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btree.go
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btree.go
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/*
* Copyright 2020 Dgraph Labs, Inc. and Contributors
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package z
import (
"fmt"
"math"
"os"
"reflect"
"strings"
"unsafe"
"github.com/etecs-ru/ristretto/z/simd"
)
var (
pageSize = os.Getpagesize()
maxKeys = (pageSize / 16) - 1
oneThird = int(float64(maxKeys) / 3)
)
const (
absoluteMax = uint64(math.MaxUint64 - 1)
minSize = 1 << 20
)
// Tree represents the structure for custom mmaped B+ tree.
// It supports keys in range [1, math.MaxUint64-1] and values [1, math.Uint64].
type Tree struct {
buffer *Buffer
data []byte
nextPage uint64
freePage uint64
stats TreeStats
}
func (t *Tree) initRootNode() {
// This is the root node.
t.newNode(0)
// This acts as the rightmost pointer (all the keys are <= this key).
t.Set(absoluteMax, 0)
}
// NewTree returns an in-memory B+ tree.
func NewTree(tag string) *Tree {
const defaultTag = "tree"
if tag == "" {
tag = defaultTag
}
t := &Tree{buffer: NewBuffer(minSize, tag)}
t.Reset()
return t
}
// NewTree returns a persistent on-disk B+ tree.
func NewTreePersistent(path string) (*Tree, error) {
t := &Tree{}
var err error
// Open the buffer from disk and set it to the maximum allocated size.
t.buffer, err = NewBufferPersistent(path, minSize)
if err != nil {
return nil, err
}
t.buffer.offset = uint64(len(t.buffer.buf))
t.data = t.buffer.Bytes()
// pageID can never be 0 if the tree has been initialized.
root := t.node(1)
isInitialized := root.pageID() != 0
if !isInitialized {
t.nextPage = 1
t.freePage = 0
t.initRootNode()
} else {
t.reinit()
}
return t, nil
}
// reinit sets the internal variables of a Tree, which are normally stored
// in-memory, but are lost when loading from disk.
func (t *Tree) reinit() {
// Calculate t.nextPage by finding the first node whose pageID is not set.
t.nextPage = 1
for int(t.nextPage)*pageSize < len(t.data) {
n := t.node(t.nextPage)
if n.pageID() == 0 {
break
}
t.nextPage++
}
maxPageId := t.nextPage - 1
// Calculate t.freePage by finding the page to which no other page points.
// This would be the head of the page linked list.
// tailPages[i] is true if pageId i+1 is not the head of the list.
tailPages := make([]bool, maxPageId)
// Mark all pages containing nodes as tail pages.
t.Iterate(func(n node) {
i := n.pageID() - 1
tailPages[i] = true
// If this is a leaf node, increment the stats.
if n.isLeaf() {
t.stats.NumLeafKeys += n.numKeys()
}
})
// pointedPages is a list of page IDs that the tail pages point to.
pointedPages := make([]uint64, 0)
for i, isTail := range tailPages {
if !isTail {
pageId := uint64(i) + 1
// Skip if nextPageId = 0, as that is equivalent to null page.
if nextPageId := t.node(pageId).uint64(0); nextPageId != 0 {
pointedPages = append(pointedPages, nextPageId)
}
t.stats.NumPagesFree++
}
}
// Mark all pages being pointed to as tail pages.
for _, pageId := range pointedPages {
i := pageId - 1
tailPages[i] = true
}
// There should only be one head page left.
for i, isTail := range tailPages {
if !isTail {
pageId := uint64(i) + 1
t.freePage = pageId
break
}
}
}
// Reset resets the tree and truncates it to maxSz.
func (t *Tree) Reset() {
// Tree relies on uninitialized data being zeroed out, so we need to Memclr
// the data before using it again.
