improve performance of LongList.union

primitiveCollections/src/jmh/java/org/lucares/collections/BenchmarkMultiwayMerge.java

@@ -21,19 +21,29 @@ import org.openjdk.jmh.annotations.Warmup;
 
 @State(Scope.Benchmark)
 @BenchmarkMode(Mode.Throughput)
-@Warmup(iterations = 10, time = 500, timeUnit = TimeUnit.MILLISECONDS)
+@Warmup(iterations = 5, time = 500, timeUnit = TimeUnit.MILLISECONDS)
-@Measurement(iterations = 5, time = 500, timeUnit = TimeUnit.MILLISECONDS)
+@Measurement(iterations = 3, time = 500, timeUnit = TimeUnit.MILLISECONDS)
-@Fork(2)
+@Fork(1)
 public class BenchmarkMultiwayMerge {
 
-	@Param({ "10000" , "20000"  })
+	private static final String OPTION_RANDOM = "random";
-	private int values;
 
-	@Param({  "3","5", "10","20" })
+	private static final String OPTION_NON_OVERLAP = "non-overlap";
-	private int numLists;
 
-	@Param({ "true" })
+	// @Param({ "3","5", "10","20", "1000" })
-	private boolean random;
+	@Param({ "1000" })
+	private int anumLists;
+
+	// @Param({ "10", "1000" , "20000" })
+	@Param({ "1000" })
+	private int bvalues;
+
+	@Param({ OPTION_RANDOM, OPTION_NON_OVERLAP })
+	// @Param({ OPTION_NON_OVERLAP})
+	private String ctype;
+
+	@Param({ "0", "500" })
+	private int dconcatNonOverlap;
 
 	private List<LongList> longSorted = null;
 
@@ -41,18 +51,37 @@ public class BenchmarkMultiwayMerge {
 	public void setup() throws Exception {
 		ThreadLocalRandom rng = ThreadLocalRandom.current();
 		longSorted = new ArrayList<>();
-		for (int i = 0; i < numLists; i++) {
+		if (ctype.equalsIgnoreCase(OPTION_NON_OVERLAP)) {
-			LongList list = new LongList(values);
+
-			if (random) {
+			final LongList list = randomList(bvalues * anumLists, rng);
-				for (int j = 0; j < values; j++) {
+			list.sort();
-					list.add(rng.nextLong());
+			for (int i = 0; i < anumLists; i++) {
-				}
+				longSorted.add(list.sublist(i * bvalues, (i + 1) * bvalues));
-				list.sort();
+			}
-			} else {
+
-				LongStream.range(0, values).forEachOrdered(list::add);
+		} else {
+			for (int i = 0; i < anumLists; i++) {
+				final LongList list;
+				if (ctype.equalsIgnoreCase(OPTION_RANDOM)) {
+					list = randomList(bvalues, rng);
+					list.sort();
+				} else {
+					list = new LongList(bvalues);
+					LongStream.range(0, bvalues).forEachOrdered(list::add);
+				}
+				longSorted.add(list);
 			}
-			longSorted.add(list);
 		}
+
+		LongList.FLAGS_UNION_CONCATENATE_NON_OVERLAPPING_AVG_MIN = dconcatNonOverlap;
+	}
+
+	private LongList randomList(int values, ThreadLocalRandom rng) {
+		final LongList list = new LongList(values);
+		for (int j = 0; j < values; j++) {
+			list.add(rng.nextLong());
+		}
+		return list;
 	}
 
 	@TearDown
@@ -66,7 +95,7 @@ public class BenchmarkMultiwayMerge {
 		LongList.union(longSorted);
 	}
 
-	@Benchmark
+	// @Benchmark
 	public void testUnionSortedLists_TwowayMergeImplementation() throws Exception {
 
 		twowayMerge(longSorted);
@@ -81,26 +110,17 @@ public class BenchmarkMultiwayMerge {
 
 	public static void main(String[] args) throws Exception {
 		System.out.println("\n\n----------------\nstart");
-		// -XX:+PrintCompilation
 
