1 files changed, 292 insertions, 0 deletions
diff --git a/vendor/github.com/beorn7/perks/quantile/stream.go b/vendor/github.com/beorn7/perks/quantile/stream.go
new file mode 100644
index 0000000..f4cabd6
--- /dev/null
+++ b/vendor/github.com/beorn7/perks/quantile/stream.go
@@ -0,0 +1,292 @@
+// Package quantile computes approximate quantiles over an unbounded data
+// stream within low memory and CPU bounds.
+//
+// A small amount of accuracy is traded to achieve the above properties.
+//
+// Multiple streams can be merged before calling Query to generate a single set
+// of results. This is meaningful when the streams represent the same type of
+// data. See Merge and Samples.
+//
+// For more detailed information about the algorithm used, see:
+//
+// Effective Computation of Biased Quantiles over Data Streams
+//
+// http://www.cs.rutgers.edu/~muthu/bquant.pdf
+package quantile
+
+import (
+	"math"
+	"sort"
+)
+
+// Sample holds an observed value and meta information for compression. JSON
+// tags have been added for convenience.
+type Sample struct {
+	Value float64 `json:",string"`
+	Width float64 `json:",string"`
+	Delta float64 `json:",string"`
+}
+
+// Samples represents a slice of samples. It implements sort.Interface.
+type Samples []Sample
+
+func (a Samples) Len() int           { return len(a) }
+func (a Samples) Less(i, j int) bool { return a[i].Value < a[j].Value }
+func (a Samples) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
+
+type invariant func(s *stream, r float64) float64
+
+// NewLowBiased returns an initialized Stream for low-biased quantiles
+// (e.g. 0.01, 0.1, 0.5) where the needed quantiles are not known a priori, but
+// error guarantees can still be given even for the lower ranks of the data
+// distribution.
+//
+// The provided epsilon is a relative error, i.e. the true quantile of a value
+// returned by a query is guaranteed to be within (1±Epsilon)*Quantile.
+//
+// See http://www.cs.rutgers.edu/~muthu/bquant.pdf for time, space, and error
+// properties.
+func NewLowBiased(epsilon float64) *Stream {
+	ƒ := func(s *stream, r float64) float64 {
+		return 2 * epsilon * r
+	}
+	return newStream(ƒ)
+}
+
+// NewHighBiased returns an initialized Stream for high-biased quantiles
+// (e.g. 0.01, 0.1, 0.5) where the needed quantiles are not known a priori, but
+// error guarantees can still be given even for the higher ranks of the data
+// distribution.
+//
+// The provided epsilon is a relative error, i.e. the true quantile of a value
+// returned by a query is guaranteed to be within 1-(1±Epsilon)*(1-Quantile).
+//
+// See http://www.cs.rutgers.edu/~muthu/bquant.pdf for time, space, and error
+// properties.
+func NewHighBiased(epsilon float64) *Stream {
+	ƒ := func(s *stream, r float64) float64 {
+		return 2 * epsilon * (s.n - r)
+	}
+	return newStream(ƒ)
+}
+
+// NewTargeted returns an initialized Stream concerned with a particular set of
+// quantile values that are supplied a priori. Knowing these a priori reduces
+// space and computation time. The targets map maps the desired quantiles to
+// their absolute errors, i.e. the true quantile of a value returned by a query
+// is guaranteed to be within (Quantile±Epsilon).
+//
+// See http://www.cs.rutgers.edu/~muthu/bquant.pdf for time, space, and error properties.
+func NewTargeted(targets map[float64]float64) *Stream {
+	ƒ := func(s *stream, r float64) float64 {
+		var m = math.MaxFloat64
+		var f float64
+		for quantile, epsilon := range targets {
+			if quantile*s.n <= r {
+				f = (2 * epsilon * r) / quantile
+			} else {
+				f = (2 * epsilon * (s.n - r)) / (1 - quantile)
+			}
+			if f < m {
+				m = f
+			}
+		}
+		return m
+	}
+	return newStream(ƒ)
+}
+
+// Stream computes quantiles for a stream of float64s. It is not thread-safe by
+// design. Take care when using across multiple goroutines.
+type Stream struct {
+	*stream
+	b      Samples
+	sorted bool
+}
+
+func newStream(ƒ invariant) *Stream {
+	x := &stream{ƒ: ƒ}
+	return &Stream{x, make(Samples, 0, 500), true}
+}
+
+// Insert inserts v into the stream.
+func (s *Stream) Insert(v float64) {
+	s.insert(Sample{Value: v, Width: 1})
+}
+
+func (s *Stream) insert(sample Sample) {
+	s.b = append(s.b, sample)
+	s.sorted = false
+	if len(s.b) == cap(s.b) {
+		s.flush()
+	}
+}
+
+// Query returns the computed qth percentiles value. If s was created with
+// NewTargeted, and q is not in the set of quantiles provided a priori, Query
+// will return an unspecified result.
