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btree.go
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btree.go
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// Btree page types.
// 'Table' are data tables. InteriorTable pages have no data, and
// points to other pages. InteriorLeaf pages have data and don't point to other
// pages.
// 'Index' tables have index keys. Both the internal and leaf pages contain
// keys.
package db
import (
"encoding/binary"
"errors"
"sort"
)
const (
// "Define the depth of a leaf b-tree to be 1 and the depth of any interior
// b-tree to be one more than the maximum depth of any of its children. In
// a well-formed database, all children of an interior b-tree have the same
// depth."
// and:
// "A "pointer" in an interior b-tree page is just the 31-bit integer page
// number of the child page."
// Ergo, in a well-formed database where every interal page only links to a
// single left branch (highly unlikely), we can't ever go deeper than 31
// levels.
maxRecursion = 31
)
// Iterate callback. Gets rowid and (possibly truncated) payload. Return true when done
type iterCB func(rowid int64, pl cellPayload) (bool, error)
type tableBtree interface {
// Iter goes over every record
Iter(int, *Database, iterCB) (bool, error)
// Scan starting from a rowid
IterMin(int, *Database, int64, iterCB) (bool, error)
// Count counts the number of records. For debugging.
Count(*Database) (int, error)
}
// indexIterCB gets the Record. It returns true when the iter should be
// stopped.
type indexIterCB func(row Record) (bool, error)
type indexBtree interface {
// Iter goes over every record
Iter(int, *Database, indexIterCB) (bool, error)
// Scan starting from a key
IterMin(int, *Database, Key, indexIterCB) (bool, error)
// Count counts the number of records. For debugging.
Count(*Database) (int, error)
}
type tableLeafCell struct {
left int64 // rowID
payload cellPayload
}
type tableLeaf struct {
cells []tableLeafCell
}
type tableInteriorCell struct {
left int
key int64
}
type tableInterior struct {
cells []tableInteriorCell
rightmost int
}
type indexLeaf struct {
cells []cellPayload
}
type indexInteriorCell struct {
left int // pageID
payload cellPayload
}
type indexInterior struct {
cells []indexInteriorCell
rightmost int
}
var (
_ tableBtree = &tableLeaf{}
_ tableBtree = &tableInterior{}
_ indexBtree = &indexLeaf{}
_ indexBtree = &indexInterior{}
)
func newBtree(b []byte, isFileHeader bool, pageSize int) (interface{}, error) {
hb := b
if isFileHeader {
hb = b[headerSize:]
}
cells := int(binary.BigEndian.Uint16(hb[3:5]))
switch typ := int(hb[0]); typ {
case 0x0d:
return newLeafTableBtree(cells, hb[8:], b, pageSize)
case 0x05:
rightmostPointer := int(binary.BigEndian.Uint32(hb[8:12]))
return newInteriorTableBtree(cells, hb[12:], b, rightmostPointer)
case 0x0a:
return newLeafIndex(cells, b[8:], b, pageSize)
case 0x02:
rightmostPointer := int(binary.BigEndian.Uint32(b[8:12]))
return newInteriorIndex(cells, b[12:], b, rightmostPointer, pageSize)
default:
return nil, errors.New("unsupported page type")
}
}
func newLeafTableBtree(
count int,
pointers []byte,
content []byte,
pageSize int,
) (*tableLeaf, error) {
cells, err := parseCellpointers(count, pointers, len(content))
if err != nil {
return nil, err
}
leafs := make([]tableLeafCell, len(cells))
for i, start := range cells {
leafs[i], err = parseTableLeaf(content[start:], pageSize)
if err != nil {
return nil, err
}
}
return &tableLeaf{
cells: leafs,
}, nil
}
func (l *tableLeaf) Count(*Database) (int, error) {
return len(l.cells), nil
}
func (l *tableLeaf) Iter(_ int, _ *Database, cb iterCB) (bool, error) {
for _, c := range l.cells {
if done, err := cb(c.left, c.payload); done || err != nil {
return done, err
}
}
return false, nil
}
func (l *tableLeaf) IterMin(_ int, db *Database, rowid int64, cb iterCB) (bool, error) {
n := sort.Search(len(l.cells), func(n int) bool {
return l.cells[n].left >= rowid
})
for _, c := range l.cells[n:] {
return cb(c.left, c.payload)
}
return false, nil
}
func newInteriorTableBtree(
count int,
pointers []byte,
content []byte,
rightmost int,
) (*tableInterior, error) {
cells, err := parseCellpointers(count, pointers, len(content))
if err != nil {
return nil, err
}
cs := make([]tableInteriorCell, len(cells))
for i, start := range cells {
cs[i], err = parseTableInterior(content[start:])
if err != nil {
return nil, err
}
}
return &tableInterior{
cells: cs,
rightmost: rightmost,
}, nil
}
type interiorIterCB func(page int) (bool, error)
func (l *tableInterior) cellIter(db *Database, cb interiorIterCB) (bool, error) {
for _, c := range l.cells {
if done, err := cb(c.left); done || err != nil {
return done, err
}
}
return cb(l.rightmost)
}
func (l *tableInterior) cellIterMin(db *Database, rowid int64, cb interiorIterCB) (bool, error) {
n := sort.Search(len(l.cells), func(n int) bool {
return l.cells[n].key >= rowid
})
for _, c := range l.cells[n:] {
if done, err := cb(c.left); done || err != nil {
return done, err
}
}
return cb(l.rightmost)
}
func (l *tableInterior) Count(db *Database) (int, error) {
total := 0
