mirror of
https://github.com/Luzifer/elb-instance-status.git
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293 lines
7.2 KiB
Go
293 lines
7.2 KiB
Go
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// Package quantile computes approximate quantiles over an unbounded data
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// stream within low memory and CPU bounds.
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//
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// A small amount of accuracy is traded to achieve the above properties.
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//
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// Multiple streams can be merged before calling Query to generate a single set
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// of results. This is meaningful when the streams represent the same type of
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// data. See Merge and Samples.
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//
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// For more detailed information about the algorithm used, see:
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//
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// Effective Computation of Biased Quantiles over Data Streams
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//
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// http://www.cs.rutgers.edu/~muthu/bquant.pdf
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package quantile
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import (
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"math"
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"sort"
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)
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// Sample holds an observed value and meta information for compression. JSON
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// tags have been added for convenience.
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type Sample struct {
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Value float64 `json:",string"`
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Width float64 `json:",string"`
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Delta float64 `json:",string"`
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}
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// Samples represents a slice of samples. It implements sort.Interface.
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type Samples []Sample
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func (a Samples) Len() int { return len(a) }
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func (a Samples) Less(i, j int) bool { return a[i].Value < a[j].Value }
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func (a Samples) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
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type invariant func(s *stream, r float64) float64
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// NewLowBiased returns an initialized Stream for low-biased quantiles
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// (e.g. 0.01, 0.1, 0.5) where the needed quantiles are not known a priori, but
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// error guarantees can still be given even for the lower ranks of the data
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// distribution.
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//
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// The provided epsilon is a relative error, i.e. the true quantile of a value
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// returned by a query is guaranteed to be within (1±Epsilon)*Quantile.
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//
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// See http://www.cs.rutgers.edu/~muthu/bquant.pdf for time, space, and error
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// properties.
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func NewLowBiased(epsilon float64) *Stream {
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ƒ := func(s *stream, r float64) float64 {
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return 2 * epsilon * r
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}
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return newStream(ƒ)
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}
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// NewHighBiased returns an initialized Stream for high-biased quantiles
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// (e.g. 0.01, 0.1, 0.5) where the needed quantiles are not known a priori, but
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// error guarantees can still be given even for the higher ranks of the data
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// distribution.
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//
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// The provided epsilon is a relative error, i.e. the true quantile of a value
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// returned by a query is guaranteed to be within 1-(1±Epsilon)*(1-Quantile).
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//
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// See http://www.cs.rutgers.edu/~muthu/bquant.pdf for time, space, and error
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// properties.
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func NewHighBiased(epsilon float64) *Stream {
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ƒ := func(s *stream, r float64) float64 {
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return 2 * epsilon * (s.n - r)
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}
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return newStream(ƒ)
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}
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// NewTargeted returns an initialized Stream concerned with a particular set of
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// quantile values that are supplied a priori. Knowing these a priori reduces
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// space and computation time. The targets map maps the desired quantiles to
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// their absolute errors, i.e. the true quantile of a value returned by a query
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// is guaranteed to be within (Quantile±Epsilon).
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//
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// See http://www.cs.rutgers.edu/~muthu/bquant.pdf for time, space, and error properties.
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func NewTargeted(targets map[float64]float64) *Stream {
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ƒ := func(s *stream, r float64) float64 {
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var m = math.MaxFloat64
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var f float64
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for quantile, epsilon := range targets {
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if quantile*s.n <= r {
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f = (2 * epsilon * r) / quantile
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} else {
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f = (2 * epsilon * (s.n - r)) / (1 - quantile)
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}
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if f < m {
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m = f
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}
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}
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return m
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}
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return newStream(ƒ)
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}
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// Stream computes quantiles for a stream of float64s. It is not thread-safe by
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// design. Take care when using across multiple goroutines.
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type Stream struct {
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*stream
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b Samples
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sorted bool
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}
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func newStream(ƒ invariant) *Stream {
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x := &stream{ƒ: ƒ}
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return &Stream{x, make(Samples, 0, 500), true}
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}
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// Insert inserts v into the stream.
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func (s *Stream) Insert(v float64) {
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s.insert(Sample{Value: v, Width: 1})
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}
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func (s *Stream) insert(sample Sample) {
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s.b = append(s.b, sample)
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s.sorted = false
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if len(s.b) == cap(s.b) {
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s.flush()
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}
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}
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// Query returns the computed qth percentiles value. If s was created with
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// NewTargeted, and q is not in the set of quantiles provided a priori, Query
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// will return an unspecified result.
