// 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 trace
// This file implements histogramming for RPC statistics collection.
import (
"bytes"
"fmt"
"html/template"
"log"
"math"
"golang.org/x/net/internal/timeseries"
)
const (
bucketCount = 38
)
// histogram keeps counts of values in buckets that are spaced
// out in powers of 2: 0-1, 2-3, 4-7...
// histogram implements timeseries.Observable
type histogram struct {
sum int64 // running total of measurements
sumOfSquares float64 // square of running total
buckets []int64 // bucketed values for histogram
value int // holds a single value as an optimization
valueCount int64 // number of values recorded for single value
}
// AddMeasurement records a value measurement observation to the histogram.
func (h *histogram) addMeasurement(value int64) {
// TODO: assert invariant
h.sum += value
h.sumOfSquares += float64(value) * float64(value)
bucketIndex := getBucket(value)
if h.valueCount == 0 || (h.valueCount > 0 && h.value == bucketIndex) {
h.value = bucketIndex
h.valueCount++
} else {
h.allocateBuckets()
h.buckets[bucketIndex]++
}
}
func (h *histogram) allocateBuckets() {
if h.buckets == nil {
h.buckets = make([]int64, bucketCount)
h.buckets[h.value] = h.valueCount
h.value = 0
h.valueCount = -1
}
}
func log2(i int64) int {
n := 0
for ; i >= 0x100; i >>= 8 {
n += 8
}
for ; i > 0; i >>= 1 {
n += 1
}
return n
}
func getBucket(i int64) (index int) {
index = log2(i) - 1
if index < 0 {
index = 0
}
if index >= bucketCount {
index = bucketCount - 1
}
return
}
// Total returns the number of recorded observations.
func (h *histogram) total() (total int64) {
if h.valueCount >= 0 {
total = h.valueCount
}
for _, val := range h.buckets {
total += int64(val)
}
return
}
// Average returns the average value of recorded observations.
func (h *histogram) average() float64 {
t := h.total()
if t == 0 {
return 0
}
return float64(h.sum) / float64(t)
}
// Variance returns the variance of recorded observations.
func (h *histogram) variance() float64 {
t := float64(h.total())
if t == 0 {
return 0
}
s := float64(h.sum) / t
return h.sumOfSquares/t - s*s
}
// StandardDeviation returns the standard deviation of recorded observations.
func (h *histogram) standardDeviation() float64 {
return math.Sqrt(h.variance())
}
// PercentileBoundary estimates the value that the given fraction of recorded
// observations are less than.
func (h *histogram) percentileBoundary(percentile float64) int64 {
total := h.total()
// Corner cases (make sure result is strictly less than Total())
if total == 0 {
return 0
} else if total == 1 {
return int64(h.average())
}
percentOfTotal := round(float64(total) * percentile)
var runningTotal int64
for i := range h.buckets {
value := h.buckets[i]
runningTotal += value
if runningTotal == percentOfTotal {
// We hit an exact bucket boundary. If the next bucket has data, it is a
// good estimate of the value. If the bucket is empty, we interpolate the
// midpoint between the next bucket's boundary and the next non-zero
// bucket. If the remaining buckets are all empty, then we use the
// boundary for the next bucket as the estimate.
j := uint8(i + 1)
min := bucketBoundary(j)
if runningTotal < total {
for h.buckets[j] == 0 {
j++
}
}
max := bucketBoundary(j)
return min + round(float64(max-min)/2)
} else if runningTotal > percentOfTotal {
// The value is in this bucket. Interpolate the value.
delta := runningTotal - percentOfTotal
percentBucket := float64(value-delta) / float64(value)
bucketMin := bucketBoundary(uint8(i))
nextBucketMin := bucketBoundary(uint8(i + 1))
bucketSize := nextBucketMin - bucketMin
return bucketMin + round(percentBucket*float64(bucketSize))
}
}
return bucketBoundary(bucketCount - 1)
}
// Median returns the estimated median of the observed values.
func (h *histogram) median() int64 {
return h.percentileBoundary(0.5)
}
// Add adds other to h.
func (h *histogram) Add(other timeseries.Observable) {
o := other.(*histogram)
if o.valueCount == 0 {
// Other histogram is empty
} else if h.valueCount >= 0 && o.valueCount > 0 && h.value == o.value {
// Both have a single bucketed value, aggregate them
h.valueCount += o.valueCount
} else {
// Two different values necessitate buckets in this histogram
h.allocateBuckets()
if o.valueCount >= 0 {
h.buckets[o.value] += o.valueCount
} else {
for i := range h.buckets {
h.buckets[i] += o.buckets[i]
}
}
}
h.sumOfSquares += o.sumOfSquares
h.sum += o.sum
}
// Clear resets the histogram to an empty state, removing all observed values.