l.cellIter(db, func(p int) (bool, error) {
page, err := db.openTable(p)
if err != nil {
return false, err
}
n, err := page.Count(db)
if err != nil {
return false, err
}
total += n
return false, nil
})
return total, nil
}
func (l *tableInterior) Iter(r int, db *Database, cb iterCB) (bool, error) {
if r == 0 {
return false, ErrRecursion
}
return l.cellIter(db, func(p int) (bool, error) {
page, err := db.openTable(p)
if err != nil {
return false, err
}
if done, err := page.Iter(r-1, db, cb); done || err != nil {
return done, err
}
return false, nil
})
}
func (l *tableInterior) IterMin(r int, db *Database, rowid int64, cb iterCB) (bool, error) {
if r == 0 {
return false, ErrRecursion
}
return l.cellIterMin(db, rowid, func(pageID int) (bool, error) {
page, err := db.openTable(pageID)
if err != nil {
return false, err
}
return page.IterMin(r-1, db, rowid, cb)
})
}
func newLeafIndex(
count int,
pointers []byte,
content []byte,
pageSize int,
) (*indexLeaf, error) {
cells, err := parseCellpointers(count, pointers, len(content))
if err != nil {
return nil, err
}
cs := make([]cellPayload, len(cells))
for i, start := range cells {
cs[i], err = parseIndexLeaf(content[start:], pageSize)
if err != nil {
return nil, err
}
}
return &indexLeaf{
cells: cs,
}, nil
}
func (l *indexLeaf) Iter(_ int, db *Database, cb indexIterCB) (bool, error) {
for _, pl := range l.cells {
full, err := addOverflow(db, pl)
if err != nil {
return false, err
}
rec, err := parseRecord(full)
if err != nil {
return false, err
}
if done, err := cb(rec); done || err != nil {
return done, err
}
}
return false, nil
}
func (l *indexLeaf) IterMin(_ int, db *Database, key Key, cb indexIterCB) (bool, error) {
var searchErr error
n := sort.Search(len(l.cells), func(n int) bool {
r, err := indexBinSearch(db, l.cells[n], key)
if err != nil {
searchErr = err
}
return r
})
if searchErr != nil {
return false, searchErr
}
for _, pl := range l.cells[n:] {
full, err := addOverflow(db, pl)
if err != nil {
return false, err
}
rec, err := parseRecord(full)
if err != nil {
return false, err
}
if done, err := cb(rec); done || err != nil {
return done, err
}
}
return false, nil
}
func (l *indexLeaf) Count(*Database) (int, error) {
return len(l.cells), nil
}
func newInteriorIndex(
count int,
pointers []byte,
content []byte,
rightmost int,
pageSize int,
) (*indexInterior, error) {
cells, err := parseCellpointers(count, pointers, len(content))
if err != nil {
return nil, err
}
cs := make([]indexInteriorCell, len(cells))
for i, start := range cells {
cs[i], err = parseIndexInterior(content[start:], pageSize)
if err != nil {
return nil, err
}
}
return &indexInterior{
cells: cs,
rightmost: rightmost,
}, nil
}
func (l *indexInterior) Iter(r int, db *Database, cb indexIterCB) (bool, error) {
if r == 0 {
return false, ErrRecursion
}
for _, c := range l.cells {
page, err := db.openIndex(c.left)
if err != nil {
return false, err
}
if done, err := page.Iter(r-1, db, cb); done || err != nil {
return done, err
}
// the btree node also has a record
full, err := addOverflow(db, c.payload)
if err != nil {
return false, err
}
rec, err := parseRecord(full)
if err != nil {
return false, err
}
if done, err := cb(rec); done || err != nil {
return done, err
}
}
page, err := db.openIndex(l.rightmost)
if err != nil {
return false, err
}
return page.Iter(r-1, db, cb)
}
func (l *indexInterior) IterMin(r int, db *Database, key Key, cb indexIterCB) (bool, error) {
if r == 0 {
return false, ErrRecursion
}
// binary search the page containing the range of the key
var searchErr error
n := sort.Search(len(l.cells), func(n int) bool {
r, err := indexBinSearch(db, l.cells[n].payload, key)
if err != nil {
searchErr = err
}
return r
})
if searchErr != nil {
return false, searchErr
}
useIter := false
for _, c := range l.cells[n:] {
page, err := db.openIndex(c.left)
if err != nil {
return false, err
}
if useIter {
if done, err := page.Iter(r-1, db, cb); done || err != nil {
return done, err
}
} else {
if done, err := page.IterMin(r-1, db, key, cb); done || err != nil {
return done, err
}
}
useIter = true // from now on we can simply scan
// the node has a record, too
full, err := addOverflow(db, c.payload)
if err != nil {
return false, err
}
rec, err := parseRecord(full)
if err != nil {
return false, err
}
if done, err := cb(rec); done || err != nil {
return done, err
}
}
page, err := db.openIndex(l.rightmost)
if err != nil {
return false, err
}
if useIter {
return page.Iter(r-1, db, cb)
} else {
return page.IterMin(r-1, db, key, cb)
}
}
func (l *indexInterior) Count(db *Database) (int, error) {
total := 0
for _, c := range l.cells {
page, err := db.openIndex(c.left)
if err != nil {
return 0, err
}
n, err := page.Count(db)
if err != nil {
return 0, err
}
total += n
total += 1 // the btree node has a record, too
}
page, err := db.openIndex(l.rightmost)
if err != nil {
return 0, err
}
n, err := page.Count(db)
return total + n, err
}
func calculateCellInPageBytes(l int64, pageSize int, maxInPagePayload int) int {
// Overflow calculation described in the file format spec. The
// variable names and magic constants are from the spec exactly.
