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      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 #define AST_REPRESENTATION_BITSET_TYPE_LIST(V)    \
    160   V(None,               0)                    \
    161   V(UntaggedBit,        1u << 22 | kSemantic) \
    162   V(UntaggedIntegral8,  1u << 23 | kSemantic) \
    163   V(UntaggedIntegral16, 1u << 24 | kSemantic) \
    164   V(UntaggedIntegral32, 1u << 25 | kSemantic) \
    165   V(UntaggedFloat32,    1u << 26 | kSemantic) \
    166   V(UntaggedFloat64,    1u << 27 | kSemantic) \
    167   V(UntaggedSimd128,    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(Simd,                1u << 15 | AST_REPRESENTATION(kTaggedPointer)) \
    201   V(OtherObject,         1u << 17 | AST_REPRESENTATION(kTaggedPointer)) \
    202   V(OtherUndetectable,   1u << 16 | AST_REPRESENTATION(kTaggedPointer)) \
    203   V(Proxy,               1u << 18 | AST_REPRESENTATION(kTaggedPointer)) \
    204   V(Function,            1u << 19 | AST_REPRESENTATION(kTaggedPointer)) \
    205   V(Hole,                1u << 20 | AST_REPRESENTATION(kTaggedPointer)) \
    206   V(OtherInternal,       1u << 21 |                                     \
    207                          AST_REPRESENTATION(kTagged | kUntagged))       \
    208   \
    209   V(Signed31,                   kUnsigned30 | kNegative31) \
    210   V(Signed32,                   kSigned31 | kOtherUnsigned31 |          \
    211                                 kOtherSigned32)                         \
    212   V(Signed32OrMinusZero,        kSigned32 | kMinusZero) \
    213   V(Signed32OrMinusZeroOrNaN,   kSigned32 | kMinusZero | kNaN) \
    214   V(Negative32,                 kNegative31 | kOtherSigned32) \
    215   V(Unsigned31,                 kUnsigned30 | kOtherUnsigned31) \
    216   V(Unsigned32,                 kUnsigned30 | kOtherUnsigned31 | \
    217                                 kOtherUnsigned32) \
    218   V(Unsigned32OrMinusZero,      kUnsigned32 | kMinusZero) \
    219   V(Unsigned32OrMinusZeroOrNaN, kUnsigned32 | kMinusZero | kNaN) \
    220   V(Integral32,                 kSigned32 | kUnsigned32) \
    221   V(PlainNumber,                kIntegral32 | kOtherNumber) \
    222   V(OrderedNumber,              kPlainNumber | kMinusZero) \
    223   V(MinusZeroOrNaN,             kMinusZero | kNaN) \
    224   V(Number,                     kOrderedNumber | kNaN) \
    225   V(String,                     kInternalizedString | kOtherString) \
    226   V(UniqueName,                 kSymbol | kInternalizedString) \
    227   V(Name,                       kSymbol | kString) \
    228   V(BooleanOrNumber,            kBoolean | kNumber) \
    229   V(BooleanOrNullOrNumber,      kBooleanOrNumber | kNull) \
    230   V(BooleanOrNullOrUndefined,   kBoolean | kNull | kUndefined) \
    231   V(NullOrNumber,               kNull | kNumber) \
    232   V(NullOrUndefined,            kNull | kUndefined) \
    233   V(Undetectable,               kNullOrUndefined | kOtherUndetectable) \
    234   V(NumberOrOddball,            kNumber | kNullOrUndefined | kBoolean | kHole) \
    235   V(NumberOrSimdOrString,       kNumber | kSimd | kString) \
    236   V(NumberOrString,             kNumber | kString) \
    237   V(NumberOrUndefined,          kNumber | kUndefined) \
    238   V(PlainPrimitive,             kNumberOrString | kBoolean | kNullOrUndefined) \
    239   V(Primitive,                  kSymbol | kSimd | kPlainPrimitive) \
    240   V(DetectableReceiver,         kFunction | kOtherObject | kProxy) \
    241   V(Object,                     kFunction | kOtherObject | kOtherUndetectable) \
    242   V(Receiver,                   kObject | kProxy) \
    243   V(StringOrReceiver,           kString | kReceiver) \
    244   V(Unique,                     kBoolean | kUniqueName | kNull | kUndefined | \
    245                                 kReceiver) \
    246   V(Internal,                   kHole | kOtherInternal) \
    247   V(NonInternal,                kPrimitive | kReceiver) \
    248   V(NonNumber,                  kUnique | kString | kInternal) \
    249   V(Any,                        0xfffffffeu)
    250 
    251 // clang-format on
    252 
    253 /*
    254  * The following diagrams show how integers (in the mathematical sense) are
    255  * divided among the different atomic numerical types.
