class AstType;
    525 
    526   static AstType* New(AstType* outer, Zone* zone) {
    527     return AsType(new (zone->New(sizeof(AstContextType)))
    528                       AstContextType(outer));  // NOLINT
    529   }
    530 
    531   static AstContextType* cast(AstType* type) {
    532     DCHECK(IsKind(type, kContext));
    533     return static_cast<AstContextType*>(FromType(type));
    534   }
    535 
    536   explicit AstContextType(AstType* outer)
    537       : AstTypeBase(kContext), outer_(outer) {}
    538 
    539   AstType* outer_;
    540 };
    541 
    542 // -----------------------------------------------------------------------------
    543 // Array types.
    544 
    545 class AstArrayType : public AstTypeBase {
    546  public:
    547   AstType* Element() { return element_; }
    548 
    549  private:
    550   friend class AstType;
    551 
    552   explicit AstArrayType(AstType* element)
    553       : AstTypeBase(kArray), element_(element) {}
    554 
    555   static AstType* New(AstType* element, Zone* zone) {
    556     return AsType(new (zone->New(sizeof(AstArrayType))) AstArrayType(element));
    557   }
    558 
    559   static AstArrayType* cast(AstType* type) {
    560     DCHECK(IsKind(type, kArray));
    561     return static_cast<AstArrayType*>(FromType(type));
    562   }
    563 
    564   AstType* element_;
    565 };
    566 
    567 // -----------------------------------------------------------------------------
    568 // Superclass for types with variable number of type fields.
    569 class AstStructuralType : public AstTypeBase {
    570  public:
    571   int LengthForTesting() { return Length(); }
    572 
    573  protected:
    574   friend class AstType;
    575 
    576   int Length() { return length_; }
    577 
    578   AstType* Get(int i) {
    579     DCHECK(0 <= i && i < this->Length());
    580     return elements_[i];
    581   }
    582 
    583   void Set(int i, AstType* type) {
    584     DCHECK(0 <= i && i < this->Length());
    585     elements_[i] = type;
    586   }
    587 
    588   void Shrink(int length) {
    589     DCHECK(2 <= length && length <= this->Length());
    590     length_ = length;
    591   }
    592 
    593   AstStructuralType(Kind kind, int length, i::Zone* zone)
    594       : AstTypeBase(kind), length_(length) {
    595     elements_ =
    596         reinterpret_cast<AstType**>(zone->New(sizeof(AstType*) * length));
    597   }
    598 
    599  private:
    600   int length_;
    601   AstType** elements_;
    602 };
    603 
    604 // -----------------------------------------------------------------------------
    605 // Function types.
    606 
    607 class AstFunctionType : public AstStructuralType {
    608  public:
    609   int Arity() { return this->Length() - 2; }
    610   AstType* Result() { return this->Get(0); }
    611   AstType* Receiver() { return this->Get(1); }
    612   AstType* Parameter(int i) { return this->Get(2 + i); }
    613 
    614   void InitParameter(int i, AstType* type) { this->Set(2 + i, type); }
    615 
    616  private:
    617   friend class AstType;
    618 
    619   AstFunctionType(AstType* result, AstType* receiver, int arity, Zone* zone)
    620       : AstStructuralType(kFunction, 2 + arity, zone) {
    621     Set(0, result);
    622     Set(1, receiver);
    623   }
    624 
    625   static AstType* New(AstType* result, AstType* receiver, int arity,
    626                       Zone* zone) {
    627     return AsType(new (zone->New(sizeof(AstFunctionType)))
    628                       AstFunctionType(result, receiver, arity, zone));
    629   }
    630 
    631   static AstFunctionType* cast(AstType* type) {
    632     DCHECK(IsKind(type, kFunction));
    633     return static_cast<AstFunctionType*>(FromType(type));
    634   }
    635 };
    636 
    637 // -----------------------------------------------------------------------------
    638 // Tuple types.
