reflect: fix StructOf hash and string

[official-gcc.git] / libgo / go / reflect / type.go

// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Package reflect implements run-time reflection, allowing a program to
// manipulate objects with arbitrary types. The typical use is to take a value
// with static type interface{} and extract its dynamic type information by
// calling TypeOf, which returns a Type.
//
// A call to ValueOf returns a Value representing the run-time data.
// Zero takes a Type and returns a Value representing a zero value
// for that type.
//
// See "The Laws of Reflection" for an introduction to reflection in Go:
// https://golang.org/doc/articles/laws_of_reflection.html
package reflect

import (
        "strconv"
        "sync"
        "unicode"
        "unicode/utf8"
        "unsafe"
)

// Type is the representation of a Go type.
//
// Not all methods apply to all kinds of types. Restrictions,
// if any, are noted in the documentation for each method.
// Use the Kind method to find out the kind of type before
// calling kind-specific methods. Calling a method
// inappropriate to the kind of type causes a run-time panic.
//
// Type values are comparable, such as with the == operator,
// so they can be used as map keys.
// Two Type values are equal if they represent identical types.
type Type interface {
        // Methods applicable to all types.

        // Align returns the alignment in bytes of a value of
        // this type when allocated in memory.
        Align() int

        // FieldAlign returns the alignment in bytes of a value of
        // this type when used as a field in a struct.
        FieldAlign() int

        // Method returns the i'th method in the type's method set.
        // It panics if i is not in the range [0, NumMethod()).
        //
        // For a non-interface type T or *T, the returned Method's Type and Func
        // fields describe a function whose first argument is the receiver.
        //
        // For an interface type, the returned Method's Type field gives the
        // method signature, without a receiver, and the Func field is nil.
        Method(int) Method

        // MethodByName returns the method with that name in the type's
        // method set and a boolean indicating if the method was found.
        //
        // For a non-interface type T or *T, the returned Method's Type and Func
        // fields describe a function whose first argument is the receiver.
        //
        // For an interface type, the returned Method's Type field gives the
        // method signature, without a receiver, and the Func field is nil.
        MethodByName(string) (Method, bool)

        // NumMethod returns the number of exported methods in the type's method set.
        NumMethod() int

        // Name returns the type's name within its package.
        // It returns an empty string for unnamed types.
        Name() string

        // PkgPath returns a named type's package path, that is, the import path
        // that uniquely identifies the package, such as "encoding/base64".
        // If the type was predeclared (string, error) or unnamed (*T, struct{}, []int),
        // the package path will be the empty string.
        PkgPath() string

        // Size returns the number of bytes needed to store
        // a value of the given type; it is analogous to unsafe.Sizeof.
        Size() uintptr

        // String returns a string representation of the type.
        // The string representation may use shortened package names
        // (e.g., base64 instead of "encoding/base64") and is not
        // guaranteed to be unique among types. To test for type identity,
        // compare the Types directly.
        String() string

        // Used internally by gccgo--the string retaining quoting.
        rawString() string

        // Kind returns the specific kind of this type.
        Kind() Kind

        // Implements reports whether the type implements the interface type u.
        Implements(u Type) bool

        // AssignableTo reports whether a value of the type is assignable to type u.
        AssignableTo(u Type) bool

        // ConvertibleTo reports whether a value of the type is convertible to type u.
        ConvertibleTo(u Type) bool

        // Comparable reports whether values of this type are comparable.
        Comparable() bool

        // Methods applicable only to some types, depending on Kind.
        // The methods allowed for each kind are:
        //
        //      Int*, Uint*, Float*, Complex*: Bits
        //      Array: Elem, Len
        //      Chan: ChanDir, Elem
        //      Func: In, NumIn, Out, NumOut, IsVariadic.
        //      Map: Key, Elem
        //      Ptr: Elem
        //      Slice: Elem
        //      Struct: Field, FieldByIndex, FieldByName, FieldByNameFunc, NumField

        // Bits returns the size of the type in bits.
        // It panics if the type's Kind is not one of the
        // sized or unsized Int, Uint, Float, or Complex kinds.
        Bits() int

        // ChanDir returns a channel type's direction.
        // It panics if the type's Kind is not Chan.
        ChanDir() ChanDir

        // IsVariadic reports whether a function type's final input parameter
        // is a "..." parameter. If so, t.In(t.NumIn() - 1) returns the parameter's
        // implicit actual type []T.
        //
        // For concreteness, if t represents func(x int, y ... float64), then
        //
        //      t.NumIn() == 2
        //      t.In(0) is the reflect.Type for "int"
        //      t.In(1) is the reflect.Type for "[]float64"
        //      t.IsVariadic() == true
        //
        // IsVariadic panics if the type's Kind is not Func.
        IsVariadic() bool

        // Elem returns a type's element type.
        // It panics if the type's Kind is not Array, Chan, Map, Ptr, or Slice.
        Elem() Type

        // Field returns a struct type's i'th field.
        // It panics if the type's Kind is not Struct.
        // It panics if i is not in the range [0, NumField()).
        Field(i int) StructField

        // FieldByIndex returns the nested field corresponding
        // to the index sequence. It is equivalent to calling Field
        // successively for each index i.
        // It panics if the type's Kind is not Struct.
        FieldByIndex(index []int) StructField

        // FieldByName returns the struct field with the given name
        // and a boolean indicating if the field was found.
        FieldByName(name string) (StructField, bool)

        // FieldByNameFunc returns the struct field with a name
        // that satisfies the match function and a boolean indicating if
        // the field was found.
        //
        // FieldByNameFunc considers the fields in the struct itself
        // and then the fields in any anonymous structs, in breadth first order,
        // stopping at the shallowest nesting depth containing one or more
        // fields satisfying the match function. If multiple fields at that depth
        // satisfy the match function, they cancel each other
        // and FieldByNameFunc returns no match.
        // This behavior mirrors Go's handling of name lookup in
        // structs containing anonymous fields.
        FieldByNameFunc(match func(string) bool) (StructField, bool)

        // In returns the type of a function type's i'th input parameter.
        // It panics if the type's Kind is not Func.
        // It panics if i is not in the range [0, NumIn()).
        In(i int) Type

        // Key returns a map type's key type.
        // It panics if the type's Kind is not Map.
        Key() Type

        // Len returns an array type's length.
        // It panics if the type's Kind is not Array.
        Len() int

        // NumField returns a struct type's field count.
        // It panics if the type's Kind is not Struct.
        NumField() int

        // NumIn returns a function type's input parameter count.
        // It panics if the type's Kind is not Func.
        NumIn() int

        // NumOut returns a function type's output parameter count.
        // It panics if the type's Kind is not Func.
        NumOut() int

        // Out returns the type of a function type's i'th output parameter.
        // It panics if the type's Kind is not Func.
        // It panics if i is not in the range [0, NumOut()).
        Out(i int) Type

        common() *rtype
        uncommon() *uncommonType
}

// BUG(rsc): FieldByName and related functions consider struct field names to be equal
// if the names are equal, even if they are unexported names originating
// in different packages. The practical effect of this is that the result of
// t.FieldByName("x") is not well defined if the struct type t contains
// multiple fields named x (embedded from different packages).
// FieldByName may return one of the fields named x or may report that there are none.
// See https://golang.org/issue/4876 for more details.

/*
 * These data structures are known to the compiler (../../cmd/internal/gc/reflect.go).
 * A few are known to ../runtime/type.go to convey to debuggers.
 * They are also known to ../runtime/type.go.
 */

// A Kind represents the specific kind of type that a Type represents.
// The zero Kind is not a valid kind.
type Kind uint

const (
        Invalid Kind = iota
        Bool
        Int
        Int8
        Int16
        Int32
        Int64
        Uint
        Uint8
        Uint16
        Uint32
        Uint64
        Uintptr
        Float32
        Float64
        Complex64
        Complex128
        Array
        Chan
        Func
        Interface
        Map
        Ptr
        Slice
        String
        Struct
        UnsafePointer
)

// rtype is the common implementation of most values.
// It is embedded in other, public struct types, but always
// with a unique tag like `reflect:"array"` or `reflect:"ptr"`
// so that code cannot convert from, say, *arrayType to *ptrType.
//
// rtype must be kept in sync with ../runtime/type.go:/^type._type.
type rtype struct {
        size       uintptr
        ptrdata    uintptr // size of memory prefix holding all pointers
        hash       uint32  // hash of type; avoids computation in hash tables
        kind       uint8   // enumeration for C
        align      int8    // alignment of variable with this type
        fieldAlign uint8   // alignment of struct field with this type
        _          uint8   // unused/padding

        hashfn  func(unsafe.Pointer, uintptr) uintptr     // hash function
        equalfn func(unsafe.Pointer, unsafe.Pointer) bool // equality function

        gcdata        *byte   // garbage collection data
        string        *string // string form; unnecessary  but undeniably useful
        *uncommonType         // (relatively) uncommon fields
        ptrToThis     *rtype  // type for pointer to this type, if used in binary or has methods
}

// Method on non-interface type
type method struct {
        name    *string        // name of method
        pkgPath *string        // nil for exported Names; otherwise import path
        mtyp    *rtype         // method type (without receiver)
        typ     *rtype         // .(*FuncType) underneath (with receiver)
        tfn     unsafe.Pointer // fn used for normal method call
}

// uncommonType is present only for types with names or methods
// (if T is a named type, the uncommonTypes for T and *T have methods).
// Using a pointer to this struct reduces the overall size required
// to describe an unnamed type with no methods.
type uncommonType struct {
        name    *string  // name of type
        pkgPath *string  // import path; nil for built-in types like int, string
        methods []method // methods associated with type
}

// ChanDir represents a channel type's direction.
type ChanDir int

const (
        RecvDir ChanDir             = 1 << iota // <-chan
        SendDir                                 // chan<-
        BothDir = RecvDir | SendDir             // chan
)

