xiangfu0 commented on code in PR #19795:
URL: https://github.com/apache/pinot/pull/19795#discussion_r4227825890


##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/PercentileTDigestAccumulator.java:
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@@ -0,0 +1,1687 @@
+/**
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you 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.
+ */
+package org.apache.pinot.segment.local.customobject;
+
+import java.nio.ByteBuffer;
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.Collection;
+import java.util.List;
+import org.apache.pinot.segment.local.utils.TDigestUtils;
+import 
org.apache.pinot.segment.local.utils.TDigestUtils.SerializedTDigestMetadata;
+import org.apache.pinot.segment.spi.customobject.TDigest;
+import org.slf4j.Logger;
+import org.slf4j.LoggerFactory;
+
+
+/// Accumulates raw values and serialized TDigests into primitive centroids 
using Pinot's K1 weight-limit rule.
+///
+/// Raw values are sorted in small batches; serialized centroids retain their 
existing sorted order. Both are
+/// linearly merged with accumulated centroids. K1 preserves Pinot's existing 
middle-quantile behavior, and the
+/// legacy verbose and small encodings preserve stored data and mixed-version 
wire compatibility.
+///
+/// Serialized state keeps its first digest pending and allocates centroid 
buffers only when another input must be
+/// merged or the digest is queried. Raw-value buffers remain unallocated 
until a raw value is added.
+///
+/// Historical corrupted payloads remain opaque and byte-exact, with NaN 
statistics. Their reported historical mass
+/// may be invalid; they cannot be mutated or mixed with another distribution. 
Such an operation fails before
+/// changing aggregate mass, because neither invented statistics nor synthetic 
NaN bytes are safe for old readers.
+///
+/// Instances are externally serialized per aggregation or group key and are 
not safe for concurrent mutation.
+public final class PercentileTDigestAccumulator extends TDigest {
+  private static final Logger LOGGER = 
LoggerFactory.getLogger(PercentileTDigestAccumulator.class);
+  private static final int MIN_RAW_BUFFER_SIZE = 256;
+  private static final int MAX_RAW_BUFFER_SIZE = 10_000;
+  private static final int MIN_COMPRESSION = 10;
+  private static final int TWO_LEVEL_COMPRESSION_MULTIPLIER = 2;
+  private static final int MIN_INCREMENTAL_COMPRESSION = 50;
+
+  private final double _compression;
+  private final boolean _useTwoLevelRawCompression;
+  private final double _workingCompression;
+  private final double _publicMaxWeightScale;
+  private final double _workingMaxWeightScale;
+  private final int _centroidCapacity;
+  private final int _pendingCentroidCapacity;
+  private double[] _rawValues;
+  private double[] _centroidMeans;
+  private double[] _centroidWeights;
+  private double[] _outputMeans;
+  private double[] _outputWeights;
+  private double[] _incomingMeans;
+  private double[] _incomingWeights;
+  private double[] _sortedIncomingMeans;
+  private double[] _sortedIncomingWeights;
+  private SerializedTDigestInput _serializedTDigestInput;
+  private byte[] _pendingSerializedTDigest;
+  private byte[] _originalFractionalBytes;
+  private SerializedTDigestMetadata _pendingSerializedMetadata;
+  private boolean _legacyDegraded;
+  private byte[] _serializedBytesForWrite;
+  private boolean _hasFractionalWeights;
+
+  private int _numRawValues;
+  private int _numCentroids;
+  private int _numIncomingCentroids;
+  private int _serializedMainCapacity;
+  private int _serializedBufferCapacity;
+  private int _mergeCount;
+  private boolean _publiclyCompressed;
+  private boolean _incomingCentroidsSorted = true;
+  private double _totalWeight;
+  private double _incomingWeight;
+  private double _min = Double.POSITIVE_INFINITY;
+  private double _max = Double.NEGATIVE_INFINITY;
+
+  public PercentileTDigestAccumulator(int compression) {
+    this(positiveCompression(compression), true, true);
+  }
+
+  public PercentileTDigestAccumulator(double compression) {
+    this(compression, true, true);
+  }
+
+  private PercentileTDigestAccumulator(double compression, boolean 
allocateRawBuffer, boolean allocateMergeBuffers) {
+    this(compression, allocateRawBuffer, allocateMergeBuffers, false);
+  }
+
+  private PercentileTDigestAccumulator(double compression, boolean 
allocateRawBuffer, boolean allocateMergeBuffers,
+      boolean useTwoLevelRawCompression) {
+    TDigestUtils.validateCompression(compression);
+    _useTwoLevelRawCompression = useTwoLevelRawCompression;
+    _compression = Math.max(MIN_COMPRESSION, compression);
+    _workingCompression = TWO_LEVEL_COMPRESSION_MULTIPLIER * _compression;
+    _publicMaxWeightScale = calculateK1MaxWeightScale(_compression);
+    _workingMaxWeightScale = calculateK1MaxWeightScale(_workingCompression);
+    long roundedCompression = (long) Math.ceil(_compression);
+    _centroidCapacity = TDigestUtils.getDefaultCentroidCapacity(_compression);
+    _pendingCentroidCapacity = getPendingCentroidCapacity(_centroidCapacity);
+    if (allocateRawBuffer) {
+      _rawValues = new double[getRawBufferSize(roundedCompression)];
+    }
+    if (allocateMergeBuffers) {
+      int initialCapacity = Math.min(_centroidCapacity, MIN_RAW_BUFFER_SIZE);
+      _centroidMeans = new double[initialCapacity];
+      _centroidWeights = new double[initialCapacity];
+      _outputMeans = new double[initialCapacity];
+      _outputWeights = new double[initialCapacity];
+    }
+  }
+
+  /// Creates a lazy digest with the legacy two-level compression used by 
Star-tree and general digest aggregation.
+  public static PercentileTDigestAccumulator forLegacyAggregation(double 
compression) {
+    return new PercentileTDigestAccumulator(compression, false, false, true);
+  }
+
+  public static PercentileTDigestAccumulator forSerializedTDigest(byte[] 
bytes) {
+    return new PercentileTDigestAccumulator(readCompression(bytes), false, 
false);
+  }
+
+  public static PercentileTDigestAccumulator 
forSerializedTDigest(SerializedTDigestInput input) {
+    return new PercentileTDigestAccumulator(input._compression, false, false);
+  }
+
+  public static PercentileTDigestAccumulator 
forSerializedTDigestWithMergeBuffers(byte[] bytes) {
+    return new PercentileTDigestAccumulator(readCompression(bytes), false, 
true);
+  }
+
+  public static PercentileTDigestAccumulator forSerializedTDigest(ByteBuffer 
input) {
+    SerializedTDigestInput serialized = new SerializedTDigestInput();
+    serialized.reset(input);
+    PercentileTDigestAccumulator accumulator = 
forSerializedTDigest(serialized);
+    accumulator.addSerializedTDigest(serialized);
+    return accumulator;
+  }
+
+  public static PercentileTDigestAccumulator forReduction(double compression) {
+    return new PercentileTDigestAccumulator(positiveCompression(compression), 
false, false);
+  }
+
+  /// Copies primitive centroids without encoding and decoding them. Zero 
weights are ignored, and unordered
+  /// means are sorted when initializing a stored, already compressed 
distribution; caller arrays are not mutated.
+  /// Subsequent inputs use the normal buffered merge. Positive weights and 
consistent extrema are required.