    639 
    640 class AstTupleType : public AstStructuralType {
    641  public:
    642   int Arity() { return this->Length(); }
    643   AstType* Element(int i) { return this->Get(i); }
    644 
    645   void InitElement(int i, AstType* type) { this->Set(i, type); }
    646 
    647  private:
    648   friend class AstType;
    649 
    650   AstTupleType(int length, Zone* zone)
    651       : AstStructuralType(kTuple, length, zone) {}
    652 
    653   static AstType* New(int length, Zone* zone) {
    654     return AsType(new (zone->New(sizeof(AstTupleType)))
    655                       AstTupleType(length, zone));
    656   }
    657 
    658   static AstTupleType* cast(AstType* type) {
    659     DCHECK(IsKind(type, kTuple));
    660     return static_cast<AstTupleType*>(FromType(type));
    661   }
    662 };
    663 
    664 // -----------------------------------------------------------------------------
    665 // Union types (internal).
    666 // A union is a structured type with the following invariants:
    667 // - its length is at least 2
    668 // - at most one field is a bitset, and it must go into index 0
    669 // - no field is a union
    670 // - no field is a subtype of any other field
    671 class AstUnionType : public AstStructuralType {
    672  private:
    673   friend AstType;
    674   friend AstBitsetType;
    675 
    676   AstUnionType(int length, Zone* zone)
    677       : AstStructuralType(kUnion, length, zone) {}
    678 
    679   static AstType* New(int length, Zone* zone) {
    680     return AsType(new (zone->New(sizeof(AstUnionType)))
    681                       AstUnionType(length, zone));
    682   }
    683 
    684   static AstUnionType* cast(AstType* type) {
    685     DCHECK(IsKind(type, kUnion));
    686     return static_cast<AstUnionType*>(FromType(type));
    687   }
    688 
    689   bool Wellformed();
    690 };
    691 
    692 class AstType {
    693  public:
    694   typedef AstBitsetType::bitset bitset;  // Internal
    695 
    696 // Constructors.
    697 #define DEFINE_TYPE_CONSTRUCTOR(type, value) \
    698   static AstType* type() { return AstBitsetType::New(AstBitsetType::k##type); }
    699   AST_PROPER_BITSET_TYPE_LIST(DEFINE_TYPE_CONSTRUCTOR)
    700 #undef DEFINE_TYPE_CONSTRUCTOR
    701 
    702   static AstType* SignedSmall() {
    703     return AstBitsetType::New(AstBitsetType::SignedSmall());
    704   }
    705   static AstType* UnsignedSmall() {
    706     return AstBitsetType::New(AstBitsetType::UnsignedSmall());
    707   }
    708 
    709   static AstType* Class(i::Handle<i::Map> map, Zone* zone) {
    710     return AstClassType::New(map, zone);
    711   }
    712   static AstType* Constant(i::Handle<i::Object> value, Zone* zone) {
    713     return AstConstantType::New(value, zone);
    714   }
    715   static AstType* Range(double min, double max, Zone* zone) {
    716     return AstRangeType::New(min, max,
    717                              AST_REPRESENTATION(AstBitsetType::kTagged |
    718                                                 AstBitsetType::kUntaggedNumber),
    719                              zone);
    720   }
    721   static AstType* Context(AstType* outer, Zone* zone) {
    722     return AstContextType::New(outer, zone);
    723   }
    724   static AstType* Array(AstType* element, Zone* zone) {
    725     return AstArrayType::New(element, zone);
    726   }
    727   static AstType* Function(AstType* result, AstType* receiver, int arity,
    728                            Zone* zone) {
    729     return AstFunctionType::New(result, receiver, arity, zone);
    730   }
    731   static AstType* Function(AstType* result, Zone* zone) {
    732     return Function(result, Any(), 0, zone);
    733   }
    734   static AstType* Function(AstType* result, AstType* param0, Zone* zone) {
    735     AstType* function = Function(result, Any(), 1, zone);
    736     function->AsFunction()->InitParameter(0, param0);
    737     return function;
    738   }
    739   static AstType* Function(AstType* result, AstType* param0, AstType* param1,
    740                            Zone* zone) {
    741     AstType* function = Function(result, Any(), 2, zone);
    742     function->AsFunction()->InitParameter(0, param0);
    743     function->AsFunction()->InitParameter(1, param1);
    744     return function;
    745   }
