xiangfu0 commented on code in PR #19795:
URL: https://github.com/apache/pinot/pull/19795#discussion_r4248116940


##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/TDigestCodec.java:
##########
@@ -0,0 +1,850 @@
+/**
+ * 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.lang.invoke.MethodHandles;
+import java.lang.invoke.VarHandle;
+import java.nio.BufferUnderflowException;
+import java.nio.ByteBuffer;
+import java.nio.ByteOrder;
+import java.util.Arrays;
+
+/// Compatibility helpers for the serialized t-digest format shared by 
t-digest 3.2 and 3.3.
+///
+/// Version 3.3 requires the first and last centroid to have unit weight 
whenever a digest is recompressed. Version
+/// 3.2 did not maintain that invariant, so an otherwise valid 3.2 digest can 
fail an assertion after being read by
+/// 3.3. Pure reads retain the legacy weighted boundary centroids. Adjacent 
equal means use Pinot's point-mass
+/// interpolation, so quantile/CDF values can change on unchanged bytes, 
including intervals next to a plateau.
+/// Mutation and serialization repair their boundaries only when unit 
endpoints can preserve their total weight and
+/// first moment; otherwise unchanged historical bytes remain readable and 
mutation fails explicitly.
+/// Serialization uses the compact form when 3.3's larger low-compression 
centroid buffer would not fit in a 3.2
+/// default buffer and every centroid is exactly representable in that format. 
Otherwise, it merges the nearest
+/// interior centroids until the verbose representation fits the 3.2 capacity. 
This keeps intermediate values readable
+/// in both directions during a rolling upgrade without silently narrowing 
double-precision values to floats.
+///
+/// Pinot owns the in-memory K1 implementation and retains these legacy bytes 
for stored columns and mixed-version
+/// intermediate results. Decoding checks lengths and numerical state before 
allocating centroid arrays.
+/// NaN means at an identifiable infinite tail are restored to that infinite 
bound without changing their weights.
+/// Other poisoned states remain byte-readable with NaN statistics because 
their distribution cannot be recovered.
+/// They retain their original bytes; attempting to mutate them or mix them 
with another distribution fails explicitly.
+/// Opaque poisoned payloads retain their original centroids even if an old 
reader's default array cannot hold them;
+/// these historical exceptions remain readable by Pinot, but are not 
guaranteed to survive a reverse upgrade.
+/// Historical fractional boundary masses below one, and singleton masses 
between one and two, retain their original
+/// bytes. Fresh serialization rejects these boundaries: t-digest 3.3's 
unit-endpoint assertion cannot be satisfied
+/// without changing their mass. Fractional interior weights remain supported.
+public final class TDigestCodec {
+  public static final int VERBOSE_ENCODING = 1;
+  public static final int SMALL_ENCODING = 2;
+  private static final int LEGACY_CAPACITY_PADDING = 10;
+  public static final int VERBOSE_HEADER_SIZE = 32;
+  public static final int VERBOSE_CENTROID_SIZE = 16;
+  public static final int SMALL_HEADER_SIZE = 30;
+  public static final int SMALL_CENTROID_SIZE = 8;
+  public static final int DEFAULT_MERGE_BUFFER_MULTIPLIER = 5;
+
+  private TDigestCodec() {
+  }
+
+  /// Reads the compression from a validated header without decoding centroid 
arrays.
+  public static double readCompression(byte[] bytes) {
+    return readSerializedHeader(ByteBuffer.wrap(bytes)).compression();
+  }
+
+  /// Rejects non-finite compression while retaining the legacy clamping of 
finite settings below ten.
+  public static void validateCompression(double compression) {
+    if (!Double.isFinite(compression)) {

Review Comment:
   Behavior change vs. the previous release: `validateCompression` only rejects 
non-finite values, and `normalizeCompression`/the accumulator clamp anything 
below 10. `PERCENTILETDIGEST(col, 95, 0)` previously failed fast with 
`IllegalArgumentException("TDigest compression must be positive: 0")`; it now 
silently executes at compression 10 (AggregationFunctionFactory only checks 
`compressionFactor >= 0`, so 0 reaches here). This restores tdunning's silent 
clamping, which may well be intended — but it deserves a release note, or a `> 
0` check at the query layer so user typos still fail fast.



##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/TDigestCodec.java:
##########
@@ -0,0 +1,850 @@
+/**
+ * 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.lang.invoke.MethodHandles;
+import java.lang.invoke.VarHandle;
+import java.nio.BufferUnderflowException;
+import java.nio.ByteBuffer;
+import java.nio.ByteOrder;
+import java.util.Arrays;
+
+/// Compatibility helpers for the serialized t-digest format shared by 
t-digest 3.2 and 3.3.
+///
+/// Version 3.3 requires the first and last centroid to have unit weight 
whenever a digest is recompressed. Version
+/// 3.2 did not maintain that invariant, so an otherwise valid 3.2 digest can 
fail an assertion after being read by
+/// 3.3. Pure reads retain the legacy weighted boundary centroids. Adjacent 
equal means use Pinot's point-mass
+/// interpolation, so quantile/CDF values can change on unchanged bytes, 
including intervals next to a plateau.
+/// Mutation and serialization repair their boundaries only when unit 
endpoints can preserve their total weight and
+/// first moment; otherwise unchanged historical bytes remain readable and 
mutation fails explicitly.
+/// Serialization uses the compact form when 3.3's larger low-compression 
centroid buffer would not fit in a 3.2
+/// default buffer and every centroid is exactly representable in that format. 
Otherwise, it merges the nearest
+/// interior centroids until the verbose representation fits the 3.2 capacity. 
This keeps intermediate values readable
+/// in both directions during a rolling upgrade without silently narrowing 
double-precision values to floats.
+///
+/// Pinot owns the in-memory K1 implementation and retains these legacy bytes 
for stored columns and mixed-version
+/// intermediate results. Decoding checks lengths and numerical state before 
allocating centroid arrays.
+/// NaN means at an identifiable infinite tail are restored to that infinite 
bound without changing their weights.
+/// Other poisoned states remain byte-readable with NaN statistics because 
their distribution cannot be recovered.
+/// They retain their original bytes; attempting to mutate them or mix them 
with another distribution fails explicitly.
+/// Opaque poisoned payloads retain their original centroids even if an old 
reader's default array cannot hold them;
+/// these historical exceptions remain readable by Pinot, but are not 
guaranteed to survive a reverse upgrade.
+/// Historical fractional boundary masses below one, and singleton masses 
between one and two, retain their original
+/// bytes. Fresh serialization rejects these boundaries: t-digest 3.3's 
unit-endpoint assertion cannot be satisfied
+/// without changing their mass. Fractional interior weights remain supported.
+public final class TDigestCodec {
+  public static final int VERBOSE_ENCODING = 1;
+  public static final int SMALL_ENCODING = 2;
+  private static final int LEGACY_CAPACITY_PADDING = 10;
+  public static final int VERBOSE_HEADER_SIZE = 32;
+  public static final int VERBOSE_CENTROID_SIZE = 16;
+  public static final int SMALL_HEADER_SIZE = 30;
+  public static final int SMALL_CENTROID_SIZE = 8;
+  public static final int DEFAULT_MERGE_BUFFER_MULTIPLIER = 5;
+
+  private TDigestCodec() {
+  }
+
+  /// Reads the compression from a validated header without decoding centroid 
arrays.
+  public static double readCompression(byte[] bytes) {
+    return readSerializedHeader(ByteBuffer.wrap(bytes)).compression();
+  }
+
+  /// Rejects non-finite compression while retaining the legacy clamping of 
finite settings below ten.
+  public static void validateCompression(double compression) {
+    if (!Double.isFinite(compression)) {
+      throw new IllegalArgumentException("Invalid TDigest compression: " + 
compression);
+    }
+  }
+
+  /// Applies the legacy minimum compression to query, ingestion and 
serialized-header settings.
+  public static double normalizeCompression(double compression) {
+    validateCompression(compression);
+    return Math.max(compression, 10.0);
+  }
+
+  /// Writes validated centroid arrays in the standard verbose encoding 
without sorting or recompression.
+  /// The caller retains the arrays; only the first `count` entries are 
written, with normalized compression.
+  public static byte[] serializeCentroids(double compression, double min, 
double max, double[] means,
+      double[] weights, int count) {
+    if (count < 0 || count > means.length || count > weights.length) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count: " + 
count);
+    }
+    ByteBuffer encoded = ByteBuffer.allocate(Math.addExact(VERBOSE_HEADER_SIZE,
+        Math.multiplyExact(VERBOSE_CENTROID_SIZE, count)));
+    
encoded.putInt(VERBOSE_ENCODING).putDouble(min).putDouble(max).putDouble(normalizeCompression(compression));
+    encoded.putInt(count);
+    for (int i = 0; i < count; i++) {
+      encoded.putDouble(weights[i]).putDouble(means[i]);
+    }
+    return encoded.array();
+  }
+
+  /// Encodes validated, sorted native centroids and selects a 
legacy-compatible representation.
+  static byte[] serializeCompatibleCentroids(double compression, double min, 
double max, double[] means,
+      double[] weights, int count, boolean inheritedFractionalBoundaries) {
+    if (count < 0 || count > 0 && (count > means.length || count > 
weights.length || !(min <= max))) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count or 
extrema");
+    }
+    ByteBuffer buffer = ByteBuffer.allocate(
+        Math.addExact(VERBOSE_HEADER_SIZE,
+            Math.multiplyExact(VERBOSE_CENTROID_SIZE, count)));
+    buffer.putInt(VERBOSE_ENCODING);
+    buffer.putDouble(min);
+    buffer.putDouble(max);
+    buffer.putDouble(compression);
+    buffer.putInt(count);
+    double encodedWeight = 0.0;
+    boolean hasNonFiniteMeans = false;
+    boolean fractionalWeights = false;
+    for (int i = 0; i < count; i++) {
+      if (!(weights[i] > 0.0) || !Double.isFinite(weights[i]) || !(means[i] >= 
min && means[i] <= max)) {
+        throw new IllegalArgumentException("Invalid TDigest centroid");
+      }
+      buffer.putDouble(weights[i]);
+      buffer.putDouble(means[i]);
+      encodedWeight += weights[i];
+      hasNonFiniteMeans |= !Double.isFinite(means[i]);
+      fractionalWeights |= weights[i] != Math.rint(weights[i]);
+    }
+    if (!Double.isFinite(encodedWeight)) {
+      throw new IllegalArgumentException("TDigest total weight exceeds the 
supported range");
+    }
+    boolean weightedBoundaries = count == 1 ? weights[0] >= 2.0
+        : count > 1 && (weights[0] > 1.0 || weights[count - 1] > 1.0);
+    // Collect exact wire metadata during the write rather than decoding and 
validating our fresh bytes again.
