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/*
* Licensed to Metamarkets Group Inc. (Metamarkets) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. Metamarkets licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*/
package io.druid.query.aggregation.histogram;
import com.fasterxml.jackson.annotation.JsonValue;
import com.google.common.base.Preconditions;
import com.google.common.collect.Lists;
import com.google.common.collect.Maps;
import com.google.common.primitives.Floats;
import com.google.common.primitives.Ints;
import com.google.common.primitives.Longs;
import com.google.common.primitives.Shorts;
import java.nio.ByteBuffer;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Map;
public class ApproximateHistogram
{
public static final int DEFAULT_HISTOGRAM_SIZE = 50;
public static final int DEFAULT_BUCKET_SIZE = 7;
// max size of the histogram (number of bincount/position pairs)
int size;
public float[] positions;
public long[] bins;
// used bincount
int binCount;
// min value that's been put into histogram
float min;
float max;
// total number of values that have been put into histogram
transient long count;
// lower limit to maintain resolution
// cutoff above which we merge bins is the difference of the limits / (size - 3)
// so we'll set size = 203, lower limit = 0, upper limit = 10.00 if we don't want
// to merge differences < 0.05
transient float lowerLimit;
transient float upperLimit;
// use sign bit to indicate approximate bin and remaining bits for bin count
private static final long APPROX_FLAG_BIT = Long.MIN_VALUE;
private static final long COUNT_BITS = Long.MAX_VALUE;
@Override
public boolean equals(Object o)
{
if (this == o) {
return true;
}
if (o == null || getClass() != o.getClass()) {
return false;
}
ApproximateHistogram that = (ApproximateHistogram) o;
if (size != that.size) {
return false;
}
if (binCount != that.binCount) {
return false;
}
if (Float.compare(that.max, max) != 0) {
return false;
}
if (Float.compare(that.min, min) != 0) {
return false;
}
for (int i = 0; i < binCount; ++i) {
if (positions[i] != that.positions[i]) {
return false;
}
}
for (int i = 0; i < binCount; ++i) {
if (bins[i] != that.bins[i]) {
return false;
}
}
return true;
}
@Override
public int hashCode()
{
int result = size;
result = 31 * result + (positions != null ? ArrayUtils.hashCode(positions, 0, binCount) : 0);
result = 31 * result + (bins != null ? ArrayUtils.hashCode(bins, 0, binCount) : 0);
result = 31 * result + binCount;
result = 31 * result + (min != +0.0f ? Float.floatToIntBits(min) : 0);
result = 31 * result + (max != +0.0f ? Float.floatToIntBits(max) : 0);
return result;
}
public ApproximateHistogram(
int size,
float[] positions,
long[] bins,
int binCount,
float min,
float max,
long count,
float lowerLimit,
float upperLimit
)
{
Preconditions.checkArgument(positions.length == bins.length, "position and bin array must have same size");
Preconditions.checkArgument(binCount <= size, "binCount must be less or equal to size");
this.size = size;
this.positions = positions;
this.bins = bins;
this.binCount = binCount;
this.min = min;
this.max = max;
this.count = count;
this.lowerLimit = lowerLimit;
this.upperLimit = upperLimit;
}
public ApproximateHistogram()
{
this(DEFAULT_HISTOGRAM_SIZE);
}
public ApproximateHistogram(int size)
{
this(
size, //size
new float[size], //positions
new long[size], //bins
0, //binCount
Float.POSITIVE_INFINITY, //min
Float.NEGATIVE_INFINITY, //max
0, //count
Float.NEGATIVE_INFINITY, //lowerLimit
Float.POSITIVE_INFINITY //upperLimit
);
}
public ApproximateHistogram(int size, float lowerLimit, float upperLimit)
{
this(
size, //size
new float[size], //positions
new long[size], //bins
0, //binCount
Float.POSITIVE_INFINITY, //min
Float.NEGATIVE_INFINITY, //max
0, //count
lowerLimit, //lowerLimit
upperLimit //upperLimit
);
}
public ApproximateHistogram(int binCount, float[] positions, long[] bins, float min, float max)
{
this(
positions.length, //size
positions, //positions
bins, //bins
binCount, //binCount
min, //min
max, //max
sumBins(bins, binCount), //count
Float.NEGATIVE_INFINITY, //lowerLimit
Float.POSITIVE_INFINITY //upperLimit
);
}
public long count() { return count; }
public float min() { return min; }
public float max() { return max; }
public int binCount() { return binCount; }
public int capacity() { return size; }
public float[] positions() { return Arrays.copyOfRange(positions, 0, binCount); }
public long[] bins()
{
long[] counts = new long[binCount];
for (int i = 0; i < binCount; ++i) {
counts[i] = bins[i] & COUNT_BITS;
}
return counts;
}
@Override
public String toString()
{
return "ApproximateHistogram{" +
"size=" + size +
", lowerLimit=" + lowerLimit +
", upperLimit=" + upperLimit +
", positions=" + Arrays.toString(positions()) +
", bins=" + getBinsString() +
", binCount=" + binCount +
", min=" + min +
", max=" + max +
", count=" + count +
'}';
}
public long getExactCount()
{
long exactCount = 0;
for (int i = 0; i < binCount; ++i) {
if ((bins[i] & APPROX_FLAG_BIT) == 0) {
exactCount += (bins[i] & COUNT_BITS);
}
}
return exactCount;
}
public float getMin() { return this.min;}
public float getMax() { return this.max;}
private static long sumBins(long[] bins, int binCount)
{
long count = 0;
for (int i = 0; i < binCount; ++i) {
count += bins[i] & COUNT_BITS;
}
return count;
}
/**
* @return a string representation of the actual bin counts
*/
protected String getBinsString()
{
StringBuilder s = new StringBuilder();
s.append('[');
for (int i = 0; i < bins.length; ++i) {
if (i > 0) {
s.append(", ");
}
if ((bins[i] & APPROX_FLAG_BIT) != 0) {
s.append("*");
}
s.append(bins[i] & COUNT_BITS);
}
s.append(']');