Memclr(t.buffer.buf)
t.buffer.Reset()
t.buffer.AllocateOffset(minSize)
t.data = t.buffer.Bytes()
t.stats = TreeStats{}
t.nextPage = 1
t.freePage = 0
t.initRootNode()
}
// Close releases the memory used by the tree.
func (t *Tree) Close() error {
if t == nil {
return nil
}
return t.buffer.Release()
}
type TreeStats struct {
Allocated int // Derived.
Bytes int // Derived.
NumLeafKeys int // Calculated.
NumPages int // Derived.
NumPagesFree int // Calculated.
Occupancy float64 // Derived.
PageSize int // Derived.
}
// Stats returns stats about the tree.
func (t *Tree) Stats() TreeStats {
numPages := int(t.nextPage - 1)
out := TreeStats{
Bytes: numPages * pageSize,
Allocated: len(t.data),
NumLeafKeys: t.stats.NumLeafKeys,
NumPages: numPages,
NumPagesFree: t.stats.NumPagesFree,
PageSize: pageSize,
}
out.Occupancy = 100.0 * float64(out.NumLeafKeys) / float64(maxKeys*numPages)
return out
}
// BytesToUint64Slice converts a byte slice to a uint64 slice.
func BytesToUint64Slice(b []byte) []uint64 {
if len(b) == 0 {
return nil
}
var u64s []uint64
hdr := (*reflect.SliceHeader)(unsafe.Pointer(&u64s))
hdr.Len = len(b) / 8
hdr.Cap = hdr.Len
hdr.Data = uintptr(unsafe.Pointer(&b[0]))
return u64s
}
func (t *Tree) newNode(bit uint64) node {
var pageId uint64
if t.freePage > 0 {
pageId = t.freePage
t.stats.NumPagesFree--
} else {
pageId = t.nextPage
t.nextPage++
offset := int(pageId) * pageSize
reqSize := offset + pageSize
if reqSize > len(t.data) {
t.buffer.AllocateOffset(reqSize - len(t.data))
t.data = t.buffer.Bytes()
}
}
n := t.node(pageId)
if t.freePage > 0 {
t.freePage = n.uint64(0)
}
zeroOut(n)
n.setBit(bit)
n.setAt(keyOffset(maxKeys), pageId)
return n
}
func getNode(data []byte) node {
return node(BytesToUint64Slice(data))
}
func zeroOut(data []uint64) {
for i := 0; i < len(data); i++ {
data[i] = 0
}
}
func (t *Tree) node(pid uint64) node {
// page does not exist
if pid == 0 {
return nil
}
start := pageSize * int(pid)
return getNode(t.data[start : start+pageSize])
}
// Set sets the key-value pair in the tree.
func (t *Tree) Set(k, v uint64) {
if k == math.MaxUint64 || k == 0 {
panic("Error setting zero or MaxUint64")
}
root := t.set(1, k, v)
if root.isFull() {
right := t.split(1)
left := t.newNode(root.bits())
// Re-read the root as the underlying buffer for tree might have changed during split.
root = t.node(1)
copy(left[:keyOffset(maxKeys)], root)
left.setNumKeys(root.numKeys())
// reset the root node.
zeroOut(root[:keyOffset(maxKeys)])
root.setNumKeys(0)
// set the pointers for left and right child in the root node.
root.set(left.maxKey(), left.pageID())
root.set(right.maxKey(), right.pageID())
}
}
// For internal nodes, they contain <key, ptr>.
// where all entries <= key are stored in the corresponding ptr.
func (t *Tree) set(pid, k, v uint64) node {
n := t.node(pid)
if n.isLeaf() {
t.stats.NumLeafKeys += n.set(k, v)
return n
}
// This is an internal node.
idx := n.search(k)
if idx >= maxKeys {
panic("search returned index >= maxKeys")
}
// If no key at idx.
if n.key(idx) == 0 {
n.setAt(keyOffset(idx), k)
n.setNumKeys(n.numKeys() + 1)
}
child := t.node(n.val(idx))
if child == nil {
child = t.newNode(bitLeaf)
n = t.node(pid)
n.setAt(valOffset(idx), child.pageID())
}
child = t.set(child.pageID(), k, v)
// Re-read n as the underlying buffer for tree might have changed during set.
n = t.node(pid)
if child.isFull() {
// Just consider the left sibling for simplicity.
