package metrics
import (
"math"
"math/rand"
"sort"
"sync"
"time"
)
const rescaleThreshold = time.Hour
// Samples maintain a statistically-significant selection of values from
// a stream.
type Sample interface {
Clear()
Count() int64
Max() int64
Mean() float64
Min() int64
Percentile(float64) float64
Percentiles([]float64) []float64
Size() int
Snapshot() Sample
StdDev() float64
Sum() int64
Update(int64)
Values() []int64
Variance() float64
}
// ExpDecaySample is an exponentially-decaying sample using a forward-decaying
// priority reservoir. See Cormode et al's "Forward Decay: A Practical Time
// Decay Model for Streaming Systems".
//
// <http://dimacs.rutgers.edu/~graham/pubs/papers/fwddecay.pdf>
type ExpDecaySample struct {
alpha float64
count int64
mutex sync.Mutex
reservoirSize int
t0, t1 time.Time
values *expDecaySampleHeap
}
// NewExpDecaySample constructs a new exponentially-decaying sample with the
// given reservoir size and alpha.
func NewExpDecaySample(reservoirSize int, alpha float64) Sample {
if !Enabled {
return NilSample{}
}
s := &ExpDecaySample{
alpha: alpha,
reservoirSize: reservoirSize,
t0: time.Now(),
values: newExpDecaySampleHeap(reservoirSize),
}
s.t1 = s.t0.Add(rescaleThreshold)
return s
}
// Clear clears all samples.
func (s *ExpDecaySample) Clear() {
s.mutex.Lock()
defer s.mutex.Unlock()
s.count = 0
s.t0 = time.Now()
s.t1 = s.t0.Add(rescaleThreshold)
s.values.Clear()
}
// Count returns the number of samples recorded, which may exceed the
// reservoir size.
func (s *ExpDecaySample) Count() int64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return s.count
}
// Max returns the maximum value in the sample, which may not be the maximum
// value ever to be part of the sample.
func (s *ExpDecaySample) Max() int64 {
return SampleMax(s.Values())
}
// Mean returns the mean of the values in the sample.
func (s *ExpDecaySample) Mean() float64 {
return SampleMean(s.Values())
}
// Min returns the minimum value in the sample, which may not be the minimum
// value ever to be part of the sample.
func (s *ExpDecaySample) Min() int64 {
return SampleMin(s.Values())
}
// Percentile returns an arbitrary percentile of values in the sample.
func (s *ExpDecaySample) Percentile(p float64) float64 {
return SamplePercentile(s.Values(), p)
}
// Percentiles returns a slice of arbitrary percentiles of values in the
// sample.
func (s *ExpDecaySample) Percentiles(ps []float64) []float64 {
return SamplePercentiles(s.Values(), ps)
}
// Size returns the size of the sample, which is at most the reservoir size.
func (s *ExpDecaySample) Size() int {
s.mutex.Lock()
defer s.mutex.Unlock()
return s.values.Size()
}
// Snapshot returns a read-only copy of the sample.
func (s *ExpDecaySample) Snapshot() Sample {
s.mutex.Lock()
defer s.mutex.Unlock()
vals := s.values.Values()
values := make([]int64, len(vals))
for i, v := range vals {
values[i] = v.v
}
return &SampleSnapshot{
count: s.count,
values: values,
}
}
// StdDev returns the standard deviation of the values in the sample.
func (s *ExpDecaySample) StdDev() float64 {
return SampleStdDev(s.Values())
}
// Sum returns the sum of the values in the sample.
func (s *ExpDecaySample) Sum() int64 {
return SampleSum(s.Values())
}
// Update samples a new value.
func (s *ExpDecaySample) Update(v int64) {
s.update(time.Now(), v)
}
// Values returns a copy of the values in the sample.
func (s *ExpDecaySample) Values() []int64 {
s.mutex.Lock()
defer s.mutex.Unlock()
vals := s.values.Values()
values := make([]int64, len(vals))
for i, v := range vals {
values[i] = v.v
}
return values
}
// Variance returns the variance of the values in the sample.