-		if (args != null) {
+		for (int i = 0; i < 80; i++) {
 			BenchmarkMultiwayMerge benchmark = new BenchmarkMultiwayMerge();
-			benchmark.numLists = 10;
+			benchmark.anumLists = 1000;
-			benchmark.values = 10000;
+			benchmark.bvalues = 1000;
+			benchmark.ctype = "non-overlapping";
+			benchmark.dconcatNonOverlap = 500;
 			benchmark.setup();
+			long start = System.nanoTime();
 			benchmark.testUnionSortedLists_MultiwayMerge();
-		} else {
+			System.out.println("total: " + (System.nanoTime() - start) / 1_000_000.0 + " ms");
-			for (int i = 0; i < 8; i++) {
-				BenchmarkMultiwayMerge benchmark = new BenchmarkMultiwayMerge();
-				benchmark.numLists = 10;
-				benchmark.values = 10000;
-				benchmark.setup();
-				System.out.println("\n\n----------------\n" + i);
-				for (int j = 0; j < 1000; j++) {
-					// benchmark.testUnionSortedLists_MultiwayMerge();
-					benchmark.testUnionSortedLists_TwowayMergeImplementation();
-				}
-			}
 		}
 		System.out.println("done");
 	}

primitiveCollections/src/main/java/org/lucares/collections/LongList.java

@@ -6,8 +6,10 @@ import java.util.Arrays;
 import java.util.Collection;
 import java.util.Iterator;
 import java.util.List;
+import java.util.Map.Entry;
 import java.util.Random;
 import java.util.Spliterator.OfLong;
+import java.util.TreeMap;
 import java.util.concurrent.ThreadLocalRandom;
 import java.util.stream.LongStream;
 import java.util.stream.StreamSupport;
@@ -31,6 +33,12 @@ public final class LongList implements Serializable, Cloneable {
 
 	private static final long[] EMPTY_ARRAY = {};
 
+	/**
+	 * If the average length of the lists is longer than this value, then we'll
+	 * first try to concatenate non-overlapping lists before the union is computed.
+	 */
+	public static int FLAGS_UNION_CONCATENATE_NON_OVERLAPPING_AVG_MIN = 500;
+
 	/**
 	 * The array containing the values. It is transient, so that we can implement
 	 * our own serialization.
@@ -606,6 +614,14 @@ public final class LongList implements Serializable, Cloneable {
 		return data[pos];
 	}
 
+	public long first() {
+		return get(0);
+	}
+
+	public long last() {
+		return get(size() - 1);
+	}
+
 	/**
 	 * Unsafe version of {@link #get(long)} that does not check for out of bounds
 	 * access if assertions are disabled. The caller has to make sure that pos is
@@ -1028,6 +1044,7 @@ public final class LongList implements Serializable, Cloneable {
 		try {
 			final LongList result = (LongList) super.clone();
 			result.data = size == 0 ? EMPTY_ARRAY : Arrays.copyOf(data, size);
+			result.sorted = sorted;
 			return result;
 		} catch (final CloneNotSupportedException e) {
 			throw new IllegalStateException(e);
@@ -1157,7 +1174,7 @@ public final class LongList implements Serializable, Cloneable {
 	 * TODO check time complexity If all lists are sorted, then the time complexity
 	 * is O(n+m), where n is the length of the first list and m the length of the
 	 * second list. If at least one list is not sorted, then the time complexity is
-	 * O(m*log(m)), where m is the length of the longer list.
+	 * O(m*log(m)), where m is the length of the longest list.
 	 *
 	 * @param longLists the lists
 	 * @return the union of both lists
@@ -1184,28 +1201,173 @@ public final class LongList implements Serializable, Cloneable {
 		case 0:
 			return new LongList();
 		case 1:
-			return longLists.iterator().next().clone();
+			// remove duplicate values
+			return unionInternal(longLists.iterator().next(), LongList.of());
 		case 2:
 			final Iterator<LongList> it = longLists.iterator();
 			final LongList a = it.next();
 			final LongList b = it.next();
 			return unionInternal(a, b);
 		default:
-			final Collection<LongList> sortedLists = subsetOfSortedLists(longLists);
+			final List<LongList> sortedLists = toSortedLists(longLists);
-			final Collection<LongList> unsortedLists = subsetOfUnsortedLists(longLists);
 