+    SerializedTDigestMetadata metadata = new 
SerializedTDigestMetadata(VERBOSE_ENCODING, min, max,
+        compression, count,
+        VERBOSE_HEADER_SIZE, VERBOSE_CENTROID_SIZE, buffer.capacity(), 
encodedWeight,
+        hasNonFiniteMeans, false, false, fractionalWeights, 
weightedBoundaries, false, compression, Double.NaN,
+        Double.NaN, Double.NaN);
+    return makeLegacyCompatible(buffer.array(), metadata, 
inheritedFractionalBoundaries);
+  }
+
+  /// Rejects fresh boundary masses that legacy readers cannot recompress 
without inventing mass.
+  /// Call after boundary normalization and removing zero-weight centroids; 
fractional interior mass is supported.
+  static void checkLegacyBoundaryWeights(int count, double firstWeight, double 
lastWeight) {
+    if (count > 0 && (firstWeight < 1.0 || lastWeight < 1.0
+        || count == 1 && firstWeight != 1.0 && firstWeight < 2.0)) {
+      throw new IllegalArgumentException("Cannot serialize fractional TDigest 
boundary mass for legacy readers");
+    }
+  }
+
+  /// Allows only unsupported endpoint means inherited from a validated legacy 
source. This is shared by native,
+  /// enclosing and generic writers; new fractional global extrema do not 
receive the historical exception.
+  /// Exact equality is intentional: endpoint repair preserves these means, 
and admitting nearby means would grant
+  /// the exception to fresh extrema. Fresh fractional input at or beyond a 
recorded endpoint permanently excludes
+  /// that endpoint, even if its historical mass was merged away or the new 
weight equals the historical weight.
+  static boolean hasInheritedFractionalBoundaryEncoding(TDigest source, int 
count, double firstMean,
+      double firstWeight, double lastMean, double lastWeight) {
+    if (count <= 0 || !source.hasValidStatistics() || !(firstWeight > 0.0) || 
!(lastWeight > 0.0)
+        || !Double.isFinite(firstWeight) || !Double.isFinite(lastWeight)) {
+      return false;
+    }
+    boolean singleton = count == 1 && firstWeight != 1.0 && firstWeight < 2.0;
+    boolean firstUnsupported = firstWeight < 1.0 || singleton;
+    boolean lastUnsupported = lastWeight < 1.0 || singleton;
+    return (firstUnsupported || lastUnsupported)
+        && (!firstUnsupported || firstMean == 
source.getHistoricalFractionalBoundaryMean(true)
+            && !(source.getFreshFractionalBoundaryMean(true) <= firstMean))
+        && (!lastUnsupported || lastMean == 
source.getHistoricalFractionalBoundaryMean(false)
+            && !(source.getFreshFractionalBoundaryMean(false) >= lastMean));
+  }
+
+  private static void checkSerializedBoundaryWeights(byte[] bytes, 
SerializedTDigestMetadata metadata) {
+    int count = metadata.centroidCount();
+    if (count > 0) {
+      ByteBuffer encoded = ByteBuffer.wrap(bytes);
+      int firstOffset = metadata.centroidOffset();
+      int lastOffset = firstOffset + (count - 1) * metadata.centroidSize();
+      double firstWeight = metadata.encoding() == VERBOSE_ENCODING
+          ? encoded.getDouble(firstOffset) : encoded.getFloat(firstOffset);
+      double lastWeight = metadata.encoding() == VERBOSE_ENCODING
+          ? encoded.getDouble(lastOffset) : encoded.getFloat(lastOffset);
+      checkLegacyBoundaryWeights(count, firstWeight, lastWeight);
+    }
+  }
+
+  /// Converts a verbose `MergingDigest` payload to a representation readable 
by t-digest 3.2 and 3.3.
+  ///
+  /// The input must use the standard verbose `MergingDigest` encoding. The 
returned payload stays verbose when it
+  /// already fits both legacy default capacities, uses compact encoding only 
when every narrowed field is exact, and
+  /// otherwise reduces interior centroids without narrowing doubles. 
Compression below ten is normalized in the
+  /// output header because the 3.2 verbose reader sizes its arrays from the 
raw header before applying that minimum.
+  /// Opaque degraded state is retained without reducing its unknown 
distribution, including over-capacity payloads.
+  /// Fresh fractional endpoints that legacy unit-boundary repair cannot 
represent are rejected without reweighting.
+  public static byte[] makeLegacyCompatible(byte[] verboseBytes) {
+    return makeLegacyCompatible(verboseBytes, 
inspectSerialized(ByteBuffer.wrap(verboseBytes), false));
+  }
+
+  /// Serializes an unchanged, independently retained payload using metadata 
validated at ingestion.
+  ///
+  /// The metadata must describe these exact bytes. This avoids another 
centroid validation walk for lazy digests.
+  public static byte[] makeLegacyCompatible(byte[] verboseBytes, 
SerializedTDigestMetadata metadata) {
+    return makeLegacyCompatible(verboseBytes, metadata, false);
+  }
+
+  /// Retains exact verbose weights for inherited historical fractional 
endpoints that cannot become unit endpoints.
+  /// All other compatibility checks apply. These payloads keep their 
historical assertion-enabled 3.3 read/merge
+  /// limitation; callers must establish inherited endpoint provenance before 
enabling this exception.
+  static byte[] makeLegacyCompatible(byte[] verboseBytes, 
SerializedTDigestMetadata metadata,
+      boolean inheritedFractionalBoundaries) {
+    if (metadata.encoding() != VERBOSE_ENCODING) {
+      throw new IllegalArgumentException("Expected verbose TDigest encoding");
+    }
+    if (metadata.needsLegacyFallback()) {
+      return verboseBytes;

Review Comment:
   The `needsLegacyFallback` early return skips both the sub-10 
compression-header normalization below and the capacity reduction. A degraded 
verbose payload whose raw header compression is < 10 and whose centroid count 
exceeds `2*ceil(rawCompression)+10` will throw ArrayIndexOutOfBoundsException 
in a t-digest 3.2-era reader, which sizes its arrays from the raw header before 
clamping. This is within the documented "not guaranteed to survive a reverse 
upgrade" carve-out, but the LegacyReader gate's `degraded-over-capacity` 
fixture doesn't cover the sub-10-header variant — worth adding a fixture so 
this failure mode stays characterized.



##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/TDigestCodec.java:
##########
@@ -0,0 +1,850 @@
+/**
+ * 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.lang.invoke.MethodHandles;
+import java.lang.invoke.VarHandle;
+import java.nio.BufferUnderflowException;
+import java.nio.ByteBuffer;
+import java.nio.ByteOrder;
+import java.util.Arrays;
+
+/// Compatibility helpers for the serialized t-digest format shared by 
t-digest 3.2 and 3.3.
+///
+/// Version 3.3 requires the first and last centroid to have unit weight 
whenever a digest is recompressed. Version
+/// 3.2 did not maintain that invariant, so an otherwise valid 3.2 digest can 
fail an assertion after being read by
+/// 3.3. Pure reads retain the legacy weighted boundary centroids. Adjacent 
equal means use Pinot's point-mass
+/// interpolation, so quantile/CDF values can change on unchanged bytes, 
including intervals next to a plateau.
+/// Mutation and serialization repair their boundaries only when unit 
endpoints can preserve their total weight and
+/// first moment; otherwise unchanged historical bytes remain readable and 
mutation fails explicitly.
+/// Serialization uses the compact form when 3.3's larger low-compression 
centroid buffer would not fit in a 3.2
+/// default buffer and every centroid is exactly representable in that format. 
Otherwise, it merges the nearest
+/// interior centroids until the verbose representation fits the 3.2 capacity. 
This keeps intermediate values readable
+/// in both directions during a rolling upgrade without silently narrowing 
double-precision values to floats.
+///
+/// Pinot owns the in-memory K1 implementation and retains these legacy bytes 
for stored columns and mixed-version
+/// intermediate results. Decoding checks lengths and numerical state before 
allocating centroid arrays.
+/// NaN means at an identifiable infinite tail are restored to that infinite 
bound without changing their weights.
+/// Other poisoned states remain byte-readable with NaN statistics because 
their distribution cannot be recovered.
+/// They retain their original bytes; attempting to mutate them or mix them 
with another distribution fails explicitly.
+/// Opaque poisoned payloads retain their original centroids even if an old 
reader's default array cannot hold them;
+/// these historical exceptions remain readable by Pinot, but are not 
guaranteed to survive a reverse upgrade.
+/// Historical fractional boundary masses below one, and singleton masses 
between one and two, retain their original
+/// bytes. Fresh serialization rejects these boundaries: t-digest 3.3's 
unit-endpoint assertion cannot be satisfied
+/// without changing their mass. Fractional interior weights remain supported.
+public final class TDigestCodec {
+  public static final int VERBOSE_ENCODING = 1;
+  public static final int SMALL_ENCODING = 2;
+  private static final int LEGACY_CAPACITY_PADDING = 10;
+  public static final int VERBOSE_HEADER_SIZE = 32;
+  public static final int VERBOSE_CENTROID_SIZE = 16;
+  public static final int SMALL_HEADER_SIZE = 30;
+  public static final int SMALL_CENTROID_SIZE = 8;
+  public static final int DEFAULT_MERGE_BUFFER_MULTIPLIER = 5;
+
+  private TDigestCodec() {
+  }
+
+  /// Reads the compression from a validated header without decoding centroid 
arrays.
+  public static double readCompression(byte[] bytes) {
+    return readSerializedHeader(ByteBuffer.wrap(bytes)).compression();
+  }
+
+  /// Rejects non-finite compression while retaining the legacy clamping of 
finite settings below ten.
+  public static void validateCompression(double compression) {
+    if (!Double.isFinite(compression)) {
+      throw new IllegalArgumentException("Invalid TDigest compression: " + 
compression);
+    }
+  }
+
+  /// Applies the legacy minimum compression to query, ingestion and 
serialized-header settings.
+  public static double normalizeCompression(double compression) {
+    validateCompression(compression);
+    return Math.max(compression, 10.0);
+  }
+
+  /// Writes validated centroid arrays in the standard verbose encoding 
without sorting or recompression.
+  /// The caller retains the arrays; only the first `count` entries are 
written, with normalized compression.
+  public static byte[] serializeCentroids(double compression, double min, 
double max, double[] means,
+      double[] weights, int count) {
+    if (count < 0 || count > means.length || count > weights.length) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count: " + 
count);
+    }
+    ByteBuffer encoded = ByteBuffer.allocate(Math.addExact(VERBOSE_HEADER_SIZE,
+        Math.multiplyExact(VERBOSE_CENTROID_SIZE, count)));
+    
encoded.putInt(VERBOSE_ENCODING).putDouble(min).putDouble(max).putDouble(normalizeCompression(compression));
+    encoded.putInt(count);
+    for (int i = 0; i < count; i++) {
+      encoded.putDouble(weights[i]).putDouble(means[i]);
+    }
+    return encoded.array();
+  }
+
+  /// Encodes validated, sorted native centroids and selects a 
legacy-compatible representation.