    256  *
    257  *   ON    OS32     N31     U30     OU31    OU32     ON
    258  * ______[_______[_______[_______[_______[_______[_______
    259  *     -2^31   -2^30     0      2^30    2^31    2^32
    260  *
    261  * E.g., OtherUnsigned32 (OU32) covers all integers from 2^31 to 2^32-1.
    262  *
    263  * Some of the atomic numerical bitsets are internal only (see
    264  * INTERNAL_BITSET_TYPE_LIST).  To a types user, they should only occur in
    265  * union with certain other bitsets.  For instance, OtherNumber should only
    266  * occur as part of PlainNumber.
    267  */
    268 
    269 #define AST_PROPER_BITSET_TYPE_LIST(V)   \
    270   AST_REPRESENTATION_BITSET_TYPE_LIST(V) \
    271   AST_SEMANTIC_BITSET_TYPE_LIST(V)
    272 
    273 #define AST_BITSET_TYPE_LIST(V)          \
    274   AST_MASK_BITSET_TYPE_LIST(V)           \
    275   AST_REPRESENTATION_BITSET_TYPE_LIST(V) \
    276   AST_INTERNAL_BITSET_TYPE_LIST(V)       \
    277   AST_SEMANTIC_BITSET_TYPE_LIST(V)
    278 
    279 class AstType;
    280 
    281 // -----------------------------------------------------------------------------
    282 // Bitset types (internal).
    283 
    284 class AstBitsetType {
    285  public:
    286   typedef uint32_t bitset;  // Internal
    287 
    288   enum : uint32_t {
    289 #define DECLARE_TYPE(type, value) k##type = (value),
    290     AST_BITSET_TYPE_LIST(DECLARE_TYPE)
    291 #undef DECLARE_TYPE
    292         kUnusedEOL = 0
    293   };
    294 
    295   static bitset SignedSmall();
    296   static bitset UnsignedSmall();
    297 
    298   bitset Bitset() {
    299     return static_cast<bitset>(reinterpret_cast<uintptr_t>(this) ^ 1u);
    300   }
    301 
    302   static bool IsInhabited(bitset bits) {
    303     return AST_SEMANTIC(bits) != kNone && AST_REPRESENTATION(bits) != kNone;
    304   }
    305 
    306   static bool SemanticIsInhabited(bitset bits) {
    307     return AST_SEMANTIC(bits) != kNone;
    308   }
    309 
    310   static bool Is(bitset bits1, bitset bits2) {
    311     return (bits1 | bits2) == bits2;
    312   }
    313 
    314   static double Min(bitset);
    315   static double Max(bitset);
    316 
    317   static bitset Glb(AstType* type);  // greatest lower bound that's a bitset
    318   static bitset Glb(double min, double max);
    319   static bitset Lub(AstType* type);  // least upper bound that's a bitset
    320   static bitset Lub(i::Map* map);
    321   static bitset Lub(i::Object* value);
    322   static bitset Lub(double value);
    323   static bitset Lub(double min, double max);
    324   static bitset ExpandInternals(bitset bits);
    325 
    326   static const char* Name(bitset);
    327   static void Print(std::ostream& os, bitset);  // NOLINT
    328 #ifdef DEBUG
    329   static void Print(bitset);
    330 #endif
    331 
    332   static bitset NumberBits(bitset bits);
    333 
    334   static bool IsBitset(AstType* type) {
    335     return reinterpret_cast<uintptr_t>(type) & 1;
    336   }
    337 
    338   static AstType* NewForTesting(bitset bits) { return New(bits); }
    339 
    340  private:
    341   friend class AstType;
    342 
    343   static AstType* New(bitset bits) {
    344     return reinterpret_cast<AstType*>(static_cast<uintptr_t>(bits | 1u));
    345   }
    346 
    347   struct Boundary {
    348     bitset internal;
    349     bitset external;
    350     double min;
    351   };
    352   static const Boundary BoundariesArray[];
    353   static inline const Boundary* Boundaries();
    354   static inline size_t BoundariesSize();
    355 };
    356 
    357 // -----------------------------------------------------------------------------
    358 // Superclass for non-bitset types (internal).
