internal/timeseries: New package.

This implements a time series data structure.
It is not a general purpose package, but will be used
by the upcoming trace package.

Change-Id: I3aa547b2f76582fea246b2b35b465b35499f3fda
Reviewed-on: https://go-review.googlesource.com/10720Reviewed-by: Andrew Gerrand <adg@golang.org>

internal/timeseries/timeseries.go

+// Copyright 2015 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package timeseries implements a time series structure for stats collection.
+package timeseries // import "golang.org/x/net/internal/timeseries"
+
+import (
+	"fmt"
+	"log"
+	"time"
+)
+
+const (
+	timeSeriesNumBuckets       = 64
+	minuteHourSeriesNumBuckets = 60
+)
+
+var timeSeriesResolutions = []time.Duration{
+	1 * time.Second,
+	10 * time.Second,
+	1 * time.Minute,
+	10 * time.Minute,
+	1 * time.Hour,
+	6 * time.Hour,
+	24 * time.Hour,          // 1 day
+	7 * 24 * time.Hour,      // 1 week
+	4 * 7 * 24 * time.Hour,  // 4 weeks
+	16 * 7 * 24 * time.Hour, // 16 weeks
+}
+
+var minuteHourSeriesResolutions = []time.Duration{
+	1 * time.Second,
+	1 * time.Minute,
+}
+
+// An Observable is a kind of data that can be aggregated in a time series.
+type Observable interface {
+	Multiply(ratio float64)    // Multiplies the data in self by a given ratio
+	Add(other Observable)      // Adds the data from a different observation to self
+	Clear()                    // Clears the observation so it can be reused.
+	CopyFrom(other Observable) // Copies the contents of a given observation to self
+}
+
+// Float attaches the methods of Observable to a float64.
+type Float float64
+
+// NewFloat returns a Float.
+func NewFloat() Observable {
+	f := Float(0)
+	return &f
+}
+
+// String returns the float as a string.
+func (f *Float) String() string { return fmt.Sprintf("%g", f.Value()) }
+
+// Value returns the float's value.
+func (f *Float) Value() float64 { return float64(*f) }
+
+func (f *Float) Multiply(ratio float64) { *f *= Float(ratio) }
+
+func (f *Float) Add(other Observable) {
+	o := other.(*Float)
+	*f += *o
+}
+
+func (f *Float) Clear() { *f = 0 }
+
+func (f *Float) CopyFrom(other Observable) {
+	o := other.(*Float)
+	*f = *o
+}
+
+// A Clock tells the current time.
+type Clock interface {
+	Time() time.Time
+}
+
+type defaultClock int
+
+var defaultClockInstance defaultClock
+
+func (defaultClock) Time() time.Time { return time.Now() }
+
+// Information kept per level. Each level consists of a circular list of
+// observations. The start of the level may be derived from end and the
+// len(buckets) * sizeInMillis.
+type tsLevel struct {
+	oldest   int               // index to oldest bucketed Observable
+	newest   int               // index to newest bucketed Observable
+	end      time.Time         // end timestamp for this level
+	size     time.Duration     // duration of the bucketed Observable
+	buckets  []Observable      // collections of observations
+	provider func() Observable // used for creating new Observable
+}
+
+func (l *tsLevel) Clear() {
+	l.oldest = 0
+	l.newest = len(l.buckets) - 1
+	l.end = time.Time{}
+	for i := range l.buckets {
+		if l.buckets[i] != nil {
+			l.buckets[i].Clear()
+			l.buckets[i] = nil
+		}
+	}
+}
+
+func (l *tsLevel) InitLevel(size time.Duration, numBuckets int, f func() Observable) {
+	l.size = size
+	l.provider = f
+	l.buckets = make([]Observable, numBuckets)
+}
+
+// Keeps a sequence of levels. Each level is responsible for storing data at
+// a given resolution. For example, the first level stores data at a one
+// minute resolution while the second level stores data at a one hour
+// resolution.
+
+// Each level is represented by a sequence of buckets. Each bucket spans an
+// interval equal to the resolution of the level. New observations are added
+// to the last bucket.