+  public void addCentroids(double[] means, double[] weights, int count, double 
min, double max,
+      boolean alreadyCompressed) {
+    requireMutable();
+    if (count < 0 || count > means.length || count > weights.length) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count: " + 
count);
+    }
+    double totalWeight = 0.0;
+    int positiveCount = 0;
+    boolean sorted = true;
+    boolean fractionalWeights = false;
+    double previousMean = Double.NEGATIVE_INFINITY;
+    for (int i = 0; i < count; i++) {
+      double weight = weights[i];
+      if (weight == 0.0) {
+        continue;
+      }
+      double mean = means[i];
+      if (!(weight > 0.0) || !Double.isFinite(weight) || !(mean >= min && mean 
<= max)) {
+        throw new IllegalArgumentException("Invalid TDigest centroid");
+      }
+      totalWeight += weight;
+      sorted &= mean >= previousMean;
+      previousMean = mean;
+      fractionalWeights |= weight != Math.rint(weight);
+      positiveCount++;
+    }
+    checkTotalWeight(getTotalWeight() + totalWeight);
+    if (positiveCount == 0) {
+      return;
+    }
+    materializePendingSerializedTDigest();
+    _originalFractionalBytes = null;
+    _hasFractionalWeights |= fractionalWeights;
+    if (hasNoInputs() && alreadyCompressed) {
+      ensureCentroidCapacity(Math.addExact(positiveCount, 2));
+      for (int i = 0; i < count; i++) {
+        if (weights[i] > 0.0) {
+          _centroidMeans[_numCentroids] = means[i];
+          _centroidWeights[_numCentroids++] = weights[i];
+        }
+      }
+      if (!sorted) {
+        it.unimi.dsi.fastutil.Arrays.mergeSort(0, _numCentroids,
+            (first, second) -> Double.compare(_centroidMeans[first], 
_centroidMeans[second]),
+            (first, second) -> {
+              double mean = _centroidMeans[first];
+              _centroidMeans[first] = _centroidMeans[second];
+              _centroidMeans[second] = mean;
+              double weight = _centroidWeights[first];
+              _centroidWeights[first] = _centroidWeights[second];
+              _centroidWeights[second] = weight;
+            });
+      }
+      _totalWeight = totalWeight;
+      _min = min;
+      _max = max;
+      normalizeBoundaryCentroids();
+      _publiclyCompressed = true;
+    } else {
+      for (int i = 0; i < count; i++) {
+        if (weights[i] > 0.0) {
+          bufferIncomingCentroid(means[i], weights[i]);
+        }
+      }
+      _min = Math.min(_min, min);
+      _max = Math.max(_max, max);
+    }
+  }
+
+  public void add(double[] values, int from, int toExclusive) {
+    if (from >= toExclusive) {
+      return;
+    }
+    requireMutable();
+    materializePendingSerializedTDigest();
+    ensureRawBuffer();
+    while (from < toExclusive) {
+      if (_numRawValues == _rawValues.length
+          || _numRawValues + _numIncomingCentroids == getPendingInputLimit()) {
+        flush();
+      }
+      int numValues = Math.min(toExclusive - from, Math.min(_rawValues.length 
- _numRawValues,
+          getPendingInputLimit() - _numRawValues - _numIncomingCentroids));
+      int rawOffset = _numRawValues;
+      for (int i = 0; i < numValues; i++) {
+        double value = values[from + i];
+        if (Double.isNaN(value)) {
+          throw new IllegalArgumentException("Cannot add NaN to t-digest");
+        }
+        _rawValues[rawOffset + i] = value;
+      }
+      _originalFractionalBytes = null;
+      from += numValues;
+      _numRawValues += numValues;
+      if (_numRawValues == _rawValues.length
+          || _numRawValues + _numIncomingCentroids == getPendingInputLimit()) {
+        flush();
+      }
+    }
+  }
+
+  @Override
+  public void add(double value) {
+    if (Double.isNaN(value)) {
+      throw new IllegalArgumentException("Cannot add NaN to t-digest");
+    }
+    requireMutable();
+    materializePendingSerializedTDigest();
+    ensureRawBuffer();
+    if (_numRawValues == _rawValues.length
+        || _numRawValues + _numIncomingCentroids == getPendingInputLimit()) {
+      flush();
+    }
+    _originalFractionalBytes = null;
+    _rawValues[_numRawValues++] = value;
+  }
+
+  @Override
+  public void add(double value, double weight) {
+    if (weight == 1) {
+      add(value);
+      return;
+    }
+    if (Double.isNaN(value)) {
+      throw new IllegalArgumentException("Cannot add NaN to t-digest");
+    }
+    if (!(weight > 0.0) || !Double.isFinite(weight)) {
+      throw new IllegalArgumentException("TDigest weight must be positive: " + 
weight);
+    }
+    requireMutable();
+    materializePendingSerializedTDigest();
+    bufferIncomingCentroid(value, weight);
+    _originalFractionalBytes = null;
+    _hasFractionalWeights |= weight != Math.rint(weight);
+    _min = Math.min(_min, value);
+    _max = Math.max(_max, value);
+  }
+
+  @Override
+  public void add(TDigest other) {
+    requireMutable();
+    if (other instanceof PercentileTDigestAccumulator) {
+      addAccumulator((PercentileTDigestAccumulator) other);
+      return;
+    }
+    if (!other.hasValidStatistics()) {
+      materializePendingSerializedTDigest();
+      SerializedTDigestInput input = getSerializedTDigestInput();
+      input.reset(ByteBuffer.wrap(TDigestUtils.serialize(other)), false);
+      addSerializedTDigest(input);
+      return;
+    }
+    materializePendingSerializedTDigest();
+    double otherWeight = other.getTotalWeight();
+    checkTotalWeight(_totalWeight + _incomingWeight + _numRawValues + 
otherWeight);
+    for (Centroid centroid : other.centroids()) {
+      double weight = centroid.weight();
+      if (weight == 0.0) {
+        continue;
+      }
+      if (!(weight > 0.0) || !Double.isFinite(weight) || 
Double.isNaN(centroid.mean())) {
+        throw new IllegalArgumentException("Invalid TDigest centroid");
+      }
+      _hasFractionalWeights |= weight != Math.rint(weight);
+      bufferIncomingCentroid(centroid.mean(), weight);
+      _originalFractionalBytes = null;
+    }
+    if (otherWeight != 0.0) {
+      _min = Math.min(_min, other.getMin());
+      _max = Math.max(_max, other.getMax());
+    }
+  }
+
+  @Override
+  public void add(List<? extends TDigest> others) {
+    for (TDigest other : others) {
+      add(other);
+    }
+  }
+
+  private void addAccumulator(PercentileTDigestAccumulator other) {
+    if (other == this) {
+      compress();
+      if (_numCentroids == 0) {
+        return;
+      }
+      // Snapshot only self-merges; fresh fractional mass need not be 
representable by a legacy wire payload.
+      addCentroids(Arrays.copyOf(_centroidMeans, _numCentroids), 
Arrays.copyOf(_centroidWeights, _numCentroids),
+          _numCentroids, _min, _max, false);
+      return;
+    }
+    if (other._originalFractionalBytes != null && _compression == 
other._compression && getTotalWeight() == 0.0) {
+      materializePendingSerializedTDigest();
+      SerializedTDigestInput input = getSerializedTDigestInput();
+      input.reset(other._originalFractionalBytes);
+      input._retainedBytes = other._originalFractionalBytes;
+      addSerializedTDigest(input);
+      return;
+    }
+    if (other._pendingSerializedTDigest != null) {
+      // Materialize before resetting the reusable reader: materialization 
uses that same reader.
+      materializePendingSerializedTDigest();
+      SerializedTDigestInput input = getSerializedTDigestInput();
+      input.reset(other._pendingSerializedTDigest, 
other._pendingSerializedMetadata);
+      input._retainedBytes = other._pendingSerializedTDigest;
+      addSerializedTDigest(input);
+      return;
+    }
+    if (other._legacyDegraded) {
+      addSerializedTDigest(other.serialize());
+      return;
+    }
+
+    // MergingDigest compressed merge sources in place. Aggregation owns these 
mutable inputs exclusively.
+    other.compress();
+    materializePendingSerializedTDigest();
+    checkTotalWeight(_totalWeight + _incomingWeight + _numRawValues + 
other._totalWeight);
+    _hasFractionalWeights |= other._hasFractionalWeights;
+    preserveSerializedCapacity(other._serializedMainCapacity, 
other._serializedBufferCapacity);
+    bufferIncomingCentroids(other._centroidMeans, other._centroidWeights, 
other._numCentroids);
+    if (other._totalWeight > 0.0) {
+      _originalFractionalBytes = null;
+    }
+    _min = Math.min(_min, other._min);
+    _max = Math.max(_max, other._max);
+  }
+
+  public void addSerializedTDigest(byte[] bytes) {
+    requireMutable();
+    materializePendingSerializedTDigest();
+    SerializedTDigestInput input = getSerializedTDigestInput();
+    input.reset(bytes);
+    addSerializedTDigest(input);
+  }
+
+  private SerializedTDigestInput getSerializedTDigestInput() {
+    if (_serializedTDigestInput == null) {
+      _serializedTDigestInput = new SerializedTDigestInput();
+    }
+    return _serializedTDigestInput;
+  }
+
+  public void addSerializedTDigest(SerializedTDigestInput input) {
+    requireMutable();
+    if (prepareSerializedTDigest(input)) {
+      mergeSerializedTDigest(input, false);
+    }
+  }
+
+  public void addSerializedTDigestDirect(SerializedTDigestInput input) {
+    requireMutable();
+    if (prepareSerializedTDigest(input)) {
+      mergeSerializedTDigest(input, true);
+    }
+  }
+
+  private boolean prepareSerializedTDigest(SerializedTDigestInput input) {
+    if (_pendingSerializedTDigest == null && hasNoInputs()) {
+      input.inspectMetadata();
+      _hasFractionalWeights |= input._metadata.fractionalWeights();
+      _pendingSerializedTDigest = input.retainBytes();
+      _pendingSerializedMetadata = input._metadata;
+      if (input.hasUnrepresentableBoundaryMass() && _compression == 
input._compression) {
+        // Alias the retained snapshot; historical fractional bytes remain 
byte-exact after read-only materialization.
