github.com/m3db/m3@v1.5.0/src/aggregator/aggregation/quantile/cm/stream.go

// Copyright (c) 2016 Uber Technologies, Inc.
//
// 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.

package cm

import (
	"math"
)

const (
	minSamplesToCompress = 3
)

var (
	nan = math.NaN()
)

type threshold struct {
	rank      int64
	threshold int64
}

// Stream represents a data stream.
type Stream struct {
	compressCursor           *Sample // compression cursor
	streamPool               StreamPool
	insertCursor             *Sample
	samples                  sampleList
	computedQuantiles        []float64   // sorted computed target quantiles
	thresholdBuf             []threshold // temporary buffer for computed thresholds
	bufLess                  minHeap     // sample buffer whose value is less than that at the insertion cursor
	bufMore                  minHeap     // sample buffer whose value is more than that at the insertion cursor
	quantiles                []float64   // sorted target quantiles
	numValues                int64       // number of values inserted into the sorted stream
	insertAndCompressCounter int         // insertion and compression counter
	insertAndCompressEvery   int         // stream insertion and compression frequency
	capacity                 int         // initial stream sample buffer capacity
	eps                      float64     // desired epsilon for errors
	compressMinRank          int64       // compression min rank
	closed                   bool        // whether the stream is closed
	flushed                  bool        // whether the stream is flushed
}

// NewStream creates a new sample stream.
func NewStream(opts Options) *Stream {
	if opts == nil {
		opts = NewOptions()
	}

	s := &Stream{
		streamPool:             opts.StreamPool(),
		eps:                    opts.Eps(),
		capacity:               opts.Capacity(),
		insertAndCompressEvery: opts.InsertAndCompressEvery(),
	}

	return s
}

// AddBatch adds a batch of sample values.
func (s *Stream) AddBatch(values []float64) {
	s.flushed = false

	if len(values) == 0 {
		return
	}

	if s.samples.Len() == 0 {
		sample := s.samples.Acquire()
		sample.value = values[0]
		sample.numRanks = 1
		sample.delta = 0
		s.samples.PushBack(sample)
		s.insertCursor = s.samples.Front()
		s.numValues++
		values = values[1:]
	}

	var (
		insertPointValue = s.insertCursor.value
		insertCounter    = s.insertAndCompressCounter
	)

	for _, value := range values {
		if value < insertPointValue {
			s.bufLess.Push(value)
		} else {
			s.bufMore.Push(value)
		}

		if insertCounter == s.insertAndCompressEvery {
			s.insert()
			s.compress()
			insertCounter = 0
		}
		insertCounter++
	}
	s.insertAndCompressCounter = insertCounter
}

// Add adds a sample value.
func (s *Stream) Add(value float64) {
	s.AddBatch([]float64{value})
}

// Flush flushes the internal buffer.
func (s *Stream) Flush() {
	if s.flushed {
		return
	}

	for s.bufLess.Len() > 0 || s.bufMore.Len() > 0 {
		if s.bufMore.Len() == 0 {
			s.resetInsertCursor()
		}
		s.insert()
		s.compress()
	}
	s.calcQuantiles()
	s.flushed = true
}

// Min returns the minimum value.
func (s *Stream) Min() float64 {
	return s.Quantile(0.0)
}

// Max returns the maximum value.
func (s *Stream) Max() float64 {
	return s.Quantile(1.0)
}

// Quantile returns the quantile value.
func (s *Stream) Quantile(q float64) float64 {
	if q < 0.0 || q > 1.0 {
		return nan
	}

	if s.samples.Empty() {
		return 0.0
	}

	if q == 0.0 {
		return s.samples.Front().value
	}
	if q == 1.0 {
		return s.samples.Back().value
	}

	for i, qt := range s.quantiles {
		if qt >= q {
			return s.computedQuantiles[i]
		}
	}
	return math.NaN()
}

// ResetSetData resets the stream and sets data.
func (s *Stream) ResetSetData(quantiles []float64) {
	s.quantiles = quantiles

	if len(quantiles) > cap(s.computedQuantiles) {
		s.computedQuantiles = make([]float64, len(quantiles))
		s.thresholdBuf = make([]threshold, len(quantiles))
	} else {
		s.computedQuantiles = s.computedQuantiles[:len(quantiles)]
		s.thresholdBuf = s.thresholdBuf[:len(quantiles)]
	}

	s.closed = false
}

// Close closes the stream.
func (s *Stream) Close() {
	if s.closed {
		return
	}
	s.closed = true

	s.bufMore.Reset()
	s.bufLess.Reset()

	s.samples.Reset()
	s.insertCursor = nil
	s.compressCursor = nil
	s.insertAndCompressCounter = 0
	s.numValues = 0
	s.compressMinRank = 0
	s.streamPool.Put(s)
}