+type timeSeries struct {
+	provider    func() Observable // make more Observable
+	numBuckets  int               // number of buckets in each level
+	levels      []*tsLevel        // levels of bucketed Observable
+	lastAdd     time.Time         // time of last Observable tracked
+	total       Observable        // convenient aggregation of all Observable
+	clock       Clock             // Clock for getting current time
+	pending     Observable        // observations not yet bucketed
+	pendingTime time.Time         // what time are we keeping in pending
+	dirty       bool              // if there are pending observations
+}
+
+// init initializes a level according to the supplied criteria.
+func (ts *timeSeries) init(resolutions []time.Duration, f func() Observable, numBuckets int, clock Clock) {
+	ts.provider = f
+	ts.numBuckets = numBuckets
+	ts.clock = clock
+	ts.levels = make([]*tsLevel, len(resolutions))
+
+	for i := range resolutions {
+		if i > 0 && resolutions[i-1] >= resolutions[i] {
+			log.Print("timeseries: resolutions must be monotonically increasing")
+			break
+		}
+		newLevel := new(tsLevel)
+		newLevel.InitLevel(resolutions[i], ts.numBuckets, ts.provider)
+		ts.levels[i] = newLevel
+	}
+
+	ts.Clear()
+}
+
+// Clear removes all observations from the time series.
+func (ts *timeSeries) Clear() {
+	ts.lastAdd = time.Time{}
+	ts.total = ts.resetObservation(ts.total)
+	ts.pending = ts.resetObservation(ts.pending)
+	ts.pendingTime = time.Time{}
+	ts.dirty = false
+
+	for i := range ts.levels {
+		ts.levels[i].Clear()
+	}
+}
+
+// Add records an observation at the current time.
+func (ts *timeSeries) Add(observation Observable) {
+	ts.AddWithTime(observation, ts.clock.Time())
+}
+
+// AddWithTime records an observation at the specified time.
+func (ts *timeSeries) AddWithTime(observation Observable, t time.Time) {
+
+	smallBucketDuration := ts.levels[0].size
+
+	if t.After(ts.lastAdd) {
+		ts.lastAdd = t
+	}
+
+	if t.After(ts.pendingTime) {
+		ts.advance(t)
+		ts.mergePendingUpdates()
+		ts.pendingTime = ts.levels[0].end
+		ts.pending.CopyFrom(observation)
+		ts.dirty = true
+	} else if t.After(ts.pendingTime.Add(-1 * smallBucketDuration)) {
+		// The observation is close enough to go into the pending bucket.
+		// This compensates for clock skewing and small scheduling delays
+		// by letting the update stay in the fast path.
+		ts.pending.Add(observation)
+		ts.dirty = true
+	} else {
+		ts.mergeValue(observation, t)
+	}
+}
+
+// mergeValue inserts the observation at the specified time in the past into all levels.
+func (ts *timeSeries) mergeValue(observation Observable, t time.Time) {
+	for _, level := range ts.levels {
+		index := (ts.numBuckets - 1) - int(level.end.Sub(t)/level.size)
+		if 0 <= index && index < ts.numBuckets {
+			bucketNumber := (level.oldest + index) % ts.numBuckets
+			if level.buckets[bucketNumber] == nil {
+				level.buckets[bucketNumber] = level.provider()
+			}
+			level.buckets[bucketNumber].Add(observation)
+		}
+	}
+	ts.total.Add(observation)
+}
+
+// mergePendingUpdates applies the pending updates into all levels.
+func (ts *timeSeries) mergePendingUpdates() {
+	if ts.dirty {
+		ts.mergeValue(ts.pending, ts.pendingTime)
+		ts.pending = ts.resetObservation(ts.pending)
+		ts.dirty = false
+	}
+}
+
+// advance cycles the buckets at each level until the latest bucket in
+// each level can hold the time specified.
+func (ts *timeSeries) advance(t time.Time) {
+	if !t.After(ts.levels[0].end) {
+		return
+	}
+	for i := 0; i < len(ts.levels); i++ {
+		level := ts.levels[i]
+		if !level.end.Before(t) {
+			break
+		}
+
+		// If the time is sufficiently far, just clear the level and advance
+		// directly.