+  static byte[] serializeCompatibleCentroids(double compression, double min, 
double max, double[] means,
+      double[] weights, int count, boolean inheritedFractionalBoundaries) {
+    if (count < 0 || count > 0 && (count > means.length || count > 
weights.length || !(min <= max))) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count or 
extrema");
+    }
+    ByteBuffer buffer = ByteBuffer.allocate(
+        Math.addExact(VERBOSE_HEADER_SIZE,
+            Math.multiplyExact(VERBOSE_CENTROID_SIZE, count)));
+    buffer.putInt(VERBOSE_ENCODING);
+    buffer.putDouble(min);
+    buffer.putDouble(max);
+    buffer.putDouble(compression);
+    buffer.putInt(count);
+    double encodedWeight = 0.0;
+    boolean hasNonFiniteMeans = false;
+    boolean fractionalWeights = false;
+    for (int i = 0; i < count; i++) {
+      if (!(weights[i] > 0.0) || !Double.isFinite(weights[i]) || !(means[i] >= 
min && means[i] <= max)) {
+        throw new IllegalArgumentException("Invalid TDigest centroid");
+      }
+      buffer.putDouble(weights[i]);
+      buffer.putDouble(means[i]);
+      encodedWeight += weights[i];
+      hasNonFiniteMeans |= !Double.isFinite(means[i]);
+      fractionalWeights |= weights[i] != Math.rint(weights[i]);
+    }
+    if (!Double.isFinite(encodedWeight)) {
+      throw new IllegalArgumentException("TDigest total weight exceeds the 
supported range");
+    }
+    boolean weightedBoundaries = count == 1 ? weights[0] >= 2.0
+        : count > 1 && (weights[0] > 1.0 || weights[count - 1] > 1.0);
+    // Collect exact wire metadata during the write rather than decoding and 
validating our fresh bytes again.
+    SerializedTDigestMetadata metadata = new 
SerializedTDigestMetadata(VERBOSE_ENCODING, min, max,
+        compression, count,
+        VERBOSE_HEADER_SIZE, VERBOSE_CENTROID_SIZE, buffer.capacity(), 
encodedWeight,
+        hasNonFiniteMeans, false, false, fractionalWeights, 
weightedBoundaries, false, compression, Double.NaN,
+        Double.NaN, Double.NaN);
+    return makeLegacyCompatible(buffer.array(), metadata, 
inheritedFractionalBoundaries);
+  }
+
+  /// Rejects fresh boundary masses that legacy readers cannot recompress 
without inventing mass.
+  /// Call after boundary normalization and removing zero-weight centroids; 
fractional interior mass is supported.
+  static void checkLegacyBoundaryWeights(int count, double firstWeight, double 
lastWeight) {
+    if (count > 0 && (firstWeight < 1.0 || lastWeight < 1.0
+        || count == 1 && firstWeight != 1.0 && firstWeight < 2.0)) {
+      throw new IllegalArgumentException("Cannot serialize fractional TDigest 
boundary mass for legacy readers");
+    }
+  }
+
+  /// Allows only unsupported endpoint means inherited from a validated legacy 
source. This is shared by native,
+  /// enclosing and generic writers; new fractional global extrema do not 
receive the historical exception.
+  /// Exact equality is intentional: endpoint repair preserves these means, 
and admitting nearby means would grant
+  /// the exception to fresh extrema. Fresh fractional input at or beyond a 
recorded endpoint permanently excludes
+  /// that endpoint, even if its historical mass was merged away or the new 
weight equals the historical weight.
+  static boolean hasInheritedFractionalBoundaryEncoding(TDigest source, int 
count, double firstMean,
+      double firstWeight, double lastMean, double lastWeight) {
+    if (count <= 0 || !source.hasValidStatistics() || !(firstWeight > 0.0) || 
!(lastWeight > 0.0)
+        || !Double.isFinite(firstWeight) || !Double.isFinite(lastWeight)) {
+      return false;
+    }
+    boolean singleton = count == 1 && firstWeight != 1.0 && firstWeight < 2.0;
+    boolean firstUnsupported = firstWeight < 1.0 || singleton;
+    boolean lastUnsupported = lastWeight < 1.0 || singleton;
+    return (firstUnsupported || lastUnsupported)
+        && (!firstUnsupported || firstMean == 
source.getHistoricalFractionalBoundaryMean(true)
+            && !(source.getFreshFractionalBoundaryMean(true) <= firstMean))
+        && (!lastUnsupported || lastMean == 
source.getHistoricalFractionalBoundaryMean(false)
+            && !(source.getFreshFractionalBoundaryMean(false) >= lastMean));
+  }
+
+  private static void checkSerializedBoundaryWeights(byte[] bytes, 
SerializedTDigestMetadata metadata) {
+    int count = metadata.centroidCount();
+    if (count > 0) {
+      ByteBuffer encoded = ByteBuffer.wrap(bytes);
+      int firstOffset = metadata.centroidOffset();
+      int lastOffset = firstOffset + (count - 1) * metadata.centroidSize();
+      double firstWeight = metadata.encoding() == VERBOSE_ENCODING
+          ? encoded.getDouble(firstOffset) : encoded.getFloat(firstOffset);
+      double lastWeight = metadata.encoding() == VERBOSE_ENCODING
+          ? encoded.getDouble(lastOffset) : encoded.getFloat(lastOffset);
+      checkLegacyBoundaryWeights(count, firstWeight, lastWeight);
+    }
+  }
+
+  /// Converts a verbose `MergingDigest` payload to a representation readable 
by t-digest 3.2 and 3.3.
+  ///
+  /// The input must use the standard verbose `MergingDigest` encoding. The 
returned payload stays verbose when it
+  /// already fits both legacy default capacities, uses compact encoding only 
when every narrowed field is exact, and
+  /// otherwise reduces interior centroids without narrowing doubles. 
Compression below ten is normalized in the
+  /// output header because the 3.2 verbose reader sizes its arrays from the 
raw header before applying that minimum.
+  /// Opaque degraded state is retained without reducing its unknown 
distribution, including over-capacity payloads.
+  /// Fresh fractional endpoints that legacy unit-boundary repair cannot 
represent are rejected without reweighting.
+  public static byte[] makeLegacyCompatible(byte[] verboseBytes) {
+    return makeLegacyCompatible(verboseBytes, 
inspectSerialized(ByteBuffer.wrap(verboseBytes), false));
+  }
+
+  /// Serializes an unchanged, independently retained payload using metadata 
validated at ingestion.
+  ///
+  /// The metadata must describe these exact bytes. This avoids another 
centroid validation walk for lazy digests.
+  public static byte[] makeLegacyCompatible(byte[] verboseBytes, 
SerializedTDigestMetadata metadata) {
+    return makeLegacyCompatible(verboseBytes, metadata, false);
+  }
+
+  /// Retains exact verbose weights for inherited historical fractional 
endpoints that cannot become unit endpoints.
+  /// All other compatibility checks apply. These payloads keep their 
historical assertion-enabled 3.3 read/merge
+  /// limitation; callers must establish inherited endpoint provenance before 
enabling this exception.
+  static byte[] makeLegacyCompatible(byte[] verboseBytes, 
SerializedTDigestMetadata metadata,
+      boolean inheritedFractionalBoundaries) {
+    if (metadata.encoding() != VERBOSE_ENCODING) {
+      throw new IllegalArgumentException("Expected verbose TDigest encoding");
+    }
+    if (metadata.needsLegacyFallback()) {
+      return verboseBytes;
+    }
+    if (!Double.isNaN(metadata.recoveredInfinityMean())) {
+      double[] means = new double[metadata.centroidCount()];
+      double[] weights = new double[means.length];
+      decodeSerializedCentroids(ByteBuffer.wrap(verboseBytes), metadata, 
means, weights);
+      if (!inheritedFractionalBoundaries) {
+        return serializeRecoveredCentroids(metadata, means, weights);
+      }
+      verboseBytes = serializeCentroids(metadata.compression(), 
metadata.min(), metadata.max(), means, weights,
+          means.length);
+      metadata = inspectSerialized(ByteBuffer.wrap(verboseBytes), false);
+    }
+    if (metadata.hasZeroWeightCentroids()) {
+      verboseBytes = removeZeroWeightCentroids(verboseBytes, metadata);
+      metadata = inspectSerialized(ByteBuffer.wrap(verboseBytes), false);
+    }
+    if (!inheritedFractionalBoundaries) {
+      checkSerializedBoundaryWeights(verboseBytes, metadata);
+    }
+    double compression = metadata.compression();
+    if (metadata.encodedCompression() != compression) {
+      verboseBytes = verboseBytes.clone();
+      ByteBuffer.wrap(verboseBytes).putDouble(20, compression);
+    }
+    int centroidCount = metadata.centroidCount();
+    int legacyCapacity =
+        Math.min(getLegacyDefaultCentroidCapacity(compression), 
getDefaultCentroidCapacity(compression));
+    if (centroidCount <= legacyCapacity) {
+      return verboseBytes;
+    }
+    int mainCapacity = getDefaultCentroidCapacity(compression);
+    long bufferCapacity = DEFAULT_MERGE_BUFFER_MULTIPLIER * (long) 
mainCapacity;
+    if (centroidCount > mainCapacity || inheritedFractionalBoundaries || 
(double) (float) compression != compression
+        || centroidCount > Short.MAX_VALUE
+        || mainCapacity > Short.MAX_VALUE || bufferCapacity > Short.MAX_VALUE) 
{
+      return reduceVerboseCentroids(verboseBytes, legacyCapacity);
+    }
+    ByteBuffer verbose = ByteBuffer.wrap(verboseBytes);
+    ByteBuffer centroids = verbose.duplicate();
+    centroids.position(metadata.centroidOffset());
+    for (int i = 0; i < centroidCount; i++) {
+      double weight = centroids.getDouble();
+      double mean = centroids.getDouble();
+      if ((double) (float) weight != weight || (double) (float) mean != mean) {
+        return reduceVerboseCentroids(verboseBytes, legacyCapacity);
+      }
+    }
+
+    ByteBuffer small = ByteBuffer.allocate(SMALL_HEADER_SIZE + 
SMALL_CENTROID_SIZE * centroidCount);
+    verbose.rewind();
+    verbose.getInt();
+    small.putInt(SMALL_ENCODING);
+    small.putDouble(verbose.getDouble());
+    small.putDouble(verbose.getDouble());
+    verbose.getDouble();
+    verbose.getInt();
+    small.putFloat((float) compression);
+    small.putShort((short) mainCapacity);
+    small.putShort((short) bufferCapacity);
+    small.putShort((short) centroidCount);
+    for (int i = 0; i < centroidCount; i++) {
+      small.putFloat((float) verbose.getDouble());
+      small.putFloat((float) verbose.getDouble());
+    }
+    return small.array();
+  }
+
+  private static byte[] serializeRecoveredCentroids(SerializedTDigestMetadata 
metadata, double[] means,
+      double[] weights) {
+    PercentileTDigestAccumulator digest = 
PercentileTDigestAccumulator.forLegacyAggregation(metadata.compression());
+    digest.addHistoricalCentroids(means, weights, means.length, 
metadata.min(), metadata.max(), true);
+    
digest.inheritHistoricalFractionalBoundaries(metadata.historicalFractionalMinMean(),
+        metadata.historicalFractionalMaxMean());
+    return digest.serialize();
+  }
+
+  private static byte[] removeZeroWeightCentroids(byte[] verboseBytes, 
SerializedTDigestMetadata metadata) {
+    ByteBuffer source = ByteBuffer.wrap(verboseBytes);
+    source.position(metadata.centroidOffset());
+    ByteBuffer filtered = ByteBuffer.allocate(metadata.encodedLength());
+    filtered.put(verboseBytes, 0, VERBOSE_HEADER_SIZE);
+    int count = 0;
+    for (int i = 0; i < metadata.centroidCount(); i++) {
+      double weight = source.getDouble();
+      double mean = source.getDouble();
+      if (weight != 0.0) {
+        filtered.putDouble(weight).putDouble(mean);
+        count++;
+      }
+    }
+    filtered.putInt(28, count);
+    return Arrays.copyOf(filtered.array(), filtered.position());
+  }
+
+  /// Validates serialized lengths and centroid values without allocating 
centroid arrays.