// arrayType represents a fixed array type.
type arrayType struct {
        rtype `reflect:"array"`
        elem  *rtype // array element type
        slice *rtype // slice type
        len   uintptr
}

// chanType represents a channel type.
type chanType struct {
        rtype `reflect:"chan"`
        elem  *rtype  // channel element type
        dir   uintptr // channel direction (ChanDir)
}

// funcType represents a function type.
type funcType struct {
        rtype     `reflect:"func"`
        dotdotdot bool     // last input parameter is ...
        in        []*rtype // input parameter types
        out       []*rtype // output parameter types
}

// imethod represents a method on an interface type
type imethod struct {
        name    *string // name of method
        pkgPath *string // nil for exported Names; otherwise import path
        typ     *rtype  // .(*FuncType) underneath
}

// interfaceType represents an interface type.
type interfaceType struct {
        rtype   `reflect:"interface"`
        methods []imethod // sorted by hash
}

// mapType represents a map type.
type mapType struct {
        rtype         `reflect:"map"`
        key           *rtype // map key type
        elem          *rtype // map element (value) type
        bucket        *rtype // internal bucket structure
        hmap          *rtype // internal map header
        keysize       uint8  // size of key slot
        indirectkey   uint8  // store ptr to key instead of key itself
        valuesize     uint8  // size of value slot
        indirectvalue uint8  // store ptr to value instead of value itself
        bucketsize    uint16 // size of bucket
        reflexivekey  bool   // true if k==k for all keys
        needkeyupdate bool   // true if we need to update key on an overwrite
}

// ptrType represents a pointer type.
type ptrType struct {
        rtype `reflect:"ptr"`
        elem  *rtype // pointer element (pointed at) type
}

// sliceType represents a slice type.
type sliceType struct {
        rtype `reflect:"slice"`
        elem  *rtype // slice element type
}

// Struct field
type structField struct {
        name       *string // name is always non-empty
        pkgPath    *string // nil for exported Names; otherwise import path
        typ        *rtype  // type of field
        tag        *string // nil if no tag
        offsetAnon uintptr // byte offset of field<<1 | isAnonymous
}

func (f *structField) offset() uintptr {
        return f.offsetAnon >> 1
}

func (f *structField) anon() bool {
        return f.offsetAnon&1 != 0
}

// structType represents a struct type.
type structType struct {
        rtype  `reflect:"struct"`
        fields []structField // sorted by offset
}

/*
 * The compiler knows the exact layout of all the data structures above.
 * The compiler does not know about the data structures and methods below.
 */

// Method represents a single method.
type Method struct {
        // Name is the method name.
        // PkgPath is the package path that qualifies a lower case (unexported)
        // method name. It is empty for upper case (exported) method names.
        // The combination of PkgPath and Name uniquely identifies a method
        // in a method set.
        // See https://golang.org/ref/spec#Uniqueness_of_identifiers
        Name    string
        PkgPath string

        Type  Type  // method type
        Func  Value // func with receiver as first argument
        Index int   // index for Type.Method
}

const (
        kindDirectIface = 1 << 5
        kindGCProg      = 1 << 6 // Type.gc points to GC program
        kindNoPointers  = 1 << 7
        kindMask        = (1 << 5) - 1
)

func (k Kind) String() string {
        if int(k) < len(kindNames) {
                return kindNames[k]
        }
        return "kind" + strconv.Itoa(int(k))
}

var kindNames = []string{
        Invalid:       "invalid",
        Bool:          "bool",
        Int:           "int",
        Int8:          "int8",
        Int16:         "int16",
        Int32:         "int32",
        Int64:         "int64",
        Uint:          "uint",
        Uint8:         "uint8",
        Uint16:        "uint16",
        Uint32:        "uint32",
        Uint64:        "uint64",
        Uintptr:       "uintptr",
        Float32:       "float32",
        Float64:       "float64",
        Complex64:     "complex64",
        Complex128:    "complex128",
        Array:         "array",
        Chan:          "chan",
        Func:          "func",
        Interface:     "interface",
        Map:           "map",
        Ptr:           "ptr",
        Slice:         "slice",
        String:        "string",
        Struct:        "struct",
        UnsafePointer: "unsafe.Pointer",
}

func (t *uncommonType) uncommon() *uncommonType {
        return t
}

func (t *uncommonType) PkgPath() string {
        if t == nil || t.pkgPath == nil {
                return ""
        }
        return *t.pkgPath
}

func (t *uncommonType) Name() string {
        if t == nil || t.name == nil {
                return ""
        }
        return *t.name
}

func (t *rtype) rawString() string { return *t.string }

func (t *rtype) String() string {
        // For gccgo, strip out quoted strings.
        s := *t.string
        var q bool
        r := make([]byte, len(s))
        j := 0
        for i := 0; i < len(s); i++ {
                if s[i] == '\t' {
                        q = !q
                } else if !q {
                        r[j] = s[i]
                        j++
                }
        }
        return string(r[:j])
}

func (t *rtype) Size() uintptr { return t.size }

func (t *rtype) Bits() int {
        if t == nil {
                panic("reflect: Bits of nil Type")
        }
        k := t.Kind()
        if k < Int || k > Complex128 {
                panic("reflect: Bits of non-arithmetic Type " + t.String())
        }
        return int(t.size) * 8
}

func (t *rtype) Align() int { return int(t.align) }

func (t *rtype) FieldAlign() int { return int(t.fieldAlign) }

func (t *rtype) Kind() Kind { return Kind(t.kind & kindMask) }

func (t *rtype) pointers() bool { return t.kind&kindNoPointers == 0 }

func (t *rtype) common() *rtype { return t }

var methodCache sync.Map // map[*rtype][]method

func (t *rtype) exportedMethods() []method {
        methodsi, found := methodCache.Load(t)
        if found {
                return methodsi.([]method)
        }

        ut := t.uncommon()
        if ut == nil {
                return nil
        }
        allm := ut.methods
        allExported := true
        for _, m := range allm {
                if m.pkgPath != nil {
                        allExported = false
                        break
                }
        }
        var methods []method
        if allExported {
                methods = allm
        } else {
                methods = make([]method, 0, len(allm))
                for _, m := range allm {
                        if m.pkgPath == nil {
                                methods = append(methods, m)
                        }
                }
                methods = methods[:len(methods):len(methods)]
        }

        methodsi, _ = methodCache.LoadOrStore(t, methods)
        return methodsi.([]method)
}

func (t *rtype) NumMethod() int {
        if t.Kind() == Interface {
                tt := (*interfaceType)(unsafe.Pointer(t))
                return tt.NumMethod()
        }
        if t.uncommonType == nil {
                return 0 // avoid methodCache synchronization
        }
        return len(t.exportedMethods())
}

func (t *rtype) Method(i int) (m Method) {
        if t.Kind() == Interface {
                tt := (*interfaceType)(unsafe.Pointer(t))
                return tt.Method(i)
        }
        methods := t.exportedMethods()
        if i < 0 || i >= len(methods) {
                panic("reflect: Method index out of range")
        }
        p := methods[i]
        if p.name != nil {
                m.Name = *p.name
        }
        fl := flag(Func)
        mt := p.typ
        m.Type = toType(mt)
        x := new(unsafe.Pointer)
        *x = unsafe.Pointer(&p.tfn)
        m.Func = Value{mt, unsafe.Pointer(x), fl | flagIndir | flagMethodFn}
        m.Index = i
        return m
}

func (t *rtype) MethodByName(name string) (m Method, ok bool) {
        if t.Kind() == Interface {
                tt := (*interfaceType)(unsafe.Pointer(t))
                return tt.MethodByName(name)
        }
        ut := t.uncommon()
        if ut == nil {
                return Method{}, false
        }
        utmethods := ut.methods
        var eidx int
        for i := 0; i < len(utmethods); i++ {
                p := utmethods[i]
                if p.pkgPath == nil {
                        if p.name != nil && *p.name == name {
                                return t.Method(eidx), true
                        }
                        eidx++
                }
        }
        return Method{}, false
}

func (t *rtype) PkgPath() string {
        return t.uncommonType.PkgPath()
}

func (t *rtype) Name() string {
        return t.uncommonType.Name()
}

func (t *rtype) ChanDir() ChanDir {
        if t.Kind() != Chan {
                panic("reflect: ChanDir of non-chan type")
        }
        tt := (*chanType)(unsafe.Pointer(t))
        return ChanDir(tt.dir)
}

func (t *rtype) IsVariadic() bool {
        if t.Kind() != Func {
                panic("reflect: IsVariadic of non-func type")
        }
        tt := (*funcType)(unsafe.Pointer(t))
        return tt.dotdotdot
}

func (t *rtype) Elem() Type {
        switch t.Kind() {
        case Array:
                tt := (*arrayType)(unsafe.Pointer(t))
                return toType(tt.elem)
        case Chan:
                tt := (*chanType)(unsafe.Pointer(t))
                return toType(tt.elem)
        case Map:
                tt := (*mapType)(unsafe.Pointer(t))
                return toType(tt.elem)
        case Ptr:
                tt := (*ptrType)(unsafe.Pointer(t))
                return toType(tt.elem)
        case Slice:
                tt := (*sliceType)(unsafe.Pointer(t))
                return toType(tt.elem)
        }
        panic("reflect: Elem of invalid type")
}

func (t *rtype) Field(i int) StructField {
        if t.Kind() != Struct {
                panic("reflect: Field of non-struct type")
        }
        tt := (*structType)(unsafe.Pointer(t))
        return tt.Field(i)
}

func (t *rtype) FieldByIndex(index []int) StructField {
        if t.Kind() != Struct {
                panic("reflect: FieldByIndex of non-struct type")
        }
        tt := (*structType)(unsafe.Pointer(t))
        return tt.FieldByIndex(index)
}

