spanner/session.go

/*
Copyright 2017 Google LLC

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 spanner

import (
	"container/heap"
	"container/list"
	"context"
	"fmt"
	"log"
	"math"
	"math/rand"
	"runtime/debug"
	"strings"
	"sync"
	"time"

	"cloud.google.com/go/internal/trace"
	vkit "cloud.google.com/go/spanner/apiv1"
	sppb "cloud.google.com/go/spanner/apiv1/spannerpb"
	"cloud.google.com/go/spanner/internal"
	"go.opencensus.io/stats"
	"go.opencensus.io/tag"
	octrace "go.opencensus.io/trace"
	"google.golang.org/grpc/codes"
	"google.golang.org/grpc/metadata"
)

const healthCheckIntervalMins = 50

// sessionHandle is an interface for transactions to access Cloud Spanner
// sessions safely. It is generated by sessionPool.take().
type sessionHandle struct {
	// mu guarantees that the inner session object is returned / destroyed only
	// once.
	mu sync.Mutex
	// session is a pointer to a session object. Transactions never need to
	// access it directly.
	session *session
	// checkoutTime is the time the session was checked out of the pool.
	checkoutTime time.Time
	// trackedSessionHandle is the linked list node which links the session to
	// the list of tracked session handles. trackedSessionHandle is only set if
	// TrackSessionHandles has been enabled in the session pool configuration.
	trackedSessionHandle *list.Element
	// stack is the call stack of the goroutine that checked out the session
	// from the pool. This can be used to track down session leak problems.
	stack []byte
}

// recycle gives the inner session object back to its home session pool. It is
// safe to call recycle multiple times but only the first one would take effect.
func (sh *sessionHandle) recycle() {
	sh.mu.Lock()
	if sh.session == nil {
		// sessionHandle has already been recycled.
		sh.mu.Unlock()
		return
	}
	p := sh.session.pool
	tracked := sh.trackedSessionHandle
	s := sh.session
	sh.session = nil
	sh.trackedSessionHandle = nil
	sh.checkoutTime = time.Time{}
	sh.stack = nil
	sh.mu.Unlock()
	s.recycle()
	if tracked != nil {
		p.mu.Lock()
		p.trackedSessionHandles.Remove(tracked)
		p.mu.Unlock()
	}
}

// getID gets the Cloud Spanner session ID from the internal session object.
// getID returns empty string if the sessionHandle is nil or the inner session
// object has been released by recycle / destroy.
func (sh *sessionHandle) getID() string {
	sh.mu.Lock()
	defer sh.mu.Unlock()
	if sh.session == nil {
		// sessionHandle has already been recycled/destroyed.
		return ""
	}
	return sh.session.getID()
}

// getClient gets the Cloud Spanner RPC client associated with the session ID
// in sessionHandle.
func (sh *sessionHandle) getClient() *vkit.Client {
	sh.mu.Lock()
	defer sh.mu.Unlock()
	if sh.session == nil {
		return nil
	}
	return sh.session.client
}

// getMetadata returns the metadata associated with the session in sessionHandle.
func (sh *sessionHandle) getMetadata() metadata.MD {
	sh.mu.Lock()
	defer sh.mu.Unlock()
	if sh.session == nil {
		return nil
	}
	return sh.session.md
}

// getTransactionID returns the transaction id in the session if available.
func (sh *sessionHandle) getTransactionID() transactionID {
	sh.mu.Lock()
	defer sh.mu.Unlock()
	if sh.session == nil {
		return nil
	}
	return sh.session.tx
}

// destroy destroys the inner session object. It is safe to call destroy
// multiple times and only the first call would attempt to
// destroy the inner session object.
func (sh *sessionHandle) destroy() {
	sh.mu.Lock()
	s := sh.session
	if s == nil {
		// sessionHandle has already been recycled.
		sh.mu.Unlock()
		return
	}
	tracked := sh.trackedSessionHandle
	sh.session = nil
	sh.trackedSessionHandle = nil
	sh.checkoutTime = time.Time{}
	sh.stack = nil
	sh.mu.Unlock()

	if tracked != nil {
		p := s.pool
		p.mu.Lock()
		p.trackedSessionHandles.Remove(tracked)
		p.mu.Unlock()
	}
	s.destroy(false)
}

// session wraps a Cloud Spanner session ID through which transactions are
// created and executed.
type session struct {
	// client is the RPC channel to Cloud Spanner. It is set only once during
	// session's creation.
	client *vkit.Client
	// id is the unique id of the session in Cloud Spanner. It is set only once
	// during session's creation.
	id string
	// pool is the session's home session pool where it was created. It is set
	// only once during session's creation.
	pool *sessionPool
	// createTime is the timestamp of the session's creation. It is set only
	// once during session's creation.
	createTime time.Time
	// logger is the logger configured for the Spanner client that created the
	// session. If nil, logging will be directed to the standard logger.
	logger *log.Logger

	// mu protects the following fields from concurrent access: both
	// healthcheck workers and transactions can modify them.
	mu sync.Mutex
	// valid marks the validity of a session.
	valid bool
	// hcIndex is the index of the session inside the global healthcheck queue.
	// If hcIndex < 0, session has been unregistered from the queue.
	hcIndex int
	// idleList is the linkedlist node which links the session to its home
	// session pool's idle list. If idleList == nil, the
	// session is not in idle list.
	idleList *list.Element
	// nextCheck is the timestamp of next scheduled healthcheck of the session.
	// It is maintained by the global health checker.
	nextCheck time.Time
	// checkingHelath is true if currently this session is being processed by
	// health checker. Must be modified under health checker lock.
	checkingHealth bool
	// md is the Metadata to be sent with each request.
	md metadata.MD
	// tx contains the transaction id if the session has been prepared for
	// write.
	tx transactionID
	// firstHCDone indicates whether the first health check is done or not.
	firstHCDone bool
}

// isValid returns true if the session is still valid for use.
func (s *session) isValid() bool {
	s.mu.Lock()
	defer s.mu.Unlock()
	return s.valid
}

// isWritePrepared returns true if the session is prepared for write.
func (s *session) isWritePrepared() bool {
	s.mu.Lock()
	defer s.mu.Unlock()
	return s.tx != nil
}

// String implements fmt.Stringer for session.
func (s *session) String() string {
	s.mu.Lock()
	defer s.mu.Unlock()
	return fmt.Sprintf("<id=%v, hcIdx=%v, idleList=%p, valid=%v, create=%v, nextcheck=%v>",
		s.id, s.hcIndex, s.idleList, s.valid, s.createTime, s.nextCheck)
}

