xiangfu0 commented on code in PR #19795:
URL: https://github.com/apache/pinot/pull/19795#discussion_r4236363656


##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/PercentileTDigestAccumulator.java:
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@@ -0,0 +1,1498 @@
+/**
+ * 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.tdigest;
+
+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.customobject.tdigest.TDigestCodec.SerializedTDigestMetadata;
+
+
+
+/// 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.
+/// Unchanged historical fractional boundaries retain their original bytes, 
including when configured compression
+/// differs. After a merge, inherited fractional endpoints retain precise 
verbose weights and finite statistics when
+/// unit endpoints cannot preserve their mass. These keep the historical 
t-digest 3.3 assertion-enabled reader and
+/// recompression limitation. Newly introduced unsupported fractional 
endpoints are rejected.
+///
+/// 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 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 double _historicalFractionalMinMean = Double.NaN;
+  private double _historicalFractionalMaxMean = Double.NaN;
+  private SerializedTDigestMetadata _pendingSerializedMetadata;
+  private boolean _legacyDegraded;
+  private boolean _hasFractionalWeights;
+
+  private int _numRawValues;
+  private int _numCentroids;
+  private int _numIncomingCentroids;
+  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) {
+    TDigestCodec.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 = TDigestCodec.getDefaultCentroidCapacity(_compression);
+    _pendingCentroidCapacity = getPendingCentroidCapacity(_centroidCapacity, 
useTwoLevelRawCompression);
+    if (allocateRawBuffer) {
+      _rawValues = new double[getInitialRawBufferSize(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);
+  }
+
+  /// Reads and retains one legacy digest, preserving the general aggregation 
compression policy.
+  public static PercentileTDigestAccumulator fromBytes(byte[] bytes) {
+    return fromBytes(ByteBuffer.wrap(bytes));
+  }
+
+  /// Reads one payload and advances the buffer past it.
+  public static PercentileTDigestAccumulator fromBytes(ByteBuffer bytes) {
+    SerializedTDigestInput input = new SerializedTDigestInput();
+    input.reset(bytes);
+    return fromBytes(input);
+  }
+
+  /// Retains an already validated input without rescanning its centroid bytes.
+  public static PercentileTDigestAccumulator fromBytes(SerializedTDigestInput 
input) {
+    PercentileTDigestAccumulator digest = 
forLegacyAggregation(input.getCompression());
+    digest.addSerializedTDigest(input);
+    return digest;
+  }
+
+  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 {
+      if (sorted && positiveCount == count) {
+        bufferIncomingCentroids(means, weights, count, totalWeight, min, max);
+      } else {
+        // Caller-owned arrays are copied only when filtering or sorting is 
necessary.
+        double[] sortedMeans = new double[positiveCount];
+        double[] sortedWeights = new double[positiveCount];
+        int index = 0;
+        for (int i = 0; i < count; i++) {
+          if (weights[i] > 0.0) {
+            sortedMeans[index] = means[i];
+            sortedWeights[index++] = weights[i];
+          }
+        }
+        if (!sorted) {
+          sortCentroids(sortedMeans, sortedWeights, positiveCount);
+        }
+        bufferIncomingCentroids(sortedMeans, sortedWeights, positiveCount, 
totalWeight, min, max);
+      }
+      _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();
+    while (from < toExclusive) {
+      ensureRawBuffer();
+      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
+          && (!_useTwoLevelRawCompression || _rawValues.length == 
_pendingCentroidCapacity)
+          || _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) {
+    if (other.hasValidStatistics() && other.getTotalWeight() == 0.0) {
+      return;
+    }
+    requireMutable();
+    if (other instanceof PercentileTDigestAccumulator) {
+      addAccumulator((PercentileTDigestAccumulator) other);
+      return;
+    }
+    if (!other.hasValidStatistics()) {
+      materializePendingSerializedTDigest();
+      SerializedTDigestInput input = getSerializedTDigestInput();
+      input.reset(ByteBuffer.wrap(other.serialize()), false);
+      addSerializedTDigest(input);
+      return;
+    }
+    double otherWeight = other.getTotalWeight();
+    checkTotalWeight(getTotalWeight() + otherWeight);
+    Collection<Centroid> centroids = other.centroids();
+    double[] means = new double[centroids.size()];
+    double[] weights = new double[means.length];
+    int count = 0;
+    for (Centroid centroid : 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");
+      }
+      means[count] = centroid.mean();
+      weights[count++] = weight;
+    }
+    // Validate all generic centroids before changing the target, then use the 
same whole-source primitive path.
+    addCentroids(means, weights, count, other.getMin(), other.getMax(), false);
+    inheritHistoricalFractionalBoundaries(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 && 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;
+    inheritHistoricalFractionalBoundaries(other._historicalFractionalMinMean, 
other._historicalFractionalMaxMean);
+    bufferIncomingCentroids(other._centroidMeans, other._centroidWeights, 
other._numCentroids, other._totalWeight,
+        other._min, other._max);
+    if (other._totalWeight > 0.0) {
+      _originalFractionalBytes = null;
+    }
+    _min = Math.min(_min, other._min);
+    _max = Math.max(_max, other._max);
+  }
+
+  public void addSerializedTDigest(byte[] bytes) {
+    if (_legacyDegraded) {
+      SerializedTDigestInput input = getSerializedTDigestInput();
+      input.reset(bytes);
+      addSerializedTDigest(input);
+      return;
+    }
+    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) {
+    if (ignoreEmptyInputForDegradedState(input)) {
+      return;
+    }
+    requireMutable();
+    if (prepareSerializedTDigest(input)) {
+      mergeSerializedTDigest(input, false);
+    }
+  }
+
+  public void addSerializedTDigestDirect(SerializedTDigestInput input) {
+    if (ignoreEmptyInputForDegradedState(input)) {
+      return;
+    }
+    requireMutable();
+    if (prepareSerializedTDigest(input)) {
+      mergeSerializedTDigest(input, true);
+    }
+  }
+
+  private boolean ignoreEmptyInputForDegradedState(SerializedTDigestInput 
input) {
+    if (!_legacyDegraded) {
+      return false;
+    }
+    input.inspectMetadata();
+    return !input._metadata.needsLegacyFallback() && 
input._metadata.totalWeight() == 0.0;
+  }
+
+  private boolean prepareSerializedTDigest(SerializedTDigestInput input) {
+    if (_pendingSerializedTDigest == null && hasNoInputs()) {
+      input.inspectMetadata();
+      _hasFractionalWeights |= input._metadata.fractionalWeights();
+      _pendingSerializedTDigest = input.retainBytes();
+      _pendingSerializedMetadata = input._metadata;
+      if (input.recordHistoricalFractionalBoundaries(this)) {
+        // Alias the retained snapshot; historical fractional bytes remain 
byte-exact after read-only materialization.
+        _originalFractionalBytes = _pendingSerializedTDigest;
+      }
+      if (input._metadata.needsLegacyFallback()) {
+        _legacyDegraded = true;
+      }
+      return false;
+    }
+    materializePendingSerializedTDigest();
+    input.decode();
+    if (input._metadata.needsLegacyFallback()) {
+      if (hasNoInputs()) {
+        _pendingSerializedTDigest = input.retainBytes();
+        _pendingSerializedMetadata = input._metadata;
+        _legacyDegraded = true;
+        return false;
+      }
+      throw corruptedMutation();
+    }
+    checkTotalWeight(_totalWeight + _incomingWeight + _numRawValues + 
input._metadata.totalWeight());
+    input.recordHistoricalFractionalBoundaries(this);
+    if (input._metadata.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._metadata.totalWeight() == 0.0) {
+      return;
+    }
+    if (hasNoInputs()) {
+      if (input._metadata.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._metadata.totalWeight();
+        _min = input._metadata.min();
+        _max = input._metadata.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._metadata.compression();
+      }
+      return;
+    }
+    if (direct) {
+      flush();
+      boolean runBackwards = (_mergeCount++ & 1) != 0;
+      if (!mergeSorted(input._means, input._weights, input._numCentroids, 
input._metadata.totalWeight(),
+          getIncrementalCompression(), runBackwards)) {
+        return;
+      }
+    } else {
+      bufferIncomingCentroids(input._means, input._weights, 
input._numCentroids, input._metadata.totalWeight(),
+          input._metadata.min(), input._metadata.max());
+    }
+    _min = Math.min(_min, input._metadata.min());
+    _max = Math.max(_max, input._metadata.max());
+  }
+
+  @Override
+  public void compress() {
+    if (_legacyDegraded) {
+      return;
+    }
+    materializePendingSerializedTDigest();
+    if (_numRawValues > 0 || _numIncomingCentroids > 0) {
+      // SQL reduction combines pending values and existing centroids directly 
at public compression, matching
+      // MergingDigest 3.3. Its writer avoids an extra working-compression 
pass that can increase reducer rank error.
+      flush(_compression);
+      _publiclyCompressed = true;
+    } else if (!_publiclyCompressed && _numCentroids > 0) {
+      recompressCentroids(_compression);
+      _publiclyCompressed = true;
+    }
+  }
+
+  @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 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 = 
TDigestCodec.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() == 
TDigestCodec.VERBOSE_CENTROID_SIZE
+            ? encoded.getDouble() : encoded.getFloat();
+        double mean = metadata.centroidSize() == 
TDigestCodec.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;
+  }
+
+  /// Bounds compatible output without flushing. Unchanged historical bytes 
and pending compact capacities can
+  /// exceed the newly encoded legacy-capacity bound and retain their actual 
length.
+  @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 = 
TDigestCodec.getMaxLegacyCompatibleByteSize(_compression, centroidCount);
+    return _pendingSerializedTDigest != null && 
_pendingSerializedMetadata.encoding() == TDigestCodec.SMALL_ENCODING