func (s *ExpDecaySample) Variance() float64 {
return SampleVariance(s.Values())
}
// update samples a new value at a particular timestamp. This is a method all
// its own to facilitate testing.
func (s *ExpDecaySample) update(t time.Time, v int64) {
s.mutex.Lock()
defer s.mutex.Unlock()
s.count++
if s.values.Size() == s.reservoirSize {
s.values.Pop()
}
s.values.Push(expDecaySample{
k: math.Exp(t.Sub(s.t0).Seconds()*s.alpha) / rand.Float64(),
v: v,
})
if t.After(s.t1) {
values := s.values.Values()
t0 := s.t0
s.values.Clear()
s.t0 = t
s.t1 = s.t0.Add(rescaleThreshold)
for _, v := range values {
v.k = v.k * math.Exp(-s.alpha*s.t0.Sub(t0).Seconds())
s.values.Push(v)
}
}
}
// NilSample is a no-op Sample.
type NilSample struct{}
// Clear is a no-op.
func (NilSample) Clear() {}
// Count is a no-op.
func (NilSample) Count() int64 { return 0 }
// Max is a no-op.
func (NilSample) Max() int64 { return 0 }
// Mean is a no-op.
func (NilSample) Mean() float64 { return 0.0 }
// Min is a no-op.
func (NilSample) Min() int64 { return 0 }
// Percentile is a no-op.
func (NilSample) Percentile(p float64) float64 { return 0.0 }
// Percentiles is a no-op.
func (NilSample) Percentiles(ps []float64) []float64 {
return make([]float64, len(ps))
}
// Size is a no-op.
func (NilSample) Size() int { return 0 }
// Sample is a no-op.
func (NilSample) Snapshot() Sample { return NilSample{} }
// StdDev is a no-op.
func (NilSample) StdDev() float64 { return 0.0 }
// Sum is a no-op.
func (NilSample) Sum() int64 { return 0 }
// Update is a no-op.
func (NilSample) Update(v int64) {}
// Values is a no-op.
func (NilSample) Values() []int64 { return []int64{} }
// Variance is a no-op.
func (NilSample) Variance() float64 { return 0.0 }
// SampleMax returns the maximum value of the slice of int64.
func SampleMax(values []int64) int64 {
if 0 == len(values) {
return 0
}
var max int64 = math.MinInt64
for _, v := range values {
if max < v {
max = v
}
}
return max
}
// SampleMean returns the mean value of the slice of int64.
func SampleMean(values []int64) float64 {
if 0 == len(values) {
return 0.0
}
return float64(SampleSum(values)) / float64(len(values))
}
// SampleMin returns the minimum value of the slice of int64.
func SampleMin(values []int64) int64 {
if 0 == len(values) {
return 0
}
var min int64 = math.MaxInt64
for _, v := range values {
if min > v {
min = v
}
}
return min
}
// SamplePercentiles returns an arbitrary percentile of the slice of int64.
func SamplePercentile(values int64Slice, p float64) float64 {
return SamplePercentiles(values, []float64{p})[0]
}
// SamplePercentiles returns a slice of arbitrary percentiles of the slice of
// int64.
func SamplePercentiles(values int64Slice, ps []float64) []float64 {
scores := make([]float64, len(ps))
size := len(values)
if size > 0 {
sort.Sort(values)
for i, p := range ps {
pos := p * float64(size+1)
if pos < 1.0 {
scores[i] = float64(values[0])
} else if pos >= float64(size) {
scores[i] = float64(values[size-1])
} else {
lower := float64(values[int(pos)-1])
upper := float64(values[int(pos)])
scores[i] = lower + (pos-math.Floor(pos))*(upper-lower)
}
}
}
return scores
}
// SampleSnapshot is a read-only copy of another Sample.
type SampleSnapshot struct {
count int64
values []int64
}
func NewSampleSnapshot(count int64, values []int64) *SampleSnapshot {
return &SampleSnapshot{
count: count,
values: values,
}
}
// Clear panics.