func (t *rtype) FieldByName(name string) (StructField, bool) {
        if t.Kind() != Struct {
                panic("reflect: FieldByName of non-struct type")
        }
        tt := (*structType)(unsafe.Pointer(t))
        return tt.FieldByName(name)
}

func (t *rtype) FieldByNameFunc(match func(string) bool) (StructField, bool) {
        if t.Kind() != Struct {
                panic("reflect: FieldByNameFunc of non-struct type")
        }
        tt := (*structType)(unsafe.Pointer(t))
        return tt.FieldByNameFunc(match)
}

func (t *rtype) In(i int) Type {
        if t.Kind() != Func {
                panic("reflect: In of non-func type")
        }
        tt := (*funcType)(unsafe.Pointer(t))
        return toType(tt.in[i])
}

func (t *rtype) Key() Type {
        if t.Kind() != Map {
                panic("reflect: Key of non-map type")
        }
        tt := (*mapType)(unsafe.Pointer(t))
        return toType(tt.key)
}

func (t *rtype) Len() int {
        if t.Kind() != Array {
                panic("reflect: Len of non-array type")
        }
        tt := (*arrayType)(unsafe.Pointer(t))
        return int(tt.len)
}

func (t *rtype) NumField() int {
        if t.Kind() != Struct {
                panic("reflect: NumField of non-struct type")
        }
        tt := (*structType)(unsafe.Pointer(t))
        return len(tt.fields)
}

func (t *rtype) NumIn() int {
        if t.Kind() != Func {
                panic("reflect: NumIn of non-func type")
        }
        tt := (*funcType)(unsafe.Pointer(t))
        return len(tt.in)
}

func (t *rtype) NumOut() int {
        if t.Kind() != Func {
                panic("reflect: NumOut of non-func type")
        }
        tt := (*funcType)(unsafe.Pointer(t))
        return len(tt.out)
}

func (t *rtype) Out(i int) Type {
        if t.Kind() != Func {
                panic("reflect: Out of non-func type")
        }
        tt := (*funcType)(unsafe.Pointer(t))
        return toType(tt.out[i])
}

// add returns p+x.
//
// The whySafe string is ignored, so that the function still inlines
// as efficiently as p+x, but all call sites should use the string to
// record why the addition is safe, which is to say why the addition
// does not cause x to advance to the very end of p's allocation
// and therefore point incorrectly at the next block in memory.
func add(p unsafe.Pointer, x uintptr, whySafe string) unsafe.Pointer {
        return unsafe.Pointer(uintptr(p) + x)
}

func (d ChanDir) String() string {
        switch d {
        case SendDir:
                return "chan<-"
        case RecvDir:
                return "<-chan"
        case BothDir:
                return "chan"
        }
        return "ChanDir" + strconv.Itoa(int(d))
}

// Method returns the i'th method in the type's method set.
func (t *interfaceType) Method(i int) (m Method) {
        if i < 0 || i >= len(t.methods) {
                return
        }
        p := &t.methods[i]
        m.Name = *p.name
        if p.pkgPath != nil {
                m.PkgPath = *p.pkgPath
        }
        m.Type = toType(p.typ)
        m.Index = i
        return
}

// NumMethod returns the number of interface methods in the type's method set.
func (t *interfaceType) NumMethod() int { return len(t.methods) }

// MethodByName method with the given name in the type's method set.
func (t *interfaceType) MethodByName(name string) (m Method, ok bool) {
        if t == nil {
                return
        }
        var p *imethod
        for i := range t.methods {
                p = &t.methods[i]
                if *p.name == name {
                        return t.Method(i), true
                }
        }
        return
}

// A StructField describes a single field in a struct.
type StructField struct {
        // Name is the field name.
        Name string
        // PkgPath is the package path that qualifies a lower case (unexported)
        // field name. It is empty for upper case (exported) field names.
        // See https://golang.org/ref/spec#Uniqueness_of_identifiers
        PkgPath string

        Type      Type      // field type
        Tag       StructTag // field tag string
        Offset    uintptr   // offset within struct, in bytes
        Index     []int     // index sequence for Type.FieldByIndex
        Anonymous bool      // is an embedded field
}

// A StructTag is the tag string in a struct field.
//
// By convention, tag strings are a concatenation of
// optionally space-separated key:"value" pairs.
// Each key is a non-empty string consisting of non-control
// characters other than space (U+0020 ' '), quote (U+0022 '"'),
// and colon (U+003A ':').  Each value is quoted using U+0022 '"'
// characters and Go string literal syntax.
type StructTag string

// Get returns the value associated with key in the tag string.
// If there is no such key in the tag, Get returns the empty string.
// If the tag does not have the conventional format, the value
// returned by Get is unspecified. To determine whether a tag is
// explicitly set to the empty string, use Lookup.
func (tag StructTag) Get(key string) string {
        v, _ := tag.Lookup(key)
        return v
}

// Lookup returns the value associated with key in the tag string.
// If the key is present in the tag the value (which may be empty)
// is returned. Otherwise the returned value will be the empty string.
// The ok return value reports whether the value was explicitly set in
// the tag string. If the tag does not have the conventional format,
// the value returned by Lookup is unspecified.
func (tag StructTag) Lookup(key string) (value string, ok bool) {
        // When modifying this code, also update the validateStructTag code
        // in cmd/vet/structtag.go.

        for tag != "" {
                // Skip leading space.
                i := 0
                for i < len(tag) && tag[i] == ' ' {
                        i++
                }
                tag = tag[i:]
                if tag == "" {
                        break
                }

                // Scan to colon. A space, a quote or a control character is a syntax error.
                // Strictly speaking, control chars include the range [0x7f, 0x9f], not just
                // [0x00, 0x1f], but in practice, we ignore the multi-byte control characters
                // as it is simpler to inspect the tag's bytes than the tag's runes.
                i = 0
                for i < len(tag) && tag[i] > ' ' && tag[i] != ':' && tag[i] != '"' && tag[i] != 0x7f {
                        i++
                }
                if i == 0 || i+1 >= len(tag) || tag[i] != ':' || tag[i+1] != '"' {
                        break
                }
                name := string(tag[:i])
                tag = tag[i+1:]

                // Scan quoted string to find value.
                i = 1
                for i < len(tag) && tag[i] != '"' {
                        if tag[i] == '\\' {
                                i++
                        }
                        i++
                }
                if i >= len(tag) {
                        break
                }
                qvalue := string(tag[:i+1])
                tag = tag[i+1:]

                if key == name {
                        value, err := strconv.Unquote(qvalue)
                        if err != nil {
                                break
                        }
                        return value, true
                }
        }
        return "", false
}

// Field returns the i'th struct field.
func (t *structType) Field(i int) (f StructField) {
        if i < 0 || i >= len(t.fields) {
                panic("reflect: Field index out of bounds")
        }
        p := &t.fields[i]
        f.Type = toType(p.typ)
        f.Name = *p.name
        f.Anonymous = p.anon()
        if p.pkgPath != nil {
                f.PkgPath = *p.pkgPath
        }
        if p.tag != nil {
                f.Tag = StructTag(*p.tag)
        }
        f.Offset = p.offset()

        // NOTE(rsc): This is the only allocation in the interface
        // presented by a reflect.Type. It would be nice to avoid,
        // at least in the common cases, but we need to make sure
        // that misbehaving clients of reflect cannot affect other
        // uses of reflect. One possibility is CL 5371098, but we
        // postponed that ugliness until there is a demonstrated
        // need for the performance. This is issue 2320.
        f.Index = []int{i}
        return
}

// TODO(gri): Should there be an error/bool indicator if the index
//            is wrong for FieldByIndex?

// FieldByIndex returns the nested field corresponding to index.
func (t *structType) FieldByIndex(index []int) (f StructField) {
        f.Type = toType(&t.rtype)
        for i, x := range index {
                if i > 0 {
                        ft := f.Type
                        if ft.Kind() == Ptr && ft.Elem().Kind() == Struct {
                                ft = ft.Elem()
                        }
                        f.Type = ft
                }
                f = f.Type.Field(x)
        }
        return
}

// A fieldScan represents an item on the fieldByNameFunc scan work list.
type fieldScan struct {
        typ   *structType
        index []int
}

// FieldByNameFunc returns the struct field with a name that satisfies the
// match function and a boolean to indicate if the field was found.
func (t *structType) FieldByNameFunc(match func(string) bool) (result StructField, ok bool) {
        // This uses the same condition that the Go language does: there must be a unique instance
        // of the match at a given depth level. If there are multiple instances of a match at the
        // same depth, they annihilate each other and inhibit any possible match at a lower level.
        // The algorithm is breadth first search, one depth level at a time.