-			final LongList unionSorted = MultiwayLongMerger.unionSorted(sortedLists);
+			final double averageLength = totalLength(longLists) / (double) longLists.size();
 
-			final LongList result;
+			final List<LongList> sortedConcatenatedLists;
-			if (unsortedLists.isEmpty()) {
+			// benchmarks showed that concatenation is beneficial for longer lists
-				result = unionSorted;
+			if (averageLength > FLAGS_UNION_CONCATENATE_NON_OVERLAPPING_AVG_MIN) 
+			{
+				final ListConcatenater listConcatenater = new ListConcatenater(sortedLists);
+				sortedConcatenatedLists = listConcatenater.concatenateNonOverlapping();
 			} else {
-				final LongList unionUnsorted = unionUnsorted(unsortedLists);
+				sortedConcatenatedLists = sortedLists;
-				result = unionInternal(unionSorted, unionUnsorted);
 			}
 
+			switch (sortedConcatenatedLists.size()) {
+			case 0:
+				return new LongList();
+			case 1:
+				// remove duplicate values
+				return unionInternal(sortedConcatenatedLists.get(0), LongList.of());
+			case 2:
+			case 3:
+			case 4:
+			case 5:
+				// benchmarks have shown that the trivial merge is faster when merging only a
+				// few lists
+				return unionRepeatedTwowayMerge(sortedConcatenatedLists);
+			default:
+				final LongList multiwayMerged = MultiwayLongMerger.unionSorted(sortedConcatenatedLists);
+				return multiwayMerged;
+			}
+		}
+	}
+
+	private static int totalLength(Collection<LongList> longLists) {
+		int totalLength = 0;
+		for (LongList longList : longLists) {
+			totalLength += longList.size();
+		}
+		return totalLength;
+	}
+
+	private static LongList unionRepeatedTwowayMerge(final List<LongList> sortedLongLists) {
+
+		LongList result = sortedLongLists.get(0);
+		for (int i = 1; i < sortedLongLists.size(); i++) {
+			result = LongList.unionSorted(result, sortedLongLists.get(i));
+		}
+
+		return result;
+	}
+
+	private static class ListConcatenater {
+
+		private static class ListLongList {
+			private final List<LongList> list = new ArrayList<>();
+
+			public ListLongList(LongList longList) {
+				list.add(longList);
+			}
+
+			public void add(ListLongList listLongList) {
+				list.addAll(listLongList.list);
+			}
+
+			public LongList toLongList() {
+				switch (list.size()) {
+				case 0:
+					return new LongList(0);
+				case 1:
+					return list.get(0);
+				default:
+					int capacity = Math.toIntExact(list.stream().mapToLong(LongList::size).sum());
+					final LongList result = new LongList(capacity);
+					result.addAll(list);
+					return result;
+				}
+			}
+
+			public long first() {
+				return list.get(0).first();
+			}
+
+			public long last() {
+				return list.get(list.size() - 1).last();
+			}
+		}
+
+		final TreeMap<Long, List<ListLongList>> lowestValueMap = new TreeMap<>();
+		final TreeMap<Long, List<ListLongList>> highestValueMap = new TreeMap<>();
+
+		public ListConcatenater(final Collection<LongList> sortedLongLists) {
+			sortedLongLists.stream().map(ListLongList::new).forEach(this::index);
+		}
+
+		private void index(ListLongList listLongList) {
+			final long lowestValue = listLongList.first();
+			final long highestValue = listLongList.last();
+			lowestValueMap.computeIfAbsent(lowestValue, k -> new ArrayList<>()).add(listLongList);
+			highestValueMap.computeIfAbsent(highestValue, k -> new ArrayList<>()).add(listLongList);
+		}
+
+		private void removeFromIndex(ListLongList listLongList) {
+			lowestValueMap.get(listLongList.first()).remove(listLongList);
+			highestValueMap.get(listLongList.last()).remove(listLongList);
+		}
+
+		public List<LongList> concatenateNonOverlapping() {
+			for (Entry<Long, List<ListLongList>> e : highestValueMap.entrySet()) {
+				final long highestValue = e.getKey();
+				if (highestValue == Long.MAX_VALUE) {
+					continue;
+				}
+
+				final Iterator<ListLongList> it = e.getValue().iterator();
+				while (it.hasNext()) {
+					final ListLongList lowList = it.next();
+					final Entry<Long, List<ListLongList>> ceilingEntry = lowestValueMap.ceilingEntry(highestValue + 1);
+					if (ceilingEntry != null && !ceilingEntry.getValue().isEmpty()) {
+						final ListLongList highList = ceilingEntry.getValue().get(0);
+						removeFromIndex(highList);
+
+						it.remove(); // prevents concurrent modification that would happen in removeFromIndex()
+						removeFromIndex(lowList);
+
+						lowList.add(highList);
+
+						index(lowList);
+					}
+				}
+			}
+
+			final List<LongList> result = new ArrayList<>();
+			for (List<ListLongList> l : highestValueMap.values()) {
+				for (ListLongList listLongList : l) {
+					result.add(listLongList.toLongList());
+				}
+			}
 			return result;
 		}
+
+	}
+
+	private static List<LongList> toSortedLists(final Collection<LongList> longLists) {
+		final List<LongList> result = new ArrayList<>();
+
+		for (LongList longList : longLists) {
+			if (longList.isEmpty()) {
+				// skip, no need to merge an empty list
+			} else if (longList.isSorted()) {
+				result.add(longList);
+			} else {
+				final LongList copy = longList.clone();
+				copy.sort();
+				result.add(copy);
+			}
+		}
+
+		return result;
 	}
 
