package io.airlift.stats;
import com.google.common.base.Ticker;
import com.google.common.collect.ImmutableList;
import com.google.common.collect.Lists;
import io.airlift.slice.Slice;
import io.airlift.testing.TestingTicker;
import org.testng.annotations.Test;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.util.concurrent.ThreadLocalRandom;
import java.util.concurrent.TimeUnit;
import static java.lang.String.format;
import static java.util.Arrays.asList;
import static org.testng.Assert.assertEquals;
import static org.testng.Assert.assertFalse;
import static org.testng.Assert.assertTrue;
public class TestQuantileDigest
{
@Test
public void testSingleAdd()
{
QuantileDigest digest = new QuantileDigest(1);
digest.add(0);
digest.validate();
// should have no compressions with so few values and the allowed error
assertEquals(digest.getConfidenceFactor(), 0.0);
assertEquals(digest.getCount(), (double) 1);
assertEquals(digest.getNodeCount(), 1);
}
@Test
public void testNegativeValues()
{
QuantileDigest digest = new QuantileDigest(1);
addAll(digest, asList(-1, -2, -3, -4, -5, 0, 1, 2, 3, 4, 5));
assertEquals(digest.getCount(), (double) 11);
}
@Test
public void testRepeatedValue()
{
QuantileDigest digest = new QuantileDigest(1);
digest.add(0);
digest.add(0);
digest.validate();
// should have no compressions with so few values and the allowed error
assertEquals(digest.getConfidenceFactor(), 0.0);
assertEquals(digest.getCount(), (double) 2);
assertEquals(digest.getNodeCount(), 1);
}
@Test
public void testTwoDistinctValues()
{
QuantileDigest digest = new QuantileDigest(1);
digest.add(0);
digest.add(Long.MAX_VALUE);
digest.validate();
// should have no compressions with so few values and the allowed error
assertEquals(digest.getConfidenceFactor(), 0.0);
assertEquals(digest.getCount(), (double) 2);
assertEquals(digest.getNodeCount(), 3);
}
@Test
public void testTreeBuilding()
{
QuantileDigest digest = new QuantileDigest(1);
List<Integer> values = asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7);
addAll(digest, values);
assertEquals(digest.getCount(), (double) values.size());
}
@Test
public void testTreeBuildingReverse()
{
QuantileDigest digest = new QuantileDigest(1);
List<Integer> values = asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7);
addAll(digest, Lists.reverse(values));
assertEquals(digest.getCount(), (double) values.size());
}
@Test
public void testBasicCompression()
{
// maxError = 0.8 so that we get compression factor = 5 with the data below
QuantileDigest digest = new QuantileDigest(0.8, 0, new TestingTicker());
List<Integer> values = asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7);
addAll(digest, values);
digest.compress();
digest.validate();
assertEquals(digest.getCount(), (double) values.size());
assertEquals(digest.getNodeCount(), 7);
assertEquals(digest.getConfidenceFactor(), 0.2);
}
@Test
public void testCompression()
throws Exception
{
QuantileDigest digest = new QuantileDigest(1, 0, new TestingTicker());
for (int loop = 0; loop < 2; ++loop) {
addRange(digest, 0, 15);
digest.compress();
digest.validate();
}
}
@Test
public void testQuantile()
{
QuantileDigest digest = new QuantileDigest(1);
addAll(digest, asList(0, 1, 2, 3, 4, 5, 6, 7, 8, 9));
// should have no compressions with so few values and the allowed error
assertEquals(digest.getConfidenceFactor(), 0.0);
assertEquals(digest.getQuantile(0.0), 0);
assertEquals(digest.getQuantile(0.1), 1);
assertEquals(digest.getQuantile(0.2), 2);
assertEquals(digest.getQuantile(0.3), 3);
assertEquals(digest.getQuantile(0.4), 4);
assertEquals(digest.getQuantile(0.5), 5);
assertEquals(digest.getQuantile(0.6), 6);
assertEquals(digest.getQuantile(0.7), 7);
assertEquals(digest.getQuantile(0.8), 8);