return s.toString();
}
public void setLowerLimit(float lowerLimit)
{
this.lowerLimit = lowerLimit;
}
public void setUpperLimit(float upperLimit)
{
this.upperLimit = upperLimit;
}
/**
* Adds the given value to the histogram
*
* @param value the value to be added
*/
public void offer(float value)
{
// update min/max
if (value < min) {
min = value;
}
if (value > max) {
max = value;
}
// initial value
if (binCount == 0) {
positions[0] = value;
bins[0] = 1;
count++;
binCount++;
return;
}
final int index = Arrays.binarySearch(positions, 0, binCount, value);
if (index >= 0) {
// we have an exact match, simply increase the count, but keep the approximate flag
bins[index] = (bins[index] & APPROX_FLAG_BIT) | ((bins[index] & COUNT_BITS) + 1);
count++;
return;
}
// otherwise merge the value into a new or existing bin at the following position
final int insertAt = -(index + 1);
if (binCount < size) {
// we have a spare slot, put the value into a new bin
shiftRight(insertAt, binCount);
positions[insertAt] = value;
bins[insertAt] = 1;
count++;
binCount++;
return;
}
// no more slots available merge the new value into and existing bin
// or merge existing bins before inserting the new one
int minPos = minDeltaIndex();
float minDelta = minPos >= 0 ? positions[minPos + 1] - positions[minPos] : Float.MAX_VALUE;
// determine the distance of new value to the nearest bins
final float deltaRight = insertAt < binCount ? positions[insertAt] - value : Float.MAX_VALUE;
final float deltaLeft = insertAt > 0 ? value - positions[insertAt - 1] : Float.MAX_VALUE;
boolean mergeValue = false;
if (deltaRight < minDelta) {
minDelta = deltaRight;
minPos = insertAt;
mergeValue = true;
}
if (deltaLeft < minDelta) {
minDelta = deltaLeft;
minPos = insertAt - 1;
mergeValue = true;
}
if (mergeValue) {
// merge new value into an existing bin and set approximate flag
final long k = bins[minPos] & COUNT_BITS;
positions[minPos] = (positions[minPos] * k + value) / (k + 1);
bins[minPos] = (k + 1) | APPROX_FLAG_BIT;
count++;
} else {
// merge the closest bins together and insert new value as a separate bin
mergeInsert(minPos, insertAt, value, 1);
}
}
protected int minDeltaIndex()
{
// determine minimum distance between existing bins
float minDelta = Float.MAX_VALUE;
int minPos = -1;
for (int i = 0; i < binCount - 1; ++i) {
float delta = (positions[i + 1] - positions[i]);
if (delta < minDelta) {
minDelta = delta;
minPos = i;
}
}
return minPos;
}
/**
* Merges the bin in the given position with the next bin
*
* @param index index of the bin to merge, index must satisfy 0 <= index < binCount - 1
*/
protected void merge(final int index)
{
mergeInsert(index, -1, 0, 0);
}
/**
* Merges the bin in the mergeAt position with the bin in position mergeAt+1
* and simultaneously inserts the given bin (v,c) as a new bin at position insertAt
*
* @param mergeAt index of the bin to be merged
* @param insertAt index to insert the new bin at
* @param v bin position
* @param c bin count
*/
protected void mergeInsert(final int mergeAt, int insertAt, final float v, final long c)
{
final long k0 = (bins[mergeAt] & COUNT_BITS);
final long k1 = (bins[mergeAt + 1] & COUNT_BITS);
final long sum = k0 + k1;
// merge bin at given position with the next bin and set approximate flag
positions[mergeAt] = (float) (((double) positions[mergeAt] * k0 + (double) positions[mergeAt + 1] * k1) / sum);
bins[mergeAt] = sum | APPROX_FLAG_BIT;
final int unusedIndex = mergeAt + 1;
if (insertAt >= 0) {
// use unused slot to shift array left or right and make space for the new bin to insert
if (insertAt < unusedIndex) {
shiftRight(insertAt, unusedIndex);
} else if (insertAt >= unusedIndex) {
shiftLeft(unusedIndex, insertAt - 1);
insertAt--;
}
positions[insertAt] = v;
bins[insertAt] = c;
count++;
} else {
// simple merging of bins, shift everything left and free up the unused bin
shiftLeft(unusedIndex, binCount - 1);
binCount--;
}
}
/**
* Shifts the given range the histogram bins one slot to the right
*
* @param start index of the first bin to shift
* @param end index of the rightmost bin to shift into
*/
protected void shiftRight(int start, int end)
{
float prevVal = positions[start];
long prevCnt = bins[start];
for (int i = start + 1; i <= end; ++i) {
float tmpVal = positions[i];
long tmpCnt = bins[i];
positions[i] = prevVal;
bins[i] = prevCnt;
prevVal = tmpVal;
prevCnt = tmpCnt;
}
}
/**
* Shifts the given range of histogram bins one slot to the left
*
* @param start index of the leftmost empty bin to shift into
* @param end index of the last bin to shift left
*/
protected void shiftLeft(int start, int end)
{
for (int i = start; i < end; ++i) {
positions[i] = positions[i + 1];
bins[i] = bins[i + 1];
}
}
public ApproximateHistogram fold(ApproximateHistogram h)
{
return fold(h, null, null, null);
}
public ApproximateHistogram fold(ApproximateHistogram h, float[] mergedPositions, long[] mergedBins, float[] deltas)
{
if (size == 0) {
return copy(h);
} else {
return foldMin(h, mergedPositions, mergedBins, deltas);
}
}
public ApproximateHistogram foldFast(ApproximateHistogram h)
{
return foldFast(h, null, null);
}
/**
* @param h histogram to be merged into the current histogram
* @param mergedPositions temporary buffer of size greater or equal to this.capacity()
* @param mergedBins temporary buffer of size greater or equal to this.capacity()
*
* @return returns this histogram with h folded into it
*/
public ApproximateHistogram foldFast(ApproximateHistogram h, float[] mergedPositions, long[] mergedBins)
{
if (size == 0) {
return copy(h);
} else {
return foldRule(h, mergedPositions, mergedBins);
}
}
/**
* Copies histogram h into the current histogram.
