package net.agkn.hll;
/*
* Copyright 2013 Aggregate Knowledge, Inc.
*
* Licensed 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.
*/
import static org.powermock.reflect.Whitebox.getInternalState;
import static org.testng.Assert.assertEquals;
import static org.testng.Assert.assertTrue;
import it.unimi.dsi.fastutil.ints.Int2ByteOpenHashMap;
import java.util.Random;
import net.agkn.hll.serialization.ISchemaVersion;
import net.agkn.hll.serialization.SerializationUtil;
import net.agkn.hll.util.HLLUtil;
import org.testng.annotations.Test;
/**
* Tests {@link HLL} of type {@link HLLType#SPARSE}.
*
* @author timon
*/
public class SparseHLLTest {
private static final int log2m = 11;
/**
* Tests {@link HLL#addRaw(long)}.
*/
@Test
public void addTest() {
{ // insert an element with register value 1 (minimum set value)
final int registerIndex = 0;
final int registerValue = 1;
final long rawValue = ProbabilisticTestUtil.constructHLLValue(log2m, registerIndex, registerValue);
final HLL hll = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, 256/*sparseThreshold, arbitrary*/, HLLType.SPARSE);
hll.addRaw(rawValue);
assertOneRegisterSet(hll, registerIndex, (byte)registerValue);
}
{ // insert an element with register value 31 (maximum set value)
final int registerIndex = 0;
final int registerValue = 31;
final long rawValue = ProbabilisticTestUtil.constructHLLValue(log2m, registerIndex, registerValue);
final HLL hll = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, 256/*sparseThreshold, arbitrary*/, HLLType.SPARSE);
hll.addRaw(rawValue);
assertOneRegisterSet(hll, registerIndex, (byte)registerValue);
}
{ // insert an element that could overflow the register (past 31)
final int registerIndex = 0;
final int registerValue = 36;
final long rawValue = ProbabilisticTestUtil.constructHLLValue(log2m, registerIndex, registerValue);
final HLL hll = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, 256/*sparseThreshold, arbitrary*/, HLLType.SPARSE);
hll.addRaw(rawValue);
assertOneRegisterSet(hll, (short)registerIndex, (byte)31/*register max*/);
}
{ // insert duplicate elements, observe no change
final int registerIndex = 0;
final int registerValue = 1;
final long rawValue = ProbabilisticTestUtil.constructHLLValue(log2m, registerIndex, registerValue);
final HLL hll = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, 256/*sparseThreshold, arbitrary*/, HLLType.SPARSE);
hll.addRaw(rawValue);
hll.addRaw(rawValue);
assertOneRegisterSet(hll, registerIndex, (byte)registerValue);
}
{ // insert elements that increase a register's value
final int registerIndex = 0;
final int registerValue = 1;
final long rawValue = ProbabilisticTestUtil.constructHLLValue(log2m, registerIndex, registerValue);
final HLL hll = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, 256/*sparseThreshold, arbitrary*/, HLLType.SPARSE);
hll.addRaw(rawValue);
final int registerValue2 = 2;
final long rawValue2 = ProbabilisticTestUtil.constructHLLValue(log2m, registerIndex, registerValue2);
hll.addRaw(rawValue2);
assertOneRegisterSet(hll, registerIndex, (byte)registerValue2);
}
{ // insert elements that have lower register values, observe no change
final int registerIndex = 0;
final int registerValue = 2;
final long rawValue = ProbabilisticTestUtil.constructHLLValue(log2m, registerIndex, registerValue);
final HLL hll = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, 256/*sparseThreshold, arbitrary*/, HLLType.SPARSE);
hll.addRaw(rawValue);
final int registerValue2 = 1;
final long rawValue2 = ProbabilisticTestUtil.constructHLLValue(log2m, registerIndex, registerValue2);
hll.addRaw(rawValue2);
assertOneRegisterSet(hll, registerIndex, (byte)registerValue);
}
}
/**
* Smoke test for {@link HLL#cardinality()} and the proper use of the small
* range correction.