        // The current and next slices are work queues:
        // current lists the fields to visit on this depth level,
        // and next lists the fields on the next lower level.
        current := []fieldScan{}
        next := []fieldScan{{typ: t}}

        // nextCount records the number of times an embedded type has been
        // encountered and considered for queueing in the 'next' slice.
        // We only queue the first one, but we increment the count on each.
        // If a struct type T can be reached more than once at a given depth level,
        // then it annihilates itself and need not be considered at all when we
        // process that next depth level.
        var nextCount map[*structType]int

        // visited records the structs that have been considered already.
        // Embedded pointer fields can create cycles in the graph of
        // reachable embedded types; visited avoids following those cycles.
        // It also avoids duplicated effort: if we didn't find the field in an
        // embedded type T at level 2, we won't find it in one at level 4 either.
        visited := map[*structType]bool{}

        for len(next) > 0 {
                current, next = next, current[:0]
                count := nextCount
                nextCount = nil

                // Process all the fields at this depth, now listed in 'current'.
                // The loop queues embedded fields found in 'next', for processing during the next
                // iteration. The multiplicity of the 'current' field counts is recorded
                // in 'count'; the multiplicity of the 'next' field counts is recorded in 'nextCount'.
                for _, scan := range current {
                        t := scan.typ
                        if visited[t] {
                                // We've looked through this type before, at a higher level.
                                // That higher level would shadow the lower level we're now at,
                                // so this one can't be useful to us. Ignore it.
                                continue
                        }
                        visited[t] = true
                        for i := range t.fields {
                                f := &t.fields[i]
                                // Find name and (for anonymous field) type for field f.
                                fname := *f.name
                                var ntyp *rtype
                                if f.anon() {
                                        // Anonymous field of type T or *T.
                                        ntyp = f.typ
                                        if ntyp.Kind() == Ptr {
                                                ntyp = ntyp.Elem().common()
                                        }
                                }

                                // Does it match?
                                if match(fname) {
                                        // Potential match
                                        if count[t] > 1 || ok {
                                                // Name appeared multiple times at this level: annihilate.
                                                return StructField{}, false
                                        }
                                        result = t.Field(i)
                                        result.Index = nil
                                        result.Index = append(result.Index, scan.index...)
                                        result.Index = append(result.Index, i)
                                        ok = true
                                        continue
                                }

                                // Queue embedded struct fields for processing with next level,
                                // but only if we haven't seen a match yet at this level and only
                                // if the embedded types haven't already been queued.
                                if ok || ntyp == nil || ntyp.Kind() != Struct {
                                        continue
                                }
                                ntyp = toType(ntyp).common()
                                styp := (*structType)(unsafe.Pointer(ntyp))
                                if nextCount[styp] > 0 {
                                        nextCount[styp] = 2 // exact multiple doesn't matter
                                        continue
                                }
                                if nextCount == nil {
                                        nextCount = map[*structType]int{}
                                }
                                nextCount[styp] = 1
                                if count[t] > 1 {
                                        nextCount[styp] = 2 // exact multiple doesn't matter
                                }
                                var index []int
                                index = append(index, scan.index...)
                                index = append(index, i)
                                next = append(next, fieldScan{styp, index})
                        }
                }
                if ok {
                        break
                }
        }
        return
}

// FieldByName returns the struct field with the given name
// and a boolean to indicate if the field was found.
func (t *structType) FieldByName(name string) (f StructField, present bool) {
        // Quick check for top-level name, or struct without anonymous fields.
        hasAnon := false
        if name != "" {
                for i := range t.fields {
                        tf := &t.fields[i]
                        if *tf.name == name {
                                return t.Field(i), true
                        }
                        if tf.anon() {
                                hasAnon = true
                        }
                }
        }
        if !hasAnon {
                return
        }
        return t.FieldByNameFunc(func(s string) bool { return s == name })
}

// TypeOf returns the reflection Type that represents the dynamic type of i.
// If i is a nil interface value, TypeOf returns nil.
func TypeOf(i interface{}) Type {
        eface := *(*emptyInterface)(unsafe.Pointer(&i))
        return toType(eface.typ)
}

// ptrMap is the cache for PtrTo.
var ptrMap sync.Map // map[*rtype]*ptrType

// PtrTo returns the pointer type with element t.
// For example, if t represents type Foo, PtrTo(t) represents *Foo.
func PtrTo(t Type) Type {
        return t.(*rtype).ptrTo()
}

func (t *rtype) ptrTo() *rtype {
        if p := t.ptrToThis; p != nil {
                return p
        }

        // Check the cache.
        if pi, ok := ptrMap.Load(t); ok {
                return &pi.(*ptrType).rtype
        }

        s := "*" + *t.string

        canonicalTypeLock.RLock()
        r, ok := canonicalType[s]
        canonicalTypeLock.RUnlock()
        if ok {
                p := (*ptrType)(unsafe.Pointer(r.(*rtype)))
                pi, _ := ptrMap.LoadOrStore(t, p)
                return &pi.(*ptrType).rtype
        }

        // Create a new ptrType starting with the description
        // of an *unsafe.Pointer.
        var iptr interface{} = (*unsafe.Pointer)(nil)
        prototype := *(**ptrType)(unsafe.Pointer(&iptr))
        pp := *prototype

        pp.string = &s
        pp.ptrToThis = nil

        // For the type structures linked into the binary, the
        // compiler provides a good hash of the string.
        // Create a good hash for the new string by using
        // the FNV-1 hash's mixing function to combine the
        // old hash and the new "*".
        // p.hash = fnv1(t.hash, '*')
        // This is the gccgo version.
        pp.hash = (t.hash << 4) + 9

        pp.uncommonType = nil
        pp.ptrToThis = nil
        pp.elem = t

        q := canonicalize(&pp.rtype)
        p := (*ptrType)(unsafe.Pointer(q.(*rtype)))

        pi, _ := ptrMap.LoadOrStore(t, p)
        return &pi.(*ptrType).rtype
}

// fnv1 incorporates the list of bytes into the hash x using the FNV-1 hash function.
func fnv1(x uint32, list ...byte) uint32 {
        for _, b := range list {
                x = x*16777619 ^ uint32(b)
        }
        return x
}

func (t *rtype) Implements(u Type) bool {
        if u == nil {
                panic("reflect: nil type passed to Type.Implements")
        }
        if u.Kind() != Interface {
                panic("reflect: non-interface type passed to Type.Implements")
        }
        return implements(u.(*rtype), t)
}

func (t *rtype) AssignableTo(u Type) bool {
        if u == nil {
                panic("reflect: nil type passed to Type.AssignableTo")
        }
        uu := u.(*rtype)
        return directlyAssignable(uu, t) || implements(uu, t)
}

func (t *rtype) ConvertibleTo(u Type) bool {
        if u == nil {
                panic("reflect: nil type passed to Type.ConvertibleTo")
        }
        uu := u.(*rtype)
        return convertOp(uu, t) != nil
}

func (t *rtype) Comparable() bool {
        switch t.Kind() {
        case Bool, Int, Int8, Int16, Int32, Int64,
                Uint, Uint8, Uint16, Uint32, Uint64, Uintptr,
                Float32, Float64, Complex64, Complex128,
                Chan, Interface, Ptr, String, UnsafePointer:
                return true

        case Func, Map, Slice:
                return false

        case Array:
                return (*arrayType)(unsafe.Pointer(t)).elem.Comparable()

        case Struct:
                tt := (*structType)(unsafe.Pointer(t))
                for i := range tt.fields {
                        if !tt.fields[i].typ.Comparable() {
                                return false
                        }
                }
                return true

        default:
                panic("reflect: impossible")
        }
}

// implements reports whether the type V implements the interface type T.
func implements(T, V *rtype) bool {
        if T.Kind() != Interface {
                return false
        }
        t := (*interfaceType)(unsafe.Pointer(T))
        if len(t.methods) == 0 {
                return true
        }

        // The same algorithm applies in both cases, but the
        // method tables for an interface type and a concrete type
        // are different, so the code is duplicated.
        // In both cases the algorithm is a linear scan over the two
        // lists - T's methods and V's methods - simultaneously.
        // Since method tables are stored in a unique sorted order
        // (alphabetical, with no duplicate method names), the scan
        // through V's methods must hit a match for each of T's
        // methods along the way, or else V does not implement T.
        // This lets us run the scan in overall linear time instead of
        // the quadratic time  a naive search would require.
        // See also ../runtime/iface.go.
        if V.Kind() == Interface {
                v := (*interfaceType)(unsafe.Pointer(V))
                i := 0
                for j := 0; j < len(v.methods); j++ {
                        tm := &t.methods[i]
                        vm := &v.methods[j]
                        if *vm.name == *tm.name && (vm.pkgPath == tm.pkgPath || (vm.pkgPath != nil && tm.pkgPath != nil && *vm.pkgPath == *tm.pkgPath)) && toType(vm.typ).common() == toType(tm.typ).common() {
                                if i++; i >= len(t.methods) {
                                        return true
                                }
                        }
                }
                return false
        }

        v := V.uncommon()
        if v == nil {
                return false
        }
        i := 0
        for j := 0; j < len(v.methods); j++ {
                tm := &t.methods[i]
                vm := &v.methods[j]
                if *vm.name == *tm.name && (vm.pkgPath == tm.pkgPath || (vm.pkgPath != nil && tm.pkgPath != nil && *vm.pkgPath == *tm.pkgPath)) && toType(vm.mtyp).common() == toType(tm.typ).common() {
                        if i++; i >= len(t.methods) {
                                return true
                        }
                }
        }
        return false
}

// directlyAssignable reports whether a value x of type V can be directly
// assigned (using memmove) to a value of type T.
// https://golang.org/doc/go_spec.html#Assignability
// Ignoring the interface rules (implemented elsewhere)
// and the ideal constant rules (no ideal constants at run time).
func directlyAssignable(T, V *rtype) bool {
        // x's type V is identical to T?
        if T == V {
                return true
        }

        // Otherwise at least one of T and V must be unnamed
        // and they must have the same kind.
        if T.Name() != "" && V.Name() != "" || T.Kind() != V.Kind() {
                return false
        }

        // x's type T and V must  have identical underlying types.
        return haveIdenticalUnderlyingType(T, V, true)
}

func haveIdenticalType(T, V Type, cmpTags bool) bool {
        if cmpTags {
                return T == V
        }

        if T.Name() != V.Name() || T.Kind() != V.Kind() {
                return false
        }

        return haveIdenticalUnderlyingType(T.common(), V.common(), false)
}

func haveIdenticalUnderlyingType(T, V *rtype, cmpTags bool) bool {
        if T == V {
                return true
        }

        kind := T.Kind()
        if kind != V.Kind() {
                return false
        }

        // Non-composite types of equal kind have same underlying type
        // (the predefined instance of the type).
        if Bool <= kind && kind <= Complex128 || kind == String || kind == UnsafePointer {
                return true
        }