+  public static double validateSerialized(byte[] bytes) {
+    return validateSerialized(ByteBuffer.wrap(bytes));
+  }
+
+  /// Validates one legacy digest without changing `input` and returns its 
total centroid weight.
+  ///
+  /// Trailing bytes remain available to the caller for intermediate values 
containing several objects.
+  public static double validateSerialized(ByteBuffer input) {
+    return validateSerialized(input, true);
+  }
+
+  private static double validateSerialized(ByteBuffer input, boolean 
checkCapacity) {
+    return inspectSerialized(input, checkCapacity).totalWeight();
+  }
+
+  /// Header and numerical metadata for one legacy byte payload. The centroid 
bytes remain owned by the caller.
+  /// Header-only inspection leaves total weight as NaN until centroid 
inspection validates the numerical fields.
+  ///
+  /// Legacy writers can emit poisoned numerical state after overflow or 
broken fractional boundary repair.
+  /// Such state is retained with degraded quantiles, rather than being passed 
to the sorted K1 kernel.
+  public record SerializedTDigestMetadata(int encoding, double min, double 
max, double compression,
+      int centroidCount, int centroidOffset, int centroidSize,
+      int encodedLength, double totalWeight, boolean hasNonFiniteMeans, 
boolean needsLegacyFallback,
+      boolean unorderedMeans, boolean fractionalWeights, boolean 
weightedBoundaries, boolean hasZeroWeightCentroids,
+      double encodedCompression, double recoveredInfinityMean, double 
historicalFractionalMinMean,
+      double historicalFractionalMaxMean) {
+    /// Whether the encoded centroid view can be used unchanged by healthy 
pending-state readers and writers.
+    public boolean isCanonicalPayload() {
+      return !needsLegacyFallback && !weightedBoundaries && !unorderedMeans && 
!hasZeroWeightCentroids
+          && Double.isNaN(recoveredInfinityMean);
+    }
+  }
+
+  /// Invocation-local parser state. Primitive byte-array reads avoid per-row 
buffer and metadata allocations.
+  /// Public metadata and retained pending payloads receive immutable 
snapshots instead of sharing this state.
+  static final class SerializedTDigestState {
+    private static final VarHandle SHORT_VIEW =
+        MethodHandles.byteArrayViewVarHandle(short[].class, 
ByteOrder.BIG_ENDIAN);
+    private static final VarHandle INT_VIEW = 
MethodHandles.byteArrayViewVarHandle(int[].class, ByteOrder.BIG_ENDIAN);
+    private static final VarHandle LONG_VIEW = 
MethodHandles.byteArrayViewVarHandle(long[].class, ByteOrder.BIG_ENDIAN);
+
+    int _encoding;
+    double _min;
+    double _max;
+    double _compression;
+    int _centroidCount;
+    int _centroidOffset;
+    int _centroidSize;
+    int _encodedLength;
+    double _totalWeight;
+    boolean _hasNonFiniteMeans;
+    boolean _needsLegacyFallback;
+    boolean _unorderedMeans;
+    boolean _fractionalWeights;
+    boolean _weightedBoundaries;
+    boolean _hasZeroWeightCentroids;
+    double _encodedCompression;
+    double _recoveredInfinityMean;
+    double _historicalFractionalMinMean;
+    double _historicalFractionalMaxMean;
+    private byte[] _bytes;
+    private ByteBuffer _buffer;
+    private int _position;
+    private int _limit;
+
+    void reset(byte[] bytes) {
+      _bytes = bytes;
+      _buffer = null;
+      _position = 0;
+      _limit = bytes.length;
+    }
+
+    void reset(ByteBuffer input) {
+      _bytes = null;
+      _buffer = input.slice().order(ByteOrder.BIG_ENDIAN);
+      _position = 0;
+      _limit = _buffer.limit();
+    }
+
+    void copyFrom(SerializedTDigestMetadata metadata) {
+      _encoding = metadata.encoding();
+      _min = metadata.min();
+      _max = metadata.max();
+      _compression = metadata.compression();
+      _centroidCount = metadata.centroidCount();
+      _centroidOffset = metadata.centroidOffset();
+      _centroidSize = metadata.centroidSize();
+      _encodedLength = metadata.encodedLength();
+      _totalWeight = metadata.totalWeight();
+      _hasNonFiniteMeans = metadata.hasNonFiniteMeans();
+      _needsLegacyFallback = metadata.needsLegacyFallback();
+      _unorderedMeans = metadata.unorderedMeans();
+      _fractionalWeights = metadata.fractionalWeights();
+      _weightedBoundaries = metadata.weightedBoundaries();
+      _hasZeroWeightCentroids = metadata.hasZeroWeightCentroids();
+      _encodedCompression = metadata.encodedCompression();
+      _recoveredInfinityMean = metadata.recoveredInfinityMean();
+      _historicalFractionalMinMean = metadata.historicalFractionalMinMean();
+      _historicalFractionalMaxMean = metadata.historicalFractionalMaxMean();
+    }
+
+    SerializedTDigestMetadata snapshot() {
+      return new SerializedTDigestMetadata(_encoding, _min, _max, 
_compression, _centroidCount, _centroidOffset,
+          _centroidSize, _encodedLength, _totalWeight, _hasNonFiniteMeans, 
_needsLegacyFallback, _unorderedMeans,
+          _fractionalWeights, _weightedBoundaries, _hasZeroWeightCentroids, 
_encodedCompression, _recoveredInfinityMean,
+          _historicalFractionalMinMean, _historicalFractionalMaxMean);
+    }
+
+    private int readPosition(int length) {
+      if (length > _limit - _position) {
+        throw new BufferUnderflowException();
+      }
+      int position = _position;
+      _position += length;
+      return position;
+    }
+
+    private int readInt() {
+      int position = readPosition(Integer.BYTES);
+      return _bytes != null ? (int) INT_VIEW.get(_bytes, position) : 
_buffer.getInt(position);
+    }
+
+    private short readShort() {
+      int position = readPosition(Short.BYTES);
+      return _bytes != null ? (short) SHORT_VIEW.get(_bytes, position) : 
_buffer.getShort(position);
+    }
+
+    private double readDouble() {
+      int position = readPosition(Double.BYTES);
+      return _bytes != null
+          ? Double.longBitsToDouble((long) LONG_VIEW.get(_bytes, position))
+          : _buffer.getDouble(position);
+    }
+
+    private float readFloat() {
+      int position = readPosition(Float.BYTES);
+      return _bytes != null ? Float.intBitsToFloat((int) INT_VIEW.get(_bytes, 
position)) : _buffer.getFloat(position);
+    }
+  }
+
+  /// Inspects one payload without mutating `input`, scanning the centroid 
values once.
+  public static SerializedTDigestMetadata inspectSerialized(ByteBuffer input) {
+    return inspectSerialized(input, true);
+  }
+
+  /// Inspects a payload, optionally enforcing the legacy decoder's declared 
centroid capacity.
+  public static SerializedTDigestMetadata inspectSerialized(ByteBuffer input, 
boolean checkCapacity) {
+    SerializedTDigestState state = new SerializedTDigestState();
+    state.reset(input);
+    readSerializedHeader(state, checkCapacity);
+    if (Double.isNaN(state._totalWeight)) {
+      inspectSerialized(state, null, null);
+    }
+    return state.snapshot();
+  }
+
+  /// Reads the fixed-size header without allocating centroid arrays; 
oversized historical state is also inspected.
+  public static SerializedTDigestMetadata readSerializedHeader(ByteBuffer 
input) {
+    return readSerializedHeader(input, true);
+  }
+
+  /// Reads a fixed-size header, optionally enforcing the declared centroid 
capacity.
+  ///
+  /// NaN or inverted nonempty extrema mark legacy degraded state. Oversized 
payloads require numerical inspection:
+  /// historical degraded state remains readable even if an old decoder's 
arrays could not hold its centroids.
