/
sublist.go
1534 lines (1398 loc) · 36.5 KB
/
sublist.go
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// Copyright 2016-2020 The NATS Authors
// 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 server
import (
"bytes"
"errors"
"strings"
"sync"
"sync/atomic"
)
// Sublist is a routing mechanism to handle subject distribution and
// provides a facility to match subjects from published messages to
// interested subscribers. Subscribers can have wildcard subjects to
// match multiple published subjects.
// Common byte variables for wildcards and token separator.
const (
pwc = '*'
pwcs = "*"
fwc = '>'
fwcs = ">"
tsep = "."
btsep = '.'
)
// Sublist related errors
var (
ErrInvalidSubject = errors.New("sublist: invalid subject")
ErrNotFound = errors.New("sublist: no matches found")
ErrNilChan = errors.New("sublist: nil channel")
ErrAlreadyRegistered = errors.New("sublist: notification already registered")
)
const (
// cacheMax is used to bound limit the frontend cache
slCacheMax = 1024
// If we run a sweeper we will drain to this count.
slCacheSweep = 512
// plistMin is our lower bounds to create a fast plist for Match.
plistMin = 256
)
// SublistResult is a result structure better optimized for queue subs.
type SublistResult struct {
psubs []*subscription
qsubs [][]*subscription // don't make this a map, too expensive to iterate
}
// A Sublist stores and efficiently retrieves subscriptions.
type Sublist struct {
sync.RWMutex
genid uint64
matches uint64
cacheHits uint64
inserts uint64
removes uint64
root *level
cache map[string]*SublistResult
ccSweep int32
notify *notifyMaps
count uint32
}
// notifyMaps holds maps of arrays of channels for notifications
// on a change of interest.
type notifyMaps struct {
insert map[string][]chan<- bool
remove map[string][]chan<- bool
}
// A node contains subscriptions and a pointer to the next level.
type node struct {
next *level
psubs map[*subscription]*subscription
qsubs map[string](map[*subscription]*subscription)
plist []*subscription
}
// A level represents a group of nodes and special pointers to
// wildcard nodes.
type level struct {
nodes map[string]*node
pwc, fwc *node
}
// Create a new default node.
func newNode() *node {
return &node{psubs: make(map[*subscription]*subscription)}
}
// Create a new default level.
func newLevel() *level {
return &level{nodes: make(map[string]*node)}
}
// In general caching is recommended however in some extreme cases where
// interest changes are high, suppressing the cache can help.
// https://github.com/nats-io/nats-server/issues/941
// FIXME(dlc) - should be more dynamic at some point based on cache thrashing.
// NewSublist will create a default sublist with caching enabled per the flag.
func NewSublist(enableCache bool) *Sublist {
if enableCache {
return &Sublist{root: newLevel(), cache: make(map[string]*SublistResult)}
}
return &Sublist{root: newLevel()}
}
// NewSublistWithCache will create a default sublist with caching enabled.
func NewSublistWithCache() *Sublist {
return NewSublist(true)
}
// NewSublistNoCache will create a default sublist with caching disabled.
func NewSublistNoCache() *Sublist {
return NewSublist(false)
}
// CacheEnabled returns whether or not caching is enabled for this sublist.
func (s *Sublist) CacheEnabled() bool {
s.RLock()
enabled := s.cache != nil
s.RUnlock()
return enabled
}
// RegisterNotification will register for notifications when interest for the given
// subject changes. The subject must be a literal publish type subject.
// The notification is true for when the first interest for a subject is inserted,
// and false when all interest in the subject is removed. Note that this interest
// needs to be exact and that wildcards will not trigger the notifications. The sublist
// will not block when trying to send the notification. Its up to the caller to make
// sure the channel send will not block.