*/
@Test
public void smallRangeSmokeTest() {
final int log2m = 11;
final int m = (1 << log2m);
final int regwidth = 5;
// only one register set
{
final HLL hll = new HLL(log2m, regwidth, 128/*explicitThreshold, arbitrary, unused*/, 256/*sparseThreshold, arbitrary*/, HLLType.SPARSE);
hll.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, 0, 1));
final long cardinality = hll.cardinality();
// Trivially true that small correction conditions hold: one register
// set implies zeroes exist, and estimator trivially smaller than 5m/2.
// Small range correction: m * log(m/V)
final long expected = (long)Math.ceil(m * Math.log((double)m / (m - 1)/*# of zeroes*/));
assertEquals(cardinality, expected);
}
// all but one register set
{
final HLL hll = new HLL(log2m, regwidth, 128/*explicitThreshold, arbitrary, unused*/, 256/*sparseThreshold, arbitrary*/, HLLType.SPARSE);
for(int i=0; i<(m - 1); i++) {
hll.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, i, 1));
}
// Trivially true that small correction conditions hold: all but
// one register set implies a zero exists, and estimator trivially
// smaller than 5m/2 since it's alpha / ((m-1)/2)
final long cardinality = hll.cardinality();
// Small range correction: m * log(m/V)
final long expected = (long)Math.ceil(m * Math.log((double)m / 1/*# of zeroes*/));
assertEquals(cardinality, expected);
}
}
/**
* Smoke test for {@link HLL#cardinality()} and the proper use of the
* uncorrected estimator.
*/
@Test
public void normalRangeSmokeTest() {
final int log2m = 11;
final int m = (1 << log2m);
final int regwidth = 5;
// regwidth = 5, so hash space is
// log2m + (2^5 - 1 - 1), so L = log2m + 30
final int l = log2m + 30;
// all registers at 'medium' value
{
final HLL hll = new HLL(log2m, regwidth, 128/*explicitThreshold, arbitrary, unused*/, m/*sparseThreshold*/, HLLType.SPARSE);
final int registerValue = 7/*chosen to ensure neither correction kicks in*/;
for(int i=0; i<m; i++) {
hll.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, i, registerValue));
}
final long cardinality = hll.cardinality();
// Simplified estimator when all registers take same value: alpha / (m/2^val)
final double estimator = HLLUtil.alphaMSquared(m)/((double)m/Math.pow(2, registerValue));
// Assert conditions for uncorrected range
assertTrue(estimator <= Math.pow(2,l)/30);
assertTrue(estimator > (5 * m /(double)2));
final long expected = (long)Math.ceil(estimator);
assertEquals(cardinality, expected);
}
}
/**
* Smoke test for {@link HLL#cardinality()} and the proper use of the large
* range correction.
*/
@Test
public void largeRangeSmokeTest() {
final int log2m = 11;
final int m = (1 << log2m);
final int regwidth = 5;
// regwidth = 5, so hash space is
// log2m + (2^5 - 1 - 1), so L = log2m + 30
final int l = log2m + 30;
// all registers at large value
{
final HLL hll = new HLL(log2m, regwidth, 128/*explicitThreshold, arbitrary, unused*/, m/*sparseThreshold*/, HLLType.SPARSE);
final int registerValue = 31/*chosen to ensure large correction kicks in*/;
for(int i=0; i<m; i++) {
hll.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, i, registerValue));
}
final long cardinality = hll.cardinality();
// Simplified estimator when all registers take same value: alpha / (m/2^val)
final double estimator = HLLUtil.alphaMSquared(m)/((double)m/Math.pow(2, registerValue));
// Assert conditions for large range
assertTrue(estimator > Math.pow(2, l)/30);
// Large range correction: -2^32 * log(1 - E/2^32)
final long expected = (long)Math.ceil(-1.0 * Math.pow(2, l) * Math.log(1.0 - estimator/Math.pow(2, l)));
assertEquals(cardinality, expected);
}
}
/**
* Tests {@link HLL#union(HLL)}.