// if t.shareWithSibling(n, idx) {
// return n
// }
nn := t.split(child.pageID())
// Re-read n and child as the underlying buffer for tree might have changed during split.
n = t.node(pid)
child = t.node(n.uint64(valOffset(idx)))
// Set child pointers in the node n.
// Note that key for right node (nn) already exist in node n, but the
// pointer is updated.
n.set(child.maxKey(), child.pageID())
n.set(nn.maxKey(), nn.pageID())
}
return n
}
// Get looks for key and returns the corresponding value.
// If key is not found, 0 is returned.
func (t *Tree) Get(k uint64) uint64 {
if k == math.MaxUint64 || k == 0 {
panic("Does not support getting MaxUint64/Zero")
}
root := t.node(1)
return t.get(root, k)
}
func (t *Tree) get(n node, k uint64) uint64 {
if n.isLeaf() {
return n.get(k)
}
// This is internal node
idx := n.search(k)
if idx == n.numKeys() || n.key(idx) == 0 {
return 0
}
child := t.node(n.uint64(valOffset(idx)))
assert(child != nil)
return t.get(child, k)
}
// DeleteBelow deletes all keys with value under ts.
func (t *Tree) DeleteBelow(ts uint64) {
root := t.node(1)
t.stats.NumLeafKeys = 0
t.compact(root, ts)
assert(root.numKeys() >= 1)
}
func (t *Tree) compact(n node, ts uint64) int {
if n.isLeaf() {
numKeys := n.compact(ts)
t.stats.NumLeafKeys += n.numKeys()
return numKeys
}
// Not leaf.
N := n.numKeys()
for i := 0; i < N; i++ {
assert(n.key(i) > 0)
childID := n.uint64(valOffset(i))
child := t.node(childID)
if rem := t.compact(child, ts); rem == 0 && i < N-1 {
// If no valid key is remaining we can drop this child. However, don't do that if this
// is the max key.
t.stats.NumLeafKeys -= child.numKeys()
child.setAt(0, t.freePage)
t.freePage = childID
n.setAt(valOffset(i), 0)
t.stats.NumPagesFree++
}
}
// We use ts=1 here because we want to delete all the keys whose value is 0, which means they no
// longer have a valid page for that key.
return n.compact(1)
}
func (t *Tree) iterate(n node, fn func(node)) {
fn(n)
if n.isLeaf() {
return
}
// Explore children.
for i := 0; i < maxKeys; i++ {
if n.key(i) == 0 {
return
}
childID := n.uint64(valOffset(i))
assert(childID > 0)
child := t.node(childID)
t.iterate(child, fn)
}
}
// Iterate iterates over the tree and executes the fn on each node.
func (t *Tree) Iterate(fn func(node)) {
root := t.node(1)
t.iterate(root, fn)
}
// IterateKV iterates through all keys and values in the tree.
// If newVal is non-zero, it will be set in the tree.
func (t *Tree) IterateKV(f func(key, val uint64) (newVal uint64)) {
t.Iterate(func(n node) {
// Only leaf nodes contain keys.
if !n.isLeaf() {
return
}
for i := 0; i < n.numKeys(); i++ {
key := n.key(i)
val := n.val(i)
// A zero value here means that this is a bogus entry.
if val == 0 {
continue
}
newVal := f(key, val)
if newVal != 0 {
n.setAt(valOffset(i), newVal)
}
}
})
}
func (t *Tree) print(n node, parentID uint64) {
n.print(parentID)
if n.isLeaf() {
return
}
pid := n.pageID()
for i := 0; i < maxKeys; i++ {
if n.key(i) == 0 {
return
}
childID := n.uint64(valOffset(i))
child := t.node(childID)
t.print(child, pid)
}
}
// Print iterates over the tree and prints all valid KVs.