*
* @param h ApproximateHistogram to copy
*
* @return this histogram
*/
public ApproximateHistogram copy(ApproximateHistogram h)
{
this.size = h.size;
this.positions = new float[size];
this.bins = new long[size];
System.arraycopy(h.positions, 0, this.positions, 0, h.binCount);
System.arraycopy(h.bins, 0, this.bins, 0, h.binCount);
this.min = h.min;
this.max = h.max;
this.binCount = h.binCount;
this.count = h.count;
return this;
}
//approximate histogram solution using min heap to store location of min deltas
protected ApproximateHistogram foldMin(
ApproximateHistogram h,
float[] mergedPositions,
long[] mergedBins,
float[] deltas
)
{
// find common min / max
float mergedMin = this.min < h.min ? this.min : h.min;
float mergedMax = this.max > h.max ? this.max : h.max;
long mergedCount = this.count + h.count;
int maxSize = this.binCount + h.binCount;
int[] next = new int[maxSize];
int[] prev = new int[maxSize];
// use preallocated arrays if passed
if (mergedPositions == null || mergedBins == null || deltas == null) {
mergedPositions = new float[maxSize];
mergedBins = new long[maxSize];
deltas = new float[maxSize];
} else {
Preconditions.checkArgument(
mergedPositions.length >= maxSize,
"temp buffer [mergedPositions] too small: length must be at least [%d], got [%d]",
maxSize,
mergedPositions.length
);
Preconditions.checkArgument(
mergedBins.length >= maxSize,
"temp buffer [mergedBins] too small: length must be at least [%d], got [%d]",
maxSize,
mergedPositions.length
);
Preconditions.checkArgument(
deltas.length >= maxSize,
"temp buffer [deltas] too small: length must be at least [%d], got [%d]",
maxSize,
mergedPositions.length
);
}
int mergedBinCount = combineBins(
this.binCount, this.positions, this.bins, h.binCount, h.positions, h.bins,
mergedPositions, mergedBins, deltas
);
if (mergedBinCount == 0) {
return this;
}
// determine how many bins to merge
int numMerge = mergedBinCount - this.size;
if (numMerge < 0) {
numMerge = 0;
}
// perform the required number of merges
mergeBins(mergedBinCount, mergedPositions, mergedBins, deltas, numMerge, next, prev);
// copy merged values
int i = 0;
int k = 0;
while (i < mergedBinCount) {
this.positions[k] = mergedPositions[i];
this.bins[k] = mergedBins[i];
++k;
i = next[i];
}
this.binCount = mergedBinCount - numMerge;
this.min = mergedMin;
this.max = mergedMax;
this.count = mergedCount;
return this;
}
protected ApproximateHistogram foldRule(ApproximateHistogram h, float[] mergedPositions, long[] mergedBins)
{
// ruleCombine bins requires at least one bin
if (h.binCount == 0) {
return this;
}
// find common min / max
float mergedMin = this.min < h.min ? this.min : h.min;
float mergedMax = this.max > h.max ? this.max : h.max;
long mergedCount = this.count + h.count;
this.min = mergedMin;
this.max = mergedMax;
// use preallocated arrays if passed
if (mergedPositions == null) {
mergedPositions = new float[this.size];
mergedBins = new long[this.size];
}
int mergedBinCount;
if (this.binCount + h.binCount <= this.size) {
// no need to merge bins
mergedBinCount = combineBins(
this.binCount, this.positions, this.bins,
h.binCount, h.positions, h.bins,
mergedPositions, mergedBins, null
);
} else {
mergedBinCount = ruleCombineBins(
this.binCount, this.positions, this.bins, h.binCount, h.positions, h.bins,
mergedPositions, mergedBins
);
}
for (int i = 0; i < mergedBinCount; ++i) {
this.positions[i] = mergedPositions[i];
this.bins[i] = mergedBins[i];
}
this.binCount = mergedBinCount;
this.count = mergedCount;
return this;
}
protected int ruleCombineBins(
int leftBinCount, float[] leftPositions, long[] leftBins,
int rightBinCount, float[] rightPositions, long[] rightBins,
float[] mergedPositions, long[] mergedBins
)
{
final float cutoff;
// assumes binCount is greater than one for both histograms
// if upper and lower limits are set, we use the first and last used values of the arrays
// for information below and above the limits, respectively
if (this.upperLimit != Float.POSITIVE_INFINITY && this.lowerLimit != Float.NEGATIVE_INFINITY) {
cutoff = (this.upperLimit - this.lowerLimit) / (size - 2 - 1);
} else {
if (this.upperLimit != Float.POSITIVE_INFINITY) {
cutoff = (this.upperLimit - this.min) / (size - 2);