+  public static SerializedTDigestMetadata readSerializedHeader(ByteBuffer 
input, boolean checkCapacity) {
+    SerializedTDigestState state = new SerializedTDigestState();
+    state.reset(input);
+    readSerializedHeader(state, checkCapacity);
+    return state.snapshot();
+  }
+
+  static void readSerializedHeader(SerializedTDigestState state, boolean 
checkCapacity) {
+    int encoding = state.readInt();
+    if (encoding != VERBOSE_ENCODING && encoding != SMALL_ENCODING) {
+      throw new IllegalStateException("Invalid format for serialized 
histogram");
+    }
+    double min = state.readDouble();
+    double max = state.readDouble();
+    double compression;
+    double encodedCompression;
+    int mainCapacity;
+    int bufferCapacity = 0;
+    int centroidCount;
+    int centroidSize;
+    if (encoding == VERBOSE_ENCODING) {
+      encodedCompression = state.readDouble();
+      compression = normalizeCompression(encodedCompression);
+      mainCapacity = Math.max(getDefaultCentroidCapacity(compression), 
getLegacyDefaultCentroidCapacity(compression));
+      centroidCount = state.readInt();
+      centroidSize = VERBOSE_CENTROID_SIZE;
+    } else {
+      encodedCompression = state.readFloat();
+      compression = normalizeCompression(encodedCompression);
+      mainCapacity = state.readShort();
+      bufferCapacity = state.readShort();
+      checkSmallArrayCapacity(mainCapacity);
+      checkSmallArrayCapacity(bufferCapacity);
+      if (mainCapacity == -1) {
+        mainCapacity = getDefaultCentroidCapacity(compression);
+      }
+      centroidCount = state.readShort();
+      centroidSize = SMALL_CENTROID_SIZE;
+    }
+    if (centroidCount < 0) {
+      throw new IllegalArgumentException("Invalid negative TDigest centroid 
count: " + centroidCount);
+    }
+    if (centroidCount > (state._limit - state._position) / centroidSize) {
+      throw new BufferUnderflowException();
+    }
+    int centroidOffset = state._position;
+    int encodedLength = centroidOffset + centroidCount * centroidSize;
+    state._encoding = encoding;
+    state._min = min;
+    state._max = max;
+    state._compression = compression;
+    state._centroidCount = centroidCount;
+    state._centroidOffset = centroidOffset;
+    state._centroidSize = centroidSize;
+    state._encodedLength = encodedLength;
+    state._totalWeight = Double.NaN;
+    state._hasNonFiniteMeans = false;
+    state._needsLegacyFallback = Double.isNaN(min) || Double.isNaN(max) || 
centroidCount > 0 && min > max;
+    state._unorderedMeans = false;
+    state._fractionalWeights = false;
+    state._weightedBoundaries = false;
+    state._hasZeroWeightCentroids = false;
+    state._encodedCompression = encodedCompression;
+    state._recoveredInfinityMean = Double.NaN;
+    state._historicalFractionalMinMean = Double.NaN;
+    state._historicalFractionalMaxMean = Double.NaN;
+    if (checkCapacity && centroidCount > mainCapacity) {
+      inspectSerialized(state, null, null);
+      if (!state._needsLegacyFallback) {
+        throw new IllegalArgumentException("TDigest centroid count exceeds 
capacity: " + centroidCount);
+      }
+    }
+  }
+
+  /// Validates centroids in one pass and optionally decodes their means and 
weights into reusable arrays.
+  ///
+  /// The header must describe this exact input, and each supplied array must 
hold all encoded centroids. Endpoint
+  /// rounding inherited from compact re-encoding or old merge arithmetic is 
restored to the double header bounds.
+  public static SerializedTDigestMetadata inspectSerialized(ByteBuffer input, 
SerializedTDigestMetadata header,
+      double[] means, double[] weights) {
+    SerializedTDigestState state = new SerializedTDigestState();
+    state.reset(input);
+    state.copyFrom(header);
+    inspectSerialized(state, means, weights);
+    return state.snapshot();
+  }
+
+  static void inspectSerialized(SerializedTDigestState state, double[] means, 
double[] weights) {
+    state._position = state._centroidOffset;
+    int centroidCount = state._centroidCount;
+    int centroidSize = state._centroidSize;
+    double min = state._min;
+    double max = state._max;
+    double totalWeight = 0.0;
+    double previousMean = Double.NEGATIVE_INFINITY;
+    boolean hasNonFiniteMeans = false;
+    boolean needsLegacyFallback = state._needsLegacyFallback;
+    boolean unorderedMeans = false;
+    boolean fractionalWeights = false;
+    boolean hasZeroWeightCentroids = false;
+    int positiveCentroidCount = 0;
+    double lowerPositiveMean = Double.POSITIVE_INFINITY;
+    double upperPositiveMean = Double.NEGATIVE_INFINITY;
+    double lowerPositiveWeight = 0.0;
+    double upperPositiveWeight = 0.0;
+    boolean withinBounds = true;
+    // Infer only a matching one-sided tail, or a distribution consisting 
entirely of one infinity. A NaN
+    // between finite centroids or in a +/-Infinity mixture has lost 
information and remains opaque.
+    double infinityMean = min == max && Double.isInfinite(min) ? min
+        : Double.isFinite(min) && max == Double.POSITIVE_INFINITY ? max
+        : min == Double.NEGATIVE_INFINITY && Double.isFinite(max) ? min : 
Double.NaN;
+    boolean hasNaNMeans = false;
+    boolean hasFiniteMeans = false;
+    boolean positiveInfinityTailStarted = false;
+    boolean negativeInfinityTailEnded = false;
+    boolean identifiableInfinityTail = true;
+    double roundedMin = (double) (float) min;
+    double roundedMax = (double) (float) max;
+    // Legacy mean += (incoming - mean) * weight / totalWeight can cancel near 
a small endpoint. Bound
+    // its value displacement using the finite input range's scale, rather 
than ULPs of the small result.
+    double roundingTolerance = 4.0 * Math.max(Double.isFinite(min) ? 
Math.ulp(min) : 0.0,
+        Double.isFinite(max) ? Math.ulp(max) : 0.0);
+    for (int i = 0; i < centroidCount; i++) {
+      double weight = centroidSize == VERBOSE_CENTROID_SIZE ? 
state.readDouble() : state.readFloat();
+      double mean = centroidSize == VERBOSE_CENTROID_SIZE ? state.readDouble() 
: state.readFloat();
+      // Legacy readers admitted raw non-finite weights. Their mass cannot be 
recovered, so preserve the bytes
+      // as opaque state while keeping the same finite-weight validation for 
newly created distributions.
+      needsLegacyFallback |= !Double.isFinite(weight);
+      // Legacy compact writers can narrow a finite double endpoint outside 
the float range to infinity.
+      // Recover that identifiable rounding before classifying non-finite 
state; verbose infinity remains opaque.
+      if (state._encoding == SMALL_ENCODING) {
+        if (mean == Double.NEGATIVE_INFINITY && Double.isFinite(min) && 
roundedMin == mean) {
+          mean = min;
+        } else if (mean == Double.POSITIVE_INFINITY && Double.isFinite(max) && 
roundedMax == mean) {
+          mean = max;
+        }
+      }
+      if (means != null) {
+        means[i] = Math.max(min, Math.min(mean, max));
+      }
+      if (weights != null) {
+        weights[i] = weight;
+      }
+      // A zero-mass centroid has no distribution to merge, even when its 
unused mean is NaN or stale.
+      if (weight == 0.0) {
+        hasZeroWeightCentroids = true;
+        continue;
+      }
+      if (weight > 0.0) {
+        positiveCentroidCount++;
+      }
+      fractionalWeights |= weight != Math.rint(weight);
+      boolean nanMean = Double.isNaN(mean);
+      hasNaNMeans |= nanMean;
+      hasFiniteMeans |= Double.isFinite(mean);
+      if (nanMean && !Double.isNaN(infinityMean)) {
+        mean = infinityMean;
+      }
+      double boundaryMean = Math.max(min, Math.min(mean, max));
+      if (weight > 0.0) {
+        // Match the stored centroid sort, including signed zeros after the 
decoder's endpoint clamp.
+        // Stable sorting keeps the first lower endpoint and the last upper 
endpoint among equal means.
+        if (lowerPositiveWeight == 0.0 || Double.compare(boundaryMean, 
lowerPositiveMean) < 0) {
+          lowerPositiveMean = boundaryMean;
+          lowerPositiveWeight = weight;
+        }
+        if (upperPositiveWeight == 0.0 || Double.compare(boundaryMean, 
upperPositiveMean) >= 0) {
+          upperPositiveMean = boundaryMean;
+          upperPositiveWeight = weight;
+        }
+      }
+      if (infinityMean == Double.POSITIVE_INFINITY) {
+        if (mean == infinityMean) {
+          positiveInfinityTailStarted = true;
+        } else if (positiveInfinityTailStarted) {
+          identifiableInfinityTail = false;
+        }
+      } else if (infinityMean == Double.NEGATIVE_INFINITY) {
+        if (mean == infinityMean && negativeInfinityTailEnded) {
+          identifiableInfinityTail = false;
+        } else if (mean != infinityMean) {
+          negativeInfinityTailEnded = true;
+        }
+      }
+      if (min == max && Double.isInfinite(min) && mean != infinityMean) {
+        identifiableInfinityTail = false;
+      }
+      // Negative residuals and unidentifiable NaN means still have an unknown 
distribution. Never normalize
+      // or sort them into plausible statistics, even if another centroid 
could be repaired as an infinite tail.
+      needsLegacyFallback |= weight < 0.0 || Double.isNaN(mean)
+          || !Double.isFinite(mean) && (mean < min || mean > max);
+      hasNonFiniteMeans |= !Double.isFinite(mean);
+      if (!Double.isNaN(mean)) {
+        unorderedMeans |= Double.compare(boundaryMean, previousMean) < 0;
+        // A compact endpoint can move between its float-rounded value and the 
double bound in later merges.
+        // Permit that finite interval and bounded legacy arithmetic roundoff, 
without widening for infinity.
+        boolean lowerRounded = Double.isFinite(mean) && Double.isFinite(min)
+            && (min - mean <= roundingTolerance || Double.isFinite(roundedMin) 
&& mean >= roundedMin);
+        boolean upperRounded = Double.isFinite(mean) && Double.isFinite(max)
+            && (mean - max <= roundingTolerance || Double.isFinite(roundedMax) 
&& mean <= roundedMax);
+        withinBounds &= (mean >= min || lowerRounded) && (mean <= max || 
upperRounded);
+        previousMean = boundaryMean;
+      }
+      totalWeight += weight;
+      needsLegacyFallback |= !Double.isFinite(totalWeight);
+    }
+    // Identifiable endpoint rounding can be restored safely. Other historical 
out-of-extrema values have an
+    // unknown distribution: retain their original bytes and NaN statistics 
instead of inventing clamped quantiles.