func (t *Tree) Print() {
root := t.node(1)
t.print(root, 0)
}
// Splits the node into two. It moves right half of the keys from the original node to a newly
// created right node. It returns the right node.
func (t *Tree) split(pid uint64) node {
n := t.node(pid)
if !n.isFull() {
panic("This should be called only when n is full")
}
// Create a new node nn, copy over half the keys from n, and set the parent to n's parent.
nn := t.newNode(n.bits())
// Re-read n as the underlying buffer for tree might have changed during newNode.
n = t.node(pid)
rightHalf := n[keyOffset(maxKeys/2):keyOffset(maxKeys)]
copy(nn, rightHalf)
nn.setNumKeys(maxKeys - maxKeys/2)
// Remove entries from node n.
zeroOut(rightHalf)
n.setNumKeys(maxKeys / 2)
return nn
}
// shareWithSiblingXXX is unused for now. The idea is to move some keys to
// sibling when a node is full. But, I don't see any special benefits in our
// access pattern. It doesn't result in better occupancy ratios.
func (t *Tree) shareWithSiblingXXX(n node, idx int) bool {
if idx == 0 {
return false
}
left := t.node(n.val(idx - 1))
ns := left.numKeys()
if ns >= maxKeys/2 {
// Sibling is already getting full.
return false
}
right := t.node(n.val(idx))
// Copy over keys from right child to left child.
copied := copy(left[keyOffset(ns):], right[:keyOffset(oneThird)])
copied /= 2 // Considering that key-val constitute one key.
left.setNumKeys(ns + copied)
// Update the max key in parent node n for the left sibling.
n.setAt(keyOffset(idx-1), left.maxKey())
// Now move keys to left for the right sibling.
until := copy(right, right[keyOffset(oneThird):keyOffset(maxKeys)])
right.setNumKeys(until / 2)
zeroOut(right[until:keyOffset(maxKeys)])
return true
}
// Each node in the node is of size pageSize. Two kinds of nodes. Leaf nodes and internal nodes.
// Leaf nodes only contain the data. Internal nodes would contain the key and the offset to the
// child node.
// Internal node would have first entry as
// <0 offset to child>, <1000 offset>, <5000 offset>, and so on...
// Leaf nodes would just have: <key, value>, <key, value>, and so on...
// Last 16 bytes of the node are off limits.
// | pageID (8 bytes) | metaBits (1 byte) | 3 free bytes | numKeys (4 bytes) |
type node []uint64
func (n node) uint64(start int) uint64 { return n[start] }
// func (n node) uint32(start int) uint32 { return *(*uint32)(unsafe.Pointer(&n[start])) }
func keyOffset(i int) int { return 2 * i }
func valOffset(i int) int { return 2*i + 1 }
func (n node) numKeys() int { return int(n.uint64(valOffset(maxKeys)) & 0xFFFFFFFF) }
func (n node) pageID() uint64 { return n.uint64(keyOffset(maxKeys)) }
func (n node) key(i int) uint64 { return n.uint64(keyOffset(i)) }
func (n node) val(i int) uint64 { return n.uint64(valOffset(i)) }
func (n node) data(i int) []uint64 { return n[keyOffset(i):keyOffset(i+1)] }
func (n node) setAt(start int, k uint64) {
n[start] = k
}
func (n node) setNumKeys(num int) {
idx := valOffset(maxKeys)
val := n[idx]
val &= 0xFFFFFFFF00000000
val |= uint64(num)
n[idx] = val
}
func (n node) moveRight(lo int) {
hi := n.numKeys()
assert(hi != maxKeys)
// copy works despite of overlap in src and dst.
