// Package hdrhistogram provides an implementation of Gil Tene's HDR Histogram
// data structure. The HDR Histogram allows for fast and accurate analysis of
// the extreme ranges of data with non-normal distributions, like latency.
package hdrhistogram
import (
"fmt"
"math"
)
// A Bracket is a part of a cumulative distribution.
type Bracket struct {
Quantile float64
Count, ValueAt int64
}
// A Snapshot is an exported view of a Histogram, useful for serializing them.
// A Histogram can be constructed from it by passing it to Import.
type Snapshot struct {
LowestTrackableValue int64
HighestTrackableValue int64
SignificantFigures int64
Counts []int64
}
// A Histogram is a lossy data structure used to record the distribution of
// non-normally distributed data (like latency) with a high degree of accuracy
// and a bounded degree of precision.
type Histogram struct {
lowestTrackableValue int64
highestTrackableValue int64
unitMagnitude int64
significantFigures int64
subBucketHalfCountMagnitude int32
subBucketHalfCount int32
subBucketMask int64
subBucketCount int32
bucketCount int32
countsLen int32
totalCount int64
counts []int64
}
// New returns a new Histogram instance capable of tracking values in the given
// range and with the given amount of precision.
func New(minValue, maxValue int64, sigfigs int) *Histogram {
if sigfigs < 1 || 5 < sigfigs {
panic(fmt.Errorf("sigfigs must be [1,5] (was %d)", sigfigs))
}
largestValueWithSingleUnitResolution := 2 * math.Pow10(sigfigs)
subBucketCountMagnitude := int32(math.Ceil(math.Log2(float64(largestValueWithSingleUnitResolution))))
subBucketHalfCountMagnitude := subBucketCountMagnitude
if subBucketHalfCountMagnitude < 1 {
subBucketHalfCountMagnitude = 1
}
subBucketHalfCountMagnitude--
unitMagnitude := int32(math.Floor(math.Log2(float64(minValue))))
if unitMagnitude < 0 {
unitMagnitude = 0
}
subBucketCount := int32(math.Pow(2, float64(subBucketHalfCountMagnitude)+1))
subBucketHalfCount := subBucketCount / 2
subBucketMask := int64(subBucketCount-1) << uint(unitMagnitude)
// determine exponent range needed to support the trackable value with no
// overflow:
smallestUntrackableValue := int64(subBucketCount) << uint(unitMagnitude)
bucketsNeeded := int32(1)
for smallestUntrackableValue < maxValue {
smallestUntrackableValue <<= 1
bucketsNeeded++
}
bucketCount := bucketsNeeded
countsLen := (bucketCount + 1) * (subBucketCount / 2)
return &Histogram{
lowestTrackableValue: minValue,
highestTrackableValue: maxValue,
unitMagnitude: int64(unitMagnitude),
significantFigures: int64(sigfigs),
subBucketHalfCountMagnitude: subBucketHalfCountMagnitude,
subBucketHalfCount: subBucketHalfCount,
subBucketMask: subBucketMask,
subBucketCount: subBucketCount,
bucketCount: bucketCount,
countsLen: countsLen,
totalCount: 0,
counts: make([]int64, countsLen),
}
}
// ByteSize returns an estimate of the amount of memory allocated to the
// histogram in bytes.
//
// N.B.: This does not take into account the overhead for slices, which are
// small, constant, and specific to the compiler version.
func (h *Histogram) ByteSize() int {
return 6*8 + 5*4 + len(h.counts)*8
}
// Merge merges the data stored in the given histogram with the receiver,
// returning the number of recorded values which had to be dropped.
func (h *Histogram) Merge(from *Histogram) (dropped int64) {
i := from.rIterator()
for i.next() {
v := i.valueFromIdx
c := i.countAtIdx
if h.RecordValues(v, c) != nil {
dropped += c
}
}
return
}
// TotalCount returns total number of values recorded.
func (h *Histogram) TotalCount() int64 {
return h.totalCount
}
// Max returns the approximate maximum recorded value.