func (s *Sublist) RegisterNotification(subject string, notify chan<- bool) error {
return s.registerNotification(subject, _EMPTY_, notify)
}
func (s *Sublist) RegisterQueueNotification(subject, queue string, notify chan<- bool) error {
return s.registerNotification(subject, queue, notify)
}
func (s *Sublist) registerNotification(subject, queue string, notify chan<- bool) error {
if subjectHasWildcard(subject) {
return ErrInvalidSubject
}
if notify == nil {
return ErrNilChan
}
var hasInterest bool
r := s.Match(subject)
if len(r.psubs)+len(r.qsubs) > 0 {
if queue == _EMPTY_ {
for _, sub := range r.psubs {
if string(sub.subject) == subject {
hasInterest = true
break
}
}
} else {
for _, qsub := range r.qsubs {
qs := qsub[0]
if string(qs.subject) == subject && string(qs.queue) == queue {
hasInterest = true
break
}
}
}
}
key := keyFromSubjectAndQueue(subject, queue)
var err error
s.Lock()
if s.notify == nil {
s.notify = ¬ifyMaps{
insert: make(map[string][]chan<- bool),
remove: make(map[string][]chan<- bool),
}
}
// Check which list to add us to.
if hasInterest {
err = s.addRemoveNotify(key, notify)
} else {
err = s.addInsertNotify(key, notify)
}
s.Unlock()
if err == nil {
sendNotification(notify, hasInterest)
}
return err
}
// Lock should be held.
func chkAndRemove(key string, notify chan<- bool, ms map[string][]chan<- bool) bool {
chs := ms[key]
for i, ch := range chs {
if ch == notify {
chs[i] = chs[len(chs)-1]
chs = chs[:len(chs)-1]
if len(chs) == 0 {
delete(ms, key)
}
return true
}
}
return false
}
func (s *Sublist) ClearNotification(subject string, notify chan<- bool) bool {
return s.clearNotification(subject, _EMPTY_, notify)
}
func (s *Sublist) ClearQueueNotification(subject, queue string, notify chan<- bool) bool {
return s.clearNotification(subject, queue, notify)
}
func (s *Sublist) clearNotification(subject, queue string, notify chan<- bool) bool {
s.Lock()
if s.notify == nil {
s.Unlock()
return false
}
key := keyFromSubjectAndQueue(subject, queue)
// Check both, start with remove.
didRemove := chkAndRemove(key, notify, s.notify.remove)
didRemove = didRemove || chkAndRemove(key, notify, s.notify.insert)
// Check if everything is gone
if len(s.notify.remove)+len(s.notify.insert) == 0 {
s.notify = nil
}
s.Unlock()
return didRemove
}
func sendNotification(ch chan<- bool, hasInterest bool) {
select {
case ch <- hasInterest:
default:
}
}
// Add a new channel for notification in insert map.
// Write lock should be held.
func (s *Sublist) addInsertNotify(subject string, notify chan<- bool) error {
return s.addNotify(s.notify.insert, subject, notify)
}
// Add a new channel for notification in removal map.
// Write lock should be held.
func (s *Sublist) addRemoveNotify(subject string, notify chan<- bool) error {
return s.addNotify(s.notify.remove, subject, notify)
}
// Add a new channel for notification.
// Write lock should be held.
func (s *Sublist) addNotify(m map[string][]chan<- bool, subject string, notify chan<- bool) error {
chs := m[subject]
if len(chs) > 0 {
// Check to see if this chan is already registered.
for _, ch := range chs {
if ch == notify {
return ErrAlreadyRegistered
}
}
}
m[subject] = append(chs, notify)
return nil
}
// To generate a key from subject and queue. We just add spc.
func keyFromSubjectAndQueue(subject, queue string) string {
if len(queue) == 0 {
return subject
}
var sb strings.Builder
sb.WriteString(subject)
sb.WriteString(" ")
sb.WriteString(queue)
return sb.String()
}
// chkForInsertNotification will check to see if we need to notify on this subject.
// Write lock should be held.
func (s *Sublist) chkForInsertNotification(subject, queue string) {
key := keyFromSubjectAndQueue(subject, queue)
// All notify subjects are also literal so just do a hash lookup here.
if chs := s.notify.insert[key]; len(chs) > 0 {
for _, ch := range chs {
sendNotification(ch, true)
}
// Move from the insert map to the remove map.
s.notify.remove[key] = append(s.notify.remove[key], chs...)
delete(s.notify.insert, key)
}
}
// chkForRemoveNotification will check to see if we need to notify on this subject.