} else if (this.lowerLimit != Float.NEGATIVE_INFINITY) {
cutoff = (this.max - this.lowerLimit) / (size - 2);
} else {
cutoff = (this.max - this.min) / (size - 1);
}
}
float lowerPosition = 0f;
long lowerBin = 0;
float upperPosition = 0f;
long upperBin = 0;
int j = 0;
int k = 0;
int pos = 0;
// continuously merge the left histogram below the lower limit
while (j != leftBinCount) {
final float m1 = leftPositions[j];
if (m1 < lowerLimit) {
final long k1 = leftBins[j] & COUNT_BITS;
float delta = (m1 - lowerPosition);
final long k0 = lowerBin & COUNT_BITS;
final long sum = k0 + k1;
final float w = (float) k0 / (float) sum;
lowerPosition = -delta * w + m1;
// set approximate flag
lowerBin = sum | APPROX_FLAG_BIT;
++j;
} else {
break;
}
}
// continuously merge the right histogram below the lower limit
while (k != rightBinCount) {
final float m1 = rightPositions[k];
if (m1 < lowerLimit) {
final long k1 = rightBins[k] & COUNT_BITS;
float delta = (m1 - lowerPosition);
final long k0 = lowerBin & COUNT_BITS;
final long sum = k0 + k1;
final float w = (float) k0 / (float) sum;
lowerPosition = -delta * w + m1;
// set approximate flag
lowerBin = sum | APPROX_FLAG_BIT;
++k;
} else {
break;
}
}
// if there are values below the lower limit, store them in array position 0
if ((lowerBin & COUNT_BITS) > 0) {
mergedPositions[0] = lowerPosition;
mergedBins[0] = lowerBin;
pos = 1;
}
// if there are values below the lower limit, fill in array position 1
// else array position 0
while (j != leftBinCount || k != rightBinCount) {
if (j != leftBinCount && (k == rightBinCount || leftPositions[j] < rightPositions[k])) {
mergedPositions[pos] = leftPositions[j];
mergedBins[pos] = leftBins[j];
++j;
break;
} else {
mergedPositions[pos] = rightPositions[k];
mergedBins[pos] = rightBins[k];
++k;
break;
}
}
while (j != leftBinCount || k != rightBinCount) {
if (j != leftBinCount && (k == rightBinCount || leftPositions[j] < rightPositions[k])) {
final float m1 = leftPositions[j];
final long k1 = leftBins[j] & COUNT_BITS;
// above the upper limit gets merged continuously in the left histogram
if (m1 > upperLimit) {
float delta = (m1 - upperPosition);
final long k0 = upperBin & COUNT_BITS;
final long sum = k0 + k1;
final float w = (float) k0 / (float) sum;
upperPosition = -delta * w + m1;
// set approximate flag
upperBin = sum | APPROX_FLAG_BIT;
++j;
continue;
}
final float delta = (m1 - mergedPositions[pos]);
if (delta <= cutoff) {
final long k0 = mergedBins[pos] & COUNT_BITS;
final long sum = k0 + k1;
final float w = (float) k0 / (float) sum;
mergedPositions[pos] = -delta * w + m1;
// set approximate flag
mergedBins[pos] = sum | APPROX_FLAG_BIT;
} else {
++pos;
mergedPositions[pos] = m1;
mergedBins[pos] = k1;
}
++j;
} else {
final float m1 = rightPositions[k];
final long k1 = rightBins[k] & COUNT_BITS;
// above the upper limit gets merged continuously in the right histogram
if (m1 > upperLimit) {
float delta = (m1 - upperPosition);
final long k0 = upperBin & COUNT_BITS;
final long sum = k0 + k1;
final float w = (float) k0 / (float) sum;
upperPosition = -delta * w + m1;
// set approximate flag
upperBin = sum | APPROX_FLAG_BIT;
++k;
continue;
}
final float delta = (m1 - mergedPositions[pos]);
if (delta <= cutoff) {
final long k0 = mergedBins[pos] & COUNT_BITS;
final long sum = k0 + k1;
final float w = (float) k0 / (float) sum;
mergedPositions[pos] = -delta * w + m1;
mergedBins[pos] = sum | APPROX_FLAG_BIT;
} else {
++pos;
mergedPositions[pos] = m1;
mergedBins[pos] = k1;
}
++k;
}
}
if ((upperBin & COUNT_BITS) > 0) {
++pos;
mergedPositions[pos] = upperPosition;
mergedBins[pos] = upperBin;
}
return pos + 1;
}
/**
* mergeBins performs the given number of bin merge operations on the given histogram
*
* It repeatedly merges the two closest bins until it has performed the requested number of merge operations.
* Merges are done in-place and unused bins have unknown state
*
* next / prev maintains a doubly-linked list of valid bin indices into the mergedBins array.
*
* Fast operation is achieved by building a min-heap of the deltas as opposed to repeatedly
* scanning the array of deltas to find the minimum. A reverse index into the heap is maintained
* to allow deleting and updating of specific deltas.