// ping verifies if the session is still alive in Cloud Spanner.
func (s *session) ping() error {
	ctx, cancel := context.WithTimeout(context.Background(), time.Second)
	defer cancel()

	// Start parent span that doesn't record.
	_, span := octrace.StartSpan(ctx, "cloud.google.com/go/spanner.ping", octrace.WithSampler(octrace.NeverSample()))
	defer span.End()

	// s.getID is safe even when s is invalid.
	_, err := s.client.ExecuteSql(contextWithOutgoingMetadata(ctx, s.md, true), &sppb.ExecuteSqlRequest{
		Session: s.getID(),
		Sql:     "SELECT 1",
	})
	return err
}

// setHcIndex atomically sets the session's index in the healthcheck queue and
// returns the old index.
func (s *session) setHcIndex(i int) int {
	s.mu.Lock()
	defer s.mu.Unlock()
	oi := s.hcIndex
	s.hcIndex = i
	return oi
}

// setIdleList atomically sets the session's idle list link and returns the old
// link.
func (s *session) setIdleList(le *list.Element) *list.Element {
	s.mu.Lock()
	defer s.mu.Unlock()
	old := s.idleList
	s.idleList = le
	return old
}

// invalidate marks a session as invalid and returns the old validity.
func (s *session) invalidate() bool {
	s.mu.Lock()
	defer s.mu.Unlock()
	ov := s.valid
	s.valid = false
	return ov
}

// setNextCheck sets the timestamp for next healthcheck on the session.
func (s *session) setNextCheck(t time.Time) {
	s.mu.Lock()
	defer s.mu.Unlock()
	s.nextCheck = t
}

// setTransactionID sets the transaction id in the session
func (s *session) setTransactionID(tx transactionID) {
	s.mu.Lock()
	defer s.mu.Unlock()
	s.tx = tx
}

// getID returns the session ID which uniquely identifies the session in Cloud
// Spanner.
func (s *session) getID() string {
	s.mu.Lock()
	defer s.mu.Unlock()
	return s.id
}

// getHcIndex returns the session's index into the global healthcheck priority
// queue.
func (s *session) getHcIndex() int {
	s.mu.Lock()
	defer s.mu.Unlock()
	return s.hcIndex
}

// getIdleList returns the session's link in its home session pool's idle list.
func (s *session) getIdleList() *list.Element {
	s.mu.Lock()
	defer s.mu.Unlock()
	return s.idleList
}

// getNextCheck returns the timestamp for next healthcheck on the session.
func (s *session) getNextCheck() time.Time {
	s.mu.Lock()
	defer s.mu.Unlock()
	return s.nextCheck
}

// recycle turns the session back to its home session pool.
func (s *session) recycle() {
	s.setTransactionID(nil)
	s.pool.mu.Lock()
	if !s.pool.recycleLocked(s) {
		// s is rejected by its home session pool because it expired and the
		// session pool currently has enough open sessions.
		s.pool.mu.Unlock()
		s.destroy(false)
		s.pool.mu.Lock()
	}
	s.pool.decNumInUseLocked(context.Background())
	s.pool.mu.Unlock()
}

// destroy removes the session from its home session pool, healthcheck queue
// and Cloud Spanner service.
func (s *session) destroy(isExpire bool) bool {
	ctx, cancel := context.WithTimeout(context.Background(), 15*time.Second)
	defer cancel()
	return s.destroyWithContext(ctx, isExpire)
}

func (s *session) destroyWithContext(ctx context.Context, isExpire bool) bool {
	// Remove s from session pool.
	if !s.pool.remove(s, isExpire) {
		return false
	}
	// Unregister s from healthcheck queue.
	s.pool.hc.unregister(s)
	return true
}

func (s *session) delete(ctx context.Context) {
	// Ignore the error because even if we fail to explicitly destroy the
	// session, it will be eventually garbage collected by Cloud Spanner.
	err := s.client.DeleteSession(contextWithOutgoingMetadata(ctx, s.md, true), &sppb.DeleteSessionRequest{Name: s.getID()})
	// Do not log DeadlineExceeded errors when deleting sessions, as these do
	// not indicate anything the user can or should act upon.
	if err != nil && ErrCode(err) != codes.DeadlineExceeded {
		logf(s.logger, "Failed to delete session %v. Error: %v", s.getID(), err)
	}
}

// SessionPoolConfig stores configurations of a session pool.
type SessionPoolConfig struct {
	// MaxOpened is the maximum number of opened sessions allowed by the session
	// pool. If the client tries to open a session and there are already
	// MaxOpened sessions, it will block until one becomes available or the
	// context passed to the client method is canceled or times out.
	//
	// Defaults to NumChannels * 100.
	MaxOpened uint64

	// MinOpened is the minimum number of opened sessions that the session pool
	// tries to maintain. Session pool won't continue to expire sessions if
	// number of opened connections drops below MinOpened. However, if a session
	// is found to be broken, it will still be evicted from the session pool,
	// therefore it is posssible that the number of opened sessions drops below
	// MinOpened.
	//
	// Defaults to 100.
	MinOpened uint64

	// MaxIdle is the maximum number of idle sessions that are allowed in the
	// session pool.
	//
	// Defaults to 0.
	MaxIdle uint64

	// MaxBurst is the maximum number of concurrent session creation requests.
	//
	// Deprecated: MaxBurst exists for historical compatibility and should not
	// be used. MaxBurst was used to limit the number of sessions that the
	// session pool could create within a time frame. This was an early safety
	// valve to prevent a client from overwhelming the backend if a large number
	// of sessions was suddenly needed. The session pool would then pause the
	// creation of sessions for a while. Such a pause is no longer needed and
	// the implementation has been removed from the pool.
	//
	// Defaults to 10.
	MaxBurst uint64

	// incStep is the number of sessions to create in one batch when at least
	// one more session is needed.
	//
	// Defaults to 25.
	incStep uint64

	// WriteSessions is the fraction of sessions we try to keep prepared for
	// write.
	//
	// Deprecated: The session pool no longer prepares a fraction of the sessions with a read/write transaction.
	// This setting therefore does not have any meaning anymore, and may be removed in the future.
	//
	// Defaults to 0.2.
	WriteSessions float64

	// HealthCheckWorkers is number of workers used by health checker for this
	// pool.
	//
	// Defaults to 10.
	HealthCheckWorkers int

	// HealthCheckInterval is how often the health checker pings a session.
	//
	// Defaults to 50m.
	HealthCheckInterval time.Duration