func (*SampleSnapshot) Clear() {
panic("Clear called on a SampleSnapshot")
}
// Count returns the count of inputs at the time the snapshot was taken.
func (s *SampleSnapshot) Count() int64 { return s.count }
// Max returns the maximal value at the time the snapshot was taken.
func (s *SampleSnapshot) Max() int64 { return SampleMax(s.values) }
// Mean returns the mean value at the time the snapshot was taken.
func (s *SampleSnapshot) Mean() float64 { return SampleMean(s.values) }
// Min returns the minimal value at the time the snapshot was taken.
func (s *SampleSnapshot) Min() int64 { return SampleMin(s.values) }
// Percentile returns an arbitrary percentile of values at the time the
// snapshot was taken.
func (s *SampleSnapshot) Percentile(p float64) float64 {
return SamplePercentile(s.values, p)
}
// Percentiles returns a slice of arbitrary percentiles of values at the time
// the snapshot was taken.
func (s *SampleSnapshot) Percentiles(ps []float64) []float64 {
return SamplePercentiles(s.values, ps)
}
// Size returns the size of the sample at the time the snapshot was taken.
func (s *SampleSnapshot) Size() int { return len(s.values) }
// Snapshot returns the snapshot.
func (s *SampleSnapshot) Snapshot() Sample { return s }
// StdDev returns the standard deviation of values at the time the snapshot was
// taken.
func (s *SampleSnapshot) StdDev() float64 { return SampleStdDev(s.values) }
// Sum returns the sum of values at the time the snapshot was taken.
func (s *SampleSnapshot) Sum() int64 { return SampleSum(s.values) }
// Update panics.
func (*SampleSnapshot) Update(int64) {
panic("Update called on a SampleSnapshot")
}
// Values returns a copy of the values in the sample.
func (s *SampleSnapshot) Values() []int64 {
values := make([]int64, len(s.values))
copy(values, s.values)
return values
}
// Variance returns the variance of values at the time the snapshot was taken.
func (s *SampleSnapshot) Variance() float64 { return SampleVariance(s.values) }
// SampleStdDev returns the standard deviation of the slice of int64.
func SampleStdDev(values []int64) float64 {
return math.Sqrt(SampleVariance(values))
}
// SampleSum returns the sum of the slice of int64.
func SampleSum(values []int64) int64 {
var sum int64
for _, v := range values {
sum += v
}
return sum
}
// SampleVariance returns the variance of the slice of int64.
func SampleVariance(values []int64) float64 {
if 0 == len(values) {
return 0.0
}
m := SampleMean(values)
var sum float64
for _, v := range values {
d := float64(v) - m
sum += d * d
}
return sum / float64(len(values))
}
// A uniform sample using Vitter's Algorithm R.
//
// <http://www.cs.umd.edu/~samir/498/vitter.pdf>
type UniformSample struct {
count int64
mutex sync.Mutex
reservoirSize int
values []int64
}
// NewUniformSample constructs a new uniform sample with the given reservoir
// size.
func NewUniformSample(reservoirSize int) Sample {
if !Enabled {
return NilSample{}
}
return &UniformSample{
reservoirSize: reservoirSize,
values: make([]int64, 0, reservoirSize),
}
}
// Clear clears all samples.
func (s *UniformSample) Clear() {
s.mutex.Lock()
defer s.mutex.Unlock()
s.count = 0
s.values = make([]int64, 0, s.reservoirSize)
}
// Count returns the number of samples recorded, which may exceed the
// reservoir size.
func (s *UniformSample) Count() int64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return s.count
}
// Max returns the maximum value in the sample, which may not be the maximum
// value ever to be part of the sample.
func (s *UniformSample) Max() int64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return SampleMax(s.values)
}
// Mean returns the mean of the values in the sample.
func (s *UniformSample) Mean() float64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return SampleMean(s.values)
}
// Min returns the minimum value in the sample, which may not be the minimum
// value ever to be part of the sample.
func (s *UniformSample) Min() int64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return SampleMin(s.values)
}
// Percentile returns an arbitrary percentile of values in the sample.