+        _originalFractionalBytes = _pendingSerializedTDigest;
+      }
+      if (input._metadata.needsLegacyFallback()) {
+        markLegacyDegraded(input);
+      }
+      return false;
+    }
+    materializePendingSerializedTDigest();
+    input.decode();
+    if (input._metadata.needsLegacyFallback()) {
+      if (hasNoInputs()) {
+        _pendingSerializedTDigest = input.retainBytes();
+        _pendingSerializedMetadata = input._metadata;
+        markLegacyDegraded(input);
+        return false;
+      }
+      throw corruptedMutation();
+    }
+    checkTotalWeight(_totalWeight + _incomingWeight + _numRawValues + 
input._totalWeight);
+    if (input._totalWeight > 0.0) {
+      _originalFractionalBytes = null;
+    }
+    _hasFractionalWeights |= input._metadata.fractionalWeights();
+    return true;
+  }
+
+  private boolean hasNoInputs() {
+    return _numCentroids == 0 && _totalWeight == 0.0 && _numRawValues == 0 && 
_numIncomingCentroids == 0;
+  }
+
+  private void mergeSerializedTDigest(SerializedTDigestInput input, boolean 
direct) {
+    if (input._totalWeight == 0.0) {
+      return;
+    }
+    preserveSerializedCapacity(input._mainCapacity, input._bufferCapacity);
+    if (hasNoInputs()) {
+      if (input._totalWeight != 0.0) {
+        ensureCentroidCapacity(input._numCentroids);
+        System.arraycopy(input._means, 0, _centroidMeans, 0, 
input._numCentroids);
+        System.arraycopy(input._weights, 0, _centroidWeights, 0, 
input._numCentroids);
+        _numCentroids = input._numCentroids;
+        _totalWeight = input._totalWeight;
+        _min = input._min;
+        _max = input._max;
+        // Stored centroids already went through the writer's public 
compression. Reading or repairing their
+        // endpoints needs another K1 pass only when the output compression 
differs from the stored compression.
+        _publiclyCompressed = _compression == input._compression;
+      }
+      return;
+    }
+    if (direct) {
+      flush();
+      boolean runBackwards = (_mergeCount++ & 1) != 0;
+      if (!mergeSorted(input._means, input._weights, input._numCentroids, 
input._totalWeight,
+          getIncrementalCompression(), runBackwards)) {
+        return;
+      }
+    } else {
+      bufferIncomingCentroids(input._means, input._weights, 
input._numCentroids);
+    }
+    _min = Math.min(_min, input._min);
+    _max = Math.max(_max, input._max);
+  }
+
+  @Override
+  public void compress() {
+    if (_legacyDegraded) {
+      return;
+    }
+    if (_pendingSerializedTDigest != null || _numRawValues > 0 || 
_numIncomingCentroids > 0
+        || !_publiclyCompressed && _numCentroids > 0) {
+      _serializedBytesForWrite = null;
+    }
+    materializePendingSerializedTDigest();
+    if (_numRawValues > 0 || _numIncomingCentroids > 0) {
+      // MergingDigest 3.3 combines pending values and existing centroids 
directly at public compression. Flushing at
+      // working compression first would add an extra lossy merge pass and 
materially increase reducer rank error.
+      flush(_compression);
+      _publiclyCompressed = true;
+    } else if (!_publiclyCompressed && _numCentroids > 0) {
+      recompressCentroids(_compression);
+      _publiclyCompressed = true;
+    }
+  }
+
+  @Override
+  public long size() {
+    return (long) getTotalWeight();
+  }
+
+  @Override
+  public boolean hasValidStatistics() {
+    return !_legacyDegraded;
+  }
+
+  @Override
+  public double getTotalWeight() {
+    return _pendingSerializedTDigest != null ? 
_pendingSerializedMetadata.totalWeight()
+        : _totalWeight + _incomingWeight + _numRawValues;
+  }
+
+  /// Bounds serialized output centroids from buffered inputs, including up to 
two boundary splits before a merge
+  /// and two more before writing, without flushing or using the potentially 
huge input mass.
+  public long getCentroidCountUpperBound() {
+    return _pendingSerializedTDigest != null ? (long) 
_pendingSerializedMetadata.centroidCount() + 4L
+        : (long) _numCentroids + _numRawValues + _numIncomingCentroids + 4L;
+  }
+
+  /// Whether fractional input weights invalidate the usual bound of one 
centroid per unit of mass.
+  public boolean hasFractionalWeights() {
+    return _hasFractionalWeights;
+  }
+
+  /// Whether unchanged historical fractional boundaries still require their 
original byte representation.
+  public boolean hasOriginalFractionalPayload() {
+    return _originalFractionalBytes != null;
+  }
+
+  @Override
+  public double cdf(double value) {
+    if (Double.isNaN(value) || Double.isInfinite(value)) {
+      throw new IllegalArgumentException(String.format("Invalid value: %f", 
value));
+    }
+    if (_legacyDegraded) {
+      return Double.NaN;
+    }
+    materializePendingSerializedTDigest();
+    flush();
+    if (_numCentroids == 0) {
+      return Double.NaN;
+    }
+    if (_numCentroids == 1) {
+      double width = _max - _min;
+      if (value < _min) {
+        return 0.0;
+      } else if (value > _max) {
+        return 1.0;
+      } else if (value - _min <= width) {
+        return 0.5;
+      } else {
+        return (value - _min) / width;
+      }
+    }
+    if (value < _min) {
+      return 0.0;
+    }
+    if (value > _max) {
+      return 1.0;
+    }
+    if (value < _centroidMeans[0]) {
+      double width = _centroidMeans[0] - _min;
+      if (width > 0.0) {
+        if (_centroidWeights[0] < 1.0) {
+          return (_centroidWeights[0] / 2.0 * (value - _min) / width) / 
_totalWeight;
+        }
+        return value == _min ? 0.5 / _totalWeight
+            : (1.0 + (value - _min) / width * (_centroidWeights[0] / 2.0 - 
1.0)) / _totalWeight;
+      }
+      return 0.0;
+    }
+    int lastIndex = _numCentroids - 1;
+    if (value > _centroidMeans[lastIndex]) {
+      double width = _max - _centroidMeans[lastIndex];
+      if (width > 0.0) {
+        if (_centroidWeights[lastIndex] < 1.0) {
+          return 1.0 - (_centroidWeights[lastIndex] / 2.0 * (_max - value) / 
width) / _totalWeight;
+        }
+        return value == _max ? 1.0 - 0.5 / _totalWeight
+            : 1.0 - (1.0 + (_max - value) / width * 
(_centroidWeights[lastIndex] / 2.0 - 1.0))
+                / _totalWeight;
+      }
+      return 1.0;
+    }
+
+    double weightSoFar = 0.0;
+    for (int i = 0; i < lastIndex; i++) {
+      if (_centroidMeans[i] == value) {
+        double equalWeight = 0.0;
+        int equalIndex = i;
+        while (equalIndex < _numCentroids && _centroidMeans[equalIndex] == 
value) {
+          equalWeight += _centroidWeights[equalIndex];
+          equalIndex++;
+        }
+        return (weightSoFar + equalWeight / 2.0) / _totalWeight;
+      }
+      if (_centroidMeans[i] <= value && _centroidMeans[i + 1] > value) {
+        if (!Double.isFinite(_centroidMeans[i]) || 
!Double.isFinite(_centroidMeans[i + 1])) {
+          return (weightSoFar + _centroidWeights[i]) / _totalWeight;
+        }
+        double width = _centroidMeans[i + 1] - _centroidMeans[i];
+        if (width > 0.0) {
+          double leftExcludedWeight = getPointMassHalfWeight(i);
+          double rightExcludedWeight = getPointMassHalfWeight(i + 1);
+          double halfWeight = (_centroidWeights[i] + _centroidWeights[i + 1]) 