	// TrackSessionHandles determines whether the session pool will keep track
	// of the stacktrace of the goroutines that take sessions from the pool.
	// This setting can be used to track down session leak problems.
	//
	// Defaults to false.
	TrackSessionHandles bool

	// healthCheckSampleInterval is how often the health checker samples live
	// session (for use in maintaining session pool size).
	//
	// Defaults to 1m.
	healthCheckSampleInterval time.Duration

	// sessionLabels for the sessions created in the session pool.
	sessionLabels map[string]string
}

// DefaultSessionPoolConfig is the default configuration for the session pool
// that will be used for a Spanner client, unless the user supplies a specific
// session pool config.
var DefaultSessionPoolConfig = SessionPoolConfig{
	MinOpened:           100,
	MaxOpened:           numChannels * 100,
	MaxBurst:            10,
	incStep:             25,
	WriteSessions:       0.2,
	HealthCheckWorkers:  10,
	HealthCheckInterval: healthCheckIntervalMins * time.Minute,
}

// errMinOpenedGTMapOpened returns error for SessionPoolConfig.MaxOpened < SessionPoolConfig.MinOpened when SessionPoolConfig.MaxOpened is set.
func errMinOpenedGTMaxOpened(maxOpened, minOpened uint64) error {
	return spannerErrorf(codes.InvalidArgument,
		"require SessionPoolConfig.MaxOpened >= SessionPoolConfig.MinOpened, got %d and %d", maxOpened, minOpened)
}

// errWriteFractionOutOfRange returns error for
// SessionPoolConfig.WriteFraction < 0 or SessionPoolConfig.WriteFraction > 1
func errWriteFractionOutOfRange(writeFraction float64) error {
	return spannerErrorf(codes.InvalidArgument,
		"require SessionPoolConfig.WriteSessions >= 0.0 && SessionPoolConfig.WriteSessions <= 1.0, got %.2f", writeFraction)
}

// errHealthCheckWorkersNegative returns error for
// SessionPoolConfig.HealthCheckWorkers < 0
func errHealthCheckWorkersNegative(workers int) error {
	return spannerErrorf(codes.InvalidArgument,
		"require SessionPoolConfig.HealthCheckWorkers >= 0, got %d", workers)
}

// errHealthCheckIntervalNegative returns error for
// SessionPoolConfig.HealthCheckInterval < 0
func errHealthCheckIntervalNegative(interval time.Duration) error {
	return spannerErrorf(codes.InvalidArgument,
		"require SessionPoolConfig.HealthCheckInterval >= 0, got %v", interval)
}

// validate verifies that the SessionPoolConfig is good for use.
func (spc *SessionPoolConfig) validate() error {
	if spc.MinOpened > spc.MaxOpened && spc.MaxOpened > 0 {
		return errMinOpenedGTMaxOpened(spc.MaxOpened, spc.MinOpened)
	}
	if spc.HealthCheckWorkers < 0 {
		return errHealthCheckWorkersNegative(spc.HealthCheckWorkers)
	}
	if spc.HealthCheckInterval < 0 {
		return errHealthCheckIntervalNegative(spc.HealthCheckInterval)
	}
	return nil
}

// sessionPool creates and caches Cloud Spanner sessions.
type sessionPool struct {
	// mu protects sessionPool from concurrent access.
	mu sync.Mutex
	// valid marks the validity of the session pool.
	valid bool
	// sc is used to create the sessions for the pool.
	sc *sessionClient
	// trackedSessionHandles contains all sessions handles that have been
	// checked out of the pool. The list is only filled if TrackSessionHandles
	// has been enabled.
	trackedSessionHandles list.List
	// idleList caches idle session IDs. Session IDs in this list can be
	// allocated for use.
	idleList list.List
	// mayGetSession is for broadcasting that session retrival/creation may
	// proceed.
	mayGetSession chan struct{}
	// sessionCreationError is the last error that occurred during session
	// creation and is propagated to any waiters waiting for a session.
	sessionCreationError error
	// numOpened is the total number of open sessions from the session pool.
	numOpened uint64
	// createReqs is the number of ongoing session creation requests.
	createReqs uint64
	// numWaiters is the number of processes waiting for a session to
	// become available.
	numWaiters uint64
	// disableBackgroundPrepareSessions indicates that the BeginTransaction
	// call for a read/write transaction failed with a permanent error, such as
	// PermissionDenied or `Database not found`. Further background calls to
	// prepare sessions will be disabled.
	disableBackgroundPrepareSessions bool
	// configuration of the session pool.
	SessionPoolConfig
	// hc is the health checker
	hc *healthChecker
	// rand is a separately sourced random generator.
	rand *rand.Rand
	// numInUse is the number of sessions that are currently in use (checked out
	// from the session pool).
	numInUse uint64
	// maxNumInUse is the maximum number of sessions in use concurrently in the
	// current 10 minute interval.
	maxNumInUse uint64
	// lastResetTime is the start time of the window for recording maxNumInUse.
	lastResetTime time.Time
	// numSessions is the number of sessions that are idle for read/write.
	numSessions uint64

	// mw is the maintenance window containing statistics for the max number of
	// sessions checked out of the pool during the last 10 minutes.
	mw *maintenanceWindow

	// tagMap is a map of all tags that are associated with the emitted metrics.
	tagMap *tag.Map
}

// newSessionPool creates a new session pool.
func newSessionPool(sc *sessionClient, config SessionPoolConfig) (*sessionPool, error) {
	if err := config.validate(); err != nil {
		return nil, err
	}
	pool := &sessionPool{
		sc:                sc,
		valid:             true,
		mayGetSession:     make(chan struct{}),
		SessionPoolConfig: config,
		mw:                newMaintenanceWindow(config.MaxOpened),
		rand:              rand.New(rand.NewSource(time.Now().UnixNano())),
	}
	if config.HealthCheckWorkers == 0 {
		// With 10 workers and assuming average latency of 5ms for
		// BeginTransaction, we will be able to prepare 2000 tx/sec in advance.
		// If the rate of takeWriteSession is more than that, it will degrade to
		// doing BeginTransaction inline.
		//
		// TODO: consider resizing the worker pool dynamically according to the load.
		config.HealthCheckWorkers = 10
	}
	if config.HealthCheckInterval == 0 {
		config.HealthCheckInterval = healthCheckIntervalMins * time.Minute
	}
	if config.healthCheckSampleInterval == 0 {
		config.healthCheckSampleInterval = time.Minute
	}

