Improve quantile interpolation stability for exponential histograms (#144588)

Author: JonasKunz

libs/exponential-histogram/src/main/java/org/elasticsearch/exponentialhistogram/ExponentialHistogramQuantile.java

@@ -70,7 +70,8 @@ public static double getQuantile(ExponentialHistogram histo, double quantile) {
         if (lowerRank == upperRank) {
             result = values.valueAtRank();
         } else {
-            result = values.valueAtPreviousRank() * (1 - upperFactor) + values.valueAtRank() * upperFactor;
+            double delta = values.valueAtRank() - values.valueAtPreviousRank();
+            result = values.valueAtPreviousRank() + delta * upperFactor;
         }
         return removeNegativeZero(result);
     }

libs/exponential-histogram/src/test/java/org/elasticsearch/exponentialhistogram/QuantileAccuracyTests.java

@@ -42,6 +42,7 @@
 import static org.elasticsearch.exponentialhistogram.ExponentialScaleUtils.computeIndex;
 import static org.hamcrest.Matchers.closeTo;
 import static org.hamcrest.Matchers.equalTo;
+import static org.hamcrest.Matchers.greaterThanOrEqualTo;
 import static org.hamcrest.Matchers.lessThan;
 import static org.hamcrest.Matchers.lessThanOrEqualTo;
 import static org.hamcrest.Matchers.notANumber;
@@ -275,22 +276,26 @@ private double testQuantileAccuracy(double[] values, int bucketCount) {
         double maxError = 0;
         double allowedError = getMaximumRelativeError(values, bucketCount);
 
+        double lastQuantile = Double.NEGATIVE_INFINITY;
         // Compare histogram quantiles with exact quantiles
         for (double q : QUANTILES_TO_TEST) {
             double percentileRank = q * (values.length - 1);
             int lowerRank = (int) Math.floor(percentileRank);
             int upperRank = (int) Math.ceil(percentileRank);
             double upperFactor = percentileRank - lowerRank;
 
+            double histoValue = ExponentialHistogramQuantile.getQuantile(histogram, q);
+            // values should be monotonically increasing
+            assertThat(histoValue, greaterThanOrEqualTo(lastQuantile));
+            lastQuantile = histoValue;
+
             if (values[lowerRank] < 0 && values[upperRank] > 0) {
                 // the percentile lies directly between a sign change and we interpolate linearly in-between
                 // in this case the relative error bound does not hold
                 continue;
             }
             double exactValue = values[lowerRank] * (1 - upperFactor) + values[upperRank] * upperFactor;
 
-            double histoValue = ExponentialHistogramQuantile.getQuantile(histogram, q);
-
             // Skip comparison if exact value is close to zero to avoid false-positives due to numerical imprecision
             if (Math.abs(exactValue) < 1e-100) {
                 continue;