/ 2.0;
+          double interpolatedWeight = halfWeight - leftExcludedWeight - 
rightExcludedWeight;
+          double base = weightSoFar + _centroidWeights[i] / 2.0 + 
leftExcludedWeight;
+          return (base + interpolatedWeight * (value - _centroidMeans[i]) / 
width) / _totalWeight;
+        }
+        return (weightSoFar + (_centroidWeights[i] + _centroidWeights[i + 1]) 
/ 2.0) / _totalWeight;
+      }
+      weightSoFar += _centroidWeights[i];
+    }
+    if (value == _centroidMeans[lastIndex]) {
+      return 1.0 - Math.min(1.0, _centroidWeights[lastIndex]) / 2.0 / 
_totalWeight;
+    }
+    throw new IllegalStateException("Unable to compute TDigest CDF");
+  }
+
+  @Override
+  public double quantile(double quantile) {
+    if (Double.isNaN(quantile) || quantile < 0.0 || quantile > 1.0) {
+      throw new IllegalArgumentException("q should be in [0,1], got " + 
quantile);
+    }
+    if (_legacyDegraded) {
+      return Double.NaN;
+    }
+    materializePendingSerializedTDigest();
+    flush();
+    if (_numCentroids == 0) {
+      return Double.NaN;
+    }
+    if (quantile == 0.0) {
+      return _min;
+    }
+    if (quantile == 1.0) {
+      return _max;
+    }
+    if (_numCentroids == 1) {
+      return _centroidMeans[0];
+    }
+
+    double index = quantile * _totalWeight;
+    double firstWeight = _centroidWeights[0];
+    if (firstWeight < 1.0 && index < firstWeight / 2.0) {
+      return weightedAverage(_min, firstWeight / 2.0 - index, 
_centroidMeans[0], index);
+    }
+    if (firstWeight >= 1.0 && index < 1.0) {
+      return _min;
+    }
+    if (_centroidWeights[0] > 1.0 && index < _centroidWeights[0] / 2.0) {
+      return _min + (index - 1.0) / (_centroidWeights[0] / 2.0 - 1.0) * 
(_centroidMeans[0] - _min);
+    }
+    int lastIndex = _numCentroids - 1;
+    double lastWeight = _centroidWeights[lastIndex];
+    if (lastWeight < 1.0 && index >= _totalWeight - lastWeight / 2.0) {
+      return weightedAverage(_centroidMeans[lastIndex], _totalWeight - index, 
_max,
+          index - (_totalWeight - lastWeight / 2.0));
+    }
+    if (lastWeight >= 1.0 && index > _totalWeight - 1.0) {
+      return _max;
+    }
+    if (_centroidWeights[lastIndex] > 1.0
+        && _totalWeight - index <= _centroidWeights[lastIndex] / 2.0) {
+      return _max - (_totalWeight - index - 1.0) / 
(_centroidWeights[lastIndex] / 2.0 - 1.0)
+          * (_max - _centroidMeans[lastIndex]);
+    }
+
+    double weightSoFar = _centroidWeights[0] / 2.0;
+    for (int i = 0; i < lastIndex; i++) {
+      double halfWeight = (_centroidWeights[i] + _centroidWeights[i + 1]) / 
2.0;
+      if (weightSoFar + halfWeight > index) {
+        double leftExcludedWeight = getPointMassHalfWeight(i);
+        if (index - weightSoFar < leftExcludedWeight) {
+          return _centroidMeans[i];
+        }
+        double rightExcludedWeight = getPointMassHalfWeight(i + 1);
+        if (weightSoFar + halfWeight - index <= rightExcludedWeight) {
+          return _centroidMeans[i + 1];
+        }
+        double leftWeight = index - weightSoFar - leftExcludedWeight;
+        double rightWeight = weightSoFar + halfWeight - index - 
rightExcludedWeight;
+        return weightedAverage(_centroidMeans[i], rightWeight, 
_centroidMeans[i + 1], leftWeight);
+      }
+      weightSoFar += halfWeight;
+    }
+    double weightToMax = index - _totalWeight - _centroidWeights[lastIndex] / 
2.0;
+    double weightFromLastCentroid = _centroidWeights[lastIndex] / 2.0 - 
weightToMax;
+    return weightedAverage(_centroidMeans[lastIndex], weightToMax, _max, 
weightFromLastCentroid);
+  }
+
+  private double getPointMassHalfWeight(int index) {
+    // Adjacent equal means establish a repeated-value plateau. Keep its 
complete mass out of interpolation at
+    // either edge; an isolated weighted centroid still represents an unknown 
distribution around its mean.
+    double mean = _centroidMeans[index];
+    boolean pointMass = _centroidWeights[index] == 1.0 || index > 0 && 
_centroidMeans[index - 1] == mean
+        || index + 1 < _numCentroids && _centroidMeans[index + 1] == mean;
+    return pointMass ? _centroidWeights[index] / 2.0 : 0.0;
+  }
+
+  private static double weightedAverage(double firstValue, double firstWeight, 
double secondValue,
+      double secondWeight) {
+    if (firstValue > secondValue) {
+      return weightedAverage(secondValue, secondWeight, firstValue, 
firstWeight);
+    }
+    if (firstWeight == 0.0) {
+      return secondValue;
+    }
+    if (secondWeight == 0.0 || firstValue == secondValue) {
+      return firstValue;
+    }
+    if (!Double.isFinite(firstValue)) {
+      return firstValue;
+    }
+    if (!Double.isFinite(secondValue)) {
+      return secondValue;
+    }
+    double average = (firstValue * firstWeight + secondValue * secondWeight) / 
(firstWeight + secondWeight);
+    return Math.max(firstValue, Math.min(average, secondValue));
+  }
+
+  @Override
+  public Collection<Centroid> centroids() {
+    if (_legacyDegraded) {
+      byte[] bytes = serialize();
+      ByteBuffer encoded = ByteBuffer.wrap(bytes);
+      SerializedTDigestMetadata metadata = 
TDigestUtils.readSerializedHeader(encoded);
+      encoded.position(metadata.centroidOffset());
+      List<Centroid> centroids = new ArrayList<>(metadata.centroidCount());
+      for (int i = 0; i < metadata.centroidCount(); i++) {
+        double weight = metadata.centroidSize() == 
TDigestUtils.VERBOSE_CENTROID_SIZE
+            ? encoded.getDouble() : encoded.getFloat();
+        double mean = metadata.centroidSize() == 
TDigestUtils.VERBOSE_CENTROID_SIZE
+            ? encoded.getDouble() : encoded.getFloat();
+        centroids.add(new Centroid(mean, weight));
+      }
+      return centroids;
+    }
+    materializePendingSerializedTDigest();
+    flush();
+    List<Centroid> centroids = new ArrayList<>(_numCentroids);
+    for (int i = 0; i < _numCentroids; i++) {
+      centroids.add(new Centroid(_centroidMeans[i], _centroidWeights[i]));
+    }
+    return centroids;
+  }
+
+  /// Copies a valid distribution's primitive centroid arrays after flushing 
buffered inputs. This does not apply
+  /// public compression or serialize a finite sub-distribution; callers can 
include surrounding infinity mass.
+  public void copyCentroids(double[] means, double[] weights, int offset) {
+    if (_legacyDegraded) {
+      throw corruptedMutation();
+    }
+    materializePendingSerializedTDigest();
+    flush();
+    if (means == weights || offset < 0 || offset > means.length - _numCentroids
+        || offset > weights.length - _numCentroids) {
+      throw new IllegalArgumentException("Insufficient distinct TDigest 
centroid arrays");
+    }
+    if (_numCentroids == 0) {
+      return;
+    }
+    System.arraycopy(_centroidMeans, 0, means, offset, _numCentroids);
+    System.arraycopy(_centroidWeights, 0, weights, offset, _numCentroids);
+  }
+
+  @Override
+  public double compression() {
+    return _compression;
+  }
+
+  /// Returns the length of the [#serialize()] bytes rather than the raw 
verbose byte size, so generic `TDigest`
+  /// serializers ([#byteSize()] followed by [#asBytes(ByteBuffer)]) emit the 
mixed-version-compatible encoding.