	_, instance, database, err := parseDatabaseName(sc.database)
	if err != nil {
		return nil, err
	}
	// Errors should not prevent initializing the session pool.
	ctx, err := tag.New(context.Background(),
		tag.Upsert(tagKeyClientID, sc.id),
		tag.Upsert(tagKeyDatabase, database),
		tag.Upsert(tagKeyInstance, instance),
		tag.Upsert(tagKeyLibVersion, internal.Version),
	)
	if err != nil {
		logf(pool.sc.logger, "Failed to create tag map, error: %v", err)
	}
	pool.tagMap = tag.FromContext(ctx)

	// On GCE VM, within the same region an healthcheck ping takes on average
	// 10ms to finish, given a 5 minutes interval and 10 healthcheck workers, a
	// healthChecker can effectively mantain
	// 100 checks_per_worker/sec * 10 workers * 300 seconds = 300K sessions.
	pool.hc = newHealthChecker(config.HealthCheckInterval, config.HealthCheckWorkers, config.healthCheckSampleInterval, pool)

	// First initialize the pool before we indicate that the healthchecker is
	// ready. This prevents the maintainer from starting before the pool has
	// been initialized, which means that we guarantee that the initial
	// sessions are created using BatchCreateSessions.
	if config.MinOpened > 0 {
		numSessions := minUint64(config.MinOpened, math.MaxInt32)
		if err := pool.initPool(numSessions); err != nil {
			return nil, err
		}
	}
	pool.recordStat(context.Background(), MaxAllowedSessionsCount, int64(config.MaxOpened))
	close(pool.hc.ready)
	return pool, nil
}

func (p *sessionPool) recordStat(ctx context.Context, m *stats.Int64Measure, n int64, tags ...tag.Tag) {
	ctx = tag.NewContext(ctx, p.tagMap)
	mutators := make([]tag.Mutator, len(tags))
	for i, t := range tags {
		mutators[i] = tag.Upsert(t.Key, t.Value)
	}
	ctx, err := tag.New(ctx, mutators...)
	if err != nil {
		logf(p.sc.logger, "Failed to tag metrics, error: %v", err)
	}
	recordStat(ctx, m, n)
}

func (p *sessionPool) initPool(numSessions uint64) error {
	p.mu.Lock()
	defer p.mu.Unlock()
	return p.growPoolLocked(numSessions, true)
}

func (p *sessionPool) growPoolLocked(numSessions uint64, distributeOverChannels bool) error {
	// Take budget before the actual session creation.
	numSessions = minUint64(numSessions, math.MaxInt32)
	p.numOpened += uint64(numSessions)
	p.recordStat(context.Background(), OpenSessionCount, int64(p.numOpened))
	p.createReqs += uint64(numSessions)
	// Asynchronously create a batch of sessions for the pool.
	return p.sc.batchCreateSessions(int32(numSessions), distributeOverChannels, p)
}

// sessionReady is executed by the SessionClient when a session has been
// created and is ready to use. This method will add the new session to the
// pool and decrease the number of sessions that is being created.
func (p *sessionPool) sessionReady(s *session) {
	p.mu.Lock()
	defer p.mu.Unlock()
	// Clear any session creation error.
	p.sessionCreationError = nil
	// Set this pool as the home pool of the session and register it with the
	// health checker.
	s.pool = p
	p.hc.register(s)
	p.createReqs--
	// Insert the session at a random position in the pool to prevent all
	// sessions affiliated with a channel to be placed at sequentially in the
	// pool.
	if p.idleList.Len() > 0 {
		pos := rand.Intn(p.idleList.Len())
		before := p.idleList.Front()
		for i := 0; i < pos; i++ {
			before = before.Next()
		}
		s.setIdleList(p.idleList.InsertBefore(s, before))
	} else {
		s.setIdleList(p.idleList.PushBack(s))
	}
	p.incNumSessionsLocked(context.Background())
	// Notify other waiters blocking on session creation.
	close(p.mayGetSession)
	p.mayGetSession = make(chan struct{})
}

// sessionCreationFailed is called by the SessionClient when the creation of one
// or more requested sessions finished with an error. sessionCreationFailed will
// decrease the number of sessions being created and notify any waiters that
// the session creation failed.
func (p *sessionPool) sessionCreationFailed(err error, numSessions int32) {
	p.mu.Lock()
	defer p.mu.Unlock()
	p.createReqs -= uint64(numSessions)
	p.numOpened -= uint64(numSessions)
	p.recordStat(context.Background(), OpenSessionCount, int64(p.numOpened))
	// Notify other waiters blocking on session creation.
	p.sessionCreationError = err
	close(p.mayGetSession)
	p.mayGetSession = make(chan struct{})
}

// isValid checks if the session pool is still valid.
func (p *sessionPool) isValid() bool {
	if p == nil {
		return false
	}
	p.mu.Lock()
	defer p.mu.Unlock()
	return p.valid
}

// close marks the session pool as closed and deletes all sessions in parallel.
// Any errors that are returned by the Delete RPC are logged but otherwise
// ignored, except for DeadlineExceeded errors, which are ignored and not
// logged.
func (p *sessionPool) close(ctx context.Context) {
	if p == nil {
		return
	}
	p.mu.Lock()
	if !p.valid {
		p.mu.Unlock()
		return
	}
	p.valid = false
	p.mu.Unlock()
	p.hc.close()
	// destroy all the sessions
	p.hc.mu.Lock()
	allSessions := make([]*session, len(p.hc.queue.sessions))
	copy(allSessions, p.hc.queue.sessions)
	p.hc.mu.Unlock()
	wg := sync.WaitGroup{}
	for _, s := range allSessions {
		wg.Add(1)
		go deleteSession(ctx, s, &wg)
	}
	wg.Wait()
}

func deleteSession(ctx context.Context, s *session, wg *sync.WaitGroup) {
	defer wg.Done()
	s.destroyWithContext(ctx, false)
}

// errInvalidSessionPool is the error for using an invalid session pool.
var errInvalidSessionPool = spannerErrorf(codes.InvalidArgument, "invalid session pool")

// errGetSessionTimeout returns error for context timeout during
// sessionPool.take().
var errGetSessionTimeout = spannerErrorf(codes.Canceled, "timeout / context canceled during getting session")

// newSessionHandle creates a new session handle for the given session for this
// session pool. The session handle will also hold a copy of the current call
// stack if the session pool has been configured to track the call stacks of
// sessions being checked out of the pool.
func (p *sessionPool) newSessionHandle(s *session) (sh *sessionHandle) {
	sh = &sessionHandle{session: s, checkoutTime: time.Now()}
	if p.TrackSessionHandles {
		p.mu.Lock()
		sh.trackedSessionHandle = p.trackedSessionHandles.PushBack(sh)
		p.mu.Unlock()
		sh.stack = debug.Stack()
	}
	return sh
}