assertEquals(digest.getQuantile(0.9), 9);
assertEquals(digest.getQuantile(1), 9);
}
@Test
public void testQuantileLowerBound()
{
QuantileDigest digest = new QuantileDigest(0.5);
addRange(digest, 1, 100);
assertEquals(digest.getQuantileLowerBound(0.0), 1);
for (int i = 1; i <= 10; i++) {
assertTrue(digest.getQuantileLowerBound(i / 10.0) <= i * 10);
if (i > 5) {
assertTrue(digest.getQuantileLowerBound(i / 10.0) >= (i - 5) * 10);
}
}
assertEquals(
digest.getQuantilesLowerBound(ImmutableList.of(0.0, 0.1, 0.2)),
ImmutableList.of(digest.getQuantileLowerBound(0.0), digest.getQuantileLowerBound(0.1), digest.getQuantileLowerBound(0.2)));
}
@Test
public void testQuantileUpperBound()
{
QuantileDigest digest = new QuantileDigest(0.5);
addRange(digest, 1, 100);
assertEquals(digest.getQuantileUpperBound(1.0), 99);
for (int i = 0; i < 10; i++) {
assertTrue(digest.getQuantileUpperBound(i / 10.0) >= i * 10);
if (i < 5) {
assertTrue(digest.getQuantileUpperBound(i / 10.0) <= (i + 5) * 10);
}
}
assertEquals(
digest.getQuantilesUpperBound(ImmutableList.of(0.8, 0.9, 1.0)),
ImmutableList.of(digest.getQuantileUpperBound(0.8), digest.getQuantileUpperBound(0.9), digest.getQuantileUpperBound(1.0)));
}
@Test
public void testWeightedValues()
{
QuantileDigest digest = new QuantileDigest(1);
digest.add(0, 3);
digest.add(2, 1);
digest.add(4, 5);
digest.add(5, 1);
digest.validate();
// should have no compressions with so few values and the allowed error
assertEquals(digest.getConfidenceFactor(), 0.0);
assertEquals(digest.getQuantile(0.0), 0);
assertEquals(digest.getQuantile(0.1), 0);
assertEquals(digest.getQuantile(0.2), 0);
assertEquals(digest.getQuantile(0.3), 2);
assertEquals(digest.getQuantile(0.4), 4);
assertEquals(digest.getQuantile(0.5), 4);
assertEquals(digest.getQuantile(0.6), 4);
assertEquals(digest.getQuantile(0.7), 4);
assertEquals(digest.getQuantile(0.8), 4);
assertEquals(digest.getQuantile(0.9), 5);
assertEquals(digest.getQuantile(1), 5);
}
@Test
public void testBatchQuantileQuery()
throws Exception
{
QuantileDigest digest = new QuantileDigest(1);
addAll(digest, asList(0, 1, 2, 3, 4, 5, 6, 7, 8, 9));
// should have no compressions with so few values and the allowed error
assertEquals(digest.getConfidenceFactor(), 0.0);
assertEquals(digest.getQuantiles(asList(0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0)),
asList(0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 9L));
}
@Test
public void testHistogramQuery()
throws Exception
{
QuantileDigest digest = new QuantileDigest(1);
addAll(digest, asList(0, 1, 2, 3, 4, 5, 6, 7, 8, 9));
// should have no compressions with so few values and the allowed error
assertEquals(digest.getConfidenceFactor(), 0.0);
assertEquals(digest.getHistogram(asList(0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L)),
asList(new QuantileDigest.Bucket(0, Double.NaN),
new QuantileDigest.Bucket(1, 0),
new QuantileDigest.Bucket(1, 1),
new QuantileDigest.Bucket(1, 2),
new QuantileDigest.Bucket(1, 3),
new QuantileDigest.Bucket(1, 4),
new QuantileDigest.Bucket(1, 5),
new QuantileDigest.Bucket(1, 6),
new QuantileDigest.Bucket(1, 7),
new QuantileDigest.Bucket(1, 8),
new QuantileDigest.Bucket(1, 9)));
assertEquals(digest.getHistogram(asList(7L, 10L)),
asList(new QuantileDigest.Bucket(7, 3),
new QuantileDigest.Bucket(3, 8)));
// test some edge conditions
assertEquals(digest.getHistogram(asList(0L)), asList(new QuantileDigest.Bucket(0, Double.NaN)));
assertEquals(digest.getHistogram(asList(9L)), asList(new QuantileDigest.Bucket(9, 4)));
assertEquals(digest.getHistogram(asList(10L)), asList(new QuantileDigest.Bucket(10, 4.5)));
assertEquals(digest.getHistogram(asList(Long.MAX_VALUE)),
asList(new QuantileDigest.Bucket(10, 4.5)));
}
@Test