        // Composite types.
        switch kind {
        case Array:
                return T.Len() == V.Len() && haveIdenticalType(T.Elem(), V.Elem(), cmpTags)

        case Chan:
                // Special case:
                // x is a bidirectional channel value, T is a channel type,
                // and x's type V and T have identical element types.
                if V.ChanDir() == BothDir && haveIdenticalType(T.Elem(), V.Elem(), cmpTags) {
                        return true
                }

                // Otherwise continue test for identical underlying type.
                return V.ChanDir() == T.ChanDir() && haveIdenticalType(T.Elem(), V.Elem(), cmpTags)

        case Func:
                t := (*funcType)(unsafe.Pointer(T))
                v := (*funcType)(unsafe.Pointer(V))
                if t.dotdotdot != v.dotdotdot || len(t.in) != len(v.in) || len(t.out) != len(v.out) {
                        return false
                }
                for i, typ := range t.in {
                        if !haveIdenticalType(typ, v.in[i], cmpTags) {
                                return false
                        }
                }
                for i, typ := range t.out {
                        if !haveIdenticalType(typ, v.out[i], cmpTags) {
                                return false
                        }
                }
                return true

        case Interface:
                t := (*interfaceType)(unsafe.Pointer(T))
                v := (*interfaceType)(unsafe.Pointer(V))
                if len(t.methods) == 0 && len(v.methods) == 0 {
                        return true
                }
                // Might have the same methods but still
                // need a run time conversion.
                return false

        case Map:
                return haveIdenticalType(T.Key(), V.Key(), cmpTags) && haveIdenticalType(T.Elem(), V.Elem(), cmpTags)

        case Ptr, Slice:
                return haveIdenticalType(T.Elem(), V.Elem(), cmpTags)

        case Struct:
                t := (*structType)(unsafe.Pointer(T))
                v := (*structType)(unsafe.Pointer(V))
                if len(t.fields) != len(v.fields) {
                        return false
                }
                for i := range t.fields {
                        tf := &t.fields[i]
                        vf := &v.fields[i]
                        if tf.name != vf.name && (tf.name == nil || vf.name == nil || *tf.name != *vf.name) {
                                return false
                        }
                        if tf.pkgPath != vf.pkgPath && (tf.pkgPath == nil || vf.pkgPath == nil || *tf.pkgPath != *vf.pkgPath) {
                                return false
                        }
                        if !haveIdenticalType(tf.typ, vf.typ, cmpTags) {
                                return false
                        }
                        if cmpTags && tf.tag != vf.tag && (tf.tag == nil || vf.tag == nil || *tf.tag != *vf.tag) {
                                return false
                        }
                        if tf.offsetAnon != vf.offsetAnon {
                                return false
                        }
                }
                return true
        }

        return false
}

// The lookupCache caches ArrayOf, ChanOf, MapOf and SliceOf lookups.
var lookupCache sync.Map // map[cacheKey]*rtype

// A cacheKey is the key for use in the lookupCache.
// Four values describe any of the types we are looking for:
// type kind, one or two subtypes, and an extra integer.
type cacheKey struct {
        kind  Kind
        t1    *rtype
        t2    *rtype
        extra uintptr
}

// The funcLookupCache caches FuncOf lookups.
// FuncOf does not share the common lookupCache since cacheKey is not
// sufficient to represent functions unambiguously.
var funcLookupCache struct {
        sync.Mutex // Guards stores (but not loads) on m.

        // m is a map[uint32][]*rtype keyed by the hash calculated in FuncOf.
        // Elements of m are append-only and thus safe for concurrent reading.
        m sync.Map
}

// ChanOf returns the channel type with the given direction and element type.
// For example, if t represents int, ChanOf(RecvDir, t) represents <-chan int.
//
// The gc runtime imposes a limit of 64 kB on channel element types.
// If t's size is equal to or exceeds this limit, ChanOf panics.
func ChanOf(dir ChanDir, t Type) Type {
        typ := t.(*rtype)

        // Look in cache.
        ckey := cacheKey{Chan, typ, nil, uintptr(dir)}
        if ch, ok := lookupCache.Load(ckey); ok {
                return ch.(*rtype)
        }

        // This restriction is imposed by the gc compiler and the runtime.
        if typ.size >= 1<<16 {
                panic("reflect.ChanOf: element size too large")
        }

        // Look in known types.
        // TODO: Precedence when constructing string.
        var s string
        switch dir {
        default:
                panic("reflect.ChanOf: invalid dir")
        case SendDir:
                s = "chan<- " + *typ.string
        case RecvDir:
                s = "<-chan " + *typ.string
        case BothDir:
                s = "chan " + *typ.string
        }

        // Make a channel type.
        var ichan interface{} = (chan unsafe.Pointer)(nil)
        prototype := *(**chanType)(unsafe.Pointer(&ichan))
        ch := *prototype
        ch.dir = uintptr(dir)
        ch.string = &s

        // gccgo uses a different hash.
        // ch.hash = fnv1(typ.hash, 'c', byte(dir))
        ch.hash = 0
        if dir&SendDir != 0 {
                ch.hash += 1
        }
        if dir&RecvDir != 0 {
                ch.hash += 2
        }
        ch.hash += typ.hash << 2
        ch.hash <<= 3
        ch.hash += 15

        ch.elem = typ
        ch.uncommonType = nil
        ch.ptrToThis = nil

        // Canonicalize before storing in lookupCache
        ti := toType(&ch.rtype)
        lookupCache.Store(ckey, ti.(*rtype))
        return ti
}

func ismapkey(*rtype) bool // implemented in runtime

// MapOf returns the map type with the given key and element types.
// For example, if k represents int and e represents string,
// MapOf(k, e) represents map[int]string.
//
// If the key type is not a valid map key type (that is, if it does
// not implement Go's == operator), MapOf panics.
func MapOf(key, elem Type) Type {
        ktyp := key.(*rtype)
        etyp := elem.(*rtype)

        if !ismapkey(ktyp) {
                panic("reflect.MapOf: invalid key type " + ktyp.String())
        }

        // Look in cache.
        ckey := cacheKey{Map, ktyp, etyp, 0}
        if mt, ok := lookupCache.Load(ckey); ok {
                return mt.(Type)
        }

        // Look in known types.
        s := "map[" + *ktyp.string + "]" + *etyp.string

        // Make a map type.
        var imap interface{} = (map[unsafe.Pointer]unsafe.Pointer)(nil)
        mt := **(**mapType)(unsafe.Pointer(&imap))
        mt.string = &s

        // gccgo uses a different hash
        // mt.hash = fnv1(etyp.hash, 'm', byte(ktyp.hash>>24), byte(ktyp.hash>>16), byte(ktyp.hash>>8), byte(ktyp.hash))
        mt.hash = ktyp.hash + etyp.hash + 2 + 14

        mt.key = ktyp
        mt.elem = etyp
        mt.uncommonType = nil
        mt.ptrToThis = nil

        mt.bucket = bucketOf(ktyp, etyp)
        if ktyp.size > maxKeySize {
                mt.keysize = uint8(ptrSize)
                mt.indirectkey = 1
        } else {
                mt.keysize = uint8(ktyp.size)
                mt.indirectkey = 0
        }
        if etyp.size > maxValSize {
                mt.valuesize = uint8(ptrSize)
                mt.indirectvalue = 1
        } else {
                mt.valuesize = uint8(etyp.size)
                mt.indirectvalue = 0
        }
        mt.bucketsize = uint16(mt.bucket.size)
        mt.reflexivekey = isReflexive(ktyp)
        mt.needkeyupdate = needKeyUpdate(ktyp)

        // Canonicalize before storing in lookupCache
        ti := toType(&mt.rtype)
        lookupCache.Store(ckey, ti.(*rtype))
        return ti
}

// FuncOf returns the function type with the given argument and result types.
// For example if k represents int and e represents string,
// FuncOf([]Type{k}, []Type{e}, false) represents func(int) string.
//
// The variadic argument controls whether the function is variadic. FuncOf
// panics if the in[len(in)-1] does not represent a slice and variadic is
// true.
func FuncOf(in, out []Type, variadic bool) Type {
        if variadic && (len(in) == 0 || in[len(in)-1].Kind() != Slice) {
                panic("reflect.FuncOf: last arg of variadic func must be slice")
        }

        // Make a func type.
        var ifunc interface{} = (func())(nil)
        prototype := *(**funcType)(unsafe.Pointer(&ifunc))
        ft := new(funcType)
        *ft = *prototype

        // Build a hash and minimally populate ft.
        var hash uint32
        var fin, fout []*rtype
        shift := uint(1)
        for _, in := range in {
                t := in.(*rtype)
                fin = append(fin, t)
                hash += t.hash << shift
                shift++
        }
        shift = 2
        for _, out := range out {
                t := out.(*rtype)
                fout = append(fout, t)
                hash += t.hash << shift
                shift++
        }
        if variadic {
                hash++
        }
        hash <<= 4
        hash += 8
        ft.hash = hash
        ft.in = fin
        ft.out = fout
        ft.dotdotdot = variadic

        // Look in cache.
        if ts, ok := funcLookupCache.m.Load(hash); ok {
                for _, t := range ts.([]*rtype) {
                        if haveIdenticalUnderlyingType(&ft.rtype, t, true) {
                                return t
                        }
                }
        }

        // Not in cache, lock and retry.
        funcLookupCache.Lock()
        defer funcLookupCache.Unlock()
        if ts, ok := funcLookupCache.m.Load(hash); ok {
                for _, t := range ts.([]*rtype) {
                        if haveIdenticalUnderlyingType(&ft.rtype, t, true) {
                                return t
                        }
                }
        }

        addToCache := func(tt *rtype) Type {
                var rts []*rtype
                if rti, ok := funcLookupCache.m.Load(hash); ok {
                        rts = rti.([]*rtype)
                }
                funcLookupCache.m.Store(hash, append(rts, tt))
                return tt
        }

        str := funcStr(ft)