+  /// Prepared bytes are cached until the next write or mutation, avoiding a 
second encoding pass for that pattern.
+  /// Emitting raw verbose bytes here could produce a digest with more 
centroids than an old reader of the same
+  /// compression allocates, which it rejects with 
[ArrayIndexOutOfBoundsException].
+  @Override
+  public int byteSize() {
+    if (_legacyDegraded || _originalFractionalBytes != null) {
+      return _legacyDegraded ? _pendingSerializedTDigest.length : 
_originalFractionalBytes.length;
+    }
+    if (_serializedBytesForWrite == null) {
+      _serializedBytesForWrite = serialize();
+    }
+    return _serializedBytesForWrite.length;
+  }
+
+  /// Bounds both compatible encodings and a widened verbose view without 
flushing. Buffered and fractional inputs
+  /// can reserve more space than their eventual bytes; retained capacities 
need not fit default compression size.
+  @Override
+  public int maxSerializedByteSize() {
+    if (_legacyDegraded) {
+      return _pendingSerializedTDigest.length;
+    }
+    if (_originalFractionalBytes != null) {
+      return _originalFractionalBytes.length;
+    }
+    long centroidCount = getCentroidCountUpperBound();
+    if (!_hasFractionalWeights) {
+      centroidCount = (long) Math.min(centroidCount, 
Math.ceil(getTotalWeight()));
+    }
+    int maximumBytes = getMaxVerboseByteSize(centroidCount);
+    return _pendingSerializedTDigest == null ? maximumBytes : 
Math.max(maximumBytes, _pendingSerializedTDigest.length);
+  }
+
+  private static int getMaxVerboseByteSize(long centroidCount) {
+    return Math.toIntExact(Math.addExact(TDigestUtils.VERBOSE_HEADER_SIZE,
+        Math.multiplyExact(TDigestUtils.VERBOSE_CENTROID_SIZE, 
centroidCount)));
+  }
+
+  /// Returns the small-encoding size unless float narrowing would overflow, 
in which case verbose bytes are used.
+  /// Historical degraded state retains its original encoding and rejects 
mutation.
+  @Override
+  public int smallByteSize() {
+    if (_legacyDegraded || _originalFractionalBytes != null) {
+      return _legacyDegraded ? _pendingSerializedTDigest.length : 
_originalFractionalBytes.length;
+    }
+    compress();
+    normalizeBoundaryCentroids();
+    checkFractionalBoundaryEncoding();
+    checkCapacityPreservingCentroidCount();
+    if (!canUseSmallEncoding()) {
+      return byteSize();
+    }
+    return Math.addExact(TDigestUtils.SMALL_HEADER_SIZE,
+        Math.multiplyExact(TDigestUtils.SMALL_CENTROID_SIZE, _numCentroids));
+  }
+
+  /// Writes the [#serialize()] bytes; see [#byteSize()]. Bytes are always 
written in big-endian order (the t-digest
+  /// wire order) regardless of the destination buffer's byte order, unlike 
the library's `asBytes`.
+  @Override
+  public void asBytes(ByteBuffer buffer) {
+    byte[] bytes = _serializedBytesForWrite;
+    _serializedBytesForWrite = null;
+    buffer.put(bytes != null ? bytes : serialize());
+  }
+
+  /// Writes the representation described by [#smallByteSize()]; readers must 
inspect the leading encoding identifier.
+  @Override
+  public void asSmallBytes(ByteBuffer buffer) {
+    if (_legacyDegraded || _originalFractionalBytes != null) {
+      buffer.put(serialize());
+      return;
+    }
+    compress();
+    normalizeBoundaryCentroids();
+    checkFractionalBoundaryEncoding();
+    checkCapacityPreservingCentroidCount();
+    if (canUseSmallEncoding()) {
+      buffer.put(toCapacityPreservingBytes());
+    } else {
+      asBytes(buffer);
+    }
+  }
+
+  @Override
+  public int centroidCount() {
+    if (_pendingSerializedTDigest != null) {
+      return !_legacyDegraded && _pendingSerializedMetadata.totalWeight() == 
0.0
+          ? 0 : _pendingSerializedMetadata.centroidCount();
+    }
+    flush();
+    return _numCentroids;
+  }
+
+  @Override
+  public double getMin() {
+    if (_pendingSerializedTDigest != null) {
+      return !_legacyDegraded && _pendingSerializedMetadata.totalWeight() == 
0.0
+          ? Double.POSITIVE_INFINITY : _pendingSerializedMetadata.min();
+    }
+    flush();
+    return _min;
+  }
+
+  @Override
+  public double getMax() {
+    if (_pendingSerializedTDigest != null) {
+      return !_legacyDegraded && _pendingSerializedMetadata.totalWeight() == 
0.0
+          ? Double.NEGATIVE_INFINITY : _pendingSerializedMetadata.max();
+    }
+    flush();
+    return _max;
+  }
+
+  public byte[] serialize() {
+    if (_legacyDegraded) {
+      return _pendingSerializedTDigest.clone();
+    }
+    if (_originalFractionalBytes != null) {
+      return _originalFractionalBytes.clone();
+    }
+    if (_pendingSerializedTDigest != null) {
+      if (_pendingSerializedMetadata.weightedBoundaries() || 
_pendingSerializedMetadata.hasZeroWeightCentroids()) {
+        materializePendingSerializedTDigest();
+      } else {
+        if (ByteBuffer.wrap(_pendingSerializedTDigest).getInt() == 
TDigestUtils.VERBOSE_ENCODING) {
+          byte[] serialized = 
TDigestUtils.makeLegacyCompatible(_pendingSerializedTDigest, 
_pendingSerializedMetadata);
+          return serialized == _pendingSerializedTDigest ? serialized.clone() 
: serialized;
+        }
+        return _pendingSerializedTDigest.clone();
+      }
+    }
+    compress();
+    normalizeBoundaryCentroids();
+    checkFractionalBoundaryEncoding();
+    return toLegacyCompatibleVerboseBytes();
+  }
+
+  private void recompressCentroids(double compression) {
+    normalizeBoundaryCentroids();
+    double[] means = _centroidMeans;
+    double[] weights = _centroidWeights;
+    int numCentroids = _numCentroids;
+    double totalWeight = _totalWeight;
+    _numCentroids = 0;
+    _totalWeight = 0.0;
+    boolean runBackwards = (_mergeCount++ & 1) != 0;
+    if (!mergeSorted(means, weights, numCentroids, totalWeight, compression, 
runBackwards)) {
+      throw new IllegalStateException("Cannot recompress an empty TDigest");
+    }
+  }
+
+  private byte[] toLegacyCompatibleVerboseBytes() {
+    ByteBuffer buffer = ByteBuffer.allocate(
+        Math.addExact(TDigestUtils.VERBOSE_HEADER_SIZE,
+            Math.multiplyExact(TDigestUtils.VERBOSE_CENTROID_SIZE, 
_numCentroids)));
+    buffer.putInt(TDigestUtils.VERBOSE_ENCODING);
+    buffer.putDouble(_min);
+    buffer.putDouble(_max);
+    buffer.putDouble(_compression);
+    buffer.putInt(_numCentroids);
+    double encodedWeight = 0.0;
+    boolean hasNonFiniteMeans = false;
+    boolean fractionalWeights = false;
+    for (int i = 0; i < _numCentroids; i++) {
+      buffer.putDouble(_centroidWeights[i]);
+      buffer.putDouble(_centroidMeans[i]);
+      encodedWeight += _centroidWeights[i];
+      hasNonFiniteMeans |= !Double.isFinite(_centroidMeans[i]);
+      fractionalWeights |= _centroidWeights[i] != 
Math.rint(_centroidWeights[i]);
+    }
+    checkTotalWeight(encodedWeight);
+    boolean weightedBoundaries = _numCentroids == 1 ? _centroidWeights[0] >= 
2.0
+        : _numCentroids > 1 && (_centroidWeights[0] > 1.0 || 
_centroidWeights[_numCentroids - 1] > 1.0);
+    // Collect exact wire metadata during the write rather than decoding and 
validating our fresh bytes again.