public void testHistogramQueryAfterCompression()
throws Exception
{
QuantileDigest digest = new QuantileDigest(0.1);
int total = 10000;
addRange(digest, 0, total);
// compression should've run at this error rate and count
assertTrue(digest.getConfidenceFactor() > 0.0);
double actualMaxError = digest.getConfidenceFactor();
for (long value = 0; value < total; ++value) {
QuantileDigest.Bucket bucket = digest.getHistogram(asList(value)).get(0);
// estimated count should have an absolute error smaller than 2 * maxError * N
assertTrue(Math.abs(bucket.getCount() - value) < 2 * actualMaxError * total);
}
}
@Test
public void testQuantileQueryError()
{
double maxError = 0.1;
QuantileDigest digest = new QuantileDigest(maxError);
int count = 10000;
addRange(digest, 0, count);
// compression should've run at this error rate and count
assertTrue(digest.getConfidenceFactor() > 0);
assertTrue(digest.getConfidenceFactor() < maxError);
for (int value = 0; value < count; ++value) {
double quantile = value * 1.0 / count;
long estimatedValue = digest.getQuantile(quantile);
// true rank of estimatedValue is == estimatedValue because
// we've inserted a list of ordered numbers starting at 0
double error = Math.abs(estimatedValue - quantile * count) * 1.0 / count;
assertTrue(error < maxError);
}
}
@Test
public void testDecayedQuantiles()
throws Exception
{
TestingTicker ticker = new TestingTicker();
QuantileDigest digest = new QuantileDigest(1, ExponentialDecay.computeAlpha(0.5, 60), ticker);
addAll(digest, asList(0, 1, 2, 3, 4, 5, 6, 7, 8, 9));
// should have no compressions with so few values and the allowed error
assertEquals(digest.getConfidenceFactor(), 0.0);
ticker.increment(60, TimeUnit.SECONDS);
addAll(digest, asList(10, 11, 12, 13, 14, 15, 16, 17, 18, 19));
// Considering that the first 10 values now have a weight of 0.5 per the alpha factor, they only contributed a count
// of 5 to rank computations. Therefore, the 50th percentile is equivalent to a weighted rank of (5 + 10) / 2 = 7.5,
// which corresponds to value 12
assertEquals(digest.getQuantile(0.5), 12);
}
@Test
public void testDecayedCounts()
throws Exception
{
TestingTicker ticker = new TestingTicker();
QuantileDigest digest = new QuantileDigest(1, ExponentialDecay.computeAlpha(0.5, 60), ticker);
addAll(digest, asList(0, 1, 2, 3, 4, 5, 6, 7, 8, 9));
// should have no compressions with so few values and the allowed error
assertEquals(digest.getConfidenceFactor(), 0.0);
ticker.increment(60, TimeUnit.SECONDS);
addAll(digest, asList(10, 11, 12, 13, 14, 15, 16, 17, 18, 19));
assertEquals(digest.getCount(), 15.0);
}
@Test
public void testDecayedCountsWithClockIncrementSmallerThanRescaleThreshold()
throws Exception
{
int targetAgeInSeconds = (int) (QuantileDigest.RESCALE_THRESHOLD_SECONDS - 1);
TestingTicker ticker = new TestingTicker();
QuantileDigest digest = new QuantileDigest(1,
ExponentialDecay.computeAlpha(0.5, targetAgeInSeconds), ticker);
addAll(digest, asList(0, 1, 2, 3, 4, 5, 6, 7, 8, 9));
ticker.increment(targetAgeInSeconds, TimeUnit.SECONDS);
addAll(digest, asList(10, 11, 12, 13, 14, 15, 16, 17, 18, 19));
assertEquals(digest.getCount(), 15.0);
}
@Test
public void testMinMax()
throws Exception
{
QuantileDigest digest = new QuantileDigest(0.01, 0, new TestingTicker());
int from = 500;
int to = 700;
addRange(digest, from, to + 1);
assertEquals(digest.getMin(), from);
assertEquals(digest.getMax(), to);
}
@Test
public void testMinMaxWithDecay()
throws Exception
{
TestingTicker ticker = new TestingTicker();
QuantileDigest digest = new QuantileDigest(0.01,
ExponentialDecay.computeAlpha(QuantileDigest.ZERO_WEIGHT_THRESHOLD, 60), ticker);
addRange(digest, 1, 10);
ticker.increment(1000, TimeUnit.SECONDS); // TODO: tighter bounds?