// See https://golang.org/pkg/builtin/#copy
copy(n[keyOffset(lo+1):keyOffset(hi+1)], n[keyOffset(lo):keyOffset(hi)])
}
const (
bitLeaf = uint64(1 << 63)
)
func (n node) setBit(b uint64) {
vo := valOffset(maxKeys)
val := n[vo]
val &= 0xFFFFFFFF
val |= b
n[vo] = val
}
func (n node) bits() uint64 {
return n.val(maxKeys) & 0xFF00000000000000
}
func (n node) isLeaf() bool {
return n.bits()&bitLeaf > 0
}
// isFull checks that the node is already full.
func (n node) isFull() bool {
return n.numKeys() == maxKeys
}
// Search returns the index of a smallest key >= k in a node.
func (n node) search(k uint64) int {
N := n.numKeys()
if N < 4 {
for i := 0; i < N; i++ {
if ki := n.key(i); ki >= k {
return i
}
}
return N
}
return int(simd.Search(n[:2*N], k))
// lo, hi := 0, N
// // Reduce the search space using binary search and then do linear search.
// for hi-lo > 32 {
// mid := (hi + lo) / 2
// km := n.key(mid)
// if k == km {
// return mid
// }
// if k > km {
// // key is greater than the key at mid, so move right.
// lo = mid + 1
// } else {
// // else move left.
// hi = mid
// }
// }
// for i := lo; i <= hi; i++ {
// if ki := n.key(i); ki >= k {
// return i
// }
// }
// return N
}
func (n node) maxKey() uint64 {
idx := n.numKeys()
// idx points to the first key which is zero.
if idx > 0 {
idx--
}
return n.key(idx)
}
// compacts the node i.e., remove all the kvs with value < lo. It returns the remaining number of
// keys.
func (n node) compact(lo uint64) int {
N := n.numKeys()
mk := n.maxKey()
var left, right int
for right = 0; right < N; right++ {
if n.val(right) < lo && n.key(right) < mk {
// Skip over this key. Don't copy it.
continue
}
// Valid data. Copy it from right to left. Advance left.
if left != right {
copy(n.data(left), n.data(right))
}
left++
}
// zero out rest of the kv pairs.
zeroOut(n[keyOffset(left):keyOffset(right)])
n.setNumKeys(left)
// If the only key we have is the max key, and its value is less than lo, then we can indicate
// to the caller by returning a zero that it's OK to drop the node.
if left == 1 && n.key(0) == mk && n.val(0) < lo {
return 0
}
return left
}
func (n node) get(k uint64) uint64 {
idx := n.search(k)
// key is not found
if idx == n.numKeys() {
return 0
}
if ki := n.key(idx); ki == k {
return n.val(idx)
}
return 0
}
// set returns true if it added a new key.
func (n node) set(k, v uint64) (numAdded int) {
idx := n.search(k)
ki := n.key(idx)
if n.numKeys() == maxKeys {
// This happens during split of non-root node, when we are updating the child pointer of
// right node. Hence, the key should already exist.
assert(ki == k)
}
if ki > k {
// Found the first entry which is greater than k. So, we need to fit k
// just before it. For that, we should move the rest of the data in the
// node to the right to make space for k.
n.moveRight(idx)
}
// If the k does not exist already, increment the number of keys.
if ki != k {
n.setNumKeys(n.numKeys() + 1)
numAdded = 1
}
if ki == 0 || ki >= k {
n.setAt(keyOffset(idx), k)
n.setAt(valOffset(idx), v)
return
}
panic("shouldn't reach here")
}
func (n node) iterate(fn func(node, int)) {
for i := 0; i < maxKeys; i++ {
if k := n.key(i); k > 0 {
fn(n, i)
} else {
break
}
}
}
func (n node) print(parentID uint64) {
var keys []string
n.iterate(func(n node, i int) {
keys = append(keys, fmt.Sprintf("%d", n.key(i)))
})
if len(keys) > 8 {
copy(keys[4:], keys[len(keys)-4:])
keys[3] = "..."
keys = keys[:8]
}
fmt.Printf("%d Child of: %d num keys: %d keys: %s\n",
n.pageID(), parentID, n.numKeys(), strings.Join(keys, " "))
}