func (h *Histogram) Max() int64 {
var max int64
i := h.iterator()
for i.next() {
if i.countAtIdx != 0 {
max = i.highestEquivalentValue
}
}
return h.highestEquivalentValue(max)
}
// Min returns the approximate minimum recorded value.
func (h *Histogram) Min() int64 {
var min int64
i := h.iterator()
for i.next() {
if i.countAtIdx != 0 && min == 0 {
min = i.highestEquivalentValue
break
}
}
return h.lowestEquivalentValue(min)
}
// Mean returns the approximate arithmetic mean of the recorded values.
func (h *Histogram) Mean() float64 {
if h.totalCount == 0 {
return 0
}
var total int64
i := h.iterator()
for i.next() {
if i.countAtIdx != 0 {
total += i.countAtIdx * h.medianEquivalentValue(i.valueFromIdx)
}
}
return float64(total) / float64(h.totalCount)
}
// StdDev returns the approximate standard deviation of the recorded values.
func (h *Histogram) StdDev() float64 {
if h.totalCount == 0 {
return 0
}
mean := h.Mean()
geometricDevTotal := 0.0
i := h.iterator()
for i.next() {
if i.countAtIdx != 0 {
dev := float64(h.medianEquivalentValue(i.valueFromIdx)) - mean
geometricDevTotal += (dev * dev) * float64(i.countAtIdx)
}
}
return math.Sqrt(geometricDevTotal / float64(h.totalCount))
}
// Reset deletes all recorded values and restores the histogram to its original
// state.
func (h *Histogram) Reset() {
h.totalCount = 0
for i := range h.counts {
h.counts[i] = 0
}
}
// RecordValue records the given value, returning an error if the value is out
// of range.
func (h *Histogram) RecordValue(v int64) error {
return h.RecordValues(v, 1)
}
// RecordCorrectedValue records the given value, correcting for stalls in the
// recording process. This only works for processes which are recording values
// at an expected interval (e.g., doing jitter analysis). Processes which are
// recording ad-hoc values (e.g., latency for incoming requests) can't take
// advantage of this.
func (h *Histogram) RecordCorrectedValue(v, expectedInterval int64) error {
if err := h.RecordValue(v); err != nil {
return err
}
if expectedInterval <= 0 || v <= expectedInterval {
return nil
}
missingValue := v - expectedInterval
for missingValue >= expectedInterval {
if err := h.RecordValue(missingValue); err != nil {
return err
}
missingValue -= expectedInterval
}
return nil
}
// RecordValues records n occurrences of the given value, returning an error if
// the value is out of range.
func (h *Histogram) RecordValues(v, n int64) error {
idx := h.countsIndexFor(v)
if idx < 0 || int(h.countsLen) <= idx {
return fmt.Errorf("value %d is too large to be recorded", v)
}
h.counts[idx] += n
h.totalCount += n
return nil
}
// ValueAtQuantile returns the recorded value at the given quantile (0..100).
func (h *Histogram) ValueAtQuantile(q float64) int64 {
if q > 100 {
q = 100
}
total := int64(0)
countAtPercentile := int64(((q / 100) * float64(h.totalCount)) + 0.5)
i := h.iterator()
for i.next() {
total += i.countAtIdx
if total >= countAtPercentile {
return h.highestEquivalentValue(i.valueFromIdx)
}
}
return 0
}
// CumulativeDistribution returns an ordered list of brackets of the
// distribution of recorded values.