        // Populate the remaining fields of ft and store in cache.
        ft.string = &str
        ft.uncommonType = nil
        ft.ptrToThis = nil

        // Canonicalize before storing in funcLookupCache
        tc := toType(&ft.rtype)
        return addToCache(tc.(*rtype))
}

// funcStr builds a string representation of a funcType.
func funcStr(ft *funcType) string {
        repr := make([]byte, 0, 64)
        repr = append(repr, "func("...)
        for i, t := range ft.in {
                if i > 0 {
                        repr = append(repr, ", "...)
                }
                if ft.dotdotdot && i == len(ft.in)-1 {
                        repr = append(repr, "..."...)
                        repr = append(repr, *(*sliceType)(unsafe.Pointer(t)).elem.string...)
                } else {
                        repr = append(repr, *t.string...)
                }
        }
        repr = append(repr, ')')
        if l := len(ft.out); l == 1 {
                repr = append(repr, ' ')
        } else if l > 1 {
                repr = append(repr, " ("...)
        }
        for i, t := range ft.out {
                if i > 0 {
                        repr = append(repr, ", "...)
                }
                repr = append(repr, *t.string...)
        }
        if len(ft.out) > 1 {
                repr = append(repr, ')')
        }
        return string(repr)
}

// isReflexive reports whether the == operation on the type is reflexive.
// That is, x == x for all values x of type t.
func isReflexive(t *rtype) bool {
        switch t.Kind() {
        case Bool, Int, Int8, Int16, Int32, Int64, Uint, Uint8, Uint16, Uint32, Uint64, Uintptr, Chan, Ptr, String, UnsafePointer:
                return true
        case Float32, Float64, Complex64, Complex128, Interface:
                return false
        case Array:
                tt := (*arrayType)(unsafe.Pointer(t))
                return isReflexive(tt.elem)
        case Struct:
                tt := (*structType)(unsafe.Pointer(t))
                for _, f := range tt.fields {
                        if !isReflexive(f.typ) {
                                return false
                        }
                }
                return true
        default:
                // Func, Map, Slice, Invalid
                panic("isReflexive called on non-key type " + t.String())
        }
}

// needKeyUpdate reports whether map overwrites require the key to be copied.
func needKeyUpdate(t *rtype) bool {
        switch t.Kind() {
        case Bool, Int, Int8, Int16, Int32, Int64, Uint, Uint8, Uint16, Uint32, Uint64, Uintptr, Chan, Ptr, UnsafePointer:
                return false
        case Float32, Float64, Complex64, Complex128, Interface, String:
                // Float keys can be updated from +0 to -0.
                // String keys can be updated to use a smaller backing store.
                // Interfaces might have floats of strings in them.
                return true
        case Array:
                tt := (*arrayType)(unsafe.Pointer(t))
                return needKeyUpdate(tt.elem)
        case Struct:
                tt := (*structType)(unsafe.Pointer(t))
                for _, f := range tt.fields {
                        if needKeyUpdate(f.typ) {
                                return true
                        }
                }
                return false
        default:
                // Func, Map, Slice, Invalid
                panic("needKeyUpdate called on non-key type " + t.String())
        }
}

// Make sure these routines stay in sync with ../../runtime/hashmap.go!
// These types exist only for GC, so we only fill out GC relevant info.
// Currently, that's just size and the GC program. We also fill in string
// for possible debugging use.
const (
        bucketSize uintptr = 8
        maxKeySize uintptr = 128
        maxValSize uintptr = 128
)

func bucketOf(ktyp, etyp *rtype) *rtype {
        // See comment on hmap.overflow in ../runtime/hashmap.go.
        var kind uint8
        if ktyp.kind&kindNoPointers != 0 && etyp.kind&kindNoPointers != 0 &&
                ktyp.size <= maxKeySize && etyp.size <= maxValSize {
                kind = kindNoPointers
        }

        if ktyp.size > maxKeySize {
                ktyp = PtrTo(ktyp).(*rtype)
        }
        if etyp.size > maxValSize {
                etyp = PtrTo(etyp).(*rtype)
        }

        // Prepare GC data if any.
        // A bucket is at most bucketSize*(1+maxKeySize+maxValSize)+2*ptrSize bytes,
        // or 2072 bytes, or 259 pointer-size words, or 33 bytes of pointer bitmap.
        // Note that since the key and value are known to be <= 128 bytes,
        // they're guaranteed to have bitmaps instead of GC programs.
        var gcdata *byte
        var ptrdata uintptr

        size := bucketSize
        size = align(size, uintptr(ktyp.fieldAlign))
        size += bucketSize * ktyp.size
        size = align(size, uintptr(etyp.fieldAlign))
        size += bucketSize * etyp.size

        maxAlign := uintptr(ktyp.fieldAlign)
        if maxAlign < uintptr(etyp.fieldAlign) {
                maxAlign = uintptr(etyp.fieldAlign)
        }
        if maxAlign > ptrSize {
                size = align(size, maxAlign)
                size += align(ptrSize, maxAlign) - ptrSize
        } else if maxAlign < ptrSize {
                size = align(size, ptrSize)
                maxAlign = ptrSize
        }

        ovoff := size
        size += ptrSize

        if kind != kindNoPointers {
                nptr := size / ptrSize
                mask := make([]byte, (nptr+7)/8)
                psize := bucketSize
                psize = align(psize, uintptr(ktyp.fieldAlign))
                base := psize / ptrSize

                if ktyp.kind&kindNoPointers == 0 {
                        if ktyp.kind&kindGCProg != 0 {
                                panic("reflect: unexpected GC program in MapOf")
                        }
                        kmask := (*[16]byte)(unsafe.Pointer(ktyp.gcdata))
                        for i := uintptr(0); i < ktyp.ptrdata/ptrSize; i++ {
                                if (kmask[i/8]>>(i%8))&1 != 0 {
                                        for j := uintptr(0); j < bucketSize; j++ {
                                                word := base + j*ktyp.size/ptrSize + i
                                                mask[word/8] |= 1 << (word % 8)
                                        }
                                }
                        }
                }
                psize += bucketSize * ktyp.size
                psize = align(psize, uintptr(etyp.fieldAlign))
                base = psize / ptrSize

                if etyp.kind&kindNoPointers == 0 {
                        if etyp.kind&kindGCProg != 0 {
                                panic("reflect: unexpected GC program in MapOf")
                        }
                        emask := (*[16]byte)(unsafe.Pointer(etyp.gcdata))
                        for i := uintptr(0); i < etyp.ptrdata/ptrSize; i++ {
                                if (emask[i/8]>>(i%8))&1 != 0 {
                                        for j := uintptr(0); j < bucketSize; j++ {
                                                word := base + j*etyp.size/ptrSize + i
                                                mask[word/8] |= 1 << (word % 8)
                                        }
                                }
                        }
                }

                word := ovoff / ptrSize
                mask[word/8] |= 1 << (word % 8)
                gcdata = &mask[0]
                ptrdata = (word + 1) * ptrSize

                // overflow word must be last
                if ptrdata != size {
                        panic("reflect: bad layout computation in MapOf")
                }
        }

        b := &rtype{
                align:      int8(maxAlign),
                fieldAlign: uint8(maxAlign),
                size:       size,
                kind:       kind,
                ptrdata:    ptrdata,
                gcdata:     gcdata,
        }
        s := "bucket(" + *ktyp.string + "," + *etyp.string + ")"
        b.string = &s
        return b
}

// SliceOf returns the slice type with element type t.
// For example, if t represents int, SliceOf(t) represents []int.
func SliceOf(t Type) Type {
        typ := t.(*rtype)

        // Look in cache.
        ckey := cacheKey{Slice, typ, nil, 0}
        if slice, ok := lookupCache.Load(ckey); ok {
                return slice.(Type)
        }

        // Look in known types.
        s := "[]" + *typ.string

        // Make a slice type.
        var islice interface{} = ([]unsafe.Pointer)(nil)
        prototype := *(**sliceType)(unsafe.Pointer(&islice))
        slice := *prototype
        slice.string = &s

        // gccgo uses a different hash.
        // slice.hash = fnv1(typ.hash, '[')
        slice.hash = typ.hash + 1 + 13

        slice.elem = typ
        slice.uncommonType = nil
        slice.ptrToThis = nil

        // Canonicalize before storing in lookupCache
        ti := toType(&slice.rtype)
        lookupCache.Store(ckey, ti.(*rtype))
        return ti
}

// The structLookupCache caches StructOf lookups.
// StructOf does not share the common lookupCache since we need to pin
// the memory associated with *structTypeFixedN.
var structLookupCache struct {
        sync.Mutex // Guards stores (but not loads) on m.