func (s *UniformSample) Percentile(p float64) float64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return SamplePercentile(s.values, p)
}
// Percentiles returns a slice of arbitrary percentiles of values in the
// sample.
func (s *UniformSample) Percentiles(ps []float64) []float64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return SamplePercentiles(s.values, ps)
}
// Size returns the size of the sample, which is at most the reservoir size.
func (s *UniformSample) Size() int {
s.mutex.Lock()
defer s.mutex.Unlock()
return len(s.values)
}
// Snapshot returns a read-only copy of the sample.
func (s *UniformSample) Snapshot() Sample {
s.mutex.Lock()
defer s.mutex.Unlock()
values := make([]int64, len(s.values))
copy(values, s.values)
return &SampleSnapshot{
count: s.count,
values: values,
}
}
// StdDev returns the standard deviation of the values in the sample.
func (s *UniformSample) StdDev() float64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return SampleStdDev(s.values)
}
// Sum returns the sum of the values in the sample.
func (s *UniformSample) Sum() int64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return SampleSum(s.values)
}
// Update samples a new value.
func (s *UniformSample) Update(v int64) {
s.mutex.Lock()
defer s.mutex.Unlock()
s.count++
if len(s.values) < s.reservoirSize {
s.values = append(s.values, v)
} else {
r := rand.Int63n(s.count)
if r < int64(len(s.values)) {
s.values[int(r)] = v
}
}
}
// Values returns a copy of the values in the sample.
func (s *UniformSample) Values() []int64 {
s.mutex.Lock()
defer s.mutex.Unlock()
values := make([]int64, len(s.values))
copy(values, s.values)
return values
}
// Variance returns the variance of the values in the sample.
func (s *UniformSample) Variance() float64 {
s.mutex.Lock()
defer s.mutex.Unlock()
return SampleVariance(s.values)
}
// expDecaySample represents an individual sample in a heap.
type expDecaySample struct {
k float64
v int64
}
func newExpDecaySampleHeap(reservoirSize int) *expDecaySampleHeap {
return &expDecaySampleHeap{make([]expDecaySample, 0, reservoirSize)}
}
// expDecaySampleHeap is a min-heap of expDecaySamples.
// The internal implementation is copied from the standard library's container/heap
type expDecaySampleHeap struct {
s []expDecaySample
}
func (h *expDecaySampleHeap) Clear() {
h.s = h.s[:0]
}
func (h *expDecaySampleHeap) Push(s expDecaySample) {
n := len(h.s)
h.s = h.s[0 : n+1]
h.s[n] = s
h.up(n)
}
func (h *expDecaySampleHeap) Pop() expDecaySample {
n := len(h.s) - 1
h.s[0], h.s[n] = h.s[n], h.s[0]
h.down(0, n)
n = len(h.s)
s := h.s[n-1]
h.s = h.s[0 : n-1]
return s
}
func (h *expDecaySampleHeap) Size() int {
return len(h.s)
}
func (h *expDecaySampleHeap) Values() []expDecaySample {
return h.s
}
func (h *expDecaySampleHeap) up(j int) {
for {
i := (j - 1) / 2 // parent
if i == j || !(h.s[j].k < h.s[i].k) {
break
}
h.s[i], h.s[j] = h.s[j], h.s[i]
j = i
}
}
func (h *expDecaySampleHeap) down(i, n int) {
for {
j1 := 2*i + 1
if j1 >= n || j1 < 0 { // j1 < 0 after int overflow
break
}
j := j1 // left child
if j2 := j1 + 1; j2 < n && !(h.s[j1].k < h.s[j2].k) {
j = j2 // = 2*i + 2 // right child
}
if !(h.s[j].k < h.s[i].k) {
break
}
h.s[i], h.s[j] = h.s[j], h.s[i]
i = j
}
}
type int64Slice []int64
func (p int64Slice) Len() int { return len(p) }
func (p int64Slice) Less(i, j int) bool { return p[i] < p[j] }
func (p int64Slice) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