+		if !t.Before(level.end.Add(level.size * time.Duration(ts.numBuckets))) {
+			for _, b := range level.buckets {
+				ts.resetObservation(b)
+			}
+			level.end = time.Unix(0, (t.UnixNano()/level.size.Nanoseconds())*level.size.Nanoseconds())
+		}
+
+		for t.After(level.end) {
+			level.end = level.end.Add(level.size)
+			level.newest = level.oldest
+			level.oldest = (level.oldest + 1) % ts.numBuckets
+			ts.resetObservation(level.buckets[level.newest])
+		}
+
+		t = level.end
+	}
+}
+
+// Latest returns the sum of the num latest buckets from the level.
+func (ts *timeSeries) Latest(level, num int) Observable {
+	now := ts.clock.Time()
+	if ts.levels[0].end.Before(now) {
+		ts.advance(now)
+	}
+
+	ts.mergePendingUpdates()
+
+	result := ts.provider()
+	l := ts.levels[level]
+	index := l.newest
+
+	for i := 0; i < num; i++ {
+		if l.buckets[index] != nil {
+			result.Add(l.buckets[index])
+		}
+		if index == 0 {
+			index = ts.numBuckets
+		}
+		index--
+	}
+
+	return result
+}
+
+// LatestBuckets returns a copy of the num latest buckets from level.
+func (ts *timeSeries) LatestBuckets(level, num int) []Observable {
+	if level < 0 || level > len(ts.levels) {
+		log.Print("timeseries: bad level argument: ", level)
+		return nil
+	}
+	if num < 0 || num >= ts.numBuckets {
+		log.Print("timeseries: bad num argument: ", num)
+		return nil
+	}
+
+	results := make([]Observable, num)
+	now := ts.clock.Time()
+	if ts.levels[0].end.Before(now) {
+		ts.advance(now)
+	}
+
+	ts.mergePendingUpdates()
+
+	l := ts.levels[level]
+	index := l.newest
+
+	for i := 0; i < num; i++ {
+		result := ts.provider()
+		results[i] = result
+		if l.buckets[index] != nil {
+			result.CopyFrom(l.buckets[index])
+		}
+
+		if index == 0 {
+			index = ts.numBuckets
+		}
+		index -= 1
+	}
+	return results
+}
+
+// ScaleBy updates observations by scaling by factor.
+func (ts *timeSeries) ScaleBy(factor float64) {
+	for _, l := range ts.levels {
+		for i := 0; i < ts.numBuckets; i++ {
+			l.buckets[i].Multiply(factor)
+		}
+	}
+
+	ts.total.Multiply(factor)
+	ts.pending.Multiply(factor)
+}
+
+// Range returns the sum of observations added over the specified time range.
+// If start or finish times don't fall on bucket boundaries of the same
+// level, then return values are approximate answers.
+func (ts *timeSeries) Range(start, finish time.Time) Observable {
+	return ts.ComputeRange(start, finish, 1)[0]
+}
+
+// Recent returns the sum of observations from the last delta.
+func (ts *timeSeries) Recent(delta time.Duration) Observable {
+	now := ts.clock.Time()
+	return ts.Range(now.Add(-delta), now)
+}
+
+// Total returns the total of all observations.
+func (ts *timeSeries) Total() Observable {
+	ts.mergePendingUpdates()
+	return ts.total
+}
+
+// ComputeRange computes a specified number of values into a slice using
+// the observations recorded over the specified time period. The return
+// values are approximate if the start or finish times don't fall on the
+// bucket boundaries at the same level or if the number of buckets spanning
+// the range is not an integral multiple of num.
+func (ts *timeSeries) ComputeRange(start, finish time.Time, num int) []Observable {
+	if start.After(finish) {
+		log.Printf("timeseries: start > finish, %v>%v", start, finish)
+		return nil
+	}
+
+	if num < 0 {
+		log.Printf("timeseries: num < 0, %v", num)
+		return nil
+	}
+
+	results := make([]Observable, num)
+
+	for _, l := range ts.levels {
+		if !start.Before(l.end.Add(-l.size * time.Duration(ts.numBuckets))) {
+			ts.extract(l, start, finish, num, results)
+			return results
+		}
+	}
+
+	// Failed to find a level that covers the desired range.  So just
+	// extract from the last level, even if it doesn't cover the entire
+	// desired range.