*/
@Test
public void unionTest() {
final int log2m = 11/*arbitrary*/;
final int sparseThreshold = 256/*arbitrary*/;
{ // two empty multisets should union to an empty set
final HLL hllA = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
final HLL hllB = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
hllA.union(hllB);
assertEquals(hllA.getType(), HLLType.SPARSE/*unchanged*/);
assertEquals(hllA.cardinality(), 0L);
}
{ // two disjoint multisets should union properly
final HLL hllA = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
hllA.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, 1, 1));
final HLL hllB = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
hllB.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, 2, 1));
hllA.union(hllB);
assertEquals(hllA.getType(), HLLType.SPARSE/*unchanged*/);
assertEquals(hllA.cardinality(), 3L/*precomputed*/);
assertRegisterPresent(hllA, 1, (byte)1);
assertRegisterPresent(hllA, 2, (byte)1);
}
{ // two exactly overlapping multisets should union properly
final HLL hllA = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
hllA.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, 1, 10));
final HLL hllB = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
hllB.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, 1, 13));
hllA.union(hllB);
assertEquals(hllA.getType(), HLLType.SPARSE/*unchanged*/);
assertEquals(hllA.cardinality(), 2L/*precomputed*/);
assertOneRegisterSet(hllA, 1, (byte)13/*max(10,13)*/);
}
{ // overlapping multisets should union properly
final HLL hllA = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
final HLL hllB = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
// register index = 3
final long rawValueA = ProbabilisticTestUtil.constructHLLValue(log2m, 3, 11);
// register index = 4
final long rawValueB = ProbabilisticTestUtil.constructHLLValue(log2m, 4, 13);
final long rawValueBPrime = ProbabilisticTestUtil.constructHLLValue(log2m, 4, 21);
// register index = 5
final long rawValueC = ProbabilisticTestUtil.constructHLLValue(log2m, 5, 14);
hllA.addRaw(rawValueA);
hllA.addRaw(rawValueB);
hllB.addRaw(rawValueBPrime);
hllB.addRaw(rawValueC);
hllA.union(hllB);
// union should have three registers set, with partition B set to the
// max of the two registers
assertRegisterPresent(hllA, 3, (byte)11);
assertRegisterPresent(hllA, 4, (byte)21/*max(21,13)*/);
assertRegisterPresent(hllA, 5, (byte)14);
}
{ // too-large unions should promote
final HLL hllA = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
final HLL hllB = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
// fill up sets to maxCapacity
for(int i=0; i<sparseThreshold; i++) {
hllA.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, i, 1));
hllB.addRaw(ProbabilisticTestUtil.constructHLLValue(log2m, (i + sparseThreshold)/*non-overlapping*/, 1));
}
hllA.union(hllB);
assertEquals(hllA.getType(), HLLType.FULL);
}
}
/**
* Tests {@link HLL#clear()}.
*/
@Test
public void clearTest() {
final HLL hll = new HLL(log2m, 5/*regwidth*/, 128/*explicitThreshold, arbitrary, unused*/, 256/*sparseThreshold, arbitrary, unused*/, HLLType.SPARSE);
hll.addRaw(1L);
hll.clear();
assertEquals(hll.cardinality(), 0L);
}
/**
* Tests {@link HLL#toBytes(ISchemaVersion)} and
* {@link HLL#fromBytes(byte[])}.