 	private static LongList unionSorted(final LongList a, final LongList b) {
@@ -1270,55 +1432,21 @@ public final class LongList implements Serializable, Cloneable {
 
 	private static LongList unionUnsorted(final LongList a, final LongList b) {
 		final LongList aSorted = new LongList(a);
-		aSorted.parallelSort();
+		if (!aSorted.isSorted()) {
+			aSorted.parallelSort();
+		}
 		final LongList bSorted = new LongList(b);
-		bSorted.parallelSort();
+		if (!bSorted.isSorted()) {
+			bSorted.parallelSort();
+		}
 
 		return unionSorted(aSorted, bSorted);
 	}
 
-	private static LongList unionUnsorted(Collection<LongList> longLists) {
-
-		final List<LongList> sortedLists = new ArrayList<>();
-		for (LongList longList : longLists) {
-			final LongList copy = new LongList(longList);
-			copy.sort();
-			sortedLists.add(copy);
-		}
-		return MultiwayLongMerger.unionSorted(sortedLists);
-	}
-
 	private void checkIfSorted() {
 		sorted = true;
 		for (int i = 1; i < size && sorted; i++) {
 			sorted = data[i - 1] <= data[i];
 		}
 	}
-
-	private static Collection<LongList> subsetOfSortedLists(Collection<LongList> longLists) {
-
-		final List<LongList> result = new ArrayList<>();
-
-		for (LongList longList : longLists) {
-			if (longList.isSorted()) {
-				result.add(longList);
-			}
-		}
-
-		return result;
-	}
-
-	private static Collection<LongList> subsetOfUnsortedLists(Collection<LongList> longLists) {
-
-		final List<LongList> result = new ArrayList<>();
-
-		for (LongList longList : longLists) {
-			if (!longList.isSorted()) {
-				result.add(longList);
-			}
-		}
-
-		return result;
-	}
-
 }

primitiveCollections/src/main/java/org/lucares/collections/MultiwayLongMerger.java