Review Comment:
   **[correctness] `maxSerializedByteSize()` under-reports for healthy VERBOSE 
pending payloads whose encoded compression exceeds the accumulator 
compression.**
   
   Only SMALL-encoded pending payloads are `Math.max`ed with the retained byte 
length, but `serialize()` passes healthy verbose pending bytes through 
unchanged at the *source* compression capacity.
   
   Verified by execution: serialize a compression-1000 digest (9536 bytes 
verbose), then `forLegacyAggregation(10).addSerializedTDigest(bytes)` (the 
state `mergeWithConfiguredCompression` creates before `compress()`): 
`maxSerializedByteSize()` returns 512 (bound from `_compression=10`) while 
`serialize()` returns the retained 9536-byte payload — an 18x under-report. The 
same violation reproduces with compressions 10 vs 100 (512 vs 1632). It 
propagates through `NonFiniteAwareTDigest.maxSerializedByteSize()` and 
`PercentileTDigestValueAggregator.updateMaxByteSize()` (star-tree forward-index 
sizing), so a consumer sizing a fixed slot from 
`getMaxAggregatedValueByteSize()` before the post-serialize max-in 
under-allocates.
   
   Suggested fix: also `Math.max` with `_pendingSerializedTDigest.length` for 
VERBOSE pending payloads (or whenever `_pendingSerializedMetadata.compression() 
!= _compression`).



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