// errGetSessionTimeout returns error for context timeout during
// sessionPool.take().
func (p *sessionPool) errGetSessionTimeout(ctx context.Context) error {
	var code codes.Code
	if ctx.Err() == context.DeadlineExceeded {
		code = codes.DeadlineExceeded
	} else {
		code = codes.Canceled
	}
	if p.TrackSessionHandles {
		return p.errGetSessionTimeoutWithTrackedSessionHandles(code)
	}
	return p.errGetBasicSessionTimeout(code)
}

// errGetBasicSessionTimeout returns error for context timout during
// sessionPool.take() without any tracked sessionHandles.
func (p *sessionPool) errGetBasicSessionTimeout(code codes.Code) error {
	return spannerErrorf(code, "timeout / context canceled during getting session.\n"+
		"Enable SessionPoolConfig.TrackSessionHandles if you suspect a session leak to get more information about the checked out sessions.")
}

// errGetSessionTimeoutWithTrackedSessionHandles returns error for context
// timout during sessionPool.take() including a stacktrace of each checked out
// session handle.
func (p *sessionPool) errGetSessionTimeoutWithTrackedSessionHandles(code codes.Code) error {
	err := spannerErrorf(code, "timeout / context canceled during getting session.")
	err.(*Error).additionalInformation = p.getTrackedSessionHandleStacksLocked()
	return err
}

// getTrackedSessionHandleStacksLocked returns a string containing the
// stacktrace of all currently checked out sessions of the pool. This method
// requires the caller to have locked p.mu.
func (p *sessionPool) getTrackedSessionHandleStacksLocked() string {
	p.mu.Lock()
	defer p.mu.Unlock()
	stackTraces := ""
	i := 1
	element := p.trackedSessionHandles.Front()
	for element != nil {
		sh := element.Value.(*sessionHandle)
		sh.mu.Lock()
		if sh.stack != nil {
			stackTraces = fmt.Sprintf("%s\n\nSession %d checked out of pool at %s by goroutine:\n%s", stackTraces, i, sh.checkoutTime.Format(time.RFC3339), sh.stack)
		}
		sh.mu.Unlock()
		element = element.Next()
		i++
	}
	return stackTraces
}

func (p *sessionPool) createSession(ctx context.Context) (*session, error) {
	trace.TracePrintf(ctx, nil, "Creating a new session")
	doneCreate := func(done bool) {
		p.mu.Lock()
		if !done {
			// Session creation failed, give budget back.
			p.numOpened--
			p.recordStat(ctx, OpenSessionCount, int64(p.numOpened))
		}
		p.createReqs--
		// Notify other waiters blocking on session creation.
		close(p.mayGetSession)
		p.mayGetSession = make(chan struct{})
		p.mu.Unlock()
	}
	s, err := p.sc.createSession(ctx)
	if err != nil {
		doneCreate(false)
		// Should return error directly because of the previous retries on
		// CreateSession RPC.
		// If the error is a timeout, there is a chance that the session was
		// created on the server but is not known to the session pool. This
		// session will then be garbage collected by the server after 1 hour.
		return nil, err
	}
	s.pool = p
	p.hc.register(s)
	doneCreate(true)
	return s, nil
}

func (p *sessionPool) isHealthy(s *session) bool {
	if s.getNextCheck().Add(2 * p.hc.getInterval()).Before(time.Now()) {
		if err := s.ping(); isSessionNotFoundError(err) {
			// The session is already bad, continue to fetch/create a new one.
			s.destroy(false)
			return false
		}
		p.hc.scheduledHC(s)
	}
	return true
}

// take returns a cached session if there are available ones; if there isn't
// any, it tries to allocate a new one.
func (p *sessionPool) take(ctx context.Context) (*sessionHandle, error) {
	trace.TracePrintf(ctx, nil, "Acquiring a session")
	for {
		var s *session

		p.mu.Lock()
		if !p.valid {
			p.mu.Unlock()
			return nil, errInvalidSessionPool
		}
		if p.idleList.Len() > 0 {
			// Idle sessions are available, get one from the top of the idle
			// list.
			s = p.idleList.Remove(p.idleList.Front()).(*session)
			trace.TracePrintf(ctx, map[string]interface{}{"sessionID": s.getID()},
				"Acquired session")
			p.decNumSessionsLocked(ctx)
		}
		if s != nil {
			s.setIdleList(nil)
			numCheckedOut := p.currSessionsCheckedOutLocked()
			p.mu.Unlock()
			p.mw.updateMaxSessionsCheckedOutDuringWindow(numCheckedOut)
			// From here, session is no longer in idle list, so healthcheck
			// workers won't destroy it. If healthcheck workers failed to
			// schedule healthcheck for the session timely, do the check here.
			// Because session check is still much cheaper than session
			// creation, they should be reused as much as possible.
			if !p.isHealthy(s) {
				continue
			}
			p.incNumInUse(ctx)
			return p.newSessionHandle(s), nil
		}

		// No session available. Start the creation of a new batch of sessions
		// if that is allowed, and then wait for a session to come available.
		if p.numWaiters >= p.createReqs {
			numSessions := minUint64(p.MaxOpened-p.numOpened, p.incStep)
			if err := p.growPoolLocked(numSessions, false); err != nil {
				p.mu.Unlock()
				return nil, err
			}
		}

		p.numWaiters++
		mayGetSession := p.mayGetSession
		p.mu.Unlock()
		trace.TracePrintf(ctx, nil, "Waiting for read-only session to become available")
		select {
		case <-ctx.Done():
			trace.TracePrintf(ctx, nil, "Context done waiting for session")
			p.recordStat(ctx, GetSessionTimeoutsCount, 1)
			p.mu.Lock()
			p.numWaiters--
			p.mu.Unlock()
			return nil, p.errGetSessionTimeout(ctx)
		case <-mayGetSession:
			p.mu.Lock()
			p.numWaiters--
			if p.sessionCreationError != nil {
				trace.TracePrintf(ctx, nil, "Error creating session: %v", p.sessionCreationError)
				err := p.sessionCreationError
				p.mu.Unlock()
				return nil, err
			}
			p.mu.Unlock()
		}
	}
}