// Write lock should be held.
func (s *Sublist) chkForRemoveNotification(subject, queue string) {
key := keyFromSubjectAndQueue(subject, queue)
if chs := s.notify.remove[key]; len(chs) > 0 {
// We need to always check that we have no interest anymore.
var hasInterest bool
r := s.matchNoLock(subject)
if len(r.psubs)+len(r.qsubs) > 0 {
if queue == _EMPTY_ {
for _, sub := range r.psubs {
if string(sub.subject) == subject {
hasInterest = true
break
}
}
} else {
for _, qsub := range r.qsubs {
qs := qsub[0]
if string(qs.subject) == subject && string(qs.queue) == queue {
hasInterest = true
break
}
}
}
}
if !hasInterest {
for _, ch := range chs {
sendNotification(ch, false)
}
// Move from the remove map to the insert map.
s.notify.insert[key] = append(s.notify.insert[key], chs...)
delete(s.notify.remove, key)
}
}
}
// Insert adds a subscription into the sublist
func (s *Sublist) Insert(sub *subscription) error {
// copy the subject since we hold this and this might be part of a large byte slice.
subject := string(sub.subject)
tsa := [32]string{}
tokens := tsa[:0]
start := 0
for i := 0; i < len(subject); i++ {
if subject[i] == btsep {
tokens = append(tokens, subject[start:i])
start = i + 1
}
}
tokens = append(tokens, subject[start:])
s.Lock()
var sfwc, haswc, isnew bool
var n *node
l := s.root
for _, t := range tokens {
lt := len(t)
if lt == 0 || sfwc {
s.Unlock()
return ErrInvalidSubject
}
if lt > 1 {
n = l.nodes[t]
} else {
switch t[0] {
case pwc:
n = l.pwc
haswc = true
case fwc:
n = l.fwc
haswc, sfwc = true, true
default:
n = l.nodes[t]
}
}
if n == nil {
n = newNode()
if lt > 1 {
l.nodes[t] = n
} else {
switch t[0] {
case pwc:
l.pwc = n
case fwc:
l.fwc = n
default:
l.nodes[t] = n
}
}
}
if n.next == nil {
n.next = newLevel()
}
l = n.next
}
if sub.queue == nil {
n.psubs[sub] = sub
isnew = len(n.psubs) == 1
if n.plist != nil {
n.plist = append(n.plist, sub)
} else if len(n.psubs) > plistMin {
n.plist = make([]*subscription, 0, len(n.psubs))
// Populate
for _, psub := range n.psubs {
n.plist = append(n.plist, psub)
}
}
} else {
if n.qsubs == nil {
n.qsubs = make(map[string]map[*subscription]*subscription)
isnew = true
}
qname := string(sub.queue)
// This is a queue subscription
subs, ok := n.qsubs[qname]
if !ok {
subs = make(map[*subscription]*subscription)
n.qsubs[qname] = subs
}
subs[sub] = sub
}
s.count++
s.inserts++
s.addToCache(subject, sub)
atomic.AddUint64(&s.genid, 1)
if s.notify != nil && isnew && !haswc && len(s.notify.insert) > 0 {
s.chkForInsertNotification(subject, string(sub.queue))
}
s.Unlock()
return nil
}
// Deep copy
func copyResult(r *SublistResult) *SublistResult {
nr := &SublistResult{}
nr.psubs = append([]*subscription(nil), r.psubs...)
for _, qr := range r.qsubs {
nqr := append([]*subscription(nil), qr...)
nr.qsubs = append(nr.qsubs, nqr)
}
return nr
}
// Adds a new sub to an existing result.
func (r *SublistResult) addSubToResult(sub *subscription) *SublistResult {
// Copy since others may have a reference.
nr := copyResult(r)
if sub.queue == nil {
nr.psubs = append(nr.psubs, sub)
} else {
if i := findQSlot(sub.queue, nr.qsubs); i >= 0 {
nr.qsubs[i] = append(nr.qsubs[i], sub)
} else {
nr.qsubs = append(nr.qsubs, []*subscription{sub})
}
}
return nr
}
// addToCache will add the new entry to the existing cache
// entries if needed. Assumes write lock is held.
// Assumes write lock is held.
func (s *Sublist) addToCache(subject string, sub *subscription) {
if s.cache == nil {
return
}
// If literal we can direct match.
if subjectIsLiteral(subject) {
if r := s.cache[subject]; r != nil {
s.cache[subject] = r.addSubToResult(sub)
}
return
}
for key, r := range s.cache {
if matchLiteral(key, subject) {
s.cache[key] = r.addSubToResult(sub)
}
}
}
// removeFromCache will remove the sub from any active cache entries.
