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vector.go
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vector.go
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// Package vector implements persistent vector.
//
// This is a Go clone of Clojure's PersistentVector type
// (https://github.com/clojure/clojure/blob/master/src/jvm/clojure/lang/PersistentVector.java).
// For an introduction to the internals, see
// https://hypirion.com/musings/understanding-persistent-vector-pt-1.
package vector
import (
"bytes"
"encoding/json"
"fmt"
)
const (
chunkBits = 5
nodeSize = 1 << chunkBits
tailMaxLen = nodeSize
chunkMask = nodeSize - 1
)
// Vector is a persistent sequential container for arbitrary values. It supports
// O(1) lookup by index, modification by index, and insertion and removal
// operations at the end. Being a persistent variant of the data structure, it
// is immutable, and provides O(1) operations to create modified versions of the
// vector that shares the underlying data structure, making it suitable for
// concurrent access. The empty value is a valid empty vector.
type Vector interface {
json.Marshaler
// Len returns the length of the vector.
Len() int
// Index returns the i-th element of the vector, if it exists. The second
// return value indicates whether the element exists.
Index(i int) (any, bool)
// Assoc returns an almost identical Vector, with the i-th element
// replaced. If the index is smaller than 0 or greater than the length of
// the vector, it returns nil. If the index is equal to the size of the
// vector, it is equivalent to Conj.
Assoc(i int, val any) Vector
// Conj returns an almost identical Vector, with an additional element
// appended to the end.
Conj(val any) Vector
// Pop returns an almost identical Vector, with the last element removed. It
// returns nil if the vector is already empty.
Pop() Vector
// SubVector returns a subvector containing the elements from i up to but
// not including j.
SubVector(i, j int) Vector
// Iterator returns an iterator over the vector.
Iterator() Iterator
}
// Iterator is an iterator over vector elements. It can be used like this:
//
// for it := v.Iterator(); it.HasElem(); it.Next() {
// elem := it.Elem()
// // do something with elem...
// }
type Iterator interface {
// Elem returns the element at the current position.
Elem() any
// HasElem returns whether the iterator is pointing to an element.
HasElem() bool
// Next moves the iterator to the next position.
Next()
}
type vector struct {
count int
// height of the tree structure, defined to be 0 when root is a leaf.
height uint
root node
tail []any
}
// Empty is an empty Vector.
var Empty Vector = &vector{}
// node is a node in the vector tree. It is always of the size nodeSize.
type node *[nodeSize]any
func newNode() node {
return node(&[nodeSize]any{})
}
func clone(n node) node {
a := *n
return node(&a)
}
func nodeFromSlice(s []any) node {
var n [nodeSize]any
copy(n[:], s)
return &n
}
// Count returns the number of elements in a Vector.
func (v *vector) Len() int {
return v.count
}
// treeSize returns the number of elements stored in the tree (as opposed to the
// tail).
func (v *vector) treeSize() int {
if v.count < tailMaxLen {
return 0
}
return ((v.count - 1) >> chunkBits) << chunkBits
}
func (v *vector) Index(i int) (any, bool) {
if i < 0 || i >= v.count {
return nil, false
}
// The following is very similar to sliceFor, but is implemented separately
// to avoid unnecessary copying.
if i >= v.treeSize() {
return v.tail[i&chunkMask], true
}
n := v.root
for shift := v.height * chunkBits; shift > 0; shift -= chunkBits {
n = n[(i>>shift)&chunkMask].(node)
}
return n[i&chunkMask], true
}
// sliceFor returns the slice where the i-th element is stored. The index must
// be in bound.
func (v *vector) sliceFor(i int) []any {
if i >= v.treeSize() {
return v.tail
}
n := v.root
for shift := v.height * chunkBits; shift > 0; shift -= chunkBits {
n = n[(i>>shift)&chunkMask].(node)
}
return n[:]
}
func (v *vector) Assoc(i int, val any) Vector {
if i < 0 || i > v.count {
return nil
} else if i == v.count {
return v.Conj(val)
}
if i >= v.treeSize() {
newTail := append([]any(nil), v.tail...)
newTail[i&chunkMask] = val
return &vector{v.count, v.height, v.root, newTail}
}
return &vector{v.count, v.height, doAssoc(v.height, v.root, i, val), v.tail}
}
// doAssoc returns an almost identical tree, with the i-th element replaced by
// val.
func doAssoc(height uint, n node, i int, val any) node {
m := clone(n)
if height == 0 {
m[i&chunkMask] = val
} else {
sub := (i >> (height * chunkBits)) & chunkMask
m[sub] = doAssoc(height-1, m[sub].(node), i, val)
}
return m
}
func (v *vector) Conj(val any) Vector {
// Room in tail?
if v.count-v.treeSize() < tailMaxLen {
newTail := make([]any, len(v.tail)+1)
copy(newTail, v.tail)
newTail[len(v.tail)] = val
return &vector{v.count + 1, v.height, v.root, newTail}
}
// Full tail; push into tree.
tailNode := nodeFromSlice(v.tail)
newHeight := v.height
var newRoot node
// Overflow root?
if (v.count >> chunkBits) > (1 << (v.height * chunkBits)) {
newRoot = newNode()
newRoot[0] = v.root
newRoot[1] = newPath(v.height, tailNode)
newHeight++
} else {
newRoot = v.pushTail(v.height, v.root, tailNode)
}
return &vector{v.count + 1, newHeight, newRoot, []any{val}}
}
// pushTail returns a tree with tail appended.