// quantilesFromBuf calculates quantiles from buffer if there were too few samples to compress
func (s *Stream) quantilesFromBuf() {
	var (
		curr = s.samples.Front()
		buf  = make([]float64, 0, minSamplesToCompress)
	)

	for curr != nil {
		buf = append(buf, curr.value)
		curr = curr.next
	}

	n := len(buf)
	for i, q := range s.quantiles {
		idx := int(q * float64(n))
		if idx >= n {
			idx = n - 1
		}
		s.computedQuantiles[i] = buf[idx]
	}
}

func (s *Stream) calcQuantiles() {
	if len(s.quantiles) == 0 || s.numValues == 0 {
		return
	} else if s.numValues <= minSamplesToCompress {
		// too few values for compress(), need to compute quantiles directly
		s.quantilesFromBuf()
		return
	}

	var (
		minRank int64
		maxRank int64
		idx     int
		curr    = s.samples.Front()
		prev    = s.samples.Front()
	)

	for i, q := range s.quantiles {
		rank := int64(math.Ceil(q * float64(s.numValues)))
		s.thresholdBuf[i].rank = rank
		s.thresholdBuf[i].threshold = int64(
			math.Ceil(float64(s.threshold(rank)) / 2.0),
		)
	}

	for curr != nil && idx < len(s.computedQuantiles) {
		maxRank = minRank + curr.numRanks + curr.delta
		rank, threshold := s.thresholdBuf[idx].rank, s.thresholdBuf[idx].threshold

		if maxRank > rank+threshold || minRank > rank {
			s.computedQuantiles[idx] = prev.value
			idx++
		}

		minRank += curr.numRanks
		prev = curr
		curr = curr.next
	}

	// check if the last sample value should satisfy unprocessed quantiles
	for i := idx; i < len(s.thresholdBuf); i++ {
		rank, threshold := s.thresholdBuf[i].rank, s.thresholdBuf[i].threshold
		if maxRank >= rank+threshold || minRank > rank {
			s.computedQuantiles[i] = prev.value
		}
	}
}

// insert inserts a sample into the stream.
func (s *Stream) insert() {
	var (
		compCur          = s.compressCursor
		compValue        = math.NaN()
		samples          = &s.samples
		insertPointValue float64
		sample           *Sample
	)

	if compCur != nil {
		compValue = compCur.value
	}

	// break heap invariant and just sort all the times, as we'll consume all of them in one go
	s.bufMore.SortDesc()

	var (
		vals = []float64(s.bufMore)
		idx  = len(vals) - 1
	)

	for s.insertCursor != nil && idx < len(vals) {
		curr := s.insertCursor
		insertPointValue = curr.value

		for idx >= 0 && vals[idx] <= insertPointValue {
			val := vals[idx]
			idx--
			sample = s.samples.Acquire()
			sample.value = val
			sample.numRanks = 1
			sample.delta = curr.numRanks + curr.delta - 1

			samples.InsertBefore(sample, curr)

			if compValue >= val {
				s.compressMinRank++
			}
			s.numValues++
		}

		s.insertCursor = s.insertCursor.next
	}

	if s.insertCursor == nil && idx < len(vals) {
		for idx >= 0 && vals[idx] >= samples.Back().value {
			val := vals[idx]
			idx--
			sample = s.samples.Acquire()
			sample.value = val
			sample.numRanks = 1
			sample.delta = 0
			samples.PushBack(sample)
			s.numValues++
		}
	}

	s.bufMore = s.bufMore[:0]
	s.resetInsertCursor()
}

// compress compresses the samples in the stream.
func (s *Stream) compress() {
	// Bail early if there is nothing to compress.
	if s.samples.Len() < minSamplesToCompress {
		return
	}

	if s.compressCursor == nil {
		s.compressCursor = s.samples.Back().prev
		s.compressMinRank = s.numValues - 1 - s.compressCursor.numRanks
		s.compressCursor = s.compressCursor.prev
	}

	var (
		numVals = s.numValues
		eps     = 2.0 * s.eps
	)

	for s.compressCursor != s.samples.Front() {
		var (
			curr = s.compressCursor
			next = curr.next
			prev = curr.prev

			maxRank = s.compressMinRank + curr.numRanks + curr.delta

			threshold   = int64(math.MaxInt64)
			quantileMin int64
		)

		for i := range s.quantiles {
			if maxRank >= int64(s.quantiles[i]*float64(numVals)) {
				quantileMin = int64(eps * float64(maxRank) / s.quantiles[i])
			} else {
				quantileMin = int64(eps * float64(numVals-maxRank) / (1.0 - s.quantiles[i]))
			}
			if quantileMin < threshold {
				threshold = quantileMin
			}
		}

		s.compressMinRank -= curr.numRanks
		testVal := curr.numRanks + next.numRanks + next.delta

		if testVal <= threshold {
			if s.insertCursor == curr {
				s.insertCursor = next
			}

			next.numRanks += curr.numRanks

			// no need to release sample here
			s.samples.Remove(curr)
		}
		s.compressCursor = prev
	}

	if s.compressCursor == s.samples.Front() {
		s.compressCursor = nil
	}
}

// threshold computes the minimum threshold value.
func (s *Stream) threshold(rank int64) int64 {
	var (
		minVal      = int64(math.MaxInt64)
		numVals     = s.numValues
		eps         = 2.0 * s.eps
		quantileMin int64
	)
	for _, quantile := range s.quantiles {
		if rank >= int64(quantile*float64(numVals)) {
			quantileMin = int64(eps * float64(rank) / quantile)
		} else {
			quantileMin = int64(eps * float64(numVals-rank) / (1.0 - quantile))
		}
		if quantileMin < minVal {
			minVal = quantileMin
		}
	}

	return minVal
}

// resetInsertCursor resets the insert cursor.
func (s *Stream) resetInsertCursor() {
	s.bufLess, s.bufMore = s.bufMore, s.bufLess
	s.insertCursor = s.samples.Front()
}