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func (s *Stream) Query(q float64) float64 {
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if !s.flushed() {
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// Fast path when there hasn't been enough data for a flush;
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// this also yields better accuracy for small sets of data.
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l := len(s.b)
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if l == 0 {
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return 0
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}
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i := int(float64(l) * q)
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if i > 0 {
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i -= 1
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}
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s.maybeSort()
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return s.b[i].Value
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}
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s.flush()
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return s.stream.query(q)
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}
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// Merge merges samples into the underlying streams samples. This is handy when
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// merging multiple streams from separate threads, database shards, etc.
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//
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// ATTENTION: This method is broken and does not yield correct results. The
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// underlying algorithm is not capable of merging streams correctly.
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func (s *Stream) Merge(samples Samples) {
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sort.Sort(samples)
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s.stream.merge(samples)
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}
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// Reset reinitializes and clears the list reusing the samples buffer memory.
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func (s *Stream) Reset() {
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s.stream.reset()
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s.b = s.b[:0]
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}
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// Samples returns stream samples held by s.
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func (s *Stream) Samples() Samples {
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if !s.flushed() {
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return s.b
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}
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s.flush()
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return s.stream.samples()
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}
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// Count returns the total number of samples observed in the stream
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// since initialization.
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func (s *Stream) Count() int {
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return len(s.b) + s.stream.count()
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}
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func (s *Stream) flush() {
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s.maybeSort()
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s.stream.merge(s.b)
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s.b = s.b[:0]
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}
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func (s *Stream) maybeSort() {
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if !s.sorted {
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s.sorted = true
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sort.Sort(s.b)
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}
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}
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func (s *Stream) flushed() bool {
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return len(s.stream.l) > 0
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}
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type stream struct {
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n float64
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l []Sample
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ƒ invariant
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}
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func (s *stream) reset() {
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s.l = s.l[:0]
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s.n = 0
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}
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func (s *stream) insert(v float64) {
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s.merge(Samples{{v, 1, 0}})
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}
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func (s *stream) merge(samples Samples) {
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// TODO(beorn7): This tries to merge not only individual samples, but
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// whole summaries. The paper doesn't mention merging summaries at
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// all. Unittests show that the merging is inaccurate. Find out how to
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// do merges properly.
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var r float64
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i := 0
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for _, sample := range samples {
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for ; i < len(s.l); i++ {
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c := s.l[i]
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if c.Value > sample.Value {
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// Insert at position i.
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s.l = append(s.l, Sample{})
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copy(s.l[i+1:], s.l[i:])
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s.l[i] = Sample{
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sample.Value,
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sample.Width,
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math.Max(sample.Delta, math.Floor(s.ƒ(s, r))-1),
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// TODO(beorn7): How to calculate delta correctly?
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}
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i++
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goto inserted
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}
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r += c.Width
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}
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s.l = append(s.l, Sample{sample.Value, sample.Width, 0})
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i++
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inserted:
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s.n += sample.Width
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r += sample.Width
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}
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s.compress()
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}
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func (s *stream) count() int {
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return int(s.n)
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}
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func (s *stream) query(q float64) float64 {
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t := math.Ceil(q * s.n)
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t += math.Ceil(s.ƒ(s, t) / 2)
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p := s.l[0]
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var r float64
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for _, c := range s.l[1:] {
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r += p.Width
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if r+c.Width+c.Delta > t {
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return p.Value
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}
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p = c
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}
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return p.Value
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}
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func (s *stream) compress() {
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if len(s.l) < 2 {
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return
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}
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x := s.l[len(s.l)-1]
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xi := len(s.l) - 1
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r := s.n - 1 - x.Width
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for i := len(s.l) - 2; i >= 0; i-- {
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c := s.l[i]
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if c.Width+x.Width+x.Delta <= s.ƒ(s, r) {
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x.Width += c.Width
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s.l[xi] = x
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// Remove element at i.
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copy(s.l[i:], s.l[i+1:])
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s.l = s.l[:len(s.l)-1]
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xi -= 1
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} else {
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x = c
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xi = i
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}
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r -= c.Width
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}
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}
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func (s *stream) samples() Samples {
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samples := make(Samples, len(s.l))
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copy(samples, s.l)
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return samples
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}
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