+func (s *Stream) Query(q float64) float64 {
+	if !s.flushed() {
+		// Fast path when there hasn't been enough data for a flush;
+		// this also yields better accuracy for small sets of data.
+		l := len(s.b)
+		if l == 0 {
+			return 0
+		}
+		i := int(math.Ceil(float64(l) * q))
+		if i > 0 {
+			i -= 1
+		}
+		s.maybeSort()
+		return s.b[i].Value
+	}
+	s.flush()
+	return s.stream.query(q)
+}
+
+// Merge merges samples into the underlying streams samples. This is handy when
+// merging multiple streams from separate threads, database shards, etc.
+//
+// ATTENTION: This method is broken and does not yield correct results. The
+// underlying algorithm is not capable of merging streams correctly.
+func (s *Stream) Merge(samples Samples) {
+	sort.Sort(samples)
+	s.stream.merge(samples)
+}
+
+// Reset reinitializes and clears the list reusing the samples buffer memory.
+func (s *Stream) Reset() {
+	s.stream.reset()
+	s.b = s.b[:0]
+}
+
+// Samples returns stream samples held by s.
+func (s *Stream) Samples() Samples {
+	if !s.flushed() {
+		return s.b
+	}
+	s.flush()
+	return s.stream.samples()
+}
+
+// Count returns the total number of samples observed in the stream
+// since initialization.
+func (s *Stream) Count() int {
+	return len(s.b) + s.stream.count()
+}
+
+func (s *Stream) flush() {
+	s.maybeSort()
+	s.stream.merge(s.b)
+	s.b = s.b[:0]
+}
+
+func (s *Stream) maybeSort() {
+	if !s.sorted {
+		s.sorted = true
+		sort.Sort(s.b)
+	}
+}
+
+func (s *Stream) flushed() bool {
+	return len(s.stream.l) > 0
+}
+
+type stream struct {
+	n float64
+	l []Sample
+	ƒ invariant
+}
+
+func (s *stream) reset() {
+	s.l = s.l[:0]
+	s.n = 0
+}
+
+func (s *stream) insert(v float64) {
+	s.merge(Samples{{v, 1, 0}})
+}
+
+func (s *stream) merge(samples Samples) {
+	// TODO(beorn7): This tries to merge not only individual samples, but
+	// whole summaries. The paper doesn't mention merging summaries at
+	// all. Unittests show that the merging is inaccurate. Find out how to
+	// do merges properly.
+	var r float64
+	i := 0
+	for _, sample := range samples {
+		for ; i < len(s.l); i++ {
+			c := s.l[i]
+			if c.Value > sample.Value {
+				// Insert at position i.
+				s.l = append(s.l, Sample{})
+				copy(s.l[i+1:], s.l[i:])
+				s.l[i] = Sample{
+					sample.Value,
+					sample.Width,
+					math.Max(sample.Delta, math.Floor(s.ƒ(s, r))-1),
+					// TODO(beorn7): How to calculate delta correctly?
+				}
+				i++
+				goto inserted
+			}
+			r += c.Width
+		}
+		s.l = append(s.l, Sample{sample.Value, sample.Width, 0})
+		i++
+	inserted:
+		s.n += sample.Width
+		r += sample.Width
+	}
+	s.compress()
+}
+
+func (s *stream) count() int {
+	return int(s.n)
+}
+
+func (s *stream) query(q float64) float64 {
+	t := math.Ceil(q * s.n)
+	t += math.Ceil(s.ƒ(s, t) / 2)
+	p := s.l[0]
+	var r float64
+	for _, c := range s.l[1:] {
+		r += p.Width
+		if r+c.Width+c.Delta > t {
+			return p.Value
+		}
+		p = c
+	}
+	return p.Value
+}
+
+func (s *stream) compress() {
+	if len(s.l) < 2 {
+		return
+	}
+	x := s.l[len(s.l)-1]
+	xi := len(s.l) - 1
+	r := s.n - 1 - x.Width
+
+	for i := len(s.l) - 2; i >= 0; i-- {
+		c := s.l[i]
+		if c.Width+x.Width+x.Delta <= s.ƒ(s, r) {
+			x.Width += c.Width
+			s.l[xi] = x
+			// Remove element at i.
+			copy(s.l[i:], s.l[i+1:])
+			s.l = s.l[:len(s.l)-1]
+			xi -= 1
+		} else {
+			x = c
+			xi = i
+		}
+		r -= c.Width
+	}
+}
+
+func (s *stream) samples() Samples {
+	samples := make(Samples, len(s.l))
+	copy(samples, s.l)
+	return samples
+}