+    SerializedTDigestMetadata metadata = new 
SerializedTDigestMetadata(TDigestUtils.VERBOSE_ENCODING, _min, _max,
+        _compression, _numCentroids, 
Math.max(TDigestUtils.getDefaultCentroidCapacity(_compression),
+        TDigestUtils.getLegacyDefaultCentroidCapacity(_compression)), 0,
+        TDigestUtils.VERBOSE_HEADER_SIZE, TDigestUtils.VERBOSE_CENTROID_SIZE, 
buffer.capacity(), encodedWeight,
+        hasNonFiniteMeans, false, false, fractionalWeights, 
weightedBoundaries, false, _compression);
+    return TDigestUtils.makeLegacyCompatible(buffer.array(), metadata);
+  }
+
+  private boolean canUseSmallEncoding() {
+    if (!Float.isFinite((float) _compression)) {
+      return false;
+    }
+    for (int i = 0; i < _numCentroids; i++) {
+      if (!Float.isFinite((float) _centroidWeights[i])
+          || Double.isFinite(_centroidMeans[i]) && !Float.isFinite((float) 
_centroidMeans[i])) {
+        return false;
+      }
+    }
+    return true;
+  }
+
+  private byte[] toCapacityPreservingBytes() {
+    checkCapacityPreservingCentroidCount();
+    int mainCapacity = Math.min(Short.MAX_VALUE,
+        Math.max(_centroidCapacity, Math.max(_numCentroids, 
_serializedMainCapacity)));
+    long defaultBufferCapacity = 
Math.multiplyExact(TDigestUtils.DEFAULT_MERGE_BUFFER_MULTIPLIER, (long) 
mainCapacity);
+    int bufferCapacity = Math.toIntExact(Math.min(Short.MAX_VALUE,
+        Math.max(Math.max((long) _serializedBufferCapacity, mainCapacity + 
1L), defaultBufferCapacity)));
+    ByteBuffer buffer = ByteBuffer.allocate(
+        TDigestUtils.SMALL_HEADER_SIZE + TDigestUtils.SMALL_CENTROID_SIZE * 
_numCentroids);
+    buffer.putInt(TDigestUtils.SMALL_ENCODING);
+    buffer.putDouble(_min);
+    buffer.putDouble(_max);
+    buffer.putFloat((float) _compression);
+    buffer.putShort((short) mainCapacity);
+    buffer.putShort((short) bufferCapacity);
+    buffer.putShort((short) _numCentroids);
+    for (int i = 0; i < _numCentroids; i++) {
+      buffer.putFloat((float) _centroidWeights[i]);
+      buffer.putFloat((float) _centroidMeans[i]);
+    }
+    return buffer.array();
+  }
+
+  private void checkCapacityPreservingCentroidCount() {
+    if (_numCentroids > Short.MAX_VALUE) {
+      throw new IllegalStateException("TDigest has too many centroids for 
capacity-preserving encoding: "
+          + _numCentroids);
+    }
+  }
+
+  private void checkFractionalBoundaryEncoding() {
+    if (_numCentroids > 0) {
+      TDigestUtils.checkLegacyBoundaryWeights(_numCentroids, 
_centroidWeights[0], _centroidWeights[_numCentroids - 1]);
+    }
+  }
+
+  private void flush() {
+    // SQL accumulators merge raw inputs incrementally at configured 
compression. General digest aggregation keeps
+    // the legacy two-level raw merge, preserving sparse Star-tree query 
accuracy. Buffered reducer inputs also
+    // retain the two-level merge for its accuracy benefit.
+    flush(_numIncomingCentroids == 0 && !_useTwoLevelRawCompression
+        ? getIncrementalCompression()
+        : _workingCompression);
+  }
+
+  private double getIncrementalCompression() {
+    // Very low compression leaves too little centroid headroom for 
incremental public-compression merges to retain
+    // t-digest 3.3's accuracy. Keep the two-level strategy for those uncommon 
configurations.
+    return _compression >= MIN_INCREMENTAL_COMPRESSION ? _compression : 
_workingCompression;
+  }
+
+  private void flush(double compression) {
+    if (_numIncomingCentroids > 0) {
+      flushIncoming(compression);
+      return;
+    }
+    if (_numRawValues == 0) {
+      return;
+    }
+
+    Arrays.sort(_rawValues, 0, _numRawValues);
+    double rawMin = _rawValues[0];
+    double rawMax = _rawValues[_numRawValues - 1];
+    boolean runBackwards = (_mergeCount++ & 1) != 0;
+    mergeSorted(_rawValues, null, _numRawValues, _numRawValues, compression, 
runBackwards);
+    _numRawValues = 0;
+    _min = Math.min(_min, rawMin);
+    _max = Math.max(_max, rawMax);
+  }
+
+  private void flushIncoming(double compression) {
+    // Match mergeSorted's association before rearranging raw or paired 
centroid buffers.
+    checkTotalWeight(_totalWeight + (_incomingWeight + _numRawValues));
+    double rawMin = Double.POSITIVE_INFINITY;
+    double rawMax = Double.NEGATIVE_INFINITY;
+    if (_numRawValues > 0) {
+      Arrays.sort(_rawValues, 0, _numRawValues);
+      rawMin = _rawValues[0];
+      rawMax = _rawValues[_numRawValues - 1];
+      ensureIncomingCapacity(Math.addExact(_numIncomingCentroids, 
_numRawValues));
+      System.arraycopy(_incomingMeans, 0, _incomingMeans, _numRawValues, 
_numIncomingCentroids);
+      System.arraycopy(_incomingWeights, 0, _incomingWeights, _numRawValues, 
_numIncomingCentroids);
+      for (int i = 0; i < _numRawValues; i++) {
+        _incomingMeans[i] = _rawValues[i];
+        _incomingWeights[i] = 1.0;
+      }
+      _numIncomingCentroids += _numRawValues;
+      _incomingWeight += _numRawValues;
+      _numRawValues = 0;
+      _incomingCentroidsSorted = false;
+    }
+
+    int incomingCount = _numIncomingCentroids;
+    double incomingWeight = _incomingWeight;
+    double[] incomingMeans = _incomingMeans;
+    double[] incomingWeights = _incomingWeights;
+    if (!_incomingCentroidsSorted) {
+      ensureSortedIncomingCapacity(incomingCount);
+      stableSortIncoming(incomingCount);
+      incomingMeans = _incomingMeans;
+      incomingWeights = _incomingWeights;
+      _incomingCentroidsSorted = true;
+    }
+    boolean runBackwards = (_mergeCount & 1) != 0;
+    if (!mergeSorted(incomingMeans, incomingWeights, incomingCount, 
incomingWeight, compression, runBackwards)) {
+      throw new IllegalStateException("Cannot flush an empty TDigest input 
buffer");
+    }
+    _mergeCount++;
+    _numIncomingCentroids = 0;
+    _incomingWeight = 0.0;
+    _incomingCentroidsSorted = true;
+    _min = Math.min(_min, rawMin);
+    _max = Math.max(_max, rawMax);
+  }
+
+  private boolean mergeSorted(double[] incomingMeans, double[] 
incomingWeights, int incomingCount,
+      double incomingWeight, double compression, boolean runBackwards) {
+    if (incomingWeight == 0.0) {
+      return false;
+    }
+
+    double newTotalWeight = _totalWeight + incomingWeight;
+    checkTotalWeight(newTotalWeight);
+    normalizeBoundaryCentroids();
+    int preferredOutputCapacity = getPreferredOutputCapacity(incomingCount);
+    ensureOutputCapacity(1);
+    double totalWeightNormalizer = 1.0 / newTotalWeight;
+    double weightNormalizer = totalWeightNormalizer / 
getK1MaxWeightScale(compression);
+    int incomingIndex = runBackwards ? incomingCount - 1 : 0;
+    int centroidIndex = runBackwards ? _numCentroids - 1 : 0;
+    int incomingLimit = runBackwards ? -1 : incomingCount;
+    int centroidLimit = runBackwards ? -1 : _numCentroids;
+    int direction = runBackwards ? -1 : 1;
+    int numInputs = incomingCount + _numCentroids;
+    int inputIndex = 0;
+    int numOutputCentroids = 0;
+    double weightSoFar = 0.0;
+    double firstInputMean = _numCentroids == 0 ? incomingMeans[0]
+        : Math.min(incomingMeans[0], _centroidMeans[0]);
+    double lastInputMean = _numCentroids == 0 ? incomingMeans[incomingCount - 
1]
+        : Math.max(incomingMeans[incomingCount - 1], 
_centroidMeans[_numCentroids - 1]);
+    boolean allFiniteMeans = Double.isFinite(firstInputMean) && 
Double.isFinite(lastInputMean);
+    boolean sameSignMeans = firstInputMean > 0.0 || lastInputMean < 0.0;
+    while (incomingIndex != incomingLimit || centroidIndex != centroidLimit) {