    746   static AstType* Function(AstType* result, AstType* param0, AstType* param1,
    747                            AstType* param2, Zone* zone) {
    748     AstType* function = Function(result, Any(), 3, zone);
    749     function->AsFunction()->InitParameter(0, param0);
    750     function->AsFunction()->InitParameter(1, param1);
    751     function->AsFunction()->InitParameter(2, param2);
    752     return function;
    753   }
    754   static AstType* Function(AstType* result, int arity, AstType** params,
    755                            Zone* zone) {
    756     AstType* function = Function(result, Any(), arity, zone);
    757     for (int i = 0; i < arity; ++i) {
    758       function->AsFunction()->InitParameter(i, params[i]);
    759     }
    760     return function;
    761   }
    762   static AstType* Tuple(AstType* first, AstType* second, AstType* third,
    763                         Zone* zone) {
    764     AstType* tuple = AstTupleType::New(3, zone);
    765     tuple->AsTuple()->InitElement(0, first);
    766     tuple->AsTuple()->InitElement(1, second);
    767     tuple->AsTuple()->InitElement(2, third);
    768     return tuple;
    769   }
    770 
    771   static AstType* Union(AstType* type1, AstType* type2, Zone* zone);
    772   static AstType* Intersect(AstType* type1, AstType* type2, Zone* zone);
    773 
    774   static AstType* Of(double value, Zone* zone) {
    775     return AstBitsetType::New(
    776         AstBitsetType::ExpandInternals(AstBitsetType::Lub(value)));
    777   }
    778   static AstType* Of(i::Object* value, Zone* zone) {
    779     return AstBitsetType::New(
    780         AstBitsetType::ExpandInternals(AstBitsetType::Lub(value)));
    781   }
    782   static AstType* Of(i::Handle<i::Object> value, Zone* zone) {
    783     return Of(*value, zone);
    784   }
    785 
    786   static AstType* For(i::Map* map) {
    787     return AstBitsetType::New(
    788         AstBitsetType::ExpandInternals(AstBitsetType::Lub(map)));
    789   }
    790   static AstType* For(i::Handle<i::Map> map) { return For(*map); }
    791 
    792   // Extraction of components.
    793   static AstType* Representation(AstType* t, Zone* zone);
    794   static AstType* Semantic(AstType* t, Zone* zone);
    795 
    796   // Predicates.
    797   bool IsInhabited() { return AstBitsetType::IsInhabited(this->BitsetLub()); }
    798 
    799   bool Is(AstType* that) { return this == that || this->SlowIs(that); }
    800   bool Maybe(AstType* that);
    801   bool Equals(AstType* that) { return this->Is(that) && that->Is(this); }
    802 
    803   // Equivalent to Constant(val)->Is(this), but avoiding allocation.
    804   bool Contains(i::Object* val);
    805   bool Contains(i::Handle<i::Object> val) { return this->Contains(*val); }
    806 
    807   // State-dependent versions of the above that consider subtyping between
    808   // a constant and its map class.
    809   static AstType* NowOf(i::Object* value, Zone* zone);
    810   static AstType* NowOf(i::Handle<i::Object> value, Zone* zone) {
    811     return NowOf(*value, zone);
    812   }
    813   bool NowIs(AstType* that);
    814   bool NowContains(i::Object* val);
    815   bool NowContains(i::Handle<i::Object> val) { return this->NowContains(*val); }
    816 
    817   bool NowStable();
    818 
    819   // Inspection.
    820   bool IsRange() { return IsKind(AstTypeBase::kRange); }
    821   bool IsClass() { return IsKind(AstTypeBase::kClass); }
    822   bool IsConstant() { return IsKind(AstTypeBase::kConstant); }
    823   bool IsContext() { return IsKind(AstTypeBase::kContext); }
    824   bool IsArray() { return IsKind(AstTypeBase::kArray); }
    825   bool IsFunction() { return IsKind(AstTypeBase::kFunction); }
    826   bool IsTuple() { return IsKind(AstTypeBase::kTuple); }
    827 
    828   AstClassType* AsClass() { return AstClassType::cast(this); }
    829   AstConstantType* AsConstant() { return AstConstantType::cast(this); }
    830   AstRangeType* AsRange() { return AstRangeType::cast(this); }
    831   AstContextType* AsContext() { return AstContextType::cast(this); }
    832   AstArrayType* AsArray() { return AstArrayType::cast(this); }
    833   AstFunctionType* AsFunction() { return AstFunctionType::cast(this); }
    834   AstTupleType* AsTuple() { return AstTupleType::cast(this); }
    835 
    836   // Minimum and maximum of a numeric type.