int from = 4;
int to = 7;
addRange(digest, from, to + 1);
digest.validate();
assertEquals(digest.getMin(), from);
assertEquals(digest.getMax(), to);
}
@Test
public void testRescaleWithDecayKeepsCompactTree()
throws Exception
{
TestingTicker ticker = new TestingTicker();
int targetAgeInSeconds = (int) (QuantileDigest.RESCALE_THRESHOLD_SECONDS);
QuantileDigest digest = new QuantileDigest(0.01,
ExponentialDecay.computeAlpha(QuantileDigest.ZERO_WEIGHT_THRESHOLD / 2, targetAgeInSeconds),
ticker);
for (int i = 0; i < 10; ++i) {
digest.add(i);
digest.validate();
// bump the clock to make all previous values decay to ~0
ticker.increment(targetAgeInSeconds, TimeUnit.SECONDS);
}
assertEquals(digest.getNodeCount(), 1);
}
@Test
public void testEquivalenceEmpty()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
assertTrue(a.equivalent(b));
}
@Test
public void testEquivalenceSingle()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
a.add(1);
b.add(1);
assertTrue(a.equivalent(b));
}
@Test
public void testEquivalenceSingleDifferent()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
a.add(1);
b.add(2);
assertFalse(a.equivalent(b));
}
@Test
public void testEquivalenceComplex()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
addAll(a, asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7));
addAll(b, asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7));
assertTrue(a.equivalent(b));
}
@Test
public void testEquivalenceComplexDifferent()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
addAll(a, asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7));
addAll(b, asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8));
assertFalse(a.equivalent(b));
}
@Test
public void testMergeEmpty()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
QuantileDigest pristineB = new QuantileDigest(0.01);
a.merge(b);
a.validate();
b.validate();
assertTrue(b.equivalent(pristineB));
assertEquals(a.getCount(), 0.0);
assertEquals(a.getNodeCount(), 0);
assertEquals(b.getCount(), 0.0);
assertEquals(b.getNodeCount(), 0);
}
@Test
public void testMergeIntoEmpty()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
QuantileDigest pristineB = new QuantileDigest(0.01);
b.add(1);
pristineB.add(1);
a.merge(b);
a.validate();
b.validate();
assertTrue(b.equivalent(pristineB));
assertEquals(a.getCount(), 1.0);
assertEquals(a.getNodeCount(), 1);
assertEquals(b.getCount(), 1.0);
assertEquals(b.getNodeCount(), 1);
}
@Test
public void testMergeWithEmpty()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
QuantileDigest pristineB = new QuantileDigest(0.01);
a.add(1);
a.merge(b);
a.validate();
b.validate();
assertTrue(b.equivalent(pristineB));
assertEquals(a.getCount(), 1.0);
assertEquals(a.getNodeCount(), 1);
assertEquals(b.getCount(), 0.0);
assertEquals(b.getNodeCount(), 0);
}
@Test
public void testMergeSample()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
a.add(1);
addAll(b, asList(2, 3));
a.merge(b);
a.validate();
assertEquals(a.getCount(), 3.0);
assertEquals(a.getNodeCount(), 5);
}
@Test
public void testMergeSeparateBranches()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
QuantileDigest pristineB = new QuantileDigest(0.01);
a.add(1);
b.add(2);
pristineB.add(2);
a.merge(b);
assertTrue(b.equivalent(pristineB));
assertEquals(a.getCount(), 2.0);
assertEquals(a.getNodeCount(), 3);
assertEquals(b.getCount(), 1.0);
assertEquals(b.getNodeCount(), 1);
}
@Test
public void testMergeWithLowerLevel()
throws Exception
{
QuantileDigest a = new QuantileDigest(1, 0, Ticker.systemTicker());
QuantileDigest b = new QuantileDigest(1, 0, Ticker.systemTicker());