+      double mean;
+      double weight;
+      boolean takeIncoming = centroidIndex == centroidLimit || (incomingIndex 
!= incomingLimit
+          && (runBackwards ? incomingMeans[incomingIndex] > 
_centroidMeans[centroidIndex]
+              : incomingMeans[incomingIndex] <= 
_centroidMeans[centroidIndex]));
+      if (takeIncoming) {
+        mean = incomingMeans[incomingIndex];
+        weight = incomingWeights == null ? 1.0 : 
incomingWeights[incomingIndex];
+        incomingIndex += direction;
+      } else {
+        mean = _centroidMeans[centroidIndex];
+        weight = _centroidWeights[centroidIndex];
+        centroidIndex += direction;
+      }
+      if (numOutputCentroids == 0) {
+        _outputMeans[0] = mean;
+        _outputWeights[0] = weight;
+        numOutputCentroids = 1;
+      } else {
+        int currentIndex = numOutputCentroids - 1;
+        double proposedWeight = _outputWeights[currentIndex] + weight;
+        double q0 = weightSoFar * totalWeightNormalizer;
+        double q2 = (weightSoFar + proposedWeight) * totalWeightNormalizer;
+        double normalizedWeight = proposedWeight * weightNormalizer;
+        double normalizedWeightSquared = normalizedWeight * normalizedWeight;
+        boolean canMerge = (allFiniteMeans || 
canMergeMeans(_outputMeans[currentIndex], mean))
+            && normalizedWeightSquared <= q0 * (1.0 - q0)
+            && normalizedWeightSquared <= q2 * (1.0 - q2);
+        if (inputIndex == 1 || inputIndex == numInputs - 1) {
+          canMerge = false;
+        }
+        if (canMerge) {
+          _outputWeights[currentIndex] = proposedWeight;
+          _outputMeans[currentIndex] =
+              TDigestUtils.weightedMean(_outputMeans[currentIndex], 
proposedWeight - weight, mean, weight,
+                  proposedWeight, sameSignMeans);
+        } else {
+          weightSoFar += _outputWeights[currentIndex];
+          ensureOutputCapacity(Math.max(preferredOutputCapacity, 
numOutputCentroids + 1));
+          _outputMeans[numOutputCentroids] = mean;
+          _outputWeights[numOutputCentroids] = weight;
+          numOutputCentroids++;
+        }
+      }
+      inputIndex++;
+    }
+    if (runBackwards) {
+      reverse(_outputMeans, numOutputCentroids);
+      reverse(_outputWeights, numOutputCentroids);
+    }
+    finishMerge(numOutputCentroids, newTotalWeight, compression);
+    return true;
+  }
+
+  private void finishMerge(int numOutputCentroids, double totalWeight, double 
compression) {
+    double[] temporary = _centroidMeans;
+    _centroidMeans = _outputMeans;
+    _outputMeans = temporary;
+    temporary = _centroidWeights;
+    _centroidWeights = _outputWeights;
+    _outputWeights = temporary;
+    _numCentroids = numOutputCentroids;
+    _totalWeight = totalWeight;
+    _publiclyCompressed = compression == _compression;
+  }
+
+  private void ensureIncomingCapacity(int capacity) {
+    if (_incomingMeans == null || capacity > _incomingMeans.length) {
+      int newCapacity = _incomingMeans == null
+          ? Math.max(capacity, Math.min(_centroidCapacity, 
_pendingCentroidCapacity))
+          : Math.max(capacity, (int) Math.min(_pendingCentroidCapacity,
+              (long) _incomingMeans.length * 
TDigestUtils.DEFAULT_MERGE_BUFFER_MULTIPLIER));
+      _incomingMeans = _incomingMeans == null ? new double[newCapacity] : 
Arrays.copyOf(_incomingMeans, newCapacity);
+      _incomingWeights =
+          _incomingWeights == null ? new double[newCapacity] : 
Arrays.copyOf(_incomingWeights, newCapacity);
+    }
+  }
+
+  private void stableSortIncoming(int count) {
+    double[] sourceMeans = _incomingMeans;
+    double[] sourceWeights = _incomingWeights;
+    double[] destinationMeans = _sortedIncomingMeans;
+    double[] destinationWeights = _sortedIncomingWeights;
+    for (int width = 1; width < count; width *= 2) {
+      for (int start = 0; start < count; start += 2 * width) {
+        int middle = Math.min(start + width, count);
+        int end = Math.min(start + 2 * width, count);
+        int left = start;
+        int right = middle;
+        int output = start;
+        while (left < middle && right < end) {
+          // Equal means keep their input order, including equal signed zeros.
+          int source = sourceMeans[left] <= sourceMeans[right] ? left++ : 
right++;
+          destinationMeans[output] = sourceMeans[source];
+          destinationWeights[output++] = sourceWeights[source];
+        }
+        int remaining = left < middle ? middle - left : end - right;
+        int source = left < middle ? left : right;
+        System.arraycopy(sourceMeans, source, destinationMeans, output, 
remaining);
+        System.arraycopy(sourceWeights, source, destinationWeights, output, 
remaining);
+      }
+      double[] temporary = sourceMeans;
+      sourceMeans = destinationMeans;
+      destinationMeans = temporary;
+      temporary = sourceWeights;
+      sourceWeights = destinationWeights;
+      destinationWeights = temporary;
+    }
+    _incomingMeans = sourceMeans;
+    _incomingWeights = sourceWeights;
+    _sortedIncomingMeans = destinationMeans;
+    _sortedIncomingWeights = destinationWeights;
+  }
+
+  private void ensureSortedIncomingCapacity(int capacity) {
+    if (_sortedIncomingMeans == null || capacity > 
_sortedIncomingMeans.length) {
+      int newCapacity = _sortedIncomingMeans == null
+          ? Math.max(capacity, Math.min(_centroidCapacity, 
_pendingCentroidCapacity))
+          : Math.max(capacity, Math.multiplyExact(_sortedIncomingMeans.length, 
2));
+      _sortedIncomingMeans = new double[newCapacity];
+      _sortedIncomingWeights = new double[newCapacity];
+    }
+  }
+
+  private void bufferIncomingCentroid(double mean, double weight) {
+    checkTotalWeight(_totalWeight + _incomingWeight + _numRawValues + weight);
+    if (_numRawValues + _numIncomingCentroids == getPendingInputLimit()) {
+      flush();
+    }
+    ensureIncomingCapacity(_numIncomingCentroids + 1);
+    if (_incomingCentroidsSorted && _numIncomingCentroids > 0
+        && mean < _incomingMeans[_numIncomingCentroids - 1]) {
+      _incomingCentroidsSorted = false;
+    }
+    _incomingMeans[_numIncomingCentroids] = mean;
+    _incomingWeights[_numIncomingCentroids] = weight;
+    _numIncomingCentroids++;
+    _incomingWeight += weight;
+  }
+
+  private void bufferIncomingCentroids(double[] means, double[] weights, int 
count) {
+    int offset = 0;
+    while (offset < count) {
+      if (_numRawValues + _numIncomingCentroids == getPendingInputLimit()) {
+        flush();
+      }
+      int copied = Math.min(count - offset,
+          getPendingInputLimit() - _numRawValues - _numIncomingCentroids);
+      int existingCount = _numIncomingCentroids;
+      int combinedCount = Math.addExact(existingCount, copied);
+      if (existingCount == 0 || !_incomingCentroidsSorted) {
+        ensureIncomingCapacity(combinedCount);
+        System.arraycopy(means, offset, _incomingMeans, existingCount, copied);
+        System.arraycopy(weights, offset, _incomingWeights, existingCount, 
copied);
+      } else {
+        ensureIncomingCapacity(combinedCount);
+        int existingIndex = existingCount - 1;
+        int addedIndex = offset + copied - 1;
+        int outputIndex = combinedCount - 1;
+        while (existingIndex >= 0 && addedIndex >= offset) {
+          // Choose the added centroid on equality while merging backwards so 
existing equal centroids retain stable
+          // order before the newly added run.