// Assumes write lock is held.
func (s *Sublist) removeFromCache(subject string, sub *subscription) {
if s.cache == nil {
return
}
// If literal we can direct match.
if subjectIsLiteral(subject) {
delete(s.cache, subject)
return
}
// Wildcard here.
for key := range s.cache {
if matchLiteral(key, subject) {
delete(s.cache, key)
}
}
}
// a place holder for an empty result.
var emptyResult = &SublistResult{}
// Match will match all entries to the literal subject.
// It will return a set of results for both normal and queue subscribers.
func (s *Sublist) Match(subject string) *SublistResult {
return s.match(subject, true)
}
func (s *Sublist) matchNoLock(subject string) *SublistResult {
return s.match(subject, false)
}
func (s *Sublist) match(subject string, doLock bool) *SublistResult {
atomic.AddUint64(&s.matches, 1)
// Check cache first.
if doLock {
s.RLock()
}
r, ok := s.cache[subject]
if doLock {
s.RUnlock()
}
if ok {
atomic.AddUint64(&s.cacheHits, 1)
return r
}
tsa := [32]string{}
tokens := tsa[:0]
start := 0
for i := 0; i < len(subject); i++ {
if subject[i] == btsep {
if i-start == 0 {
return emptyResult
}
tokens = append(tokens, subject[start:i])
start = i + 1
}
}
if start >= len(subject) {
return emptyResult
}
tokens = append(tokens, subject[start:])
// FIXME(dlc) - Make shared pool between sublist and client readLoop?
result := &SublistResult{}
// Get result from the main structure and place into the shared cache.
// Hold the read lock to avoid race between match and store.
var n int
if doLock {
s.Lock()
}
matchLevel(s.root, tokens, result)
// Check for empty result.
if len(result.psubs) == 0 && len(result.qsubs) == 0 {
result = emptyResult
}
if s.cache != nil {
s.cache[subject] = result
n = len(s.cache)
}
if doLock {
s.Unlock()
}
// Reduce the cache count if we have exceeded our set maximum.
if n > slCacheMax && atomic.CompareAndSwapInt32(&s.ccSweep, 0, 1) {
go s.reduceCacheCount()
}
return result
}
// Remove entries in the cache until we are under the maximum.
// TODO(dlc) this could be smarter now that its not inline.
func (s *Sublist) reduceCacheCount() {
defer atomic.StoreInt32(&s.ccSweep, 0)
// If we are over the cache limit randomly drop until under the limit.
s.Lock()
for key := range s.cache {
delete(s.cache, key)
if len(s.cache) <= slCacheSweep {
break
}
}
s.Unlock()
}
// Helper function for auto-expanding remote qsubs.
func isRemoteQSub(sub *subscription) bool {
return sub != nil && sub.queue != nil && sub.client != nil && sub.client.kind == ROUTER
}
// UpdateRemoteQSub should be called when we update the weight of an existing
// remote queue sub.
func (s *Sublist) UpdateRemoteQSub(sub *subscription) {
// We could search to make sure we find it, but probably not worth
// it unless we are thrashing the cache. Just remove from our L2 and update
// the genid so L1 will be flushed.
s.Lock()
s.removeFromCache(string(sub.subject), sub)
atomic.AddUint64(&s.genid, 1)
s.Unlock()
}
// This will add in a node's results to the total results.
func addNodeToResults(n *node, results *SublistResult) {
// Normal subscriptions
if n.plist != nil {
results.psubs = append(results.psubs, n.plist...)