    359 class AstTypeBase {
    360  protected:
    361   friend class AstType;
    362 
    363   enum Kind {
    364     kClass,
    365     kConstant,
    366     kContext,
    367     kArray,
    368     kFunction,
    369     kTuple,
    370     kUnion,
    371     kRange
    372   };
    373 
    374   Kind kind() const { return kind_; }
    375   explicit AstTypeBase(Kind kind) : kind_(kind) {}
    376 
    377   static bool IsKind(AstType* type, Kind kind) {
    378     if (AstBitsetType::IsBitset(type)) return false;
    379     AstTypeBase* base = reinterpret_cast<AstTypeBase*>(type);
    380     return base->kind() == kind;
    381   }
    382 
    383   // The hacky conversion to/from AstType*.
    384   static AstType* AsType(AstTypeBase* type) {
    385     return reinterpret_cast<AstType*>(type);
    386   }
    387   static AstTypeBase* FromType(AstType* type) {
    388     return reinterpret_cast<AstTypeBase*>(type);
    389   }
    390 
    391  private:
    392   Kind kind_;
    393 };
    394 
    395 // -----------------------------------------------------------------------------
    396 // Class types.
    397 
    398 class AstClassType : public AstTypeBase {
    399  public:
    400   i::Handle<i::Map> Map() { return map_; }
    401 
    402  private:
    403   friend class AstType;
    404   friend class AstBitsetType;
    405 
    406   static AstType* New(i::Handle<i::Map> map, Zone* zone) {
    407     return AsType(new (zone->New(sizeof(AstClassType)))
    408                       AstClassType(AstBitsetType::Lub(*map), map));
    409   }
    410 
    411   static AstClassType* cast(AstType* type) {
    412     DCHECK(IsKind(type, kClass));
    413     return static_cast<AstClassType*>(FromType(type));
    414   }
    415 
    416   AstClassType(AstBitsetType::bitset bitset, i::Handle<i::Map> map)
    417       : AstTypeBase(kClass), bitset_(bitset), map_(map) {}
    418 
    419   AstBitsetType::bitset Lub() { return bitset_; }
    420 
    421   AstBitsetType::bitset bitset_;
    422   Handle<i::Map> map_;
    423 };
    424 
    425 // -----------------------------------------------------------------------------
    426 // Constant types.
    427 
    428 class AstConstantType : public AstTypeBase {
    429  public:
    430   i::Handle<i::Object> Value() { return object_; }
    431 
    432  private:
    433   friend class AstType;
    434   friend class AstBitsetType;
    435 
    436   static AstType* New(i::Handle<i::Object> value, Zone* zone) {
    437     AstBitsetType::bitset bitset = AstBitsetType::Lub(*value);
    438     return AsType(new (zone->New(sizeof(AstConstantType)))
    439                       AstConstantType(bitset, value));
    440   }
    441 
    442   static AstConstantType* cast(AstType* type) {
    443     DCHECK(IsKind(type, kConstant));
    444     return static_cast<AstConstantType*>(FromType(type));
    445   }
    446 
    447   AstConstantType(AstBitsetType::bitset bitset, i::Handle<i::Object> object)
    448       : AstTypeBase(kConstant), bitset_(bitset), object_(object) {}
    449 
    450   AstBitsetType::bitset Lub() { return bitset_; }
    451 
    452   AstBitsetType::bitset bitset_;
    453   Handle<i::Object> object_;
    454 };
    455 // TODO(neis): Also cache value if numerical.
    456 // TODO(neis): Allow restricting the representation.
    457 
    458 // -----------------------------------------------------------------------------
    459 // Range types.
    460 
    461 class AstRangeType : public AstTypeBase {
    462  public:
    463   struct Limits {
    464     double min;
    465     double max;
    466     Limits(double min, double max) : min(min), max(max) {}
    467     explicit Limits(AstRangeType* range)
    468         : min(range->Min()), max(range->Max()) {}
    469     bool IsEmpty();
    470     static Limits Empty() { return Limits(1, 0); }
    471     static Limits Intersect(Limits lhs, Limits rhs);
    472     static Limits Union(Limits lhs, Limits rhs);
    473   };
    474 
    475   double Min() { return limits_.min; }
    476   double Max() { return limits_.max; }
    477 
    478  private:
    479   friend class AstType;
    480   friend class AstBitsetType;
    481   friend class AstUnionType;
    482 
    483   static AstType* New(double min, double max,
    484                       AstBitsetType::bitset representation, Zone* zone) {
    485     return New(Limits(min, max), representation, zone);
    486   }
    487 
    488   static bool IsInteger(double x) {
    489     return nearbyint(x) == x && !i::IsMinusZero(x);  // Allows for infinities.