func (h *Histogram) CumulativeDistribution() []Bracket {
var result []Bracket
i := h.pIterator(1)
for i.next() {
result = append(result, Bracket{
Quantile: i.percentile,
Count: i.countToIdx,
ValueAt: i.highestEquivalentValue,
})
}
return result
}
// SignificantFigures returns the significant figures used to create the
// histogram
func (h *Histogram) SignificantFigures() int64 {
return h.significantFigures
}
// LowestTrackableValue returns the lower bound on values that will be added
// to the histogram
func (h *Histogram) LowestTrackableValue() int64 {
return h.lowestTrackableValue
}
// HighestTrackableValue returns the upper bound on values that will be added
// to the histogram
func (h *Histogram) HighestTrackableValue() int64 {
return h.highestTrackableValue
}
// Histogram bar for plotting
type Bar struct {
From, To, Count int64
}
// Pretty print as csv for easy plotting
func (b Bar) String() string {
return fmt.Sprintf("%v, %v, %v\n", b.From, b.To, b.Count)
}
// Distribution returns an ordered list of bars of the
// distribution of recorded values, counts can be normalized to a probability
func (h *Histogram) Distribution() (result []Bar) {
i := h.iterator()
for i.next() {
result = append(result, Bar{
Count: i.countAtIdx,
From: h.lowestEquivalentValue(i.valueFromIdx),
To: i.highestEquivalentValue,
})
}
return result
}
// Equals returns true if the two Histograms are equivalent, false if not.
func (h *Histogram) Equals(other *Histogram) bool {
switch {
case
h.lowestTrackableValue != other.lowestTrackableValue,
h.highestTrackableValue != other.highestTrackableValue,
h.unitMagnitude != other.unitMagnitude,
h.significantFigures != other.significantFigures,
h.subBucketHalfCountMagnitude != other.subBucketHalfCountMagnitude,
h.subBucketHalfCount != other.subBucketHalfCount,
h.subBucketMask != other.subBucketMask,
h.subBucketCount != other.subBucketCount,
h.bucketCount != other.bucketCount,
h.countsLen != other.countsLen,
h.totalCount != other.totalCount:
return false
default:
for i, c := range h.counts {
if c != other.counts[i] {
return false
}
}
}
return true
}
// Export returns a snapshot view of the Histogram. This can be later passed to
// Import to construct a new Histogram with the same state.
func (h *Histogram) Export() *Snapshot {
return &Snapshot{
LowestTrackableValue: h.lowestTrackableValue,
HighestTrackableValue: h.highestTrackableValue,
SignificantFigures: h.significantFigures,
Counts: append([]int64(nil), h.counts...), // copy
}
}
// Import returns a new Histogram populated from the Snapshot data (which the
// caller must stop accessing).
func Import(s *Snapshot) *Histogram {
h := New(s.LowestTrackableValue, s.HighestTrackableValue, int(s.SignificantFigures))
h.counts = s.Counts
totalCount := int64(0)
for i := int32(0); i < h.countsLen; i++ {
countAtIndex := h.counts[i]
if countAtIndex > 0 {
totalCount += countAtIndex
}
}
h.totalCount = totalCount
return h
}
func (h *Histogram) iterator() *iterator {
return &iterator{
h: h,
subBucketIdx: -1,
}
}
func (h *Histogram) rIterator() *rIterator {
return &rIterator{
iterator: iterator{
h: h,
subBucketIdx: -1,
},
}
}
func (h *Histogram) pIterator(ticksPerHalfDistance int32) *pIterator {
return &pIterator{
iterator: iterator{
h: h,
subBucketIdx: -1,
},
ticksPerHalfDistance: ticksPerHalfDistance,
}
}
func (h *Histogram) sizeOfEquivalentValueRange(v int64) int64 {
bucketIdx := h.getBucketIndex(v)
subBucketIdx := h.getSubBucketIdx(v, bucketIdx)
adjustedBucket := bucketIdx
if subBucketIdx >= h.subBucketCount {
adjustedBucket++
}
