MATH-1277: Fixed incorrect Kendall's tau coefficient calculation due to

internal integer overflow. Thanks to Marc Rosen.

src/changes/changes.xml

@@ -54,6 +54,9 @@ If the output is not quite correct, check for invisible trailing spaces!
     </release>
 
     <release version="4.0" date="XXXX-XX-XX" description="">
+      <action dev="oertl" type="fix" issue="MATH-1277" due-to="Marc Rosen"> <!-- backported to 3.6 -->
+        Fixed incorrect Kendall's tau coefficient calculation due to internal integer overflow.
+      </action>
       <action dev="oertl" type="update" issue="MATH-1274"> <!-- backported to 3.6 -->
         Representation of Kolmogorov-Smirnov statistic as integral value.
       </action>

src/main/java/org/apache/commons/math4/stat/correlation/KendallsCorrelation.java

@@ -201,7 +201,7 @@ public class KendallsCorrelation {
         tiedXPairs += sum(consecutiveXTies - 1);
         tiedXYPairs += sum(consecutiveXYTies - 1);
 
-        int swaps = 0;
+        long swaps = 0;
         @SuppressWarnings("unchecked")
         Pair<Double, Double>[] pairsDestination = new Pair[n];
         for (int segmentSize = 1; segmentSize < n; segmentSize <<= 1) {

src/test/java/org/apache/commons/math4/stat/correlation/KendallsCorrelationTest.java

@@ -21,6 +21,8 @@ import java.util.Arrays;
 import org.apache.commons.math4.TestUtils;
 import org.apache.commons.math4.linear.BlockRealMatrix;
 import org.apache.commons.math4.linear.RealMatrix;
+import org.apache.commons.math4.random.RandomGenerator;
+import org.apache.commons.math4.random.Well1024a;
 import org.apache.commons.math4.stat.correlation.KendallsCorrelation;
 import org.junit.Assert;
 import org.junit.Before;
@@ -259,4 +261,21 @@ public class KendallsCorrelationTest extends PearsonsCorrelationTest {
 
         Assert.assertEquals(1.0, correlation.correlation(xArray, xArray), 1e-6);
     }
+
+    @Test
+    public void testMath1277() {
+        // example that led to a correlation coefficient outside of [-1, 1]
+        // due to a bug reported in MATH-1277
+        RandomGenerator rng = new Well1024a(0);
+        double[] xArray = new double[120000];
+        double[] yArray = new double[120000];
+        for (int i = 0; i < xArray.length; ++i) {
+            xArray[i] =  rng.nextDouble();
+        }
+        for (int i = 0; i < yArray.length; ++i) {
+            yArray[i] =  rng.nextDouble();
+        }
+        double coefficient = correlation.correlation(xArray, yArray);
+        Assert.assertTrue(1.0 >= coefficient && -1.0 <= coefficient);
+    }
 }