    490   }
    491 
    492   static AstType* New(Limits lim, AstBitsetType::bitset representation,
    493                       Zone* zone) {
    494     DCHECK(IsInteger(lim.min) && IsInteger(lim.max));
    495     DCHECK(lim.min <= lim.max);
    496     DCHECK(AST_REPRESENTATION(representation) == representation);
    497     AstBitsetType::bitset bits =
    498         AST_SEMANTIC(AstBitsetType::Lub(lim.min, lim.max)) | representation;
    499 
    500     return AsType(new (zone->New(sizeof(AstRangeType)))
    501                       AstRangeType(bits, lim));
    502   }
    503 
    504   static AstRangeType* cast(AstType* type) {
    505     DCHECK(IsKind(type, kRange));
    506     return static_cast<AstRangeType*>(FromType(type));
    507   }
    508 
    509   AstRangeType(AstBitsetType::bitset bitset, Limits limits)
    510       : AstTypeBase(kRange), bitset_(bitset), limits_(limits) {}
    511 
    512   AstBitsetType::bitset Lub() { return bitset_; }
    513 
    514   AstBitsetType::bitset bitset_;
    515   Limits limits_;
    516 };
    517 
    518 // -----------------------------------------------------------------------------
    519 // Context types.
    520 
    521 class AstContextType : public AstTypeBase {
    522  public:
    523   AstType* Outer() { return outer_; }
    524 
    525  private:
    526   friend class AstType;
    527 
    528   static AstType* New(AstType* outer, Zone* zone) {
    529     return AsType(new (zone->New(sizeof(AstContextType)))
    530                       AstContextType(outer));  // NOLINT
    531   }
    532 
    533   static AstContextType* cast(AstType* type) {
    534     DCHECK(IsKind(type, kContext));
    535     return static_cast<AstContextType*>(FromType(type));
    536   }
    537 
    538   explicit AstContextType(AstType* outer)
    539       : AstTypeBase(kContext), outer_(outer) {}
    540 
    541   AstType* outer_;
    542 };
    543 
    544 // -----------------------------------------------------------------------------
    545 // Array types.
    546 
    547 class AstArrayType : public AstTypeBase {
    548  public:
    549   AstType* Element() { return element_; }
    550 
    551  private:
    552   friend class AstType;
    553 
    554   explicit AstArrayType(AstType* element)
    555       : AstTypeBase(kArray), element_(element) {}
    556 
    557   static AstType* New(AstType* element, Zone* zone) {
    558     return AsType(new (zone->New(sizeof(AstArrayType))) AstArrayType(element));
    559   }
    560 
    561   static AstArrayType* cast(AstType* type) {
    562     DCHECK(IsKind(type, kArray));
    563     return static_cast<AstArrayType*>(FromType(type));
    564   }
    565 
    566   AstType* element_;
    567 };
    568 
    569 // -----------------------------------------------------------------------------
    570 // Superclass for types with variable number of type fields.
    571 class AstStructuralType : public AstTypeBase {
    572  public:
    573   int LengthForTesting() { return Length(); }
    574 
    575  protected:
    576   friend class AstType;
    577 
    578   int Length() { return length_; }
    579 
    580   AstType* Get(int i) {
    581     DCHECK(0 <= i && i < this->Length());
    582     return elements_[i];
    583   }
    584 
    585   void Set(int i, AstType* type) {
    586     DCHECK(0 <= i && i < this->Length());
    587     elements_[i] = type;
    588   }
    589 
    590   void Shrink(int length) {
    591     DCHECK(2 <= length && length <= this->Length());
    592     length_ = length;
    593   }
    594 
    595   AstStructuralType(Kind kind, int length, i::Zone* zone)
    596       : AstTypeBase(kind), length_(length) {
    597     elements_ =
    598         reinterpret_cast<AstType**>(zone->New(sizeof(AstType*) * length));
    599   }
    600 
    601  private:
    602   int length_;
    603   AstType** elements_;
    604 };
    605 
    606 // -----------------------------------------------------------------------------
    607 // Function types.