+	ts.extract(ts.levels[len(ts.levels)-1], start, finish, num, results)
+
+	return results
+}
+
+// RecentList returns the specified number of values in slice over the most
+// recent time period of the specified range.
+func (ts *timeSeries) RecentList(delta time.Duration, num int) []Observable {
+	if delta < 0 {
+		return nil
+	}
+	now := ts.clock.Time()
+	return ts.ComputeRange(now.Add(-delta), now, num)
+}
+
+// extract returns a slice of specified number of observations from a given
+// level over a given range.
+func (ts *timeSeries) extract(l *tsLevel, start, finish time.Time, num int, results []Observable) {
+	ts.mergePendingUpdates()
+
+	srcInterval := l.size
+	dstInterval := finish.Sub(start) / time.Duration(num)
+	dstStart := start
+	srcStart := l.end.Add(-srcInterval * time.Duration(ts.numBuckets))
+
+	srcIndex := 0
+
+	// Where should scanning start?
+	if dstStart.After(srcStart) {
+		advance := dstStart.Sub(srcStart) / srcInterval
+		srcIndex += int(advance)
+		srcStart = srcStart.Add(advance * srcInterval)
+	}
+
+	// The i'th value is computed as show below.
+	// interval = (finish/start)/num
+	// i'th value = sum of observation in range
+	//   [ start + i       * interval,
+	//     start + (i + 1) * interval )
+	for i := 0; i < num; i++ {
+		results[i] = ts.resetObservation(results[i])
+		dstEnd := dstStart.Add(dstInterval)
+		for srcIndex < ts.numBuckets && srcStart.Before(dstEnd) {
+			srcEnd := srcStart.Add(srcInterval)
+			if srcEnd.After(ts.lastAdd) {
+				srcEnd = ts.lastAdd
+			}
+
+			if !srcEnd.Before(dstStart) {
+				srcValue := l.buckets[(srcIndex+l.oldest)%ts.numBuckets]
+				if !srcStart.Before(dstStart) && !srcEnd.After(dstEnd) {
+					// dst completely contains src.
+					if srcValue != nil {
+						results[i].Add(srcValue)
+					}
+				} else {
+					// dst partially overlaps src.
+					overlapStart := maxTime(srcStart, dstStart)
+					overlapEnd := minTime(srcEnd, dstEnd)
+					base := srcEnd.Sub(srcStart)
+					fraction := overlapEnd.Sub(overlapStart).Seconds() / base.Seconds()
+
+					used := ts.provider()
+					if srcValue != nil {
+						used.CopyFrom(srcValue)
+					}
+					used.Multiply(fraction)
+					results[i].Add(used)
+				}
+
+				if srcEnd.After(dstEnd) {
+					break
+				}
+			}
+			srcIndex++
+			srcStart = srcStart.Add(srcInterval)
+		}
+		dstStart = dstStart.Add(dstInterval)
+	}
+}
+
+// resetObservation clears the content so the struct may be reused.
+func (ts *timeSeries) resetObservation(observation Observable) Observable {
+	if observation == nil {
+		observation = ts.provider()
+	} else {
+		observation.Clear()
+	}
+	return observation
+}
+
+// TimeSeries tracks data at granularities from 1 second to 16 weeks.
+type TimeSeries struct {
+	timeSeries
+}
+
+// NewTimeSeries creates a new TimeSeries using the function provided for creating new Observable.
+func NewTimeSeries(f func() Observable) *TimeSeries {
+	return NewTimeSeriesWithClock(f, defaultClockInstance)
+}
+
+// NewTimeSeriesWithClock creates a new TimeSeries using the function provided for creating new Observable and the clock for
+// assigning timestamps.