// recycle puts session s back to the session pool's idle list, it returns true
// if the session pool successfully recycles session s.
func (p *sessionPool) recycle(s *session) bool {
	p.mu.Lock()
	defer p.mu.Unlock()
	return p.recycleLocked(s)
}

func (p *sessionPool) recycleLocked(s *session) bool {
	if !s.isValid() || !p.valid {
		// Reject the session if session is invalid or pool itself is invalid.
		return false
	}
	ctx := context.Background()
	// Put session at the top of the list to be handed out in LIFO order for load balancing
	// across channels.
	s.setIdleList(p.idleList.PushFront(s))
	p.incNumSessionsLocked(ctx)
	// Broadcast that a session has been returned to idle list.
	close(p.mayGetSession)
	p.mayGetSession = make(chan struct{})
	return true
}

// remove atomically removes session s from the session pool and invalidates s.
// If isExpire == true, the removal is triggered by session expiration and in
// such cases, only idle sessions can be removed.
func (p *sessionPool) remove(s *session, isExpire bool) bool {
	p.mu.Lock()
	defer p.mu.Unlock()
	if isExpire && (p.numOpened <= p.MinOpened || s.getIdleList() == nil) {
		// Don't expire session if the session is not in idle list (in use), or
		// if number of open sessions is going below p.MinOpened.
		return false
	}
	ol := s.setIdleList(nil)
	ctx := context.Background()
	// If the session is in the idlelist, remove it.
	if ol != nil {
		// Remove from the list it is in.
		p.idleList.Remove(ol)
		p.decNumSessionsLocked(ctx)
	}
	if s.invalidate() {
		// Decrease the number of opened sessions.
		p.numOpened--
		p.recordStat(ctx, OpenSessionCount, int64(p.numOpened))
		// Broadcast that a session has been destroyed.
		close(p.mayGetSession)
		p.mayGetSession = make(chan struct{})
		return true
	}
	return false
}

func (p *sessionPool) currSessionsCheckedOutLocked() uint64 {
	return p.numOpened - uint64(p.idleList.Len())
}

func (p *sessionPool) incNumInUse(ctx context.Context) {
	p.mu.Lock()
	p.incNumInUseLocked(ctx)
	p.mu.Unlock()
}

func (p *sessionPool) incNumInUseLocked(ctx context.Context) {
	p.numInUse++
	p.recordStat(ctx, SessionsCount, int64(p.numInUse), tagNumInUseSessions)
	p.recordStat(ctx, AcquiredSessionsCount, 1)
	if p.numInUse > p.maxNumInUse {
		p.maxNumInUse = p.numInUse
		p.recordStat(ctx, MaxInUseSessionsCount, int64(p.maxNumInUse))
	}
}

func (p *sessionPool) decNumInUseLocked(ctx context.Context) {
	p.numInUse--
	p.recordStat(ctx, SessionsCount, int64(p.numInUse), tagNumInUseSessions)
	p.recordStat(ctx, ReleasedSessionsCount, 1)
}

func (p *sessionPool) incNumSessionsLocked(ctx context.Context) {
	p.numSessions++
	p.recordStat(ctx, SessionsCount, int64(p.numSessions), tagNumSessions)
}

func (p *sessionPool) decNumSessionsLocked(ctx context.Context) {
	p.numSessions--
	p.recordStat(ctx, SessionsCount, int64(p.numSessions), tagNumSessions)
}

// hcHeap implements heap.Interface. It is used to create the priority queue for
// session healthchecks.
type hcHeap struct {
	sessions []*session
}

// Len implements heap.Interface.Len.
func (h hcHeap) Len() int {
	return len(h.sessions)
}

// Less implements heap.Interface.Less.
func (h hcHeap) Less(i, j int) bool {
	return h.sessions[i].getNextCheck().Before(h.sessions[j].getNextCheck())
}

// Swap implements heap.Interface.Swap.
func (h hcHeap) Swap(i, j int) {
	h.sessions[i], h.sessions[j] = h.sessions[j], h.sessions[i]
	h.sessions[i].setHcIndex(i)
	h.sessions[j].setHcIndex(j)
}

// Push implements heap.Interface.Push.
func (h *hcHeap) Push(s interface{}) {
	ns := s.(*session)
	ns.setHcIndex(len(h.sessions))
	h.sessions = append(h.sessions, ns)
}

// Pop implements heap.Interface.Pop.
func (h *hcHeap) Pop() interface{} {
	old := h.sessions
	n := len(old)
	s := old[n-1]
	h.sessions = old[:n-1]
	s.setHcIndex(-1)
	return s
}

// maintenanceWindowSize specifies the number of health check cycles that
// defines a maintenance window. The maintenance window keeps track of a
// rolling set of numbers for the number of maximum checked out sessions during
// the maintenance window. This is used by the maintainer to determine the
// number of sessions to create or delete at the end of each health check
// cycle.
const maintenanceWindowSize = 10

// maintenanceWindow contains the statistics that are gathered during a health
// check maintenance window.
type maintenanceWindow struct {
	mu sync.Mutex
	// maxSessionsCheckedOut contains the maximum number of sessions that was
	// checked out of the session pool during a health check cycle. This number
	// indicates the number of sessions that was actually needed by the pool to
	// serve the load during that cycle. The values are kept as a rolling set
	// containing the values for the past 10 cycles (minutes). The maintainer
	// uses these values to determine the number of sessions to keep at the end
	// of each cycle.
	maxSessionsCheckedOut [maintenanceWindowSize]uint64
}

// maxSessionsCheckedOutDuringWindow returns the maximum number of sessions
// that has been checked out during the last maintenance window of 10 cycles
// (minutes).
func (mw *maintenanceWindow) maxSessionsCheckedOutDuringWindow() uint64 {
	mw.mu.Lock()
	defer mw.mu.Unlock()
	var max uint64
	for _, cycleMax := range mw.maxSessionsCheckedOut {
		max = maxUint64(max, cycleMax)
	}
	return max
}

// updateMaxSessionsCheckedOutDuringWindow updates the maximum number of
// sessions that has been checked out of the pool during the current
// cycle of the maintenance window. A maintenance window consists of 10
// maintenance cycles. Each cycle keeps track of the max number of sessions in
// use during that cycle. The rolling maintenance window of 10 cycles is used
// to determine the number of sessions to keep at the end of a cycle by
// calculating the max in use during the last 10 cycles.
func (mw *maintenanceWindow) updateMaxSessionsCheckedOutDuringWindow(currNumSessionsCheckedOut uint64) {
	mw.mu.Lock()
	defer mw.mu.Unlock()
	mw.maxSessionsCheckedOut[0] = maxUint64(currNumSessionsCheckedOut, mw.maxSessionsCheckedOut[0])
}

// startNewCycle starts a new health check cycle with the specified number of
// checked out sessions as its initial value.
func (mw *maintenanceWindow) startNewCycle(currNumSessionsCheckedOut uint64) {
	mw.mu.Lock()
	defer mw.mu.Unlock()
	copy(mw.maxSessionsCheckedOut[1:], mw.maxSessionsCheckedOut[:9])
	mw.maxSessionsCheckedOut[0] = currNumSessionsCheckedOut
}