    608 
    609 class AstFunctionType : public AstStructuralType {
    610  public:
    611   int Arity() { return this->Length() - 2; }
    612   AstType* Result() { return this->Get(0); }
    613   AstType* Receiver() { return this->Get(1); }
    614   AstType* Parameter(int i) { return this->Get(2 + i); }
    615 
    616   void InitParameter(int i, AstType* type) { this->Set(2 + i, type); }
    617 
    618  private:
    619   friend class AstType;
    620 
    621   AstFunctionType(AstType* result, AstType* receiver, int arity, Zone* zone)
    622       : AstStructuralType(kFunction, 2 + arity, zone) {
    623     Set(0, result);
    624     Set(1, receiver);
    625   }
    626 
    627   static AstType* New(AstType* result, AstType* receiver, int arity,
    628                       Zone* zone) {
    629     return AsType(new (zone->New(sizeof(AstFunctionType)))
    630                       AstFunctionType(result, receiver, arity, zone));
    631   }
    632 
    633   static AstFunctionType* cast(AstType* type) {
    634     DCHECK(IsKind(type, kFunction));
    635     return static_cast<AstFunctionType*>(FromType(type));
    636   }
    637 };
    638 
    639 // -----------------------------------------------------------------------------
    640 // Tuple types.
    641 
    642 class AstTupleType : public AstStructuralType {
    643  public:
    644   int Arity() { return this->Length(); }
    645   AstType* Element(int i) { return this->Get(i); }
    646 
    647   void InitElement(int i, AstType* type) { this->Set(i, type); }
    648 
    649  private:
    650   friend class AstType;
    651 
    652   AstTupleType(int length, Zone* zone)
    653       : AstStructuralType(kTuple, length, zone) {}
    654 
    655   static AstType* New(int length, Zone* zone) {
    656     return AsType(new (zone->New(sizeof(AstTupleType)))
    657                       AstTupleType(length, zone));
    658   }
    659 
    660   static AstTupleType* cast(AstType* type) {
    661     DCHECK(IsKind(type, kTuple));
    662     return static_cast<AstTupleType*>(FromType(type));
    663   }
    664 };
    665 
    666 // -----------------------------------------------------------------------------
    667 // Union types (internal).
    668 // A union is a structured type with the following invariants:
    669 // - its length is at least 2
    670 // - at most one field is a bitset, and it must go into index 0
    671 // - no field is a union
    672 // - no field is a subtype of any other field
    673 class AstUnionType : public AstStructuralType {
    674  private:
    675   friend AstType;
    676   friend AstBitsetType;
    677 
    678   AstUnionType(int length, Zone* zone)
    679       : AstStructuralType(kUnion, length, zone) {}
    680 
    681   static AstType* New(int length, Zone* zone) {
    682     return AsType(new (zone->New(sizeof(AstUnionType)))
    683                       AstUnionType(length, zone));
    684   }
    685 
    686   static AstUnionType* cast(AstType* type) {
    687     DCHECK(IsKind(type, kUnion));
    688     return static_cast<AstUnionType*>(FromType(type));
    689   }
    690 
    691   bool Wellformed();
    692 };
    693 
    694 class AstType {
    695  public:
    696   typedef AstBitsetType::bitset bitset;  // Internal
    697 
    698 // Constructors.
    699 #define DEFINE_TYPE_CONSTRUCTOR(type, value) \
    700   static AstType* type() { return AstBitsetType::New(AstBitsetType::k##type); }
    701   AST_PROPER_BITSET_TYPE_LIST(DEFINE_TYPE_CONSTRUCTOR)
    702 #undef DEFINE_TYPE_CONSTRUCTOR
    703 
    704   static AstType* SignedSmall() {
    705     return AstBitsetType::New(AstBitsetType::SignedSmall());
    706   }
    707   static AstType* UnsignedSmall() {
    708     return AstBitsetType::New(AstBitsetType::UnsignedSmall());
    709   }
    710 
    711   static AstType* Class(i::Handle<i::Map> map, Zone* zone) {
    712     return AstClassType::New(map, zone);
    713   }
    714   static AstType* Constant(i::Handle<i::Object> value, Zone* zone) {
    715     return AstConstantType::New(value, zone);
    716   }
    717   static AstType* Range(double min, double max, Zone* zone) {
    718     return AstRangeType::New(min, max,
    719                              AST_REPRESENTATION(AstBitsetType::kTagged |
    720                                                 AstBitsetType::kUntaggedNumber),
    721                              zone);
    722   }
    723   static AstType* Context(AstType* outer, Zone* zone) {
    724     return AstContextType::New(outer, zone);
    725   }
    726   static AstType* Array(AstType* element, Zone* zone) {