} else {
for _, psub := range n.psubs {
results.psubs = append(results.psubs, psub)
}
}
// Queue subscriptions
for qname, qr := range n.qsubs {
if len(qr) == 0 {
continue
}
// Need to find matching list in results
var i int
if i = findQSlot([]byte(qname), results.qsubs); i < 0 {
i = len(results.qsubs)
nqsub := make([]*subscription, 0, len(qr))
results.qsubs = append(results.qsubs, nqsub)
}
for _, sub := range qr {
if isRemoteQSub(sub) {
ns := atomic.LoadInt32(&sub.qw)
// Shadow these subscriptions
for n := 0; n < int(ns); n++ {
results.qsubs[i] = append(results.qsubs[i], sub)
}
} else {
results.qsubs[i] = append(results.qsubs[i], sub)
}
}
}
}
// We do not use a map here since we want iteration to be past when
// processing publishes in L1 on client. So we need to walk sequentially
// for now. Keep an eye on this in case we start getting large number of
// different queue subscribers for the same subject.
func findQSlot(queue []byte, qsl [][]*subscription) int {
if queue == nil {
return -1
}
for i, qr := range qsl {
if len(qr) > 0 && bytes.Equal(queue, qr[0].queue) {
return i
}
}
return -1
}
// matchLevel is used to recursively descend into the trie.
func matchLevel(l *level, toks []string, results *SublistResult) {
var pwc, n *node
for i, t := range toks {
if l == nil {
return
}
if l.fwc != nil {
addNodeToResults(l.fwc, results)
}
if pwc = l.pwc; pwc != nil {
matchLevel(pwc.next, toks[i+1:], results)
}
n = l.nodes[t]
if n != nil {
l = n.next
} else {
l = nil
}
}
if n != nil {
addNodeToResults(n, results)
}
if pwc != nil {
addNodeToResults(pwc, results)
}
}
// lnt is used to track descent into levels for a removal for pruning.
type lnt struct {
l *level
n *node
t string
}
// Raw low level remove, can do batches with lock held outside.
func (s *Sublist) remove(sub *subscription, shouldLock bool, doCacheUpdates bool) error {
subject := string(sub.subject)
tsa := [32]string{}
tokens := tsa[:0]
start := 0
for i := 0; i < len(subject); i++ {
if subject[i] == btsep {
tokens = append(tokens, subject[start:i])
start = i + 1
}
}
tokens = append(tokens, subject[start:])
if shouldLock {
s.Lock()
defer s.Unlock()
}
var sfwc, haswc bool
var n *node
l := s.root
// Track levels for pruning
var lnts [32]lnt
levels := lnts[:0]
for _, t := range tokens {
lt := len(t)
if lt == 0 || sfwc {
return ErrInvalidSubject
}
if l == nil {
return ErrNotFound
}
if lt > 1 {
n = l.nodes[t]
} else {
switch t[0] {
case pwc:
n = l.pwc
haswc = true
case fwc:
n = l.fwc
haswc, sfwc = true, true
default:
n = l.nodes[t]
}
}
if n != nil {
levels = append(levels, lnt{l, n, t})
l = n.next
} else {
l = nil
}
}
removed, last := s.removeFromNode(n, sub)
if !removed {
return ErrNotFound
}
s.count--
s.removes++
for i := len(levels) - 1; i >= 0; i-- {
l, n, t := levels[i].l, levels[i].n, levels[i].t
if n.isEmpty() {
l.pruneNode(n, t)
}
}
if doCacheUpdates {
s.removeFromCache(subject, sub)
atomic.AddUint64(&s.genid, 1)
}
if s.notify != nil && last && !haswc && len(s.notify.remove) > 0 {
s.chkForRemoveNotification(subject, string(sub.queue))
}
return nil
}
// Remove will remove a subscription.
func (s *Sublist) Remove(sub *subscription) error {
return s.remove(sub, true, true)
}
// RemoveBatch will remove a list of subscriptions.
func (s *Sublist) RemoveBatch(subs []*subscription) error {
if len(subs) == 0 {
return nil
}
s.Lock()
defer s.Unlock()
// TODO(dlc) - We could try to be smarter here for a client going away but the account
// has a large number of subscriptions compared to this client. Quick and dirty testing
// though said just disabling all the time best for now.