QuantileDigest pristineB = new QuantileDigest(1, 0, Ticker.systemTicker());
a.add(6);
a.compress();
List<Integer> values = asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5);
addAll(b, values);
b.compress();
addAll(pristineB, values);
pristineB.compress();
a.merge(b);
assertTrue(b.equivalent(pristineB));
assertEquals(a.getCount(), 14.0);
assertEquals(b.getCount(), 13.0);
}
@Test
public void testMergeWithHigherLevel()
throws Exception
{
QuantileDigest a = new QuantileDigest(1, 0, Ticker.systemTicker());
QuantileDigest b = new QuantileDigest(1, 0, Ticker.systemTicker());
QuantileDigest pristineB = new QuantileDigest(1, 0, Ticker.systemTicker());
addAll(a, asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5));
a.compress();
addAll(b, asList(6, 7));
addAll(pristineB, asList(6, 7));
a.merge(b);
assertTrue(b.equivalent(pristineB));
assertEquals(a.getCount(), 15.0);
assertEquals(a.getNodeCount(), 7);
assertEquals(b.getCount(), 2.0);
assertEquals(b.getNodeCount(), 3);
}
// test merging two digests that have a node at the highest level to make sure
// we handle boundary conditions properly
@Test
public void testMergeMaxLevel()
throws Exception
{
QuantileDigest a = new QuantileDigest(0.01);
QuantileDigest b = new QuantileDigest(0.01);
QuantileDigest pristineB = new QuantileDigest(0.01);
addAll(a, asList(-1, 1));
addAll(b, asList(-2, 2));
addAll(pristineB, asList(-2, 2));
a.merge(b);
a.validate();
b.validate();
assertTrue(b.equivalent(pristineB));
assertEquals(a.getCount(), 4.0);
assertEquals(a.getNodeCount(), 7);
}
@Test
public void testMergeSameLevel()
throws Exception
{
QuantileDigest a = new QuantileDigest(1, 0, Ticker.systemTicker());
QuantileDigest b = new QuantileDigest(1, 0, Ticker.systemTicker());
QuantileDigest pristineB = new QuantileDigest(1, 0, Ticker.systemTicker());
a.add(0);
b.add(0);
pristineB.add(0);
a.merge(b);
assertTrue(b.equivalent(pristineB));
assertEquals(a.getCount(), 2.0);
assertEquals(a.getNodeCount(), 1);
assertEquals(b.getCount(), 1.0);
assertEquals(b.getNodeCount(), 1);
}
@Test
public void testSerializationEmpty()
throws Exception
{
QuantileDigest digest = new QuantileDigest(0.01);
QuantileDigest deserialized = deserialize(digest.serialize());
assertTrue(digest.equivalent(deserialized));
}
@Test
public void testSerializationSingle()
throws Exception
{
QuantileDigest digest = new QuantileDigest(0.01);
digest.add(1);
assertTrue(digest.equivalent(deserialize(digest.serialize())));
}
@Test
public void testSerializationComplex()
throws Exception
{
QuantileDigest digest = new QuantileDigest(1);
addAll(digest, asList(0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7));
assertTrue(digest.equivalent(deserialize(digest.serialize())));
digest.compress();
assertTrue(digest.equivalent(deserialize(digest.serialize())));
}
@Test(invocationCount = 1000)
public void testSerializationRandom()
throws Exception
{
QuantileDigest digest = new QuantileDigest(1);
List<Integer> values = new ArrayList<>();
for (int i = 0; i < 1000; i++) {
values.add(ThreadLocalRandom.current().nextInt(Integer.MAX_VALUE));
}
addAll(digest, values);
assertTrue(digest.equivalent(deserialize(digest.serialize())), format("Serialization roundtrip failed for input: %s", values));
}
private QuantileDigest deserialize(Slice serialized)
throws IOException
{
QuantileDigest result = new QuantileDigest(serialized);
result.validate();
return result;
}
private void addAll(QuantileDigest digest, List<Integer> values)
{
for (int value : values) {
digest.add(value);
}
digest.validate();
}
private void addRange(QuantileDigest digest, int from, int to)
{
for (int i = from; i < to; ++i) {
digest.add(i);
}
digest.validate();
}
}