3 files changed, 343 insertions, 0 deletions
diff --git a/vendor/github.com/beorn7/perks/LICENSE b/vendor/github.com/beorn7/perks/LICENSE
new file mode 100644
index 000000000..339177be6
--- /dev/null
+++ b/vendor/github.com/beorn7/perks/LICENSE
@@ -0,0 +1,20 @@
+Copyright (C) 2013 Blake Mizerany
+
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of this software and associated documentation files (the
+"Software"), to deal in the Software without restriction, including
+without limitation the rights to use, copy, modify, merge, publish,
+distribute, sublicense, and/or sell copies of the Software, and to
+permit persons to whom the Software is furnished to do so, subject to
+the following conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
+LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
+WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
diff --git a/vendor/github.com/beorn7/perks/README.md b/vendor/github.com/beorn7/perks/README.md
new file mode 100644
index 000000000..fc0577770
--- /dev/null
+++ b/vendor/github.com/beorn7/perks/README.md
@@ -0,0 +1,31 @@
+# Perks for Go (golang.org)
+
+Perks contains the Go package quantile that computes approximate quantiles over
+an unbounded data stream within low memory and CPU bounds.
+
+For more information and examples, see:
+http://godoc.org/github.com/bmizerany/perks
+
+A very special thank you and shout out to Graham Cormode (Rutgers University),
+Flip Korn (AT&T Labs–Research), S. Muthukrishnan (Rutgers University), and
+Divesh Srivastava (AT&T Labs–Research) for their research and publication of
+[Effective Computation of Biased Quantiles over Data Streams](http://www.cs.rutgers.edu/~muthu/bquant.pdf)
+
+Thank you, also:
+* Armon Dadgar (@armon)
+* Andrew Gerrand (@nf)
+* Brad Fitzpatrick (@bradfitz)
+* Keith Rarick (@kr)
+
+FAQ:
+
+Q: Why not move the quantile package into the project root?
+A: I want to add more packages to perks later.
+
+Copyright (C) 2013 Blake Mizerany
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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 000000000..587b1fc5b
--- /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(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
+}