@@ -250,10 +250,4 @@ class MultiwayLongMerger {
 		}
 
 	}
-
-	public static void main(String[] args) {
-		for (int i = 0; i < 20; i++) {
-			System.out.println(i + " " + (Long.highestOneBit(i - 1) << 1));
-		}
-	}
 }

primitiveCollections/src/test/java/org/lucares/collections/LongListTest.java

@@ -5,7 +5,9 @@ import java.io.ByteArrayOutputStream;
 import java.io.IOException;
 import java.io.ObjectInputStream;
 import java.io.ObjectOutputStream;
+import java.util.ArrayList;
 import java.util.Arrays;
+import java.util.Collections;
 import java.util.List;
 import java.util.Random;
 import java.util.concurrent.ConcurrentLinkedQueue;
@@ -1620,25 +1622,125 @@ public class LongListTest {
 		final LongList b = LongList.of(2, 4, 6);
 		final LongList c = LongList.of(3, 5, 7);
 
-		final LongList actual = LongList.union(a, b,  c);
+		final LongList actual = LongList.union(a, b, c);
-		Assertions.assertEquals(LongList.of(1,2,3,4,5,6,7), actual);
+		Assertions.assertEquals(LongList.of(1, 2, 3, 4, 5, 6, 7), actual);
 		Assertions.assertEquals(LongList.union(a, b, c), LongList.union(b, c, a));
 		Assertions.assertEquals(LongList.union(a, b, c), LongList.union(b, a, c));
 	}
 
 	@Test
 	public void testUnionSortedLists_four_LongMinValue() {
-		final LongList a = LongList.of(Long.MIN_VALUE, 2, 3,Long.MAX_VALUE);
+		final LongList a = LongList.of(Long.MIN_VALUE, 2, 3, Long.MAX_VALUE);
 		final LongList b = LongList.of(2, 4, 6, Long.MAX_VALUE);
 		final LongList c = LongList.of(Long.MIN_VALUE, 5, 7);
 		final LongList d = LongList.of(Long.MIN_VALUE, Long.MIN_VALUE);
 
-		final LongList actual = LongList.union(a, b,  c, d);
+		final LongList actual = LongList.union(a, b, c, d);
-		Assertions.assertEquals(LongList.of(Long.MIN_VALUE,2,3,4,5,6,7, Long.MAX_VALUE), actual);
+		Assertions.assertEquals(LongList.of(Long.MIN_VALUE, 2, 3, 4, 5, 6, 7, Long.MAX_VALUE), actual);
 		Assertions.assertEquals(LongList.union(a, b, c, d), LongList.union(b, c, a, d));
 		Assertions.assertEquals(LongList.union(a, b, c, d), LongList.union(d, b, a, c));
 	}
 