+          if (_incomingMeans[existingIndex] > means[addedIndex]) {
+            _incomingMeans[outputIndex] = _incomingMeans[existingIndex];
+            _incomingWeights[outputIndex--] = 
_incomingWeights[existingIndex--];
+          } else {
+            _incomingMeans[outputIndex] = means[addedIndex];
+            _incomingWeights[outputIndex--] = weights[addedIndex--];
+          }
+        }
+        if (addedIndex >= offset) {
+          int remaining = addedIndex - offset + 1;
+          System.arraycopy(means, offset, _incomingMeans, 0, remaining);
+          System.arraycopy(weights, offset, _incomingWeights, 0, remaining);
+        }
+      }
+      for (int i = 0; i < copied; i++) {
+        _incomingWeight += weights[offset + i];
+      }
+      offset += copied;
+      _numIncomingCentroids = combinedCount;
+    }
+  }
+
+  private void materializePendingSerializedTDigest() {
+    if (_pendingSerializedTDigest != null && !_legacyDegraded) {
+      _serializedBytesForWrite = null;
+      byte[] bytes = _pendingSerializedTDigest;
+      SerializedTDigestMetadata metadata = _pendingSerializedMetadata;
+      _pendingSerializedTDigest = null;
+      _pendingSerializedMetadata = null;
+      SerializedTDigestInput input = getSerializedTDigestInput();
+      input.reset(bytes, metadata);
+      input._retainedBytes = bytes;
+      input.decode();
+      mergeSerializedTDigest(input, false);
+    }
+  }
+
+  private void markLegacyDegraded(SerializedTDigestInput input) {
+    if (!_legacyDegraded) {
+      LOGGER.warn("Retaining historical TDigest numerical corruption: input 
centroids={}, input weight={}, "
+              + "accumulated weight={}. Percentiles for this aggregation state 
are NaN.",
+          input._numCentroids, input._totalWeight, _totalWeight + 
_incomingWeight + _numRawValues);
+      _legacyDegraded = true;
+    }
+  }
+
+  private void ensureCentroidCapacity(int capacity) {
+    if (capacity > 0 && (_centroidMeans == null || capacity > 
_centroidMeans.length)) {
+      _centroidMeans = new double[capacity];
+      _centroidWeights = new double[capacity];
+    }
+  }
+
+  private void normalizeBoundaryCentroids() {
+    if (_numCentroids == 0 || (_centroidWeights[0] == 1.0
+        && _centroidWeights[_numCentroids - 1] == 1.0)) {
+      return;
+    }
+    int requiredCapacity = Math.addExact(_numCentroids, 2);
+    if (_centroidMeans.length < requiredCapacity) {
+      _centroidMeans = Arrays.copyOf(_centroidMeans, requiredCapacity);
+      _centroidWeights = Arrays.copyOf(_centroidWeights, requiredCapacity);
+    }
+    _numCentroids = normalizeBoundaries(_centroidMeans, _centroidWeights, 
_numCentroids, _min, _max);
+  }
+
+  private static int normalizeBoundaries(double[] means, double[] weights, int 
count, double min, double max) {
+    if (count == 0 || (weights[0] == 1.0 && weights[count - 1] == 1.0)) {
+      return count;
+    }
+    if (count == 1) {
+      double weight = weights[0];
+      if (weight < 2.0) {
+        return count;
+      }
+      double mean = means[0];
+      means[0] = min;
+      weights[0] = 1.0;
+      if (weight == 2.0) {
+        means[1] = max;
+        weights[1] = 1.0;
+        return 2;
+      }
+      means[1] = residualMean(mean, weight, min, max, weight - 2.0, min, max);
+      weights[1] = weight - 2.0;
+      means[2] = max;
+      weights[2] = 1.0;
+      return 3;
+    }
+
+    if (weights[0] > 1.0) {
+      System.arraycopy(means, 1, means, 2, count - 1);
+      System.arraycopy(weights, 1, weights, 2, count - 1);
+      double weight = weights[0];
+      double mean = means[0];
+      means[0] = min;
+      weights[0] = 1.0;
+      means[1] = residualMean(mean, weight, min, 0.0, weight - 1.0, min, 
means[2]);
+      weights[1] = weight - 1.0;
+      count++;
+    }
+    int lastIndex = count - 1;
+    if (weights[lastIndex] > 1.0) {
+      double weight = weights[lastIndex];
+      double mean = means[lastIndex];
+      means[lastIndex] = residualMean(mean, weight, max, 0.0, weight - 1.0, 
means[lastIndex - 1], max);
+      weights[lastIndex] = weight - 1.0;
+      means[count] = max;
+      weights[count] = 1.0;
+      count++;
+    }
+    return count;
+  }
+
+  private void ensureRawBuffer() {
+    if (_rawValues == null) {
+      _rawValues = new double[getRawBufferSize((long) 
Math.ceil(_compression))];
+    }
+  }
+
+  private static int getRawBufferSize(long roundedCompression) {

Review Comment:
   Fixed in 
[d27edc192f](https://github.com/apache/pinot/commit/d27edc192f9440dd7bd2c15a56d44cb1e250a84f).
 Legacy ingestion now grows raw storage toward the historical 5 x main-capacity 
buffer, including the pending budget and scalar/bulk paths: compression 100 
reaches 1,050 slots and compression 10,000 reaches 100,050. Growth is lazy, 
including extreme legacy compression, and existing tests pin both flush 
thresholds. Query/reduction buffering keeps its bounded policy; this restores 
merge frequency without claiming an unmeasured throughput improvement.



##########
pinot-core/src/main/java/org/apache/pinot/core/query/aggregation/function/PercentileTDigestAggregationFunction.java:
##########
@@ -327,7 +328,7 @@ public Double extractFinalResult(@Nullable TDigest 
intermediateResult) {
     // A null intermediate result means nothing was aggregated, and so does an 
empty digest, which is what a
     // deserialized peer can still carry. With null handling enabled the 
percentile of nothing is NULL; with it
     // disabled it is what `quantile` returns for an empty digest, which is 
NaN.
-    if (intermediateResult == null || intermediateResult.size() == 0L) {
+    if (intermediateResult == null || intermediateResult.isEmpty()) {

Review Comment:
   Fixed in 
[d27edc192f](https://github.com/apache/pinot/commit/d27edc192f9440dd7bd2c15a56d44cb1e250a84f).
 Expanded the existing zero-total-weight corrupt-byte regression to both 
null-handling modes and both merge orders, with an actual empty digest as the 
control. It verifies NaN for the unknown distribution, SQL NULL only for an 
actual empty state when enabled, unchanged healthy mass after the rejected 
merge, and exact retention of corrupt bytes. Added the explicit upgrade 
behavior to compatibility-verifier/README.md.



##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/aggregator/PercentileTDigestValueAggregator.java:
##########
@@ -592,98 +601,77 @@ private void invalidateCaches() {
       _serializedBytes = null;
     }
 
-    private static void appendInfinityCentroids(List<Centroid> centroids, 
double value, long weight,
+    private static void appendInfinityCentroids(List<Centroid> centroids, 
double value, double weight,
         boolean unitWeightAtStart, boolean unitWeightAtEnd) {
       appendCentroids(centroids, value, weight, unitWeightAtStart, 
unitWeightAtEnd);
     }
 
-    private static void appendCentroids(List<Centroid> centroids, double 
value, long weight,
+    private static void appendCentroids(List<Centroid> centroids, double 
value, double weight,

Review Comment:
   Fixed in 
[d27edc192f](https://github.com/apache/pinot/commit/d27edc192f9440dd7bd2c15a56d44cb1e250a84f).
 List construction, primitive array writing and centroid counting now delegate 
to one primitive splitting helper. Counting allocates no temporary arrays or 
centroid objects; 144 boundary-weight/flag/sign comparisons preserve the 
previous split exactly, and the existing registered-size tests pass.



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