+    needsLegacyFallback |= !withinBounds
+        || hasNaNMeans && (!identifiableInfinityTail || min != max && 
!hasFiniteMeans);
+    double recoveredInfinityMean = hasNaNMeans && !needsLegacyFallback ? 
infinityMean : Double.NaN;
+    if (means != null && !Double.isNaN(recoveredInfinityMean)) {
+      for (int i = 0; i < centroidCount; i++) {
+        if (Double.isNaN(means[i])) {
+          means[i] = recoveredInfinityMean;
+        }
+      }
+    }
+    boolean weightedBoundaries = positiveCentroidCount == 1 ? 
lowerPositiveWeight >= 2.0
+        : positiveCentroidCount > 1 && (lowerPositiveWeight > 1.0 || 
upperPositiveWeight > 1.0);
+    boolean fractionalSingleton = positiveCentroidCount == 1 && 
lowerPositiveWeight != 1.0
+        && lowerPositiveWeight < 2.0;
+    double historicalFractionalMinMean = !needsLegacyFallback && 
positiveCentroidCount > 0
+        && (lowerPositiveWeight < 1.0 || fractionalSingleton) ? 
lowerPositiveMean : Double.NaN;
+    double historicalFractionalMaxMean = !needsLegacyFallback && 
positiveCentroidCount > 0
+        && (upperPositiveWeight < 1.0 || fractionalSingleton) ? 
upperPositiveMean : Double.NaN;
+    state._totalWeight = totalWeight;
+    state._hasNonFiniteMeans = hasNonFiniteMeans;
+    state._needsLegacyFallback = needsLegacyFallback;
+    state._unorderedMeans = unorderedMeans;
+    state._fractionalWeights = fractionalWeights;
+    state._weightedBoundaries = weightedBoundaries;
+    state._hasZeroWeightCentroids = hasZeroWeightCentroids;
+    state._recoveredInfinityMean = recoveredInfinityMean;
+    state._historicalFractionalMinMean = historicalFractionalMinMean;
+    state._historicalFractionalMaxMean = historicalFractionalMaxMean;
+  }
+
+  /// Materializes previously validated centroids without repeating numerical 
inspection. The metadata must describe
+  /// these exact bytes; each supplied array must hold the encoded centroid 
count. Identified NaN infinity tails and
+  /// compact endpoint rounding are restored in the same way as the inspecting 
decoder.
+  public static void decodeSerializedCentroids(ByteBuffer input, 
SerializedTDigestMetadata metadata, double[] means,
+      double[] weights) {
+    SerializedTDigestState state = new SerializedTDigestState();
+    state.reset(input);
+    state.copyFrom(metadata);
+    decodeSerializedCentroids(state, means, weights);
+  }
+
+  static void decodeSerializedCentroids(SerializedTDigestState state, double[] 
means, double[] weights) {
+    state._position = state._centroidOffset;
+    for (int i = 0; i < state._centroidCount; i++) {
+      weights[i] = state._centroidSize == VERBOSE_CENTROID_SIZE ? 
state.readDouble() : state.readFloat();
+      double mean = state._centroidSize == VERBOSE_CENTROID_SIZE ? 
state.readDouble() : state.readFloat();
+      means[i] = Double.isNaN(mean) ? state._recoveredInfinityMean

Review Comment:
   The endpoint clamp + NaN-infinity restore rule is implemented twice: here in 
`decodeSerializedCentroids` and in `inspectSerialized`'s fill path above. The 
comment says they restore "in the same way", but nothing enforces it — if the 
rounding whitelist or infinity recovery changes in one place only, a digest 
held pending and later materialized decodes different centroid means than the 
same bytes merged directly, silently diverging quantiles. Consider extracting 
one shared per-centroid restore helper that both paths call.



##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/NonFiniteAwareTDigest.java:
##########
@@ -0,0 +1,732 @@
+/**
+ * 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.util.ArrayList;
+import java.util.Collection;
+import java.util.List;
+import javax.annotation.Nullable;
+import 
org.apache.pinot.segment.local.customobject.tdigest.TDigestCodec.SerializedTDigestMetadata;
+
+
+/// Stores non-finite values as tail masses while delegating finite values to 
an owned native digest.
+/// Emits legacy t-digest bytes and preserves historical fractional endpoint 
provenance across merges and copies.
+/// Instances are mutable and require external synchronization.
+public final class NonFiniteAwareTDigest extends TDigest {
+  private PercentileTDigestAccumulator _finiteDigest;
+  private double _negativeInfinityWeight;
+  private double _positiveInfinityWeight;
+  private List<Centroid> _finiteCentroids;
+  private byte[] _originalBytes;
+  private boolean _unrepresentableInfinityTail;
+  private boolean _pendingHistoricalBoundaryRepair;
+  private double _historicalMin;
+  private double _historicalMax;
+
+  public static NonFiniteAwareTDigest forLegacyAggregation(double compression) 
{
+    return new 
NonFiniteAwareTDigest(PercentileTDigestAccumulator.forLegacyAggregation(compression),
 0.0, 0.0);
+  }
+
+  private NonFiniteAwareTDigest(PercentileTDigestAccumulator finiteDigest, 
double negativeInfinityWeight,
+      double positiveInfinityWeight) {
+    _finiteDigest = finiteDigest;
+    _negativeInfinityWeight = negativeInfinityWeight;
+    _positiveInfinityWeight = positiveInfinityWeight;
+  }
+
+  /// Snapshots the aggregation without flushing or compressing the source's 
buffered inputs.
+  public NonFiniteAwareTDigest copy() {
+    NonFiniteAwareTDigest copy =
+        new NonFiniteAwareTDigest(_finiteDigest.copy(), 
_negativeInfinityWeight, _positiveInfinityWeight);
+    copy._originalBytes = _originalBytes == null ? null : 
_originalBytes.clone();
+    copy._unrepresentableInfinityTail = _unrepresentableInfinityTail;
+    copy._pendingHistoricalBoundaryRepair = _pendingHistoricalBoundaryRepair;
+    copy._historicalMin = _historicalMin;
+    copy._historicalMax = _historicalMax;
+    return copy;
+  }
+
+  /// Copies a digest, snapshotting native accumulator buffers before any 
consuming conversion.
+  public static NonFiniteAwareTDigest copyOf(TDigest digest) {
+    if (digest instanceof NonFiniteAwareTDigest) {
+      return ((NonFiniteAwareTDigest) digest).copy();
+    }
+    NonFiniteAwareTDigest copy = forLegacyAggregation(digest.compression());
+    copy.add(digest instanceof PercentileTDigestAccumulator ? 
((PercentileTDigestAccumulator) digest).copy() : digest);
+    return copy;
+  }
+
+  public static NonFiniteAwareTDigest fromBytes(byte[] bytes) {
+    SerializedTDigestInput validated = new SerializedTDigestInput();
+    validated.reset(bytes);
+    SerializedTDigestMetadata metadata = validated.getMetadata();
+    if (!metadata.hasNonFiniteMeans() || metadata.needsLegacyFallback()) {
+      return new 
NonFiniteAwareTDigest(PercentileTDigestAccumulator.fromBytes(validated), 0.0, 
0.0);
+    }
+    validated.decode();
+    if (!PercentileTDigestAccumulator.canNormalizeBoundaries(validated._means, 
validated._weights,
+        validated._numCentroids, metadata.min(), metadata.max())) {
+      return new 
NonFiniteAwareTDigest(PercentileTDigestAccumulator.fromBytes(validated), 0.0, 
0.0);
+    }
+    double encodedMin = metadata.min();
+    double encodedMax = metadata.max();
+    double compression = metadata.compression();
+    int centroidCount = validated._numCentroids;
+    double negativeInfinityWeight = 0.0;
+    double positiveInfinityWeight = 0.0;
+    double[] finiteMeans = validated._means;
+    double[] finiteWeights = validated._weights;
+    int finiteCount = 0;
+    double finiteMin = Double.POSITIVE_INFINITY;
+    double finiteMax = Double.NEGATIVE_INFINITY;
+    for (int i = 0; i < centroidCount; i++) {
+      double weight = finiteWeights[i];
+      double mean = finiteMeans[i];
+      if (weight == 0.0) {
+        continue;
+      }
+      if (mean == Double.NEGATIVE_INFINITY) {
+        negativeInfinityWeight += weight;
+      } else if (mean == Double.POSITIVE_INFINITY) {
+        positiveInfinityWeight += weight;
+      } else {
+        finiteWeights[finiteCount] = weight;
+        finiteMeans[finiteCount] = mean;
+        finiteMin = Math.min(finiteMin, mean);
+        finiteMax = Math.max(finiteMax, mean);
+        finiteCount++;
+      }
+    }
+
+    PercentileTDigestAccumulator finiteDigest =
+        PercentileTDigestAccumulator.forLegacyAggregation(compression);
+    if (negativeInfinityWeight > 0.0 || positiveInfinityWeight > 0.0) {
+      finiteDigest.deferBoundaryNormalization();
+    }
+    if (finiteCount > 0) {
+      finiteMin = Double.isFinite(encodedMin) ? encodedMin : finiteMin;
+      finiteMax = Double.isFinite(encodedMax) ? encodedMax : finiteMax;
+      finiteDigest.addHistoricalCentroids(finiteMeans, finiteWeights, 
finiteCount, finiteMin, finiteMax, true);
+    }
+    validated.recordHistoricalFractionalBoundaries(finiteDigest);
+    NonFiniteAwareTDigest wrapped =
+        new NonFiniteAwareTDigest(finiteDigest, negativeInfinityWeight, 
positiveInfinityWeight);
+    wrapped._pendingHistoricalBoundaryRepair = metadata.weightedBoundaries();
+    wrapped._historicalMin = encodedMin;
+    wrapped._historicalMax = encodedMax;
+    wrapped._unrepresentableInfinityTail = 
!canSplitInfinityWeight(negativeInfinityWeight)
+        || !canSplitInfinityWeight(positiveInfinityWeight);
+    if (metadata.fractionalWeights() || wrapped._unrepresentableInfinityTail) {
+      wrapped._originalBytes = bytes.clone();
+    }
+    return wrapped;
+  }
+
+  @Override
+  public void add(double value) {
+    add(value, 1);
+  }
+
+  @Override
+  public void add(double value, double weight) {
+    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);
+    }
+    PercentileTDigestAccumulator.checkTotalWeight(getTotalWeight() + weight);
+    double infinityWeight = 0.0;
+    if (value == Double.NEGATIVE_INFINITY) {
+      addInfinityWeight(_negativeInfinityWeight, weight);
+      infinityWeight = 
addInfinityWeight(boundaryPreparedView()._negativeInfinityWeight, weight);
+    } else if (value == Double.POSITIVE_INFINITY) {
+      addInfinityWeight(_positiveInfinityWeight, weight);
+      infinityWeight = 
addInfinityWeight(boundaryPreparedView()._positiveInfinityWeight, weight);
+    }
+    checkSplittableInfinityWeight(infinityWeight);
+    requireMutable();
+    if (value == Double.NEGATIVE_INFINITY) {
+      _finiteDigest.deferBoundaryNormalization();
+      _finiteDigest.recordFreshFractionalMean(value, weight);
+      _negativeInfinityWeight = infinityWeight;
+    } else if (value == Double.POSITIVE_INFINITY) {
+      _finiteDigest.deferBoundaryNormalization();
+      _finiteDigest.recordFreshFractionalMean(value, weight);
+      _positiveInfinityWeight = infinityWeight;
+    } else {
+      _finiteDigest.add(value, weight);
+    }
+    mutated();
+  }
+
+  @Override
+  public void add(TDigest other) {
+    if (other.isEmpty()) {
+      return;
+    }
+    if (!hasValidStatistics()) {
+      throw PercentileTDigestAccumulator.corruptedMutation();
+    }
+    if (!other.hasValidStatistics() && !isEmpty()) {
+      throw PercentileTDigestAccumulator.corruptedMutation();
+    }
+    if (other.hasValidStatistics()) {
+      PercentileTDigestAccumulator.checkTotalWeight(getTotalWeight() + 
other.getTotalWeight());
+    }
+    if (other instanceof NonFiniteAwareTDigest) {
+      NonFiniteAwareTDigest wrapped = (NonFiniteAwareTDigest) other;
+      if (isEmpty() && wrapped._unrepresentableInfinityTail) {
+        _finiteDigest = wrapped._finiteDigest.copy();
+        _negativeInfinityWeight = wrapped._negativeInfinityWeight;
+        _positiveInfinityWeight = wrapped._positiveInfinityWeight;
+        _originalBytes = wrapped._originalBytes.clone();
+        _unrepresentableInfinityTail = true;
+        _pendingHistoricalBoundaryRepair = 
wrapped._pendingHistoricalBoundaryRepair;
+        _historicalMin = wrapped._historicalMin;
+        _historicalMax = wrapped._historicalMax;
+        invalidateDerivedCaches();
+        return;
+      }
+      addInfinityWeight(_negativeInfinityWeight, 
wrapped._negativeInfinityWeight);
+      addInfinityWeight(_positiveInfinityWeight, 
wrapped._positiveInfinityWeight);
+      NonFiniteAwareTDigest preparedReceiver = boundaryPreparedView();
+      NonFiniteAwareTDigest preparedSource = wrapped.boundaryPreparedView();
+      double negativeInfinityWeight =
+          addInfinityWeight(preparedReceiver._negativeInfinityWeight, 
preparedSource._negativeInfinityWeight);
+      double positiveInfinityWeight =
+          addInfinityWeight(preparedReceiver._positiveInfinityWeight, 
preparedSource._positiveInfinityWeight);
+      checkSplittableInfinityWeight(negativeInfinityWeight);
+      checkSplittableInfinityWeight(positiveInfinityWeight);
+      requireMutable();
+      wrapped.prepareHistoricalBoundaries();
+      if (negativeInfinityWeight > 0.0 || positiveInfinityWeight > 0.0) {
+        _finiteDigest.deferBoundaryNormalization();
+      }
+      try {
+        if (!wrapped._finiteDigest.isEmpty()) {
+          _finiteDigest.add(wrapped._finiteDigest);
+        }
+      } catch (RuntimeException | Error e) {
+        restoreBoundaryNormalizationAfterFailedMerge();
+        throw e;
+      } finally {
+        // Native merging can compress the source before a later validation 
failure.