// newMaintenanceWindow creates a new maintenance window with all values for
// maxSessionsCheckedOut set to maxOpened. This ensures that a complete
// maintenance window must pass before the maintainer will start to delete any
// sessions.
func newMaintenanceWindow(maxOpened uint64) *maintenanceWindow {
	mw := &maintenanceWindow{}
	// Initialize the rolling window with max values to prevent the maintainer
	// from deleting sessions before a complete window of 10 cycles has
	// finished.
	for i := 0; i < maintenanceWindowSize; i++ {
		mw.maxSessionsCheckedOut[i] = maxOpened
	}
	return mw
}

// healthChecker performs periodical healthchecks on registered sessions.
type healthChecker struct {
	// mu protects concurrent access to healthChecker.
	mu sync.Mutex
	// queue is the priority queue for session healthchecks. Sessions with lower
	// nextCheck rank higher in the queue.
	queue hcHeap
	// interval is the average interval between two healthchecks on a session.
	interval time.Duration
	// workers is the number of concurrent healthcheck workers.
	workers int
	// waitWorkers waits for all healthcheck workers to exit
	waitWorkers sync.WaitGroup
	// pool is the underlying session pool.
	pool *sessionPool
	// sampleInterval is the interval of sampling by the maintainer.
	sampleInterval time.Duration
	// ready is used to signal that maintainer can start running.
	ready chan struct{}
	// done is used to signal that health checker should be closed.
	done chan struct{}
	// once is used for closing channel done only once.
	once             sync.Once
	maintainerCancel func()
}

// newHealthChecker initializes new instance of healthChecker.
func newHealthChecker(interval time.Duration, workers int, sampleInterval time.Duration, pool *sessionPool) *healthChecker {
	if workers <= 0 {
		workers = 1
	}
	hc := &healthChecker{
		interval:         interval,
		workers:          workers,
		pool:             pool,
		sampleInterval:   sampleInterval,
		ready:            make(chan struct{}),
		done:             make(chan struct{}),
		maintainerCancel: func() {},
	}
	hc.waitWorkers.Add(1)
	go hc.maintainer()
	for i := 1; i <= hc.workers; i++ {
		hc.waitWorkers.Add(1)
		go hc.worker(i)
	}
	return hc
}

// close closes the healthChecker and waits for all healthcheck workers to exit.
func (hc *healthChecker) close() {
	hc.mu.Lock()
	hc.maintainerCancel()
	hc.mu.Unlock()
	hc.once.Do(func() { close(hc.done) })
	hc.waitWorkers.Wait()
}

// isClosing checks if a healthChecker is already closing.
func (hc *healthChecker) isClosing() bool {
	select {
	case <-hc.done:
		return true
	default:
		return false
	}
}

// getInterval gets the healthcheck interval.
func (hc *healthChecker) getInterval() time.Duration {
	hc.mu.Lock()
	defer hc.mu.Unlock()
	return hc.interval
}

// scheduledHCLocked schedules next healthcheck on session s with the assumption
// that hc.mu is being held.
func (hc *healthChecker) scheduledHCLocked(s *session) {
	var constPart, randPart float64
	if !s.firstHCDone {
		// The first check will be scheduled in a large range to make requests
		// more evenly distributed. The first healthcheck will be scheduled
		// after [interval*0.2, interval*1.1) ns.
		constPart = float64(hc.interval) * 0.2
		randPart = hc.pool.rand.Float64() * float64(hc.interval) * 0.9
		s.firstHCDone = true
	} else {
		// The next healthcheck will be scheduled after
		// [interval*0.9, interval*1.1) ns.
		constPart = float64(hc.interval) * 0.9
		randPart = hc.pool.rand.Float64() * float64(hc.interval) * 0.2
	}
	// math.Ceil makes the value to be at least 1 ns.
	nsFromNow := int64(math.Ceil(constPart + randPart))
	s.setNextCheck(time.Now().Add(time.Duration(nsFromNow)))
	if hi := s.getHcIndex(); hi != -1 {
		// Session is still being tracked by healthcheck workers.
		heap.Fix(&hc.queue, hi)
	}
}

// scheduledHC schedules next healthcheck on session s. It is safe to be called
// concurrently.
func (hc *healthChecker) scheduledHC(s *session) {
	hc.mu.Lock()
	defer hc.mu.Unlock()
	hc.scheduledHCLocked(s)
}

// register registers a session with healthChecker for periodical healthcheck.
func (hc *healthChecker) register(s *session) {
	hc.mu.Lock()
	defer hc.mu.Unlock()
	hc.scheduledHCLocked(s)
	heap.Push(&hc.queue, s)
}

// unregister unregisters a session from healthcheck queue.
func (hc *healthChecker) unregister(s *session) {
	hc.mu.Lock()
	defer hc.mu.Unlock()
	oi := s.setHcIndex(-1)
	if oi >= 0 {
		heap.Remove(&hc.queue, oi)
	}
}

// markDone marks that health check for session has been performed.
func (hc *healthChecker) markDone(s *session) {
	hc.mu.Lock()
	defer hc.mu.Unlock()
	s.checkingHealth = false
}

// healthCheck checks the health of the session and pings it if needed.
func (hc *healthChecker) healthCheck(s *session) {
	defer hc.markDone(s)
	if !s.pool.isValid() {
		// Session pool is closed, perform a garbage collection.
		s.destroy(false)
		return
	}
	if err := s.ping(); isSessionNotFoundError(err) {
		// Ping failed, destroy the session.
		s.destroy(false)
	}
}

// worker performs the healthcheck on sessions in healthChecker's priority
// queue.
func (hc *healthChecker) worker(i int) {
	// Returns a session which we should ping to keep it alive.
	getNextForPing := func() *session {
		hc.pool.mu.Lock()
		defer hc.pool.mu.Unlock()
		hc.mu.Lock()
		defer hc.mu.Unlock()
		if hc.queue.Len() <= 0 {
			// Queue is empty.
			return nil
		}
		s := hc.queue.sessions[0]
		if s.getNextCheck().After(time.Now()) && hc.pool.valid {
			// All sessions have been checked recently.
			return nil
		}
		hc.scheduledHCLocked(s)
		if !s.checkingHealth {
			s.checkingHealth = true
			return s
		}
		return nil
	}

	for {
		if hc.isClosing() {
			// Exit when the pool has been closed and all sessions have been
			// destroyed or when health checker has been closed.
			hc.waitWorkers.Done()
			return
		}
		rs := getNextForPing()
		if rs == nil {
			// No work to be done so sleep to avoid burning CPU.
			pause := int64(100 * time.Millisecond)
			if pause > int64(hc.interval) {
				pause = int64(hc.interval)
			}
			select {
			case <-time.After(time.Duration(rand.Int63n(pause) + pause/2)):
			case <-hc.done:
			}
			continue
		}
		hc.healthCheck(rs)
	}
}