+	@Test
+	public void testUnionSortedLists_Concatenating_with_empty_list() {
+		// aims to use the ListConcatenater in LongList.union()
+		// that means we need at least three lists and they must all be non-overlapping
+		final LongList a = LongList.of(1, 2, 3);
+		final LongList b = LongList.of();
+		final LongList c = LongList.of(10,11);
+
+		final LongList actual = LongList.union(a, b, c);
+		Assertions.assertEquals(LongList.of(1,2,3,10,11), actual);
+		Assertions.assertEquals(LongList.union(a, b, c), LongList.union(b, c, a));
+		Assertions.assertEquals(LongList.union(a, b, c), LongList.union( b, a, c));
+	}
+	
+	@Test
+	public void testUnionSortedLists_Concatenating_results_in_one_list() {
+		// aims to use the ListConcatenater in LongList.union()
+		// that means we need at least three lists and they must all be non-overlapping
+		final LongList a = LongList.of(1, 2, 3);
+		final LongList b = LongList.of(4);
+		final LongList c = LongList.of(10,11);
+
+		final LongList actual = LongList.union(a, b, c);
+		Assertions.assertEquals(LongList.of(1,2,3,4,10,11), actual);
+		Assertions.assertEquals(LongList.union(a, b, c), LongList.union(b, c, a));
+		Assertions.assertEquals(LongList.union(a, b, c), LongList.union( b, a, c));
+	}
+
+	@Test
+	public void testUnionSortedLists_Concatenating_results_in_two_lists() {
+		// aims to use the ListConcatenater in LongList.union()
+		// that means we need at least three lists
+		final LongList a = LongList.of(1, 2, 3);
+		final LongList b = LongList.of(3, 4);
+		final LongList c = LongList.of(4, 10,11); // can be concatenated to a
+
+		final LongList actual = LongList.union(a, b, c);
+		Assertions.assertEquals(LongList.of(1,2,3,4,10,11), actual);
+		Assertions.assertEquals(LongList.union(a, b, c), LongList.union(b, c, a));
+		Assertions.assertEquals(LongList.union(a, b, c), LongList.union( b, a, c));
+	}
+	
+	@Test
+	public void testUnionSortedLists_Multiway_merge () {
+		// aims to use the MultiwayLongMerge 
+		// that means we need overlapping lists so that ListConcatenater will return at least six lists
+		// this is done by adding 1 to all six lists
+		final LongList a = LongList.of(1, 2, 3);
+		final LongList b = LongList.of(1, 3, 4);
+		final LongList c = LongList.of(1, 4, 10,11);
+		final LongList d = LongList.of(1, 6,9);
+		final LongList e = LongList.of(1, 123, 144);
+		final LongList f = LongList.of(1, 411, 1011,1111);  
+
+		final LongList actual = LongList.union(a, b, c,d,e,f);
+		Assertions.assertEquals(LongList.of(1,2,3,4,6,9,10,11,123,144,411,1011,1111), actual);
+		Assertions.assertEquals(LongList.union(a, b, c,d,e,f), LongList.union(b, c, a,d,e,f));
+		Assertions.assertEquals(LongList.union(a, b, c,d,e,f), LongList.union( b, d,f,a,e, c));
+	}
+
+	@Test
+	public void testUnionSortedLists_ten_lists_fifteen_elements_random() {
+		testUnionSortedLists(10, 15, true);
+	}
+
+	@Test
+	public void testUnionSortedLists_ten_lists_fifteen_elements_equal() {
+		testUnionSortedLists(10, 15, false);
+	}
+
+	private void testUnionSortedLists(int numLists, int values, boolean random) {
+		ThreadLocalRandom rng = ThreadLocalRandom.current();
+		List<LongList> longSorted = new ArrayList<>();
+		for (int i = 0; i < numLists; i++) {
+			LongList list = new LongList(values);
+			if (random) {
+				for (int j = 0; j < values; j++) {
+					list.add(rng.nextLong());
+				}
+				list.sort();
+			} else {
+				LongStream.range(0, values).forEachOrdered(list::add);
+			}
+			longSorted.add(list);
+		}
+
+		final LongList actual = LongList.union(longSorted);
+
+		final LongList concatenatedList = new LongList();
+		concatenatedList.addAll(longSorted);
+		final LongList expected = LongList.union(concatenatedList, LongList.of());
+		Assertions.assertEquals(expected, actual);
+
+		Collections.shuffle(longSorted);
+		final LongList unionShuffled1 = LongList.union(longSorted);
+		Collections.shuffle(longSorted);
+		final LongList unionShuffled2 = LongList.union(longSorted);
+		Assertions.assertEquals(unionShuffled1, unionShuffled2);
+	}
+
 	@Test
 	public void testUnionUnsortedLists() {
 		final LongList a = LongList.of(1, 0, 3, 4);