*
* next and prev arrays are used to maintain indices to the previous / next valid bin from a given bin index
*
* Its effect is equivalent to running the following code:
*
*
*
* @param mergedBinCount
* @param mergedPositions
* @param mergedBins
* @param deltas
* @param numMerge
* @param next
* @param prev
*
* @return the last valid index into the mergedPositions and mergedBins arrays
*/
private static void mergeBins(
int mergedBinCount, float[] mergedPositions,
long[] mergedBins,
float[] deltas,
int numMerge,
int[] next,
int[] prev
)
{
// repeatedly search for two closest bins, merge them and update the corresponding deltas
// maintain index to the last valid bin
int lastValidIndex = mergedBinCount - 1;
// initialize prev / next lookup arrays
for (int i = 0; i < mergedBinCount; ++i) {
next[i] = i + 1;
}
for (int i = 0; i < mergedBinCount; ++i) {
prev[i] = i - 1;
}
// initialize min-heap of deltas and the reverse index into the heap
int heapSize = mergedBinCount - 1;
int[] heap = new int[heapSize];
int[] reverseIndex = new int[heapSize];
for (int i = 0; i < heapSize; ++i) {
heap[i] = i;
}
for (int i = 0; i < heapSize; ++i) {
reverseIndex[i] = i;
}
heapify(heap, reverseIndex, heapSize, deltas);
{
int i = 0;
while (i < numMerge) {
// find the smallest delta within the range used for bins
// pick minimum delta by scanning array
//int currentIndex = minIndex(deltas, lastValidIndex);
// pick minimum delta index using min-heap
int currentIndex = heap[0];
final int nextIndex = next[currentIndex];
final int prevIndex = prev[currentIndex];
final long k0 = mergedBins[currentIndex] & COUNT_BITS;
final long k1 = mergedBins[nextIndex] & COUNT_BITS;
final float m0 = mergedPositions[currentIndex];
final float m1 = mergedPositions[nextIndex];
final float d1 = deltas[nextIndex];
final long sum = k0 + k1;
final float w = (float) k0 / (float) sum;
// merge bin at given position with the next bin
final float mm0 = (m0 - m1) * w + m1;
mergedPositions[currentIndex] = mm0;
//mergedPositions[nextIndex] = Float.MAX_VALUE; // for debugging
mergedBins[currentIndex] = sum | APPROX_FLAG_BIT;
//mergedBins[nextIndex] = -1; // for debugging
// update deltas and min-heap
if (nextIndex == lastValidIndex) {
// merged bin is the last => remove the current bin delta from the heap
heapSize = heapDelete(heap, reverseIndex, heapSize, reverseIndex[currentIndex], deltas);
//deltas[currentIndex] = Float.MAX_VALUE; // for debugging
} else {
// merged bin is not the last => remove the merged bin delta from the heap
heapSize = heapDelete(heap, reverseIndex, heapSize, reverseIndex[nextIndex], deltas);
// updated current delta
deltas[currentIndex] = m1 - mm0 + d1;
// updated delta is necessarily larger than existing one, therefore we only need to push it down the heap
siftDown(heap, reverseIndex, reverseIndex[currentIndex], heapSize - 1, deltas);
}
if (prevIndex >= 0) {
// current bin is not the first, therefore update the previous bin delta
deltas[prevIndex] = mm0 - mergedPositions[prevIndex];
// updated previous bin delta is necessarily larger than its existing value => push down the heap
siftDown(heap, reverseIndex, reverseIndex[prevIndex], heapSize - 1, deltas);
}
// mark the merged bin as invalid
// deltas[nextIndex] = Float.MAX_VALUE; // for debugging
// update last valid index if we merged the last bin
if (nextIndex == lastValidIndex) {
lastValidIndex = currentIndex;
}
next[currentIndex] = next[nextIndex];
if (nextIndex < lastValidIndex) {
prev[next[nextIndex]] = currentIndex;
}
++i;
}
}
}
/**
* Builds a min-heap and a reverseIndex into the heap from the given array of values
*
* @param heap min-heap stored as indices into the array of values
* @param reverseIndex reverse index from the array of values into the heap
* @param count current size of the heap
* @param values values to be stored in the heap
*/
private static void heapify(int[] heap, int[] reverseIndex, int count, float[] values)
{
int start = (count - 2) / 2;
while (start >= 0) {
siftDown(heap, reverseIndex, start, count - 1, values);
start--;
}
}
/**
* Rebalances the min-heap by pushing values from the top down and simultaneously updating the reverse index
*
* @param heap min-heap stored as indices into the array of values
* @param reverseIndex reverse index from the array of values into the heap
* @param start index to start re-balancing from
* @param end index to stop re-balancing at
* @param values values stored in the heap
*/
private static void siftDown(int[] heap, int[] reverseIndex, int start, int end, float[] values)
{
int root = start;
while (root * 2 + 1 <= end) {
int child = root * 2 + 1;
int swap = root;
if (values[heap[swap]] > values[heap[child]]) {
swap = child;
}
if (child + 1 <= end && values[heap[swap]] > values[heap[child + 1]]) {
swap = child + 1;
}
if (swap != root) {
// swap
int tmp = heap[swap];
heap[swap] = heap[root];
heap[root] = tmp;
// heap index from delta index
reverseIndex[heap[swap]] = swap;
reverseIndex[heap[root]] = root;
root = swap;
} else {
return;
}
}
}
/**
* Deletes an item from the min-heap and updates the reverse index
*
* @param heap min-heap stored as indices into the array of values
* @param reverseIndex reverse index from the array of values into the heap
* @param count current size of the heap
* @param heapIndex index of the item to be deleted
* @param values values stored in the heap
*/
private static int heapDelete(int[] heap, int[] reverseIndex, int count, int heapIndex, float[] values)
{
int end = count - 1;
reverseIndex[heap[heapIndex]] = -1;
heap[heapIndex] = heap[end];
reverseIndex[heap[heapIndex]] = heapIndex;
end--;
siftDown(heap, reverseIndex, heapIndex, end, values);
return count - 1;
}
private static int minIndex(float[] deltas, int lastValidIndex)
{
int minIndex = -1;
float min = Float.MAX_VALUE;
for (int k = 0; k < lastValidIndex; ++k) {
float value = deltas[k];
if (value < min) {
minIndex = k;
min = value;
}
}
return minIndex;
}
/**
* Combines two sets of histogram bins using merge-sort and computes the delta between consecutive bin positions.
* Duplicate bins are merged together.