return int64(1) << uint(h.unitMagnitude+int64(adjustedBucket))
}
func (h *Histogram) valueFromIndex(bucketIdx, subBucketIdx int32) int64 {
return int64(subBucketIdx) << uint(int64(bucketIdx)+h.unitMagnitude)
}
func (h *Histogram) lowestEquivalentValue(v int64) int64 {
bucketIdx := h.getBucketIndex(v)
subBucketIdx := h.getSubBucketIdx(v, bucketIdx)
return h.valueFromIndex(bucketIdx, subBucketIdx)
}
func (h *Histogram) nextNonEquivalentValue(v int64) int64 {
return h.lowestEquivalentValue(v) + h.sizeOfEquivalentValueRange(v)
}
func (h *Histogram) highestEquivalentValue(v int64) int64 {
return h.nextNonEquivalentValue(v) - 1
}
func (h *Histogram) medianEquivalentValue(v int64) int64 {
return h.lowestEquivalentValue(v) + (h.sizeOfEquivalentValueRange(v) >> 1)
}
func (h *Histogram) getCountAtIndex(bucketIdx, subBucketIdx int32) int64 {
return h.counts[h.countsIndex(bucketIdx, subBucketIdx)]
}
func (h *Histogram) countsIndex(bucketIdx, subBucketIdx int32) int32 {
bucketBaseIdx := (bucketIdx + 1) << uint(h.subBucketHalfCountMagnitude)
offsetInBucket := subBucketIdx - h.subBucketHalfCount
return bucketBaseIdx + offsetInBucket
}
func (h *Histogram) getBucketIndex(v int64) int32 {
pow2Ceiling := bitLen(v | h.subBucketMask)
return int32(pow2Ceiling - int64(h.unitMagnitude) -
int64(h.subBucketHalfCountMagnitude+1))
}
func (h *Histogram) getSubBucketIdx(v int64, idx int32) int32 {
return int32(v >> uint(int64(idx)+int64(h.unitMagnitude)))
}
func (h *Histogram) countsIndexFor(v int64) int {
bucketIdx := h.getBucketIndex(v)
subBucketIdx := h.getSubBucketIdx(v, bucketIdx)
return int(h.countsIndex(bucketIdx, subBucketIdx))
}
type iterator struct {
h *Histogram
bucketIdx, subBucketIdx int32
countAtIdx, countToIdx, valueFromIdx int64
highestEquivalentValue int64
}
func (i *iterator) next() bool {
if i.countToIdx >= i.h.totalCount {
return false
}
// increment bucket
i.subBucketIdx++
if i.subBucketIdx >= i.h.subBucketCount {
i.subBucketIdx = i.h.subBucketHalfCount
i.bucketIdx++
}
if i.bucketIdx >= i.h.bucketCount {
return false
}
i.countAtIdx = i.h.getCountAtIndex(i.bucketIdx, i.subBucketIdx)
i.countToIdx += i.countAtIdx
i.valueFromIdx = i.h.valueFromIndex(i.bucketIdx, i.subBucketIdx)
i.highestEquivalentValue = i.h.highestEquivalentValue(i.valueFromIdx)
return true
}
type rIterator struct {
iterator
countAddedThisStep int64
}
func (r *rIterator) next() bool {
for r.iterator.next() {
if r.countAtIdx != 0 {
r.countAddedThisStep = r.countAtIdx
return true
}
}
return false
}
type pIterator struct {
iterator
seenLastValue bool
ticksPerHalfDistance int32
percentileToIteratorTo float64
percentile float64
}
func (p *pIterator) next() bool {
if !(p.countToIdx < p.h.totalCount) {
if p.seenLastValue {
return false
}
p.seenLastValue = true
p.percentile = 100
return true
}
if p.subBucketIdx == -1 && !p.iterator.next() {
return false
}
var done = false
for !done {
currentPercentile := (100.0 * float64(p.countToIdx)) / float64(p.h.totalCount)
if p.countAtIdx != 0 && p.percentileToIteratorTo <= currentPercentile {
p.percentile = p.percentileToIteratorTo
halfDistance := math.Trunc(math.Pow(2, math.Trunc(math.Log2(100.0/(100.0-p.percentileToIteratorTo)))+1))
percentileReportingTicks := float64(p.ticksPerHalfDistance) * halfDistance
p.percentileToIteratorTo += 100.0 / percentileReportingTicks
return true
}
done = !p.iterator.next()
}
return true
}
func bitLen(x int64) (n int64) {
for ; x >= 0x8000; x >>= 16 {
n += 16
}
if x >= 0x80 {
x >>= 8
n += 8
}
if x >= 0x8 {
x >>= 4
n += 4
}
if x >= 0x2 {
x >>= 2
n += 2
}
if x >= 0x1 {
n++
}
return
}