    837   // These functions do not distinguish between -0 and +0.  If the type equals
    838   // kNaN, they return NaN; otherwise kNaN is ignored.  Only call these
    839   // functions on subtypes of Number.
    840   double Min();
    841   double Max();
    842 
    843   // Extracts a range from the type: if the type is a range or a union
    844   // containing a range, that range is returned; otherwise, NULL is returned.
    845   AstType* GetRange();
    846 
    847   static bool IsInteger(i::Object* x);
    848   static bool IsInteger(double x) {
    849     return nearbyint(x) == x && !i::IsMinusZero(x);  // Allows for infinities.
    850   }
    851 
    852   int NumClasses();
    853   int NumConstants();
    854 
    855   template <class T>
    856   class Iterator {
    857    public:
    858     bool Done() const { return index_ < 0; }
    859     i::Handle<T> Current();
    860     void Advance();
    861 
    862    private:
    863     friend class AstType;
    864 
    865     Iterator() : index_(-1) {}
    866     explicit Iterator(AstType* type) : type_(type), index_(-1) { Advance(); }
    867 
    868     inline bool matches(AstType* type);
    869     inline AstType* get_type();
    870 
    871     AstType* type_;
    872     int index_;
    873   };
    874 
    875   Iterator<i::Map> Classes() {
    876     if (this->IsBitset()) return Iterator<i::Map>();
    877     return Iterator<i::Map>(this);
    878   }
    879   Iterator<i::Object> Constants() {
    880     if (this->IsBitset()) return Iterator<i::Object>();
    881     return Iterator<i::Object>(this);
    882   }
    883 
    884   // Printing.
    885 
    886   enum PrintDimension { BOTH_DIMS, SEMANTIC_DIM, REPRESENTATION_DIM };
    887 
    888   void PrintTo(std::ostream& os, PrintDimension dim = BOTH_DIMS);  // NOLINT
    889 
    890 #ifdef DEBUG
    891   void Print();
    892 #endif
    893 
    894   // Helpers for testing.
    895   bool IsBitsetForTesting() { return IsBitset(); }
    896   bool IsUnionForTesting() { return IsUnion(); }
    897   bitset AsBitsetForTesting() { return AsBitset(); }
    898   AstUnionType* AsUnionForTesting() { return AsUnion(); }
    899 
    900  private:
    901   // Friends.
    902   template <class>
    903   friend class Iterator;
    904   friend AstBitsetType;
    905   friend AstUnionType;
    906 
    907   // Internal inspection.
    908   bool IsKind(AstTypeBase::Kind kind) {
    909     return AstTypeBase::IsKind(this, kind);
    910   }
    911 
    912   bool IsNone() { return this == None(); }
    913   bool IsAny() { return this == Any(); }
    914   bool IsBitset() { return AstBitsetType::IsBitset(this); }
    915   bool IsUnion() { return IsKind(AstTypeBase::kUnion); }
    916 
    917   bitset AsBitset() {
    918     DCHECK(this->IsBitset());
    919     return reinterpret_cast<AstBitsetType*>(this)->Bitset();
    920   }
    921   AstUnionType* AsUnion() { return AstUnionType::cast(this); }
    922 
    923   bitset Representation();
    924 
    925   // Auxiliary functions.