        // m is a map[uint32][]Type keyed by the hash calculated in StructOf.
        // Elements in m are append-only and thus safe for concurrent reading.
        m sync.Map
}

// isLetter returns true if a given 'rune' is classified as a Letter.
func isLetter(ch rune) bool {
        return 'a' <= ch && ch <= 'z' || 'A' <= ch && ch <= 'Z' || ch == '_' || ch >= utf8.RuneSelf && unicode.IsLetter(ch)
}

// isValidFieldName checks if a string is a valid (struct) field name or not.
//
// According to the language spec, a field name should be an identifier.
//
// identifier = letter { letter | unicode_digit } .
// letter = unicode_letter | "_" .
func isValidFieldName(fieldName string) bool {
        for i, c := range fieldName {
                if i == 0 && !isLetter(c) {
                        return false
                }

                if !(isLetter(c) || unicode.IsDigit(c)) {
                        return false
                }
        }

        return len(fieldName) > 0
}

// StructOf returns the struct type containing fields.
// The Offset and Index fields are ignored and computed as they would be
// by the compiler.
//
// StructOf currently does not generate wrapper methods for embedded fields.
// This limitation may be lifted in a future version.
func StructOf(fields []StructField) Type {
        var (
                hash       = uint32(12)
                size       uintptr
                typalign   int8
                comparable = true
                hashable   = true

                fs   = make([]structField, len(fields))
                repr = make([]byte, 0, 64)
                fset = map[string]struct{}{} // fields' names

                hasPtr    = false // records whether at least one struct-field is a pointer
                hasGCProg = false // records whether a struct-field type has a GCProg
        )

        lastzero := uintptr(0)
        repr = append(repr, "struct {"...)
        for i, field := range fields {
                if field.Name == "" {
                        panic("reflect.StructOf: field " + strconv.Itoa(i) + " has no name")
                }
                if !isValidFieldName(field.Name) {
                        panic("reflect.StructOf: field " + strconv.Itoa(i) + " has invalid name")
                }
                if field.Type == nil {
                        panic("reflect.StructOf: field " + strconv.Itoa(i) + " has no type")
                }
                f := runtimeStructField(field)
                ft := f.typ
                if ft.kind&kindGCProg != 0 {
                        hasGCProg = true
                }
                if ft.pointers() {
                        hasPtr = true
                }

                // Update string and hash
                name := *f.name
                hash = (hash << 1) + ft.hash
                if !f.anon() {
                        repr = append(repr, (" " + name)...)
                } else {
                        // Embedded field
                        repr = append(repr, " ?"...)
                        if f.typ.Kind() == Ptr {
                                // Embedded ** and *interface{} are illegal
                                elem := ft.Elem()
                                if k := elem.Kind(); k == Ptr || k == Interface {
                                        panic("reflect.StructOf: illegal anonymous field type " + ft.String())
                                }
                                name = elem.String()
                        } else {
                                name = ft.String()
                        }

                        switch f.typ.Kind() {
                        case Interface:
                                ift := (*interfaceType)(unsafe.Pointer(ft))
                                if len(ift.methods) > 0 {
                                        panic("reflect.StructOf: embedded field with methods not implemented")
                                }
                        case Ptr:
                                ptr := (*ptrType)(unsafe.Pointer(ft))
                                if unt := ptr.uncommon(); unt != nil {
                                        if len(unt.methods) > 0 {
                                                panic("reflect.StructOf: embedded field with methods not implemented")
                                        }
                                }
                                if unt := ptr.elem.uncommon(); unt != nil {
                                        if len(unt.methods) > 0 {
                                                panic("reflect.StructOf: embedded field with methods not implemented")
                                        }
                                }
                        default:
                                if unt := ft.uncommon(); unt != nil {
                                        if len(unt.methods) > 0 {
                                                panic("reflect.StructOf: embedded field with methods not implemented")
                                        }
                                }
                        }
                }
                if _, dup := fset[name]; dup {
                        panic("reflect.StructOf: duplicate field " + name)
                }
                fset[name] = struct{}{}

                repr = append(repr, (" " + *ft.string)...)
                if f.tag != nil {
                        repr = append(repr, (" " + strconv.Quote(*f.tag))...)
                }
                if i < len(fields)-1 {
                        repr = append(repr, ';')
                }

                comparable = comparable && (ft.equalfn != nil)
                hashable = hashable && (ft.hashfn != nil)

                offset := align(size, uintptr(ft.fieldAlign))
                if int8(ft.fieldAlign) > typalign {
                        typalign = int8(ft.fieldAlign)
                }
                size = offset + ft.size
                f.offsetAnon |= offset << 1

                if ft.size == 0 {
                        lastzero = size
                }

                fs[i] = f
        }

        if size > 0 && lastzero == size {
                // This is a non-zero sized struct that ends in a
                // zero-sized field. We add an extra byte of padding,
                // to ensure that taking the address of the final
                // zero-sized field can't manufacture a pointer to the
                // next object in the heap. See issue 9401.
                size++
        }

        if len(fs) > 0 {
                repr = append(repr, ' ')
        }
        repr = append(repr, '}')
        hash <<= 2
        str := string(repr)

        // Round the size up to be a multiple of the alignment.
        size = align(size, uintptr(typalign))

        // Make the struct type.
        var istruct interface{} = struct{}{}
        prototype := *(**structType)(unsafe.Pointer(&istruct))
        typ := new(structType)
        *typ = *prototype
        typ.fields = fs

        // Look in cache.
        if ts, ok := structLookupCache.m.Load(hash); ok {
                for _, st := range ts.([]Type) {
                        t := st.common()
                        if haveIdenticalUnderlyingType(&typ.rtype, t, true) {
                                return t
                        }
                }
        }

        // Not in cache, lock and retry.
        structLookupCache.Lock()
        defer structLookupCache.Unlock()
        if ts, ok := structLookupCache.m.Load(hash); ok {
                for _, st := range ts.([]Type) {
                        t := st.common()
                        if haveIdenticalUnderlyingType(&typ.rtype, t, true) {
                                return t
                        }
                }
        }

        addToCache := func(t Type) Type {
                var ts []Type
                if ti, ok := structLookupCache.m.Load(hash); ok {
                        ts = ti.([]Type)
                }
                structLookupCache.m.Store(hash, append(ts, t))
                return t
        }

        typ.string = &str
        typ.hash = hash
        typ.size = size
        typ.align = typalign
        typ.fieldAlign = uint8(typalign)
        if !hasPtr {
                typ.kind |= kindNoPointers
        } else {
                typ.kind &^= kindNoPointers
        }

        if hasGCProg {
                lastPtrField := 0
                for i, ft := range fs {
                        if ft.typ.pointers() {
                                lastPtrField = i
                        }
                }
                prog := []byte{0, 0, 0, 0} // will be length of prog
                for i, ft := range fs {
                        if i > lastPtrField {
                                // gcprog should not include anything for any field after
                                // the last field that contains pointer data
                                break
                        }
                        // FIXME(sbinet) handle padding, fields smaller than a word
                        elemGC := (*[1 << 30]byte)(unsafe.Pointer(ft.typ.gcdata))[:]
                        elemPtrs := ft.typ.ptrdata / ptrSize
                        switch {
                        case ft.typ.kind&kindGCProg == 0 && ft.typ.ptrdata != 0:
                                // Element is small with pointer mask; use as literal bits.
                                mask := elemGC
                                // Emit 120-bit chunks of full bytes (max is 127 but we avoid using partial bytes).
                                var n uintptr
                                for n := elemPtrs; n > 120; n -= 120 {
                                        prog = append(prog, 120)
                                        prog = append(prog, mask[:15]...)
                                        mask = mask[15:]
                                }
                                prog = append(prog, byte(n))
                                prog = append(prog, mask[:(n+7)/8]...)
                        case ft.typ.kind&kindGCProg != 0:
                                // Element has GC program; emit one element.
                                elemProg := elemGC[4 : 4+*(*uint32)(unsafe.Pointer(&elemGC[0]))-1]
                                prog = append(prog, elemProg...)
                        }
                        // Pad from ptrdata to size.
                        elemWords := ft.typ.size / ptrSize
                        if elemPtrs < elemWords {
                                // Emit literal 0 bit, then repeat as needed.
                                prog = append(prog, 0x01, 0x00)
                                if elemPtrs+1 < elemWords {
                                        prog = append(prog, 0x81)
                                        prog = appendVarint(prog, elemWords-elemPtrs-1)
                                }
                        }
                }
                *(*uint32)(unsafe.Pointer(&prog[0])) = uint32(len(prog) - 4)
                typ.kind |= kindGCProg
                typ.gcdata = &prog[0]
        } else {
                typ.kind &^= kindGCProg
                bv := new(bitVector)
                addTypeBits(bv, 0, typ.common())
                if len(bv.data) > 0 {
                        typ.gcdata = &bv.data[0]
                }
        }
        typ.ptrdata = typeptrdata(typ.common())

        if hashable {
                typ.hashfn = func(p unsafe.Pointer, seed uintptr) uintptr {
                        o := seed
                        for _, ft := range typ.fields {
                                pi := add(p, ft.offset(), "&x.field safe")
                                o = ft.typ.hashfn(pi, o)
                        }
                        return o
                }
        } else {
                typ.hashfn = nil
        }

        if comparable {
                typ.equalfn = func(p, q unsafe.Pointer) bool {
                        for _, ft := range typ.fields {
                                pi := add(p, ft.offset(), "&x.field safe")
                                qi := add(q, ft.offset(), "&x.field safe")
                                if !ft.typ.equalfn(pi, qi) {
                                        return false
                                }
                        }
                        return true
                }
        } else {
                typ.equalfn = nil
        }

        typ.kind &^= kindDirectIface
        typ.uncommonType = nil
        typ.ptrToThis = nil

        // Canonicalize before storing in structLookupCache
        ti := toType(&typ.rtype)
        return addToCache(ti.(*rtype))
}

func runtimeStructField(field StructField) structField {
        if field.PkgPath != "" {
                panic("reflect.StructOf: StructOf does not allow unexported fields")
        }

        // Best-effort check for misuse.
        // Since PkgPath is empty, not much harm done if Unicode lowercase slips through.
        c := field.Name[0]
        if 'a' <= c && c <= 'z' || c == '_' {
                panic("reflect.StructOf: field \"" + field.Name + "\" is unexported but missing PkgPath")
        }

        offsetAnon := uintptr(0)
        if field.Anonymous {
                offsetAnon |= 1
        }

        s := field.Name
        name := &s

        var tag *string
        if field.Tag != "" {
                st := string(field.Tag)
                tag = &st
        }

        return structField{
                name:       name,
                pkgPath:    nil,
                typ:        field.Type.common(),
                tag:        tag,
                offsetAnon: offsetAnon,
        }
}