func (h *histogram) Clear() {
h.buckets = nil
h.value = 0
h.valueCount = 0
h.sum = 0
h.sumOfSquares = 0
}
// CopyFrom copies from other, which must be a *histogram, into h.
func (h *histogram) CopyFrom(other timeseries.Observable) {
o := other.(*histogram)
if o.valueCount == -1 {
h.allocateBuckets()
copy(h.buckets, o.buckets)
}
h.sum = o.sum
h.sumOfSquares = o.sumOfSquares
h.value = o.value
h.valueCount = o.valueCount
}
// Multiply scales the histogram by the specified ratio.
func (h *histogram) Multiply(ratio float64) {
if h.valueCount == -1 {
for i := range h.buckets {
h.buckets[i] = int64(float64(h.buckets[i]) * ratio)
}
} else {
h.valueCount = int64(float64(h.valueCount) * ratio)
}
h.sum = int64(float64(h.sum) * ratio)
h.sumOfSquares = h.sumOfSquares * ratio
}
// New creates a new histogram.
func (h *histogram) New() timeseries.Observable {
r := new(histogram)
r.Clear()
return r
}
func (h *histogram) String() string {
return fmt.Sprintf("%d, %f, %d, %d, %v",
h.sum, h.sumOfSquares, h.value, h.valueCount, h.buckets)
}
// round returns the closest int64 to the argument
func round(in float64) int64 {
return int64(math.Floor(in + 0.5))
}
// bucketBoundary returns the first value in the bucket.
func bucketBoundary(bucket uint8) int64 {
if bucket == 0 {
return 0
}
return 1 << bucket
}
// bucketData holds data about a specific bucket for use in distTmpl.
type bucketData struct {
Lower, Upper int64
N int64
Pct, CumulativePct float64
GraphWidth int
}
// data holds data about a Distribution for use in distTmpl.
type data struct {
Buckets []*bucketData
Count, Median int64
Mean, StandardDeviation float64
}
// maxHTMLBarWidth is the maximum width of the HTML bar for visualizing buckets.
const maxHTMLBarWidth = 350.0
// newData returns data representing h for use in distTmpl.
func (h *histogram) newData() *data {
// Force the allocation of buckets to simplify the rendering implementation
h.allocateBuckets()
// We scale the bars on the right so that the largest bar is
// maxHTMLBarWidth pixels in width.
maxBucket := int64(0)
for _, n := range h.buckets {
if n > maxBucket {
maxBucket = n
}
}
total := h.total()
barsizeMult := maxHTMLBarWidth / float64(maxBucket)
var pctMult float64
if total == 0 {
pctMult = 1.0
} else {
pctMult = 100.0 / float64(total)
}
buckets := make([]*bucketData, len(h.buckets))
runningTotal := int64(0)
for i, n := range h.buckets {
if n == 0 {
continue
}
runningTotal += n
var upperBound int64
if i < bucketCount-1 {
upperBound = bucketBoundary(uint8(i + 1))
} else {
upperBound = math.MaxInt64
}
buckets[i] = &bucketData{
Lower: bucketBoundary(uint8(i)),
Upper: upperBound,
N: n,
Pct: float64(n) * pctMult,
CumulativePct: float64(runningTotal) * pctMult,
GraphWidth: int(float64(n) * barsizeMult),
}
}
return &data{
Buckets: buckets,
Count: total,
Median: h.median(),
Mean: h.average(),
StandardDeviation: h.standardDeviation(),
}
}
func (h *histogram) html() template.HTML {
buf := new(bytes.Buffer)
if err := distTmpl.Execute(buf, h.newData()); err != nil {
buf.Reset()
log.Printf("net/trace: couldn't execute template: %v", err)
}
return template.HTML(buf.String())
}
// Input: data
var distTmpl = template.Must(template.New("distTmpl").Parse(`
<table>
<tr>
<td style="padding:0.25em">Count: {{.Count}}</td>
<td style="padding:0.25em">Mean: {{printf "%.0f" .Mean}}</td>
<td style="padding:0.25em">StdDev: {{printf "%.0f" .StandardDeviation}}</td>
<td style="padding:0.25em">Median: {{.Median}}</td>
</tr>
</table>
<hr>
<table>
{{range $b := .Buckets}}
{{if $b}}
<tr>
<td style="padding:0 0 0 0.25em">[</td>
<td style="text-align:right;padding:0 0.25em">{{.Lower}},</td>
<td style="text-align:right;padding:0 0.25em">{{.Upper}})</td>
<td style="text-align:right;padding:0 0.25em">{{.N}}</td>
<td style="text-align:right;padding:0 0.25em">{{printf "%#.3f" .Pct}}%</td>
<td style="text-align:right;padding:0 0.25em">{{printf "%#.3f" .CumulativePct}}%</td>
<td><div style="background-color: blue; height: 1em; width: {{.GraphWidth}};"></div></td>
</tr>
{{end}}
{{end}}
</table>
`))