    727     return AstArrayType::New(element, zone);
    728   }
    729   static AstType* Function(AstType* result, AstType* receiver, int arity,
    730                            Zone* zone) {
    731     return AstFunctionType::New(result, receiver, arity, zone);
    732   }
    733   static AstType* Function(AstType* result, Zone* zone) {
    734     return Function(result, Any(), 0, zone);
    735   }
    736   static AstType* Function(AstType* result, AstType* param0, Zone* zone) {
    737     AstType* function = Function(result, Any(), 1, zone);
    738     function->AsFunction()->InitParameter(0, param0);
    739     return function;
    740   }
    741   static AstType* Function(AstType* result, AstType* param0, AstType* param1,
    742                            Zone* zone) {
    743     AstType* function = Function(result, Any(), 2, zone);
    744     function->AsFunction()->InitParameter(0, param0);
    745     function->AsFunction()->InitParameter(1, param1);
    746     return function;
    747   }
    748   static AstType* Function(AstType* result, AstType* param0, AstType* param1,
    749                            AstType* param2, Zone* zone) {
    750     AstType* function = Function(result, Any(), 3, zone);
    751     function->AsFunction()->InitParameter(0, param0);
    752     function->AsFunction()->InitParameter(1, param1);
    753     function->AsFunction()->InitParameter(2, param2);
    754     return function;
    755   }
    756   static AstType* Function(AstType* result, int arity, AstType** params,
    757                            Zone* zone) {
    758     AstType* function = Function(result, Any(), arity, zone);
    759     for (int i = 0; i < arity; ++i) {
    760       function->AsFunction()->InitParameter(i, params[i]);
    761     }
    762     return function;
    763   }
    764   static AstType* Tuple(AstType* first, AstType* second, AstType* third,
    765                         Zone* zone) {
    766     AstType* tuple = AstTupleType::New(3, zone);
    767     tuple->AsTuple()->InitElement(0, first);
    768     tuple->AsTuple()->InitElement(1, second);
    769     tuple->AsTuple()->InitElement(2, third);
    770     return tuple;
    771   }
    772 
    773 #define CONSTRUCT_SIMD_TYPE(NAME, Name, name, lane_count, lane_type) \
    774   static AstType* Name(Isolate* isolate, Zone* zone);
    775   SIMD128_TYPES(CONSTRUCT_SIMD_TYPE)
    776 #undef CONSTRUCT_SIMD_TYPE
    777 
    778   static AstType* Union(AstType* type1, AstType* type2, Zone* zone);
    779   static AstType* Intersect(AstType* type1, AstType* type2, Zone* zone);
    780 
    781   static AstType* Of(double value, Zone* zone) {
    782     return AstBitsetType::New(
    783         AstBitsetType::ExpandInternals(AstBitsetType::Lub(value)));
    784   }
    785   static AstType* Of(i::Object* value, Zone* zone) {
    786     return AstBitsetType::New(
    787         AstBitsetType::ExpandInternals(AstBitsetType::Lub(value)));
    788   }
    789   static AstType* Of(i::Handle<i::Object> value, Zone* zone) {
    790     return Of(*value, zone);
    791   }
    792 
    793   static AstType* For(i::Map* map) {
    794     return AstBitsetType::New(
    795         AstBitsetType::ExpandInternals(AstBitsetType::Lub(map)));
    796   }
    797   static AstType* For(i::Handle<i::Map> map) { return For(*map); }
    798 
    799   // Extraction of components.
    800   static AstType* Representation(AstType* t, Zone* zone);
    801   static AstType* Semantic(AstType* t, Zone* zone);
    802 
    803   // Predicates.
    804   bool IsInhabited() { return AstBitsetType::IsInhabited(this->BitsetLub()); }
    805 
    806   bool Is(AstType* that) { return this == that || this->SlowIs(that); }
    807   bool Maybe(AstType* that);
    808   bool Equals(AstType* that) { return this->Is(that) && that->Is(this); }
    809 
    810   // Equivalent to Constant(val)->Is(this), but avoiding allocation.
    811   bool Contains(i::Object* val);
    812   bool Contains(i::Handle<i::Object> val) { return this->Contains(*val); }
    813 
    814   // State-dependent versions of the above that consider subtyping between
    815   // a constant and its map class.
    816   static AstType* NowOf(i::Object* value, Zone* zone);
    817   static AstType* NowOf(i::Handle<i::Object> value, Zone* zone) {
    818     return NowOf(*value, zone);
    819   }
    820   bool NowIs(AstType* that);
    821   bool NowContains(i::Object* val);
    822   bool NowContains(i::Handle<i::Object> val) { return this->NowContains(*val); }
    823 
    824   bool NowStable();
    825 
    826   // Inspection.