// typeptrdata returns the length in bytes of the prefix of t
// containing pointer data. Anything after this offset is scalar data.
// keep in sync with ../cmd/compile/internal/gc/reflect.go
func typeptrdata(t *rtype) uintptr {
        if !t.pointers() {
                return 0
        }
        switch t.Kind() {
        case Struct:
                st := (*structType)(unsafe.Pointer(t))
                // find the last field that has pointers.
                field := 0
                for i := range st.fields {
                        ft := st.fields[i].typ
                        if ft.pointers() {
                                field = i
                        }
                }
                f := st.fields[field]
                return f.offset() + f.typ.ptrdata

        default:
                panic("reflect.typeptrdata: unexpected type, " + t.String())
        }
}

// See cmd/compile/internal/gc/reflect.go for derivation of constant.
const maxPtrmaskBytes = 2048

// ArrayOf returns the array type with the given count and element type.
// For example, if t represents int, ArrayOf(5, t) represents [5]int.
//
// If the resulting type would be larger than the available address space,
// ArrayOf panics.
func ArrayOf(count int, elem Type) Type {
        typ := elem.(*rtype)

        // Look in cache.
        ckey := cacheKey{Array, typ, nil, uintptr(count)}
        if array, ok := lookupCache.Load(ckey); ok {
                return array.(Type)
        }

        // Look in known types.
        s := "[" + strconv.Itoa(count) + "]" + *typ.string

        // Make an array type.
        var iarray interface{} = [1]unsafe.Pointer{}
        prototype := *(**arrayType)(unsafe.Pointer(&iarray))
        array := *prototype
        array.string = &s

        // gccgo uses a different hash.
        // array.hash = fnv1(typ.hash, '[')
        // for n := uint32(count); n > 0; n >>= 8 {
        //      array.hash = fnv1(array.hash, byte(n))
        // }
        // array.hash = fnv1(array.hash, ']')
        array.hash = typ.hash + 1 + 13

        array.elem = typ
        array.ptrToThis = nil
        if typ.size > 0 {
                max := ^uintptr(0) / typ.size
                if uintptr(count) > max {
                        panic("reflect.ArrayOf: array size would exceed virtual address space")
                }
        }
        array.size = typ.size * uintptr(count)
        if count > 0 && typ.ptrdata != 0 {
                array.ptrdata = typ.size*uintptr(count-1) + typ.ptrdata
        }
        array.align = typ.align
        array.fieldAlign = typ.fieldAlign
        array.uncommonType = nil
        array.len = uintptr(count)
        array.slice = SliceOf(elem).(*rtype)

        array.kind &^= kindNoPointers
        switch {
        case typ.kind&kindNoPointers != 0 || array.size == 0:
                // No pointers.
                array.kind |= kindNoPointers
                array.gcdata = nil
                array.ptrdata = 0

        case count == 1:
                // In memory, 1-element array looks just like the element.
                array.kind |= typ.kind & kindGCProg
                array.gcdata = typ.gcdata
                array.ptrdata = typ.ptrdata

        case typ.kind&kindGCProg == 0 && array.size <= maxPtrmaskBytes*8*ptrSize:
                // Element is small with pointer mask; array is still small.
                // Create direct pointer mask by turning each 1 bit in elem
                // into count 1 bits in larger mask.
                mask := make([]byte, (array.ptrdata/ptrSize+7)/8)
                elemMask := (*[1 << 30]byte)(unsafe.Pointer(typ.gcdata))[:]
                elemWords := typ.size / ptrSize
                for j := uintptr(0); j < typ.ptrdata/ptrSize; j++ {
                        if (elemMask[j/8]>>(j%8))&1 != 0 {
                                for i := uintptr(0); i < array.len; i++ {
                                        k := i*elemWords + j
                                        mask[k/8] |= 1 << (k % 8)
                                }
                        }
                }
                array.gcdata = &mask[0]

        default:
                // Create program that emits one element
                // and then repeats to make the array.
                prog := []byte{0, 0, 0, 0} // will be length of prog
                elemGC := (*[1 << 30]byte)(unsafe.Pointer(typ.gcdata))[:]
                elemPtrs := typ.ptrdata / ptrSize
                if typ.kind&kindGCProg == 0 {
                        // Element is small with pointer mask; use as literal bits.
                        mask := elemGC
                        // Emit 120-bit chunks of full bytes (max is 127 but we avoid using partial bytes).
                        var n uintptr
                        for n = elemPtrs; n > 120; n -= 120 {
                                prog = append(prog, 120)
                                prog = append(prog, mask[:15]...)
                                mask = mask[15:]
                        }
                        prog = append(prog, byte(n))
                        prog = append(prog, mask[:(n+7)/8]...)
                } else {
                        // Element has GC program; emit one element.
                        elemProg := elemGC[4 : 4+*(*uint32)(unsafe.Pointer(&elemGC[0]))-1]
                        prog = append(prog, elemProg...)
                }
                // Pad from ptrdata to size.
                elemWords := typ.size / ptrSize
                if elemPtrs < elemWords {
                        // Emit literal 0 bit, then repeat as needed.
                        prog = append(prog, 0x01, 0x00)
                        if elemPtrs+1 < elemWords {
                                prog = append(prog, 0x81)
                                prog = appendVarint(prog, elemWords-elemPtrs-1)
                        }
                }
                // Repeat count-1 times.
                if elemWords < 0x80 {
                        prog = append(prog, byte(elemWords|0x80))
                } else {
                        prog = append(prog, 0x80)
                        prog = appendVarint(prog, elemWords)
                }
                prog = appendVarint(prog, uintptr(count)-1)
                prog = append(prog, 0)
                *(*uint32)(unsafe.Pointer(&prog[0])) = uint32(len(prog) - 4)
                array.kind |= kindGCProg
                array.gcdata = &prog[0]
                array.ptrdata = array.size // overestimate but ok; must match program
        }

        array.kind &^= kindDirectIface

        esize := typ.size

        if typ.equalfn == nil {
                array.equalfn = nil
        } else {
                eequal := typ.equalfn
                array.equalfn = func(p, q unsafe.Pointer) bool {
                        for i := 0; i < count; i++ {
                                pi := arrayAt(p, i, esize, "i < count")
                                qi := arrayAt(q, i, esize, "i < count")
                                if !eequal(pi, qi) {
                                        return false
                                }
                        }
                        return true
                }
        }

        if typ.hashfn == nil {
                array.hashfn = nil
        } else {
                ehash := typ.hashfn
                array.hashfn = func(ptr unsafe.Pointer, seed uintptr) uintptr {
                        o := seed
                        for i := 0; i < count; i++ {
                                o = ehash(arrayAt(ptr, i, esize, "i < count"), o)
                        }
                        return o
                }
        }

        // Canonicalize before storing in lookupCache
        ti := toType(&array.rtype)
        lookupCache.Store(ckey, ti.(*rtype))
        return ti
}

func appendVarint(x []byte, v uintptr) []byte {
        for ; v >= 0x80; v >>= 7 {
                x = append(x, byte(v|0x80))
        }
        x = append(x, byte(v))
        return x
}

// toType converts from a *rtype to a Type that can be returned
// to the client of package reflect. In gc, the only concern is that
// a nil *rtype must be replaced by a nil Type, but in gccgo this
// function takes care of ensuring that multiple *rtype for the same
// type are coalesced into a single Type.
var canonicalType = make(map[string]Type)

var canonicalTypeLock sync.RWMutex

func canonicalize(t Type) Type {
        if t == nil {
                return nil
        }
        s := t.rawString()
        canonicalTypeLock.RLock()
        if r, ok := canonicalType[s]; ok {
                canonicalTypeLock.RUnlock()
                return r
        }
        canonicalTypeLock.RUnlock()
        canonicalTypeLock.Lock()
        if r, ok := canonicalType[s]; ok {
                canonicalTypeLock.Unlock()
                return r
        }
        canonicalType[s] = t
        canonicalTypeLock.Unlock()
        return t
}

func toType(p *rtype) Type {
        if p == nil {
                return nil
        }
        return canonicalize(p)
}

// ifaceIndir reports whether t is stored indirectly in an interface value.
func ifaceIndir(t *rtype) bool {
        return t.kind&kindDirectIface == 0
}

// Layout matches runtime.gobitvector (well enough).
type bitVector struct {
        n    uint32 // number of bits
        data []byte
}

// append a bit to the bitmap.
func (bv *bitVector) append(bit uint8) {
        if bv.n%8 == 0 {
                bv.data = append(bv.data, 0)
        }
        bv.data[bv.n/8] |= bit << (bv.n % 8)
        bv.n++
}

func addTypeBits(bv *bitVector, offset uintptr, t *rtype) {
        if t.kind&kindNoPointers != 0 {
                return
        }

        switch Kind(t.kind & kindMask) {
        case Chan, Func, Map, Ptr, Slice, String, UnsafePointer:
                // 1 pointer at start of representation
                for bv.n < uint32(offset/uintptr(ptrSize)) {
                        bv.append(0)
                }
                bv.append(1)

        case Interface:
                // 2 pointers
                for bv.n < uint32(offset/uintptr(ptrSize)) {
                        bv.append(0)
                }
                bv.append(1)
                bv.append(1)

        case Array:
                // repeat inner type
                tt := (*arrayType)(unsafe.Pointer(t))
                for i := 0; i < int(tt.len); i++ {
                        addTypeBits(bv, offset+uintptr(i)*tt.elem.size, tt.elem)
                }

        case Struct:
                // apply fields
                tt := (*structType)(unsafe.Pointer(t))
                for i := range tt.fields {
                        f := &tt.fields[i]
                        addTypeBits(bv, offset+f.offset(), f.typ)
                }
        }
}