*
* @param leftBinCount
* @param leftPositions
* @param leftBins
* @param rightBinCount
* @param rightPositions
* @param rightBins
* @param mergedPositions array to store the combined bin positions (size must be at least leftBinCount + rightBinCount)
* @param mergedBins array to store the combined bin counts (size must be at least leftBinCount + rightBinCount)
* @param deltas deltas between consecutive bin positions in the merged bins (size must be at least leftBinCount + rightBinCount)
*
* @return the number of combined bins
*/
private static int combineBins(
int leftBinCount, float[] leftPositions, long[] leftBins,
int rightBinCount, float[] rightPositions, long[] rightBins,
float[] mergedPositions, long[] mergedBins, float[] deltas
)
{
int i = 0;
int j = 0;
int k = 0;
while (j < leftBinCount || k < rightBinCount) {
if (j < leftBinCount && (k == rightBinCount || leftPositions[j] < rightPositions[k])) {
mergedPositions[i] = leftPositions[j];
mergedBins[i] = leftBins[j];
++j;
} else if (k < rightBinCount && (j == leftBinCount || leftPositions[j] > rightPositions[k])) {
mergedPositions[i] = rightPositions[k];
mergedBins[i] = rightBins[k];
++k;
} else {
// combine overlapping bins
mergedPositions[i] = leftPositions[j];
mergedBins[i] = leftBins[j] + rightBins[k];
++j;
++k;
}
if (deltas != null && i > 0) {
deltas[i - 1] = mergedPositions[i] - mergedPositions[i - 1];
}
++i;
}
return i;
}
/**
* Returns a byte-array representation of this ApproximateHistogram object
*
* @return byte array representation
*/
@JsonValue
public byte[] toBytes()
{
ByteBuffer buf = ByteBuffer.allocate(getMinStorageSize());
toBytes(buf);
return buf.array();
}
public int getDenseStorageSize()
{
return Ints.BYTES * 2 + Floats.BYTES * size + Longs.BYTES * size + Floats.BYTES * 2;
}
public int getSparseStorageSize()
{
return Ints.BYTES * 2 + Floats.BYTES * binCount + Longs.BYTES * binCount + Floats.BYTES * 2;
}
public int getCompactStorageSize()
{
// ensures exactCount and (count - exactCount) can safely be cast to (int)
Preconditions.checkState(canStoreCompact(), "Approximate histogram cannot be stored in compact form");
final long exactCount = getExactCount();
if (exactCount == count) {
return Shorts.BYTES + 1 + Floats.BYTES * (int) exactCount;
} else {
return Shorts.BYTES
+ 1
+ Floats.BYTES * (int) exactCount
+ 1
+ Floats.BYTES * (int) (count - exactCount)
+ Floats.BYTES * 2;
}
}
public int getMaxStorageSize()
{
return getDenseStorageSize();
}
/**
* Returns the minimum number of bytes required to store this ApproximateHistogram object
*
* @return required number of bytes
*/
public int getMinStorageSize()
{
// sparse is always small than dense, so no need to check
if (canStoreCompact() && getCompactStorageSize() < getSparseStorageSize()) {
return getCompactStorageSize();
} else {
return getSparseStorageSize();
}
}
/**
* Checks whether this approximate histogram can be stored in a compact form
*
* @return true if yes, false otherwise
*/
public boolean canStoreCompact()
{
final long exactCount = getExactCount();
return (
size <= Short.MAX_VALUE
&& exactCount <= Byte.MAX_VALUE
&& (count - exactCount) <= Byte.MAX_VALUE
);
}
/**
* Writes the representation of this ApproximateHistogram object to the given byte-buffer
*
* @param buf ByteBuffer to write the ApproximateHistogram to
*/
public void toBytes(ByteBuffer buf)
{
if (canStoreCompact() && getCompactStorageSize() < getSparseStorageSize()) {
// store compact
toBytesCompact(buf);
} else {
// store sparse
toBytesSparse(buf);
}
}
/**
* Writes the dense representation of this ApproximateHistogram object to the given byte-buffer
*
* Requires 16 + 12 * size bytes of storage
*
* @param buf ByteBuffer to write the ApproximateHistogram to
*/
public void toBytesDense(ByteBuffer buf)
{
buf.putInt(size);
buf.putInt(binCount);
buf.asFloatBuffer().put(positions);
buf.position(buf.position() + Floats.BYTES * positions.length);
buf.asLongBuffer().put(bins);
buf.position(buf.position() + Longs.BYTES * bins.length);
buf.putFloat(min);
buf.putFloat(max);
}
/**
* Writes the sparse representation of this ApproximateHistogram object to the given byte-buffer
*
* Requires 16 + 12 * binCount bytes of storage
*
* @param buf ByteBuffer to write the ApproximateHistogram to
*/
public void toBytesSparse(ByteBuffer buf)
{
buf.putInt(size);
buf.putInt(-1 * binCount); // use negative binCount to indicate sparse storage
for (int i = 0; i < binCount; ++i) {
buf.putFloat(positions[i]);
}
for (int i = 0; i < binCount; ++i) {
buf.putLong(bins[i]);
}
buf.putFloat(min);
buf.putFloat(max);
}
/**
* Returns a compact byte-buffer representation of this ApproximateHistogram object
* storing actual values as opposed to histogram bins
*
* Requires 3 + 4 * count bytes of storage with count <= 127
*
* @param buf ByteBuffer to write the ApproximateHistogram to
*/
public void toBytesCompact(ByteBuffer buf)
{
Preconditions.checkState(canStoreCompact(), "Approximate histogram cannot be stored in compact form");
buf.putShort((short) (-1 * size)); // use negative size to indicate compact storage
final long exactCount = getExactCount();
if (exactCount != count) {
// use negative count to indicate approximate bins
buf.put((byte) (-1 * (count - exactCount)));
// store actual values instead of bins
for (int i = 0; i < binCount; ++i) {
// repeat each value bins[i] times for approximate bins
if ((bins[i] & APPROX_FLAG_BIT) != 0) {
for (int k = 0; k < (bins[i] & COUNT_BITS); ++k) {
buf.putFloat(positions[i]);
}
}
}
// tack on min and max since they may be lost int the approximate bins
buf.putFloat(min);
buf.putFloat(max);
}
buf.put((byte) exactCount);
// store actual values instead of bins
for (int i = 0; i < binCount; ++i) {
// repeat each value bins[i] times for exact bins
if ((bins[i] & APPROX_FLAG_BIT) == 0) {
for (int k = 0; k < (bins[i] & COUNT_BITS); ++k) {
buf.putFloat(positions[i]);
}
}
}
}
/**