    827   bool IsRange() { return IsKind(AstTypeBase::kRange); }
    828   bool IsClass() { return IsKind(AstTypeBase::kClass); }
    829   bool IsConstant() { return IsKind(AstTypeBase::kConstant); }
    830   bool IsContext() { return IsKind(AstTypeBase::kContext); }
    831   bool IsArray() { return IsKind(AstTypeBase::kArray); }
    832   bool IsFunction() { return IsKind(AstTypeBase::kFunction); }
    833   bool IsTuple() { return IsKind(AstTypeBase::kTuple); }
    834 
    835   AstClassType* AsClass() { return AstClassType::cast(this); }
    836   AstConstantType* AsConstant() { return AstConstantType::cast(this); }
    837   AstRangeType* AsRange() { return AstRangeType::cast(this); }
    838   AstContextType* AsContext() { return AstContextType::cast(this); }
    839   AstArrayType* AsArray() { return AstArrayType::cast(this); }
    840   AstFunctionType* AsFunction() { return AstFunctionType::cast(this); }
    841   AstTupleType* AsTuple() { return AstTupleType::cast(this); }
    842 
    843   // Minimum and maximum of a numeric type.
    844   // These functions do not distinguish between -0 and +0.  If the type equals
    845   // kNaN, they return NaN; otherwise kNaN is ignored.  Only call these
    846   // functions on subtypes of Number.
    847   double Min();
    848   double Max();
    849 
    850   // Extracts a range from the type: if the type is a range or a union
    851   // containing a range, that range is returned; otherwise, NULL is returned.
    852   AstType* GetRange();
    853 
    854   static bool IsInteger(i::Object* x);
    855   static bool IsInteger(double x) {
    856     return nearbyint(x) == x && !i::IsMinusZero(x);  // Allows for infinities.
    857   }
    858 
    859   int NumClasses();
    860   int NumConstants();
    861 
    862   template <class T>
    863   class Iterator {
    864    public:
    865     bool Done() const { return index_ < 0; }
    866     i::Handle<T> Current();
    867     void Advance();
    868 
    869    private:
    870     friend class AstType;
    871 
    872     Iterator() : index_(-1) {}
    873     explicit Iterator(AstType* type) : type_(type), index_(-1) { Advance(); }
    874 
    875     inline bool matches(AstType* type);
    876     inline AstType* get_type();
    877 
    878     AstType* type_;
    879     int index_;
    880   };
    881 
    882   Iterator<i::Map> Classes() {
    883     if (this->IsBitset()) return Iterator<i::Map>();
    884     return Iterator<i::Map>(this);
    885   }
    886   Iterator<i::Object> Constants() {
    887     if (this->IsBitset()) return Iterator<i::Object>();
    888     return Iterator<i::Object>(this);
    889   }
    890 
    891   // Printing.
    892 
    893   enum PrintDimension { BOTH_DIMS, SEMANTIC_DIM, REPRESENTATION_DIM };
    894 
    895   void PrintTo(std::ostream& os, PrintDimension dim = BOTH_DIMS);  // NOLINT
    896 
    897 #ifdef DEBUG
    898   void Print();
    899 #endif
    900 
    901   // Helpers for testing.
    902   bool IsBitsetForTesting() { return IsBitset(); }
    903   bool IsUnionForTesting() { return IsUnion(); }
    904   bitset AsBitsetForTesting() { return AsBitset(); }
    905   AstUnionType* AsUnionForTesting() { return AsUnion(); }
    906 
    907  private:
    908   // Friends.
    909   template <class>
    910   friend class Iterator;
    911   friend AstBitsetType;
    912   friend AstUnionType;
    913 
    914   // Internal inspection.
    915   bool IsKind(AstTypeBase::Kind kind) {
    916     return AstTypeBase::IsKind(this, kind);
    917   }
    918 
    919   bool IsNone() { return this == None(); }
    920   bool IsAny() { return this == Any(); }
    921   bool IsBitset() { return AstBitsetType::IsBitset(this); }
    922   bool IsUnion() { return IsKind(AstTypeBase::kUnion); }
    923 
    924   bitset AsBitset() {
    925     DCHECK(this->IsBitset());
    926     return reinterpret_cast<AstBitsetType*>(this)->Bitset();
    927   }
    928   AstUnionType* AsUnion() { return AstUnionType::cast(this); }
    929 
    930   bitset Representation();
    931 
    932   // Auxiliary functions.