+func NewTimeSeriesWithClock(f func() Observable, clock Clock) *TimeSeries {
+	ts := new(TimeSeries)
+	ts.timeSeries.init(timeSeriesResolutions, f, timeSeriesNumBuckets, clock)
+	return ts
+}
+
+// MinuteHourSeries tracks data at granularities of 1 minute and 1 hour.
+type MinuteHourSeries struct {
+	timeSeries
+}
+
+// NewMinuteHourSeries creates a new MinuteHourSeries using the function provided for creating new Observable.
+func NewMinuteHourSeries(f func() Observable) *MinuteHourSeries {
+	return NewMinuteHourSeriesWithClock(f, defaultClockInstance)
+}
+
+// NewMinuteHourSeriesWithClock creates a new MinuteHourSeries using the function provided for creating new Observable and the clock for
+// assigning timestamps.
+func NewMinuteHourSeriesWithClock(f func() Observable, clock Clock) *MinuteHourSeries {
+	ts := new(MinuteHourSeries)
+	ts.timeSeries.init(minuteHourSeriesResolutions, f,
+		minuteHourSeriesNumBuckets, clock)
+	return ts
+}
+
+func (ts *MinuteHourSeries) Minute() Observable {
+	return ts.timeSeries.Latest(0, 60)
+}
+
+func (ts *MinuteHourSeries) Hour() Observable {
+	return ts.timeSeries.Latest(1, 60)
+}
+
+func minTime(a, b time.Time) time.Time {
+	if a.Before(b) {
+		return a
+	}
+	return b
+}
+
+func maxTime(a, b time.Time) time.Time {
+	if a.After(b) {
+		return a
+	}
+	return b
+}

internal/timeseries/timeseries_test.go

+// Copyright 2015 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package timeseries
+
+import (
+	"math"
+	"testing"
+	"time"
+)
+
+func isNear(x *Float, y float64, tolerance float64) bool {
+	return math.Abs(x.Value()-y) < tolerance
+}
+
+func isApproximate(x *Float, y float64) bool {
+	return isNear(x, y, 1e-2)
+}
+
+func checkApproximate(t *testing.T, o Observable, y float64) {
+	x := o.(*Float)
+	if !isApproximate(x, y) {
+		t.Errorf("Wanted %g, got %g", y, x.Value())
+	}
+}
+
+func checkNear(t *testing.T, o Observable, y, tolerance float64) {
+	x := o.(*Float)
+	if !isNear(x, y, tolerance) {
+		t.Errorf("Wanted %g +- %g, got %g", y, tolerance, x.Value())
+	}
+}
+
+var baseTime = time.Date(2013, 1, 1, 0, 0, 0, 0, time.UTC)
+
+func tu(s int64) time.Time {
+	return baseTime.Add(time.Duration(s) * time.Second)
+}
+
+func tu2(s int64, ns int64) time.Time {
+	return baseTime.Add(time.Duration(s)*time.Second + time.Duration(ns)*time.Nanosecond)
+}
+
+func TestBasicTimeSeries(t *testing.T) {
+	ts := NewTimeSeries(NewFloat)
+	fo := new(Float)
+	*fo = Float(10)
+	ts.AddWithTime(fo, tu(1))
+	ts.AddWithTime(fo, tu(1))
+	ts.AddWithTime(fo, tu(1))
+	ts.AddWithTime(fo, tu(1))
+	checkApproximate(t, ts.Range(tu(0), tu(1)), 40)
+	checkApproximate(t, ts.Total(), 40)
+	ts.AddWithTime(fo, tu(3))
+	ts.AddWithTime(fo, tu(3))
+	ts.AddWithTime(fo, tu(3))
+	checkApproximate(t, ts.Range(tu(0), tu(2)), 40)
+	checkApproximate(t, ts.Range(tu(2), tu(4)), 30)
+	checkApproximate(t, ts.Total(), 70)
+	ts.AddWithTime(fo, tu(1))
+	ts.AddWithTime(fo, tu(1))
+	checkApproximate(t, ts.Range(tu(0), tu(2)), 60)