* Constructs an Approximate Histogram object from the given byte-array representation
*
* @param bytes byte array to construct an ApproximateHistogram from
*
* @return ApproximateHistogram constructed from the given byte array
*/
public static ApproximateHistogram fromBytes(byte[] bytes)
{
ByteBuffer buf = ByteBuffer.wrap(bytes);
return fromBytes(buf);
}
/**
* Constructs an ApproximateHistogram object from the given dense byte-buffer representation
*
* @param buf ByteBuffer to construct an ApproximateHistogram from
*
* @return ApproximateHistogram constructed from the given ByteBuffer
*/
public static ApproximateHistogram fromBytesDense(ByteBuffer buf)
{
int size = buf.getInt();
int binCount = buf.getInt();
float[] positions = new float[size];
long[] bins = new long[size];
buf.asFloatBuffer().get(positions);
buf.position(buf.position() + Floats.BYTES * positions.length);
buf.asLongBuffer().get(bins);
buf.position(buf.position() + Longs.BYTES * bins.length);
float min = buf.getFloat();
float max = buf.getFloat();
return new ApproximateHistogram(binCount, positions, bins, min, max);
}
/**
* Constructs an ApproximateHistogram object from the given dense byte-buffer representation
*
* @param buf ByteBuffer to construct an ApproximateHistogram from
*
* @return ApproximateHistogram constructed from the given ByteBuffer
*/
public static ApproximateHistogram fromBytesSparse(ByteBuffer buf)
{
int size = buf.getInt();
int binCount = -1 * buf.getInt();
float[] positions = new float[size];
long[] bins = new long[size];
for (int i = 0; i < binCount; ++i) {
positions[i] = buf.getFloat();
}
for (int i = 0; i < binCount; ++i) {
bins[i] = buf.getLong();
}
float min = buf.getFloat();
float max = buf.getFloat();
return new ApproximateHistogram(binCount, positions, bins, min, max);
}
/**
* Constructs an ApproximateHistogram object from the given compact byte-buffer representation
*
* @param buf ByteBuffer to construct an ApproximateHistogram from
*
* @return ApproximateHistogram constructed from the given ByteBuffer
*/
public static ApproximateHistogram fromBytesCompact(ByteBuffer buf)
{
short size = (short) (-1 * buf.getShort());
byte count = buf.get();
if (count >= 0) {
// only exact bins
ApproximateHistogram histogram = new ApproximateHistogram(size);
for (int i = 0; i < count; ++i) {
histogram.offer(buf.getFloat());
}
return histogram;
} else {
byte approxCount = (byte) (-1 * count);
Map approx = Maps.newHashMap();
for (int i = 0; i < approxCount; ++i) {
final float value = buf.getFloat();
if (approx.containsKey(value)) {
approx.put(value, approx.get(value) + 1);
} else {
approx.put(value, 1L);
}
}
float min = buf.getFloat();
float max = buf.getFloat();
byte exactCount = buf.get();
Map exact = Maps.newHashMap();
for (int i = 0; i < exactCount; ++i) {
final float value = buf.getFloat();
if (exact.containsKey(value)) {
exact.put(value, exact.get(value) + 1);
} else {
exact.put(value, 1L);
}
}
int binCount = exact.size() + approx.size();
List pos = Lists.newArrayList();
pos.addAll(exact.keySet());
pos.addAll(approx.keySet());
Collections.sort(pos);
float[] positions = new float[size];
long[] bins = new long[size];
for (int i = 0; i < pos.size(); ++i) {
positions[i] = pos.get(i);
}
for (int i = 0; i < pos.size(); ++i) {
final float value = pos.get(i);
if (exact.containsKey(value)) {
bins[i] = exact.get(value);
} else {
bins[i] = approx.get(value) | APPROX_FLAG_BIT;
}
}
return new ApproximateHistogram(binCount, positions, bins, min, max);
}
}
/**
* Constructs an ApproximateHistogram object from the given byte-buffer representation
*
* @param buf ByteBuffer to construct an ApproximateHistogram from
*
* @return ApproximateHistogram constructed from the given ByteBuffer
*/
public static ApproximateHistogram fromBytes(ByteBuffer buf)
{
ByteBuffer copy = buf.asReadOnlyBuffer();
// negative size indicates compact representation
// this works regardless of whether we use int or short for the size since the leftmost bit is the sign bit
if (copy.getShort(buf.position()) < 0) {
return fromBytesCompact(buf);
} else {
// ignore size
copy.getInt();
// determine if sparse or dense based on sign of binCount
if (copy.getInt() < 0) {
return fromBytesSparse(buf);
} else {
return fromBytesDense(buf);
}
}
}
/**
* Returns the approximate number of items less than or equal to b in the histogram
*
* @param b the cutoff
*
* @return the approximate number of items less than or equal to b
*/
public double sum(final float b)
{
if (b < min) {
return 0;
}
if (b >= max) {
return count;
}
int index = Arrays.binarySearch(positions, 0, binCount, b);
boolean exactMatch = index >= 0;
index = exactMatch ? index : -(index + 1);
// we want positions[index] <= b < positions[index+1]
if (!exactMatch) {
index--;
}
final boolean outerLeft = index < 0;
final boolean outerRight = index >= (binCount - 1);
final long m0 = outerLeft ? 0 : (bins[index] & COUNT_BITS);
final long m1 = outerRight ? 0 : (bins[index + 1] & COUNT_BITS);
final double p0 = outerLeft ? min : positions[index];
final double p1 = outerRight ? max : positions[index + 1];
final boolean exact0 = (!outerLeft && (bins[index] & APPROX_FLAG_BIT) == 0);
final boolean exact1 = (!outerRight && (bins[index + 1] & APPROX_FLAG_BIT) == 0);
// handle case when p0 = p1, which happens if the first bin = min or the last bin = max
final double l = (p1 == p0) ? 0 : (b - p0) / (p1 - p0);
// don't include exact counts in the trapezoid calculation
long tm0 = m0;
long tm1 = m1;
if (exact0) {
tm0 = 0;
}
if (exact1) {
tm1 = 0;
}
final double mb = tm0 + (tm1 - tm0) * l;
double s = 0.5 * (tm0 + mb) * l;
for (int i = 0; i < index; ++i) {
s += (bins[i] & COUNT_BITS);
}
// add full bin count if left bin count is exact
if (exact0) {
return (s + m0);
}
// otherwise add only the left half of the bin
else {
return (s + 0.5 * m0);
}
}
/**
* Returns the approximate quantiles corresponding to the given probabilities.