// Turn off our cache if enabled.
wasEnabled := s.cache != nil
s.cache = nil
for _, sub := range subs {
if err := s.remove(sub, false, false); err != nil {
return err
}
}
// Turn caching back on here.
atomic.AddUint64(&s.genid, 1)
if wasEnabled {
s.cache = make(map[string]*SublistResult)
}
return nil
}
// pruneNode is used to prune an empty node from the tree.
func (l *level) pruneNode(n *node, t string) {
if n == nil {
return
}
if n == l.fwc {
l.fwc = nil
} else if n == l.pwc {
l.pwc = nil
} else {
delete(l.nodes, t)
}
}
// isEmpty will test if the node has any entries. Used
// in pruning.
func (n *node) isEmpty() bool {
if len(n.psubs) == 0 && len(n.qsubs) == 0 {
if n.next == nil || n.next.numNodes() == 0 {
return true
}
}
return false
}
// Return the number of nodes for the given level.
func (l *level) numNodes() int {
num := len(l.nodes)
if l.pwc != nil {
num++
}
if l.fwc != nil {
num++
}
return num
}
// Remove the sub for the given node.
func (s *Sublist) removeFromNode(n *node, sub *subscription) (found, last bool) {
if n == nil {
return false, true
}
if sub.queue == nil {
_, found = n.psubs[sub]
delete(n.psubs, sub)
if found && n.plist != nil {
// This will brute force remove the plist to perform
// correct behavior. Will get re-populated on a call
// to Match as needed.
n.plist = nil
}
return found, len(n.psubs) == 0
}
// We have a queue group subscription here
qsub := n.qsubs[string(sub.queue)]
_, found = qsub[sub]
delete(qsub, sub)
if len(qsub) == 0 {
delete(n.qsubs, string(sub.queue))
last = len(n.qsubs) == 0
}
return found, last
}
// Count returns the number of subscriptions.
func (s *Sublist) Count() uint32 {
s.RLock()
defer s.RUnlock()
return s.count
}
// CacheCount returns the number of result sets in the cache.
func (s *Sublist) CacheCount() int {
s.RLock()
cc := len(s.cache)
s.RUnlock()
return cc
}
// SublistStats are public stats for the sublist
type SublistStats struct {
NumSubs uint32 `json:"num_subscriptions"`
NumCache uint32 `json:"num_cache"`
NumInserts uint64 `json:"num_inserts"`
NumRemoves uint64 `json:"num_removes"`
NumMatches uint64 `json:"num_matches"`
CacheHitRate float64 `json:"cache_hit_rate"`
MaxFanout uint32 `json:"max_fanout"`
AvgFanout float64 `json:"avg_fanout"`
totFanout int
cacheCnt int
}
func (s *SublistStats) add(stat *SublistStats) {
s.NumSubs += stat.NumSubs
s.NumCache += stat.NumCache
s.NumInserts += stat.NumInserts
s.NumRemoves += stat.NumRemoves
s.NumMatches += stat.NumMatches
s.CacheHitRate += stat.CacheHitRate
if s.MaxFanout < stat.MaxFanout {
s.MaxFanout = stat.MaxFanout
}
// ignore slStats.AvgFanout, collect the values
// it's based on instead
s.totFanout += stat.totFanout
s.cacheCnt += stat.cacheCnt
if s.totFanout > 0 {
s.AvgFanout = float64(s.totFanout) / float64(s.cacheCnt)
}
}
// Stats will return a stats structure for the current state.
func (s *Sublist) Stats() *SublistStats {
st := &SublistStats{}
s.RLock()
cache := s.cache
cc := len(s.cache)
st.NumSubs = s.count
st.NumInserts = s.inserts
st.NumRemoves = s.removes
s.RUnlock()
st.NumCache = uint32(cc)
st.NumMatches = atomic.LoadUint64(&s.matches)
if st.NumMatches > 0 {
st.CacheHitRate = float64(atomic.LoadUint64(&s.cacheHits)) / float64(st.NumMatches)
}
// whip through cache for fanout stats, this can be off if cache is full and doing evictions.
// If this is called frequently, which it should not be, this could hurt performance.
if cache != nil {
tot, max, clen := 0, 0, 0
s.RLock()
for _, r := range s.cache {
clen++
l := len(r.psubs) + len(r.qsubs)
tot += l
if l > max {
max = l
}
}
s.RUnlock()
st.totFanout = tot
st.cacheCnt = clen
st.MaxFanout = uint32(max)
if tot > 0 {
st.AvgFanout = float64(tot) / float64(clen)
}
}
return st
}
// numLevels will return the maximum number of levels
// contained in the Sublist tree.
func (s *Sublist) numLevels() int {
return visitLevel(s.root, 0)
}
// visitLevel is used to descend the Sublist tree structure
// recursively.
func visitLevel(l *level, depth int) int {