*/
@Test
public void toFromBytesTest() {
final int log2m = 11/*arbitrary*/;
final int regwidth = 5/*arbitrary*/;
final int sparseThreshold = 256/*arbitrary*/;
final int shortWordLength = 16/*log2m + regwidth = 11 + 5*/;
final ISchemaVersion schemaVersion = SerializationUtil.DEFAULT_SCHEMA_VERSION;
final HLLType type = HLLType.SPARSE;
final int padding = schemaVersion.paddingBytes(type);
{// Should work on an empty element
final HLL hll = new HLL(log2m, regwidth, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
final byte[] bytes = hll.toBytes(schemaVersion);
// output should just be padding since no registers are used
assertEquals(bytes.length, padding);
final HLL inHLL = HLL.fromBytes(bytes);
// assert register values correct
assertElementsEqual(hll, inHLL);
}
{// Should work on a partially filled element
final HLL hll = new HLL(log2m, regwidth, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
for(int i=0; i<3; i++) {
final long rawValue = ProbabilisticTestUtil.constructHLLValue(log2m, i, (i+9));
hll.addRaw(rawValue);
}
final byte[] bytes = hll.toBytes(schemaVersion);
assertEquals(bytes.length, padding + ProbabilisticTestUtil.getRequiredBytes(shortWordLength, 3/*registerCount*/));
final HLL inHLL = HLL.fromBytes(bytes);
// assert register values correct
assertElementsEqual(hll, inHLL);
}
{// Should work on a full set
final HLL hll = new HLL(log2m, regwidth, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
for(int i=0; i<sparseThreshold; i++) {
final long rawValue = ProbabilisticTestUtil.constructHLLValue(log2m, i, (i % 9) + 1);
hll.addRaw(rawValue);
}
final byte[] bytes = hll.toBytes(schemaVersion);
// 'short words' should be 12 bits + 5 bits = 17 bits long
assertEquals(bytes.length, padding + ProbabilisticTestUtil.getRequiredBytes(shortWordLength, sparseThreshold));
final HLL inHLL = HLL.fromBytes(bytes);
// assert register values correct
assertElementsEqual(hll, inHLL);
}
}
/**
* Smoke tests the multisets by adding random values.
*/
@Test
public void randomValuesTest() {
final int log2m = 11/*arbitrary*/;
final int regwidth = 5/*arbitrary*/;
final int sparseThreshold = 256/*arbitrary*/;
final long seed = 1L;
final Random random = new Random(seed);
for(int run=0; run<100; run++) {
final HLL hll = new HLL(log2m, regwidth, 128/*explicitThreshold, arbitrary, unused*/, sparseThreshold, HLLType.SPARSE);
final Int2ByteOpenHashMap map = new Int2ByteOpenHashMap();
map.defaultReturnValue((byte)0);
for(int i=0; i<sparseThreshold; i++) {
final long rawValue = random.nextLong();
final short registerIndex = ProbabilisticTestUtil.getRegisterIndex(rawValue, log2m);
final byte registerValue = ProbabilisticTestUtil.getRegisterValue(rawValue, log2m);
if(map.get(registerIndex) < registerValue) {
map.put(registerIndex, registerValue);
}
hll.addRaw(rawValue);
}
for(int key : map.keySet()) {
final byte expectedRegisterValue = map.get(key);
assertRegisterPresent(hll, key, expectedRegisterValue);
}
}
}
//*************************************************************************
// assertion helpers
/**
* Asserts that the register at the specified index is set to the specified
* value.
*/
private static void assertRegisterPresent(final HLL hll,
final int registerIndex,
final int registerValue) {
final Int2ByteOpenHashMap sparseProbabilisticStorage = (Int2ByteOpenHashMap)getInternalState(hll, "sparseProbabilisticStorage");
assertEquals(sparseProbabilisticStorage.get(registerIndex), registerValue);
}
/**
* Asserts that only the specified register is set and has the specified value.
*/
private static void assertOneRegisterSet(final HLL hll,
final int registerIndex,
final byte registerValue) {
final Int2ByteOpenHashMap sparseProbabilisticStorage = (Int2ByteOpenHashMap)getInternalState(hll, "sparseProbabilisticStorage");
assertEquals(sparseProbabilisticStorage.size(), 1);
assertEquals(sparseProbabilisticStorage.get(registerIndex), registerValue);
}
/**
* Asserts that all registers in the two {@link HLL} instances are identical.
*/
private static void assertElementsEqual(final HLL hllA, final HLL hllB) {
final Int2ByteOpenHashMap sparseProbabilisticStorageA = (Int2ByteOpenHashMap)getInternalState(hllA, "sparseProbabilisticStorage");
final Int2ByteOpenHashMap sparseProbabilisticStorageB = (Int2ByteOpenHashMap)getInternalState(hllB, "sparseProbabilisticStorage");
assertEquals(sparseProbabilisticStorageA.size(), sparseProbabilisticStorageB.size());
for(final int index : sparseProbabilisticStorageA.keySet()) {
assertEquals(sparseProbabilisticStorageA.get(index), sparseProbabilisticStorageB.get(index));
}
}
}