    933   bool SemanticMaybe(AstType* that);
    934 
    935   bitset BitsetGlb() { return AstBitsetType::Glb(this); }
    936   bitset BitsetLub() { return AstBitsetType::Lub(this); }
    937 
    938   bool SlowIs(AstType* that);
    939   bool SemanticIs(AstType* that);
    940 
    941   static bool Overlap(AstRangeType* lhs, AstRangeType* rhs);
    942   static bool Contains(AstRangeType* lhs, AstRangeType* rhs);
    943   static bool Contains(AstRangeType* range, AstConstantType* constant);
    944   static bool Contains(AstRangeType* range, i::Object* val);
    945 
    946   static int UpdateRange(AstType* type, AstUnionType* result, int size,
    947                          Zone* zone);
    948 
    949   static AstRangeType::Limits IntersectRangeAndBitset(AstType* range,
    950                                                       AstType* bits,
    951                                                       Zone* zone);
    952   static AstRangeType::Limits ToLimits(bitset bits, Zone* zone);
    953 
    954   bool SimplyEquals(AstType* that);
    955 
    956   static int AddToUnion(AstType* type, AstUnionType* result, int size,
    957                         Zone* zone);
    958   static int IntersectAux(AstType* type, AstType* other, AstUnionType* result,
    959                           int size, AstRangeType::Limits* limits, Zone* zone);
    960   static AstType* NormalizeUnion(AstType* unioned, int size, Zone* zone);
    961   static AstType* NormalizeRangeAndBitset(AstType* range, bitset* bits,
    962                                           Zone* zone);
    963 };
    964 
    965 // -----------------------------------------------------------------------------
    966 // Type bounds. A simple struct to represent a pair of lower/upper types.
    967 
    968 struct AstBounds {
    969   AstType* lower;
    970   AstType* upper;
    971 
    972   AstBounds()
    973       :  // Make sure accessing uninitialized bounds crashes big-time.
    974         lower(nullptr),
    975         upper(nullptr) {}
    976   explicit AstBounds(AstType* t) : lower(t), upper(t) {}
    977   AstBounds(AstType* l, AstType* u) : lower(l), upper(u) {
    978     DCHECK(lower->Is(upper));
    979   }
    980 
    981   // Unrestricted bounds.
    982   static AstBounds Unbounded() {
    983     return AstBounds(AstType::None(), AstType::Any());
    984   }
    985 
    986   // Meet: both b1 and b2 are known to hold.
    987   static AstBounds Both(AstBounds b1, AstBounds b2, Zone* zone) {
    988     AstType* lower = AstType::Union(b1.lower, b2.lower, zone);
    989     AstType* upper = AstType::Intersect(b1.upper, b2.upper, zone);
    990     // Lower bounds are considered approximate, correct as necessary.
    991     if (!lower->Is(upper)) lower = upper;
    992     return AstBounds(lower, upper);
    993   }
    994 
    995   // Join: either b1 or b2 is known to hold.
    996   static AstBounds Either(AstBounds b1, AstBounds b2, Zone* zone) {
    997     AstType* lower = AstType::Intersect(b1.lower, b2.lower, zone);
    998     AstType* upper = AstType::Union(b1.upper, b2.upper, zone);
    999     return AstBounds(lower, upper);
   1000   }
   1001 
   1002   static AstBounds NarrowLower(AstBounds b, AstType* t, Zone* zone) {
   1003     AstType* lower = AstType::Union(b.lower, t, zone);
   1004     // Lower bounds are considered approximate, correct as necessary.
   1005     if (!lower->Is(b.upper)) lower = b.upper;
   1006     return AstBounds(lower, b.upper);
   1007   }
   1008   static AstBounds NarrowUpper(AstBounds b, AstType* t, Zone* zone) {
   1009     AstType* lower = b.lower;
   1010     AstType* upper = AstType::Intersect(b.upper, t, zone);
   1011     // Lower bounds are considered approximate, correct as necessary.
   1012     if (!lower->Is(upper)) lower = upper;
   1013     return AstBounds(lower, upper);
   1014   }
   1015 
   1016   bool Narrows(AstBounds that) {
   1017     return that.lower->Is(this->lower) && this->upper->Is(that.upper);
   1018   }
   1019 };
   1020 
   1021 }  // namespace internal
   1022 }  // namespace v8
   1023 
   1024 #endif  // V8_AST_AST_TYPES_H_
   1025