+        wrapped.invalidateDerivedCaches();
+      }
+      if (wrapped.hasValidStatistics()) {
+        _finiteDigest.inheritHistoricalFractionalBoundaries(wrapped);
+      }
+      _negativeInfinityWeight = negativeInfinityWeight;
+      _positiveInfinityWeight = positiveInfinityWeight;
+      mutated();
+      return;
+    }
+    if (!other.hasValidStatistics() || Double.isFinite(other.getMin()) && 
Double.isFinite(other.getMax())) {
+      requireMutable();
+      _finiteDigest.add(other);
+      mutated();
+      return;
+    }
+    // Read precise centroid weights directly; generic sources need no full 
digest serialization for their tails.
+    if (other instanceof PercentileTDigestAccumulator) {
+      PercentileTDigestAccumulator nativeDigest = 
(PercentileTDigestAccumulator) other;
+      if (isEmpty() && nativeDigest.hasUnrepresentableBoundaryPayload()) {
+        _finiteDigest = nativeDigest.copy();
+        mutated();
+        return;
+      }
+    }
+    Collection<Centroid> centroids = other.centroids();
+    double[] finiteMeans = new double[Math.addExact(centroids.size(), 2)];
+    double[] finiteWeights = new double[finiteMeans.length];
+    int count = 0;
+    double sourceMin = other.getMin();
+    double sourceMax = other.getMax();
+    double negativeInfinityWeight = 0.0;
+    double positiveInfinityWeight = 0.0;
+    for (Centroid centroid : centroids) {
+      double mean = centroid.mean();
+      double weight = centroid.weight();
+      if (weight == 0.0) {
+        continue;
+      }
+      if (!(weight > 0.0) || !Double.isFinite(weight) || !(mean >= sourceMin 
&& mean <= sourceMax)) {
+        throw new IllegalArgumentException("Invalid TDigest centroid");
+      }
+      if (mean == Double.NEGATIVE_INFINITY) {
+        negativeInfinityWeight = addInfinityWeight(negativeInfinityWeight, 
weight);
+      } else if (mean == Double.POSITIVE_INFINITY) {
+        positiveInfinityWeight = addInfinityWeight(positiveInfinityWeight, 
weight);
+      }
+      finiteMeans[count] = mean;
+      finiteWeights[count++] = weight;
+    }
+    checkSplittableInfinityWeight(negativeInfinityWeight);
+    checkSplittableInfinityWeight(positiveInfinityWeight);
+    // Original contributions exclude unit endpoints introduced by boundary 
repair.
+    addInfinityWeight(_negativeInfinityWeight, negativeInfinityWeight);
+    addInfinityWeight(_positiveInfinityWeight, positiveInfinityWeight);
+    PercentileTDigestAccumulator.sortCentroids(finiteMeans, finiteWeights, 
count);
+    count = PercentileTDigestAccumulator.normalizeSerializedBoundaries(
+        finiteMeans, finiteWeights, count, sourceMin, sourceMax);
+    negativeInfinityWeight = 0.0;
+    positiveInfinityWeight = 0.0;
+    int finiteCount = 0;
+    double finiteMin = Double.POSITIVE_INFINITY;
+    double finiteMax = Double.NEGATIVE_INFINITY;
+    double totalWeight = getTotalWeight();
+    for (int i = 0; i < count; i++) {
+      double mean = finiteMeans[i];
+      double weight = finiteWeights[i];
+      totalWeight += weight;
+      if (mean == Double.NEGATIVE_INFINITY) {
+        negativeInfinityWeight += weight;
+      } else if (mean == Double.POSITIVE_INFINITY) {
+        positiveInfinityWeight += weight;
+      } else {
+        finiteMeans[finiteCount] = mean;
+        finiteWeights[finiteCount++] = weight;
+        finiteMin = Math.min(finiteMin, mean);
+        finiteMax = Math.max(finiteMax, mean);
+      }
+    }
+    PercentileTDigestAccumulator.checkTotalWeight(totalWeight);
+    // Repair may relocate tail mass into a finite header endpoint; merge only 
the remaining tail mass.
+    NonFiniteAwareTDigest preparedReceiver = boundaryPreparedView();
+    negativeInfinityWeight = 
addInfinityWeight(preparedReceiver._negativeInfinityWeight, 
negativeInfinityWeight);
+    positiveInfinityWeight = 
addInfinityWeight(preparedReceiver._positiveInfinityWeight, 
positiveInfinityWeight);
+    checkSplittableInfinityWeight(negativeInfinityWeight);
+    checkSplittableInfinityWeight(positiveInfinityWeight);
+    requireMutable();
+    if (negativeInfinityWeight > 0.0 || positiveInfinityWeight > 0.0) {
+      _finiteDigest.deferBoundaryNormalization();
+    }
+    try {
+      if (finiteCount > 0) {
+        finiteMin = Double.isFinite(other.getMin()) ? other.getMin() : 
finiteMin;
+        finiteMax = Double.isFinite(other.getMax()) ? other.getMax() : 
finiteMax;
+        if (other instanceof PercentileTDigestAccumulator) {
+          _finiteDigest.addHistoricalCentroids(finiteMeans, finiteWeights, 
finiteCount, finiteMin, finiteMax, false);
+        } else {
+          _finiteDigest.addCentroids(finiteMeans, finiteWeights, finiteCount, 
finiteMin, finiteMax, false);
+        }
+      }
+    } catch (RuntimeException | Error e) {
+      restoreBoundaryNormalizationAfterFailedMerge();
+      throw e;
+    }
+    if (!(other instanceof PercentileTDigestAccumulator)) {
+      for (Centroid centroid : centroids) {
+        if (Double.isInfinite(centroid.mean())) {
+          _finiteDigest.recordFreshFractionalMean(centroid.mean(), 
centroid.weight());
+        }
+      }
+    }
+    _finiteDigest.inheritHistoricalFractionalBoundaries(other);
+    _negativeInfinityWeight = negativeInfinityWeight;
+    _positiveInfinityWeight = positiveInfinityWeight;
+    mutated();
+  }
+
+  private static double addInfinityWeight(double currentWeight, double 
addedWeight) {
+    double totalWeight = currentWeight + addedWeight;
+    if (currentWeight > 0.0 && addedWeight > 0.0
+        && (totalWeight == currentWeight || totalWeight == addedWeight)) {
+      throw new IllegalArgumentException("TDigest infinity-tail weight 
addition would absorb positive mass");
+    }
+    return totalWeight;
+  }
+
+  private void requireMutable() {
+    checkMutableInfinityTails();
+    if (!hasValidStatistics()) {
+      throw PercentileTDigestAccumulator.corruptedMutation();
+    }
+    if (_negativeInfinityWeight == 0.0 && _positiveInfinityWeight == 0.0) {
+      _finiteDigest.prepareForMutation();
+    } else {
+      prepareHistoricalBoundaries();
+    }
+  }
+
+  private void checkMutableInfinityTails() {
+    if (_unrepresentableInfinityTail) {
+      throw new IllegalArgumentException(
+          "Cannot normalize historical TDigest infinity-tail weight without 
losing mass");
+    }
+  }
+
+  private void prepareHistoricalBoundaries() {
+    checkMutableInfinityTails();
+    if (!_pendingHistoricalBoundaryRepair) {
+      return;
+    }
+    double encodedMin = getMin();
+    double encodedMax = getMax();
+    List<Centroid> centroids = getFiniteCentroids();
+    double[] means = new double[Math.addExact(centroids.size(), 4)];
+    double[] weights = new double[means.length];
+    int count = 0;
+    if (_negativeInfinityWeight > 0.0) {
+      means[count] = Double.NEGATIVE_INFINITY;
+      weights[count++] = _negativeInfinityWeight;
+    }
+    for (Centroid centroid : centroids) {
+      means[count] = centroid.mean();
+      weights[count++] = centroid.weight();
+    }
+    if (_positiveInfinityWeight > 0.0) {
+      means[count] = Double.POSITIVE_INFINITY;
+      weights[count++] = _positiveInfinityWeight;
+    }
+    count = PercentileTDigestAccumulator.normalizeSerializedBoundaries(means, 
weights, count, encodedMin, encodedMax);
+    int finiteCount = 0;
+    double min = Double.POSITIVE_INFINITY;
+    double max = Double.NEGATIVE_INFINITY;
+    double negativeInfinityWeight = 0.0;
+    double positiveInfinityWeight = 0.0;
+    for (int i = 0; i < count; i++) {
+      if (means[i] == Double.NEGATIVE_INFINITY) {
+        negativeInfinityWeight += weights[i];
+      } else if (means[i] == Double.POSITIVE_INFINITY) {
+        positiveInfinityWeight += weights[i];
+      } else {
+        means[finiteCount] = means[i];
+        weights[finiteCount++] = weights[i];
+        min = Math.min(min, means[i]);
+        max = Math.max(max, means[i]);
+      }
+    }
+    PercentileTDigestAccumulator finiteDigest = 
PercentileTDigestAccumulator.forLegacyAggregation(compression());
+    finiteDigest.deferBoundaryNormalization();
+    min = Double.isFinite(encodedMin) ? encodedMin : min;
+    max = Double.isFinite(encodedMax) ? encodedMax : max;
+    finiteDigest.addHistoricalCentroids(means, weights, finiteCount, min, max, 
true);
+    finiteDigest.inheritHistoricalFractionalBoundaries(_finiteDigest);
+    _finiteDigest = finiteDigest;
+    _negativeInfinityWeight = negativeInfinityWeight;
