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Implement shortcut for 0.0 and 1.0 percentile calculations, and add two new tests #382

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merged 5 commits into from
May 21, 2021
Merged

Implement shortcut for 0.0 and 1.0 percentile calculations, and add two new tests #382

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934fe92
Implement shortcut for 0.0 and 1.0 percentile calculations, and add t…
JingHuaMan Apr 23, 2021
8fd0eee
Implement shortcut for 0.0 and 1.0 percentile calculations, and add …
JingHuaMan Apr 23, 2021
dabfeaf
Modify the javadoc for the function PERCENTILEBY
JingHuaMan Apr 23, 2021
d3b7bce
Modify javadoc for PERCENTILEBY
JingHuaMan Apr 25, 2021
7a4a5cd
Modify javadoc for PERCENTILEBY
JingHuaMan Apr 25, 2021
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21 changes: 16 additions & 5 deletions jOOL-java-8/src/main/java/org/jooq/lambda/Agg.java
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Original file line number Diff line number Diff line change
Expand Up @@ -906,11 +906,27 @@ else if (l1[0] == null)

/**
* Get a {@link Collector} that calculates the derived <code>PERCENTILE_DISC(percentile)</code> function given a specific ordering.
*
* @param function map the items in the streams into values
* @param comparator comparator used for sorting the items
* @return a collector that calculates the derived <code>PERCENTILE_DISC(percentile)</code> function
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It's probably a good idea to document these in general, but I prefer this be done in a separate task, for the entire API, not just this method. I've created a new issue to track this: #388.

*/
public static <T, U> Collector<T, ?, Optional<T>> percentileBy(double percentile, Function<? super T, ? extends U> function, Comparator<? super U> comparator) {
if (percentile < 0.0 || percentile > 1.0)
throw new IllegalArgumentException("Percentile must be between 0.0 and 1.0");

// CS304 Issue link: https://github.com/jOOQ/jOOL/issues/376
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I don't know what CS304 means. Some reference to some external tracking system? There's no need for this, I will remove it. The convention to track github issues (if necessary) would be to use:

// [#376] Rationale

if (percentile == 0.0)
// If percentile is 0, this is the same as taking the item with the minimum value.
return minBy(function, comparator);
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The comment says the same thing as the method call, so it isn't really necessary. I'll remove it again after merging.

else if (percentile == 1.0)
// If percentile is 1, this is the same as taking the item with the maximum value,
// If there are multiple maxima, take the last one.
return maxBy(function, (o1, o2) -> {
int compareResult = comparator.compare(o1, o2);
return compareResult == 0 ? -1 : compareResult;
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This hack violates the Comparator contract. We can't implement it like this.

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This seems to be the correct way to implement this:

collectingAndThen(maxAllBy(function, comparator), s -> s.findLast())

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Emmm, I think my solution is not incorrect, because the function maxBy will not sort the elements but compare them one by one, and the input comparator will not be modified. So even though this implementation violates the design philosophy of Comparator, it works and there seems no potential problem with it.

It's perfectly fine to implement this with maxAllBy, but in the worst case the space complexity will be O(n). That's my concern.

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It's incorrect. If comparator.compare(o1, o2) == 0, then comparator.compare(o2, o1) == 0, yet you return -1 in both cases. I don't want to spend the time now to find an edge case where this breaks sorting algorithms, but it should be easy to get an intuition about how this hack feels very wrong

because the function maxBy will not sort the elements but compare them one by one

You shouldn't rely on such an implementation detail.

So even though this implementation violates the design philosophy of Comparator, it works and there seems no potential problem with it.

Famous last words :)

It's perfectly fine to implement this with maxAllBy, but in the worst case the space complexity will be O(n). That's my concern.

I'm open to other suggestions, but correctness always beats performance.

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Yes, you are right. Thanks for your reply!

});

// At a later stage, we'll optimise this implementation in case that function is the identity function
return Collector.of(
() -> new ArrayList<Tuple2<T, U>>(),
Expand All @@ -929,11 +945,6 @@ else if (size == 1)

l.sort(Comparator.comparing(t -> t.v2, comparator));

if (percentile == 0.0)
return Optional.of(l.get(0).v1);
else if (percentile == 1.0)
return Optional.of(l.get(size - 1).v1);