func (v *vector) pushTail(height uint, n node, tail node) node {
if height == 0 {
return tail
}
idx := ((v.count - 1) >> (height * chunkBits)) & chunkMask
m := clone(n)
child := n[idx]
if child == nil {
m[idx] = newPath(height-1, tail)
} else {
m[idx] = v.pushTail(height-1, child.(node), tail)
}
return m
}
// newPath creates a left-branching tree of specified height and leaf.
func newPath(height uint, leaf node) node {
if height == 0 {
return leaf
}
ret := newNode()
ret[0] = newPath(height-1, leaf)
return ret
}
func (v *vector) Pop() Vector {
switch v.count {
case 0:
return nil
case 1:
return Empty
}
if v.count-v.treeSize() > 1 {
newTail := make([]any, len(v.tail)-1)
copy(newTail, v.tail)
return &vector{v.count - 1, v.height, v.root, newTail}
}
newTail := v.sliceFor(v.count - 2)
newRoot := v.popTail(v.height, v.root)
newHeight := v.height
if v.height > 0 && newRoot[1] == nil {
newRoot = newRoot[0].(node)
newHeight--
}
return &vector{v.count - 1, newHeight, newRoot, newTail}
}
// popTail returns a new tree with the last leaf removed.
func (v *vector) popTail(level uint, n node) node {
idx := ((v.count - 2) >> (level * chunkBits)) & chunkMask
if level > 1 {
newChild := v.popTail(level-1, n[idx].(node))
if newChild == nil && idx == 0 {
return nil
}
m := clone(n)
if newChild == nil {
// This is needed since `m[idx] = newChild` would store an
// interface{} with a non-nil type part, which is non-nil
m[idx] = nil
} else {
m[idx] = newChild
}
return m
} else if idx == 0 {
return nil
} else {
m := clone(n)
m[idx] = nil
return m
}
}
func (v *vector) SubVector(begin, end int) Vector {
if begin < 0 || begin > end || end > v.count {
return nil
}
return &subVector{v, begin, end}
}
func (v *vector) Iterator() Iterator {
return newIterator(v)
}
func (v *vector) MarshalJSON() ([]byte, error) {
return marshalJSON(v.Iterator())
}
type subVector struct {
v *vector
begin int
end int
}
func (s *subVector) Len() int {
return s.end - s.begin
}
func (s *subVector) Index(i int) (any, bool) {
if i < 0 || s.begin+i >= s.end {
return nil, false
}
return s.v.Index(s.begin + i)
}
func (s *subVector) Assoc(i int, val any) Vector {
if i < 0 || s.begin+i > s.end {
return nil
} else if s.begin+i == s.end {
return s.Conj(val)
}
return s.v.Assoc(s.begin+i, val).SubVector(s.begin, s.end)
}
func (s *subVector) Conj(val any) Vector {
return s.v.Assoc(s.end, val).SubVector(s.begin, s.end+1)
}
func (s *subVector) Pop() Vector {
switch s.Len() {
case 0:
return nil
case 1:
return Empty
default:
return s.v.SubVector(s.begin, s.end-1)
}
}
func (s *subVector) SubVector(i, j int) Vector {
return s.v.SubVector(s.begin+i, s.begin+j)
}
func (s *subVector) Iterator() Iterator {
return newIteratorWithRange(s.v, s.begin, s.end)
}
func (s *subVector) MarshalJSON() ([]byte, error) {
return marshalJSON(s.Iterator())
}
type iterator struct {
v *vector
treeSize int
index int
end int
path []pathEntry
}
type pathEntry struct {
node node
index int
}
func (e pathEntry) current() any {
return e.node[e.index]
}
func newIterator(v *vector) *iterator {
return newIteratorWithRange(v, 0, v.Len())
}
func newIteratorWithRange(v *vector, begin, end int) *iterator {
it := &iterator{v, v.treeSize(), begin, end, nil}
if it.index >= it.treeSize {
return it
}
// Find the node for begin, remembering all nodes along the path.
n := v.root
for shift := v.height * chunkBits; shift > 0; shift -= chunkBits {
idx := (begin >> shift) & chunkMask
it.path = append(it.path, pathEntry{n, idx})
n = n[idx].(node)
}
it.path = append(it.path, pathEntry{n, begin & chunkMask})
return it
}
func (it *iterator) Elem() any {
if it.index >= it.treeSize {
return it.v.tail[it.index-it.treeSize]
}
return it.path[len(it.path)-1].current()
}
func (it *iterator) HasElem() bool {
return it.index < it.end
}
func (it *iterator) Next() {
if it.index+1 >= it.treeSize {
// Next element is in tail. Just increment the index.
it.index++
return
}
// Find the deepest level that can be advanced.
var i int
for i = len(it.path) - 1; i >= 0; i-- {
e := it.path[i]
if e.index+1 < len(e.node) {
break
}
}
if i == -1 {
panic("cannot advance; vector iterator bug")
}
// Advance on this node, and re-populate all deeper levels.
it.path[i].index++
for i++; i < len(it.path); i++ {
it.path[i] = pathEntry{it.path[i-1].current().(node), 0}
}
it.index++
}
type marshalError struct {
index int
cause error
}
func (err *marshalError) Error() string {
return fmt.Sprintf("element %d: %s", err.index, err.cause)
}
func marshalJSON(it Iterator) ([]byte, error) {
var buf bytes.Buffer
buf.WriteByte('[')
index := 0
for ; it.HasElem(); it.Next() {
if index > 0 {
buf.WriteByte(',')
}
elemBytes, err := json.Marshal(it.Elem())
if err != nil {
return nil, &marshalError{index, err}
}
buf.Write(elemBytes)
index++
}
buf.WriteByte(']')
return buf.Bytes(), nil
}