+    _positiveInfinityWeight = positiveInfinityWeight;
+    _pendingHistoricalBoundaryRepair = false;
+    invalidateDerivedCaches();
+  }
+
+  private NonFiniteAwareTDigest boundaryPreparedView() {
+    if (!_pendingHistoricalBoundaryRepair) {
+      return this;
+    }
+    NonFiniteAwareTDigest prepared = copy();
+    prepared.prepareHistoricalBoundaries();
+    return prepared;
+  }
+
+  private void restoreBoundaryNormalizationAfterFailedMerge() {
+    invalidateDerivedCaches();
+    if (_negativeInfinityWeight == 0.0 && _positiveInfinityWeight == 0.0) {
+      _finiteDigest.resetBoundaryNormalization();
+    }
+  }
+
+  @Nullable
+  PercentileTDigestAccumulator finiteDigestIfNoTails() {
+    if (_negativeInfinityWeight == 0.0 && _positiveInfinityWeight == 0.0) {
+      invalidateDerivedCaches();
+      return _finiteDigest;
+    }
+    return null;
+  }
+
+  private void mutated() {
+    _originalBytes = null;
+    invalidateDerivedCaches();
+  }
+
+  @Override
+  public void compress() {
+    _finiteDigest.compress();
+    invalidateDerivedCaches();
+  }
+
+  @Override
+  public double getTotalWeight() {
+    return _finiteDigest.getTotalWeight() + _negativeInfinityWeight + 
_positiveInfinityWeight;
+  }
+
+  @Override
+  double getHistoricalFractionalBoundaryMean(boolean lowerBoundary) {
+    return _finiteDigest.getHistoricalFractionalBoundaryMean(lowerBoundary);
+  }
+
+  @Override
+  double getFreshFractionalBoundaryMean(boolean lowerBoundary) {
+    return _finiteDigest.getFreshFractionalBoundaryMean(lowerBoundary);
+  }
+
+  @Override
+  public boolean hasValidStatistics() {
+    return _finiteDigest.hasValidStatistics();
+  }
+
+  @Override
+  public double cdf(double value) {
+    if (Double.isNaN(value) || Double.isInfinite(value)) {
+      throw new IllegalArgumentException(String.format("Invalid value: %f", 
value));
+    }
+    double size = getTotalWeight();
+    if (size == 0.0 || !hasValidStatistics()) {
+      return Double.NaN;
+    }
+    double finiteSize = _finiteDigest.getTotalWeight();
+    double finiteWeight = finiteSize == 0L ? 0.0 : _finiteDigest.cdf(value) * 
finiteSize;
+    return (_negativeInfinityWeight + finiteWeight) / size;
+  }
+
+  @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);
+    }
+    double size = getTotalWeight();
+    if (size == 0.0 || !hasValidStatistics()) {
+      return Double.NaN;
+    }
+    double index = quantile * size;
+    if (_negativeInfinityWeight > 0L && index < _negativeInfinityWeight) {
+      return Double.NEGATIVE_INFINITY;
+    }
+    if (_positiveInfinityWeight > 0L && index >= size - 
_positiveInfinityWeight) {
+      return Double.POSITIVE_INFINITY;
+    }
+    double finiteSize = _finiteDigest.getTotalWeight();
+    if (finiteSize == 0L) {
+      return _negativeInfinityWeight > 0L ? Double.NEGATIVE_INFINITY : 
Double.POSITIVE_INFINITY;
+    }
+    double finiteQuantile = (index - _negativeInfinityWeight) / finiteSize;
+    return _finiteDigest.quantile(Math.max(0.0, Math.min(finiteQuantile, 
1.0)));
+  }
+
+  @Override
+  public Collection<Centroid> centroids() {
+    return getAllCentroids();
+  }
+
+  @Override
+  public double compression() {
+    return _finiteDigest.compression();
+  }
+
+  @Override
+  public int maxSerializedByteSize() {
+    if (_originalBytes != null) {
+      return _originalBytes.length;
+    }
+    if (_negativeInfinityWeight == 0.0 && _positiveInfinityWeight == 0.0) {
+      return _finiteDigest.maxSerializedByteSize();
+    }
+    int finiteByteSize = _finiteDigest.maxSerializedByteSize();
+    PercentileTDigestAccumulator finiteDigest = _finiteDigest;
+    if (finiteDigest.hasOriginalFractionalPayload()) {
+      // Infinite tails can make retained fractional boundaries interior; 
their finite view may split endpoints.
+      finiteByteSize = Math.max(finiteByteSize,
+          TDigestCodec.getMaxLegacyCompatibleByteSize(compression(), 
finiteDigest.getCentroidCountUpperBound()));
+    }
+    boolean hasFiniteValues = _finiteDigest.getTotalWeight() > 0.0;
+    int negativeInfinityCount = 
getInfinityCentroidCount(_negativeInfinityWeight, true,
+        !hasFiniteValues && _positiveInfinityWeight == 0.0);
+    int positiveInfinityCount = 
getInfinityCentroidCount(_positiveInfinityWeight,
+        !hasFiniteValues && _negativeInfinityWeight == 0.0, true);
+    int tailCount = Math.addExact(negativeInfinityCount, 
positiveInfinityCount);
+    int tailByteSize = Math.multiplyExact(TDigestCodec.VERBOSE_CENTROID_SIZE, 
tailCount);
+    long finiteCount = hasFiniteValues ? 
finiteDigest.getCentroidCountUpperBound() : 0L;
+    int compatibleBound =
+        TDigestCodec.getMaxLegacyCompatibleByteSize(compression(), 
Math.addExact(finiteCount, tailCount));
+    return Math.min(Math.addExact(finiteByteSize, tailByteSize), 
compatibleBound);
+  }
+
+  @Override
+  public int centroidCount() {
+    return getAllCentroids().size();
+  }
+
+  @Override
+  public double getMin() {
+    if (_pendingHistoricalBoundaryRepair) {
+      return _historicalMin;
+    }
+    if (_negativeInfinityWeight > 0L) {
+      return Double.NEGATIVE_INFINITY;
+    }
+    if (!_finiteDigest.isEmpty()) {
+      return _finiteDigest.getMin();
+    }
+    return Double.POSITIVE_INFINITY;
+  }
+
+  @Override
+  public double getMax() {
+    if (_pendingHistoricalBoundaryRepair) {
+      return _historicalMax;
+    }
+    if (_positiveInfinityWeight > 0L) {
+      return Double.POSITIVE_INFINITY;
+    }
+    if (!_finiteDigest.isEmpty()) {
+      return _finiteDigest.getMax();
+    }
+    return Double.NEGATIVE_INFINITY;
+  }
+
+  private List<Centroid> getFiniteCentroids() {
+    if (_finiteCentroids == null) {
+      // Centroid reads use the native working-compression view; only 
serialization applies public compression.
+      _finiteCentroids = new ArrayList<>(_finiteDigest.centroids());
+    }
+    return _finiteCentroids;
+  }
+
+  private List<Centroid> getAllCentroids() {
+    List<Centroid> finiteCentroids = getFiniteCentroids();
+    boolean hasFiniteValues = _finiteDigest.getTotalWeight() > 0.0;
+    List<Centroid> centroids = new ArrayList<>(finiteCentroids.size() + 6);
+    if (_unrepresentableInfinityTail) {
+      if (_negativeInfinityWeight > 0.0) {
+        centroids.add(new Centroid(Double.NEGATIVE_INFINITY, 
_negativeInfinityWeight));
+      }
+      centroids.addAll(finiteCentroids);
+      if (_positiveInfinityWeight > 0.0) {
+        centroids.add(new Centroid(Double.POSITIVE_INFINITY, 
_positiveInfinityWeight));
+      }
+      return centroids;
+    }
+    appendInfinityCentroids(centroids, Double.NEGATIVE_INFINITY, 
_negativeInfinityWeight, true,
+        !hasFiniteValues && _positiveInfinityWeight == 0L);
+    centroids.addAll(finiteCentroids);
+    appendInfinityCentroids(centroids, Double.POSITIVE_INFINITY, 
_positiveInfinityWeight,
+        !hasFiniteValues && _negativeInfinityWeight == 0L, true);
+    return centroids;
+  }
+
+  @Override
+  public byte[] serialize() {
+    if (_originalBytes != null) {
+      return _originalBytes.clone();
+    }
+    if (_pendingHistoricalBoundaryRepair) {
+      return boundaryPreparedView().serialize();
+    }
+    if (_negativeInfinityWeight == 0.0 && _positiveInfinityWeight == 0.0) {
+      byte[] bytes = _finiteDigest.serialize();
+      invalidateDerivedCaches();
+      return bytes;
+    }
+    // Repair boundaries only after enclosing infinity tails establish the 
complete distribution's extrema.
+    _finiteDigest.compress();
+    invalidateDerivedCaches();
+    int finiteCentroidCount = _finiteDigest.centroidCount();
+    boolean hasFiniteValues = _finiteDigest.getTotalWeight() > 0.0;
+    int negativeInfinityCentroidCount = 
getInfinityCentroidCount(_negativeInfinityWeight, true,

Review Comment:
   The infinity-tail split is computed twice per call site with hand-duplicated 
flag expressions: these `getInfinityCentroidCount(...)` calls must pass exactly 
the same `(!hasFiniteValues && _positiveInfinityWeight == 0.0)`-style flag 
pairs as the matching `appendInfinityCentroids(...)` fill calls below (the same 
pairs recur in `maxSerializedByteSize` and `getAllCentroids`). A mismatch 
between a count call and its fill call mis-offsets the serialize arrays. 
Computing the split (or at least the flag pair) once per call site and reusing 
it for both count and fill would remove the lock-step requirement.



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