+	checkApproximate(t, ts.Range(tu(2), tu(4)), 30)
+	checkApproximate(t, ts.Total(), 90)
+	*fo = Float(100)
+	ts.AddWithTime(fo, tu(100))
+	checkApproximate(t, ts.Range(tu(99), tu(100)), 100)
+	checkApproximate(t, ts.Range(tu(0), tu(4)), 36)
+	checkApproximate(t, ts.Total(), 190)
+	*fo = Float(10)
+	ts.AddWithTime(fo, tu(1))
+	ts.AddWithTime(fo, tu(1))
+	checkApproximate(t, ts.Range(tu(0), tu(4)), 44)
+	checkApproximate(t, ts.Range(tu(37), tu2(100, 100e6)), 100)
+	checkApproximate(t, ts.Range(tu(50), tu2(100, 100e6)), 100)
+	checkApproximate(t, ts.Range(tu(99), tu2(100, 100e6)), 100)
+	checkApproximate(t, ts.Total(), 210)
+
+	for i, l := range ts.ComputeRange(tu(36), tu(100), 64) {
+		if i == 63 {
+			checkApproximate(t, l, 100)
+		} else {
+			checkApproximate(t, l, 0)
+		}
+	}
+
+	checkApproximate(t, ts.Range(tu(0), tu(100)), 210)
+	checkApproximate(t, ts.Range(tu(10), tu(100)), 100)
+
+	for i, l := range ts.ComputeRange(tu(0), tu(100), 100) {
+		if i < 10 {
+			checkApproximate(t, l, 11)
+		} else if i >= 90 {
+			checkApproximate(t, l, 10)
+		} else {
+			checkApproximate(t, l, 0)
+		}
+	}
+}
+
+func TestFloat(t *testing.T) {
+	f := Float(1)
+	if g, w := f.String(), "1"; g != w {
+		t.Errorf("Float(1).String = %q; want %q", g, w)
+	}
+	f2 := Float(2)
+	var o Observable = &f2
+	f.Add(o)
+	if g, w := f.Value(), 3.0; g != w {
+		t.Errorf("Float post-add = %v; want %v", g, w)
+	}
+	f.Multiply(2)
+	if g, w := f.Value(), 6.0; g != w {
+		t.Errorf("Float post-multiply = %v; want %v", g, w)
+	}
+	f.Clear()
+	if g, w := f.Value(), 0.0; g != w {
+		t.Errorf("Float post-clear = %v; want %v", g, w)
+	}
+	f.CopyFrom(&f2)
+	if g, w := f.Value(), 2.0; g != w {
+		t.Errorf("Float post-CopyFrom = %v; want %v", g, w)
+	}
+}
+
+type mockClock struct {
+	time time.Time
+}
+
+func (m *mockClock) Time() time.Time { return m.time }
+func (m *mockClock) Set(t time.Time) { m.time = t }
+
+const buckets = 6
+
+var testResolutions = []time.Duration{
+	10 * time.Second,  // level holds one minute of observations
+	100 * time.Second, // level holds ten minutes of observations
+	10 * time.Minute,  // level holds one hour of observations
+}
+
+// TestTimeSeries uses a small number of buckets to force a higher
+// error rate on approximations from the timeseries.
+type TestTimeSeries struct {
+	timeSeries
+}
+
+func TestExpectedErrorRate(t *testing.T) {
+	ts := new(TestTimeSeries)
+	fake := new(mockClock)
+	fake.Set(time.Now())
+	ts.timeSeries.init(testResolutions, NewFloat, buckets, fake)
+	for i := 1; i <= 61*61; i++ {
+		fake.Set(fake.Time().Add(1 * time.Second))
+		ob := Float(1)
+		ts.AddWithTime(&ob, fake.Time())
+
+		// The results should be accurate within one missing bucket (1/6) of the observations recorded.
+		checkNear(t, ts.Latest(0, buckets), min(float64(i), 60), 10)
+		checkNear(t, ts.Latest(1, buckets), min(float64(i), 600), 100)
+		checkNear(t, ts.Latest(2, buckets), min(float64(i), 3600), 600)
+	}
+}
+
+func min(a, b float64) float64 {
+	if a < b {
+		return a
+	}
+	return b
+}