* probabilities = [.5f] returns [median]
* probabilities = [.25f, .5f, .75f] returns the quartiles, [25%ile, median, 75%ile]
*
* @param probabilities array of probabilities
*
* @return an array of length probabilities.length representing the the approximate sample quantiles
* corresponding to the given probabilities
*/
public float[] getQuantiles(float[] probabilities)
{
for (float p : probabilities) {
Preconditions.checkArgument(0 < p & p < 1, "quantile probabilities must be strictly between 0 and 1");
}
float[] quantiles = new float[probabilities.length];
Arrays.fill(quantiles, Float.NaN);
if (this.count() == 0) {
return quantiles;
}
final long[] bins = this.bins();
for (int j = 0; j < probabilities.length; ++j) {
final double s = probabilities[j] * this.count();
int i = 0;
int sum = 0;
int k = 1;
long count = 0;
while (k <= this.binCount()) {
count = bins[k - 1];
if (sum + count > s) {
i = k - 1;
break;
} else {
sum += count;
}
++k;
}
if (i == 0) {
quantiles[j] = this.min();
} else {
final double d = s - sum;
final double c = -2 * d;
final long a = bins[i] - bins[i - 1];
final long b = 2 * bins[i - 1];
double z = 0;
if (a == 0) {
z = -c / b;
} else {
z = (-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a);
}
final double uj = this.positions[i - 1] + (this.positions[i] - this.positions[i - 1]) * z;
quantiles[j] = (float) uj;
}
}
return quantiles;
}
/**
* Computes a visual representation of the approximate histogram with bins laid out according to the given breaks
*
* @param breaks breaks defining the histogram bins
*
* @return visual representation of the histogram
*/
public Histogram toHistogram(final float[] breaks)
{
final double[] approximateBins = new double[breaks.length - 1];
double prev = sum(breaks[0]);
for (int i = 1; i < breaks.length; ++i) {
double s = sum(breaks[i]);
approximateBins[i - 1] = (float) (s - prev);
prev = s;
}
return new Histogram(breaks, approximateBins);
}
/**
* Computes a visual representation of the approximate histogram with a given number of equal-sized bins
*
* @param size number of equal-sized bins to divide the histogram into
*
* @return visual representation of the histogram
*/
public Histogram toHistogram(int size)
{
Preconditions.checkArgument(size > 1, "histogram size must be greater than 1");
float[] breaks = new float[size + 1];
float delta = (max - min) / (size - 1);
breaks[0] = min - delta;
for (int i = 1; i < breaks.length - 1; ++i) {
breaks[i] = breaks[i - 1] + delta;
}
breaks[breaks.length - 1] = max;
return toHistogram(breaks);
}
/**
* Computes a visual representation given an initial breakpoint, offset, and a bucket size.
*
* @param bucketSize the size of each bucket
* @param offset the location of one breakpoint
*
* @return visual representation of the histogram
*/
public Histogram toHistogram(final float bucketSize, final float offset)
{
final float minFloor = (float) Math.floor((min() - offset) / bucketSize) * bucketSize + offset;
final float lowerLimitFloor = (float) Math.floor((lowerLimit - offset) / bucketSize) * bucketSize + offset;
final float firstBreak = Math.max(minFloor, lowerLimitFloor);
final float maxCeil = (float) Math.ceil((max() - offset) / bucketSize) * bucketSize + offset;
final float upperLimitCeil = (float) Math.ceil((upperLimit - offset) / bucketSize) * bucketSize + offset;
final float lastBreak = Math.min(maxCeil, upperLimitCeil);
final float cutoff = 0.1f;
final ArrayList breaks = new ArrayList();
// to deal with left inclusivity when the min is the same as a break
final float bottomBreak = minFloor - bucketSize;
if (bottomBreak != firstBreak && (sum(firstBreak) - sum(bottomBreak) > cutoff)) {
breaks.add(bottomBreak);
}
float left = firstBreak;
boolean leftSet = false;
//the + bucketSize / 10 is because floating point addition is always slightly incorrect and so we need to account for that
while (left + bucketSize <= lastBreak + (bucketSize / 10)) {
final float right = left + bucketSize;
if (sum(right) - sum(left) > cutoff) {
if (!leftSet) {
breaks.add(left);
}
breaks.add(right);
leftSet = true;
} else {
leftSet = false;
}
left = right;
}
if (breaks.get(breaks.size() - 1) != maxCeil && (sum(maxCeil) - sum(breaks.get(breaks.size() - 1)) > cutoff)) {
breaks.add(maxCeil);
}
return toHistogram(Floats.toArray(breaks));
}
}