// maintainer maintains the number of sessions in the pool based on the session
// pool configuration and the current and historical number of sessions checked
// out of the pool. The maintainer will:
//  1. Ensure that the session pool contains at least MinOpened sessions.
//  2. If the current number of sessions in the pool exceeds the greatest number
//     of checked out sessions (=sessions in use) during the last 10 minutes,
//     and the delta is larger than MaxIdleSessions, the maintainer will reduce
//     the number of sessions to maxSessionsInUseDuringWindow+MaxIdleSessions.
func (hc *healthChecker) maintainer() {
	// Wait until the pool is ready.
	<-hc.ready

	for iteration := uint64(0); ; iteration++ {
		if hc.isClosing() {
			hc.waitWorkers.Done()
			return
		}

		hc.pool.mu.Lock()
		currSessionsOpened := hc.pool.numOpened
		maxIdle := hc.pool.MaxIdle
		minOpened := hc.pool.MinOpened

		// Reset the start time for recording the maximum number of sessions
		// in the pool.
		now := time.Now()
		if now.After(hc.pool.lastResetTime.Add(10 * time.Minute)) {
			hc.pool.maxNumInUse = hc.pool.numInUse
			hc.pool.recordStat(context.Background(), MaxInUseSessionsCount, int64(hc.pool.maxNumInUse))
			hc.pool.lastResetTime = now
		}
		hc.pool.mu.Unlock()
		// Get the maximum number of sessions in use during the current
		// maintenance window.
		maxSessionsInUseDuringWindow := hc.pool.mw.maxSessionsCheckedOutDuringWindow()
		hc.mu.Lock()
		ctx, cancel := context.WithTimeout(context.Background(), hc.sampleInterval)
		hc.maintainerCancel = cancel
		hc.mu.Unlock()

		// Grow or shrink pool if needed.
		// The number of sessions in the pool should be in the range
		// [Config.MinOpened, Config.MaxIdle+maxSessionsInUseDuringWindow]
		if currSessionsOpened < minOpened {
			if err := hc.growPoolInBatch(ctx, minOpened); err != nil {
				logf(hc.pool.sc.logger, "failed to grow pool: %v", err)
			}
		} else if maxIdle+maxSessionsInUseDuringWindow < currSessionsOpened {
			hc.shrinkPool(ctx, maxIdle+maxSessionsInUseDuringWindow)
		}

		select {
		case <-ctx.Done():
		case <-hc.done:
			cancel()
		}
		// Cycle the maintenance window. This will remove the oldest cycle and
		// add a new cycle at the beginning of the maintenance window with the
		// currently checked out number of sessions as the max number of
		// sessions in use in this cycle. This value will be increased during
		// the next cycle if it increases.
		hc.pool.mu.Lock()
		currSessionsInUse := hc.pool.currSessionsCheckedOutLocked()
		hc.pool.mu.Unlock()
		hc.pool.mw.startNewCycle(currSessionsInUse)
	}
}

func (hc *healthChecker) growPoolInBatch(ctx context.Context, growToNumSessions uint64) error {
	hc.pool.mu.Lock()
	defer hc.pool.mu.Unlock()
	numSessions := growToNumSessions - hc.pool.numOpened
	return hc.pool.growPoolLocked(numSessions, false)
}

// shrinkPool scales down the session pool. The method will stop deleting
// sessions when shrinkToNumSessions number of sessions in the pool has
// been reached. The method will also stop deleting sessions if it detects that
// another process has started creating sessions for the pool again, for
// example through the take() method.
func (hc *healthChecker) shrinkPool(ctx context.Context, shrinkToNumSessions uint64) {
	hc.pool.mu.Lock()
	maxSessionsToDelete := int(hc.pool.numOpened - shrinkToNumSessions)
	hc.pool.mu.Unlock()
	var deleted int
	var prevNumOpened uint64 = math.MaxUint64
	for {
		if ctx.Err() != nil {
			return
		}

		p := hc.pool
		p.mu.Lock()
		// Check if the number of open sessions has increased. If it has, we
		// should stop deleting sessions, as the load has increased and
		// additional sessions are needed.
		if p.numOpened >= prevNumOpened {
			p.mu.Unlock()
			break
		}
		prevNumOpened = p.numOpened

		// Check on both whether we have reached the number of open sessions as
		// well as the number of sessions to delete, in case sessions have been
		// deleted by other methods because they have expired or deemed
		// invalid.
		if shrinkToNumSessions >= p.numOpened || deleted >= maxSessionsToDelete {
			p.mu.Unlock()
			break
		}

		var s *session
		if p.idleList.Len() > 0 {
			s = p.idleList.Front().Value.(*session)
		}
		p.mu.Unlock()
		if s != nil {
			deleted++
			// destroy session as expire.
			s.destroy(true)
		} else {
			break
		}
	}
}

// maxUint64 returns the maximum of two uint64.
func maxUint64(a, b uint64) uint64 {
	if a > b {
		return a
	}
	return b
}

// minUint64 returns the minimum of two uint64.
func minUint64(a, b uint64) uint64 {
	if a > b {
		return b
	}
	return a
}

// sessionResourceType is the type name of Spanner sessions.
const sessionResourceType = "type.googleapis.com/google.spanner.v1.Session"

// isSessionNotFoundError returns true if the given error is a
// `Session not found` error.
func isSessionNotFoundError(err error) bool {
	if err == nil {
		return false
	}
	if ErrCode(err) == codes.NotFound {
		if rt, ok := extractResourceType(err); ok {
			return rt == sessionResourceType
		}
	}
	return strings.Contains(err.Error(), "Session not found")
}

func isFailedInlineBeginTransaction(err error) bool {
	if err == nil {
		return false
	}
	return ErrCode(err) == codes.Internal && strings.Contains(err.Error(), errInlineBeginTransactionFailed().Error())
}

// isClientClosing returns true if the given error is a
// `Connection is closing` error.
func isClientClosing(err error) bool {
	if err == nil {
		return false
	}
	return ErrCode(err) == codes.Canceled && strings.Contains(err.Error(), "the client connection is closing")
}