    926   bool SemanticMaybe(AstType* that);
    927 
    928   bitset BitsetGlb() { return AstBitsetType::Glb(this); }
    929   bitset BitsetLub() { return AstBitsetType::Lub(this); }
    930 
    931   bool SlowIs(AstType* that);
    932   bool SemanticIs(AstType* that);
    933 
    934   static bool Overlap(AstRangeType* lhs, AstRangeType* rhs);
    935   static bool Contains(AstRangeType* lhs, AstRangeType* rhs);
    936   static bool Contains(AstRangeType* range, AstConstantType* constant);
    937   static bool Contains(AstRangeType* range, i::Object* val);
    938 
    939   static int UpdateRange(AstType* type, AstUnionType* result, int size,
    940                          Zone* zone);
    941 
    942   static AstRangeType::Limits IntersectRangeAndBitset(AstType* range,
    943                                                       AstType* bits,
    944                                                       Zone* zone);
    945   static AstRangeType::Limits ToLimits(bitset bits, Zone* zone);
    946 
    947   bool SimplyEquals(AstType* that);
    948 
    949   static int AddToUnion(AstType* type, AstUnionType* result, int size,
    950                         Zone* zone);
    951   static int IntersectAux(AstType* type, AstType* other, AstUnionType* result,
    952                           int size, AstRangeType::Limits* limits, Zone* zone);
    953   static AstType* NormalizeUnion(AstType* unioned, int size, Zone* zone);
    954   static AstType* NormalizeRangeAndBitset(AstType* range, bitset* bits,
    955                                           Zone* zone);
    956 };
    957 
    958 // -----------------------------------------------------------------------------
    959 // Type bounds. A simple struct to represent a pair of lower/upper types.
    960 
    961 struct AstBounds {
    962   AstType* lower;
    963   AstType* upper;
    964 
    965   AstBounds()
    966       :  // Make sure accessing uninitialized bounds crashes big-time.
    967         lower(nullptr),
    968         upper(nullptr) {}
    969   explicit AstBounds(AstType* t) : lower(t), upper(t) {}
    970   AstBounds(AstType* l, AstType* u) : lower(l), upper(u) {
    971     DCHECK(lower->Is(upper));
    972   }
    973 
    974   // Unrestricted bounds.
    975   static AstBounds Unbounded() {
    976     return AstBounds(AstType::None(), AstType::Any());
    977   }
    978 
    979   // Meet: both b1 and b2 are known to hold.
    980   static AstBounds Both(AstBounds b1, AstBounds b2, Zone* zone) {
    981     AstType* lower = AstType::Union(b1.lower, b2.lower, zone);
    982     AstType* upper = AstType::Intersect(b1.upper, b2.upper, zone);
    983     // Lower bounds are considered approximate, correct as necessary.
    984     if (!lower->Is(upper)) lower = upper;
    985     return AstBounds(lower, upper);
    986   }
    987 
    988   // Join: either b1 or b2 is known to hold.
    989   static AstBounds Either(AstBounds b1, AstBounds b2, Zone* zone) {
    990     AstType* lower = AstType::Intersect(b1.lower, b2.lower, zone);
    991     AstType* upper = AstType::Union(b1.upper, b2.upper, zone);
    992     return AstBounds(lower, upper);
    993   }
    994 
    995   static AstBounds NarrowLower(AstBounds b, AstType* t, Zone* zone) {
    996     AstType* lower = AstType::Union(b.lower, t, zone);
    997     // Lower bounds are considered approximate, correct as necessary.
    998     if (!lower->Is(b.upper)) lower = b.upper;
    999     return AstBounds(lower, b.upper);
   1000   }
   1001   static AstBounds NarrowUpper(AstBounds b, AstType* t, Zone* zone) {
   1002     AstType* lower = b.lower;
   1003     AstType* upper = AstType::Intersect(b.upper, t, zone);
   1004     // Lower bounds are considered approximate, correct as necessary.
   1005     if (!lower->Is(upper)) lower = upper;
   1006     return AstBounds(lower, upper);
   1007   }
   1008 
   1009   bool Narrows(AstBounds that) {
   1010     return that.lower->Is(this->lower) && this->upper->Is(that.upper);
   1011   }
   1012 };
   1013 
   1014 }  // namespace internal
   1015 }  // namespace v8
   1016 
   1017 #endif  // V8_AST_AST_TYPES_H_
   1018