u := int64(pageSize)
p := l
x := int64(maxInPagePayload)
m := ((u - 12) * 32 / 255) - 23
k := m + ((p - m) % (u - 4))
if p <= x {
return int(l)
} else if k <= x {
return int(k)
} else {
return int(m)
}
}
// shared code for parsing payload from cells
func parsePayload(l int64, c []byte, pageSize int, maxInPagePayload int) (cellPayload, error) {
overflow := 0
inPageBytes := calculateCellInPageBytes(l, pageSize, maxInPagePayload)
if l < 0 {
return cellPayload{}, ErrCorrupted
}
if int64(inPageBytes) == l {
return cellPayload{l, c, 0}, nil
}
if len(c) < inPageBytes+4 {
return cellPayload{}, ErrCorrupted
}
c, overflow = c[:inPageBytes], int(binary.BigEndian.Uint32(c[inPageBytes:inPageBytes+4]))
if overflow == 0 {
return cellPayload{}, ErrCorrupted
}
return cellPayload{l, c, overflow}, nil
}
func parseTableLeaf(c []byte, pageSize int) (tableLeafCell, error) {
l, n := readVarint(c)
if n < 0 {
return tableLeafCell{}, ErrCorrupted
}
c = c[n:]
rowid, n := readVarint(c)
if n < 0 {
return tableLeafCell{}, ErrCorrupted
}
pl, err := parsePayload(l, c[n:], pageSize, pageSize-35)
return tableLeafCell{
left: rowid,
payload: pl,
}, err
}
func parseTableInterior(c []byte) (tableInteriorCell, error) {
if len(c) < 4 {
return tableInteriorCell{}, ErrCorrupted
}
left := int(binary.BigEndian.Uint32(c[:4]))
key, n := readVarint(c[4:])
if n < 0 {
return tableInteriorCell{}, ErrCorrupted
}
return tableInteriorCell{
left: left,
key: key,
}, nil
}
func parseIndexLeaf(c []byte, pageSize int) (cellPayload, error) {
l, n := readVarint(c)
if n < 0 {
return cellPayload{}, ErrCorrupted
}
return parsePayload(l, c[n:], pageSize, ((pageSize-12)*64/255)-23)
}
func parseIndexInterior(c []byte, pageSize int) (indexInteriorCell, error) {
if len(c) < 4 {
return indexInteriorCell{}, ErrCorrupted
}
left := int(binary.BigEndian.Uint32(c[:4]))
c = c[4:]
l, n := readVarint(c)
if n < 0 {
return indexInteriorCell{}, ErrCorrupted
}
pl, err := parsePayload(l, c[n:], pageSize, ((pageSize-12)*64/255)-23)
return indexInteriorCell{
left: int(left),
payload: pl,
}, err
}
// Parse the list of pointers to cells into byte offsets for each cell
// This format is used in all four page types.
// N is the nr of cells, pointers point to the start of the cells, until end of
// the page, maxLen is the length of the page (because cell pointers use page
// offsets).
func parseCellpointers(
n int,
pointers []byte,
maxLen int,
) ([]int, error) {
if len(pointers) < n*2 {
return nil, errors.New("invalid cell pointer array")
}
cs := make([]int, n)
// cell pointers go [p1, p2, p3], actual cell content can be in any order.
for i := range cs {
start := int(binary.BigEndian.Uint16(pointers[2*i : 2*i+2]))
if start > maxLen {
return nil, errors.New("invalid cell pointer")
}
cs[i] = start
}
return cs, nil
}
func indexBinSearch(db *Database, pl cellPayload, key Key) (bool, error) {
// It would be possible to not load the record by default but compare with
// what's available, and to only call addOverflow() when that data is
// needed.
full, err := addOverflow(db, pl)
if err != nil {
return true, err
}
rec, err := parseRecord(full)
if err != nil {
return true, err
}
return Search(key, rec), nil
}