// x.5 should be rounded down
return Optional.of(l.get((int) -Math.round(-(size * percentile + 0.5)) - 1).v1);
}
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148 changes: 148 additions & 0 deletions jOOL-java-8/src/test/java/org/jooq/lambda/CollectorTests.java
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Original file line number Diff line number Diff line change
Expand Up @@ -36,6 +36,7 @@
import java.util.Optional;
import java.util.stream.Collector;
import java.util.stream.Stream;
import java.util.function.Function;

import org.jooq.lambda.tuple.Tuple;
import org.jooq.lambda.tuple.Tuple9;
Expand Down Expand Up @@ -307,6 +308,153 @@ public void testPercentileWithStringsAndFunction() {
Utils.assertThrows(IllegalArgumentException.class, () -> Stream.of("a").collect(percentileBy(-1, String::length)));
Utils.assertThrows(IllegalArgumentException.class, () -> Stream.of("a").collect(percentileBy(2, String::length)));
}

@Test
public void testPercentileWithStringsAndFunctionWithDifferentValues() {

// CS304 (manually written) Issue link: https://github.com/jOOQ/jOOL/issues/376
// In the test testPercentileWithStringsAndFunction, the values (length) of the items are all the same,
// The function used in this test will take the first character of each string to be compared.
Function<String, Character> getFirstLetter = s -> s.length() == 0 ? 0 : s.charAt(0);

// Min
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(0.0, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(0.0, getFirstLetter)));

// 0.25 percentile
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(0.25, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(0.25, getFirstLetter)));

// Median
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c", "d").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(0.5, getFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(0.5, getFirstLetter)));

// 0.75 percentile
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("i"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("i"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("i"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(0.75, getFirstLetter)));
assertEquals(Optional.of("t"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(0.75, getFirstLetter)));

// Max
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("t"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("u"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(1.0, getFirstLetter)));
assertEquals(Optional.of("v"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(1.0, getFirstLetter)));
}

@Test
public void testPercentileWithStringsAndFunctionWithDifferentValues2() {

// CS304 (manually written) Issue link: https://github.com/jOOQ/jOOL/issues/376
// The function used in this test will take the minus value of the first character of each string to be compared.
Function<String, Integer> getMinusValueOfFirstLetter = s -> s.length() == 0 ? 0 : (int) -s.charAt(0);

// Min
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("t"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("u"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("v"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(0.0, getMinusValueOfFirstLetter)));

// 0.25
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("i"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("i"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("i"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("i"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("j"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("t"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(0.25, getMinusValueOfFirstLetter)));

// 0.5
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("d"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(0.5, getMinusValueOfFirstLetter)));

// 0.75
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c", "d").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("b"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("c"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(0.75, getMinusValueOfFirstLetter)));

// Max
assertEquals(Optional.of("a"), Stream.of("a").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
assertEquals(Optional.of("a"), Stream.of("a", "b", "c", "d", "j", "i", "c", "c", "t", "u", "v").collect(percentileBy(1.0, getMinusValueOfFirstLetter)));
}

@Test
public void testRank() {
Expand Down
21 changes: 16 additions & 5 deletions jOOL/src/main/java/org/jooq/lambda/Agg.java
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -906,11 +906,27 @@ else if (l1[0] == null)

/**
* Get a {@link Collector} that calculates the derived <code>PERCENTILE_DISC(percentile)</code> function given a specific ordering.
*
* @param function map the items in the streams into values
* @param comparator comparator used for sorting the items
* @return a collector that calculates the derived <code>PERCENTILE_DISC(percentile)</code> function
*/
public static <T, U> Collector<T, ?, Optional<T>> percentileBy(double percentile, Function<? super T, ? extends U> function, Comparator<? super U> comparator) {
if (percentile < 0.0 || percentile > 1.0)
throw new IllegalArgumentException("Percentile must be between 0.0 and 1.0");

// CS304 Issue link: https://github.com/jOOQ/jOOL/issues/376
if (percentile == 0.0)
// If percentile is 0, this is the same as taking the item with the minimum value.
return minBy(function, comparator);
else if (percentile == 1.0)
// If percentile is 1, this is the same as taking the item with the maximum value,
// If there are multiple maxima, take the last one.
return maxBy(function, (o1, o2) -> {
int compareResult = comparator.compare(o1, o2);
return compareResult == 0 ? -1 : compareResult;
});

// At a later stage, we'll optimise this implementation in case that function is the identity function
return Collector.of(
() -> new ArrayList<Tuple2<T, U>>(),
Expand All @@ -929,11 +945,6 @@ else if (size == 1)

l.sort(Comparator.comparing(t -> t.v2, comparator));

if (percentile == 0.0)
return Optional.of(l.get(0).v1);
else if (percentile == 1.0)
return Optional.of(l.get(size - 1).v1);

// x.5 should be rounded down
return Optional.of(l.get((int) -Math.round(-(size * percentile + 0.5)) - 1).v1);
}
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