viirya commented on code in PR #56334:
URL: https://github.com/apache/spark/pull/56334#discussion_r3522717166


##########
sql/core/src/main/scala/org/apache/spark/sql/execution/columnar/ArrowCachedBatchSerializer.scala:
##########
@@ -0,0 +1,1601 @@
+/*
+ * 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.spark.sql.execution.columnar
+
+import java.io.{ByteArrayInputStream, ByteArrayOutputStream}
+import java.nio.channels.Channels
+
+import scala.jdk.CollectionConverters._
+
+import org.apache.arrow.compression.{Lz4CompressionCodec, ZstdCompressionCodec}
+import org.apache.arrow.vector.{VectorLoader, VectorSchemaRoot, VectorUnloader}
+import org.apache.arrow.vector.compression.{CompressionCodec, 
NoCompressionCodec}
+import org.apache.arrow.vector.ipc.{ReadChannel, WriteChannel}
+import org.apache.arrow.vector.ipc.message.{ArrowRecordBatch, 
MessageSerializer}
+
+import org.apache.spark.{SparkException, TaskContext}
+import org.apache.spark.rdd.RDD
+import org.apache.spark.sql.catalyst.InternalRow
+import org.apache.spark.sql.catalyst.expressions.Attribute
+import org.apache.spark.sql.catalyst.expressions.codegen.UnsafeRowWriter
+import org.apache.spark.sql.catalyst.types.DataTypeUtils
+import org.apache.spark.sql.catalyst.util.DateTimeUtils
+import org.apache.spark.sql.columnar.{CachedBatch, 
SimpleMetricsCachedBatchSerializer}
+import org.apache.spark.sql.errors.ExecutionErrors
+import org.apache.spark.sql.execution.arrow.ArrowWriter
+import org.apache.spark.sql.internal.SQLConf
+import org.apache.spark.sql.types._
+import org.apache.spark.sql.util.ArrowUtils
+import org.apache.spark.sql.vectorized.{ArrowColumnVector, ColumnarBatch, 
ColumnVector}
+import org.apache.spark.storage.StorageLevel
+import org.apache.spark.unsafe.types.UTF8String
+import org.apache.spark.util.Utils
+
+/**
+ * A [[CachedBatchSerializer]] that uses Apache Arrow as the cache format.
+ *
+ * This serializer:
+ *  - Supports both row-based (InternalRow) and columnar (ColumnarBatch) input
+ *  - Stores each batch as an internal, schema-less encapsulated Arrow 
RecordBatch message with
+ *    optional compression (zstd/lz4); the schema is reconstructed from the 
relation's attributes
+ *    on read (see [[ArrowCachedBatch]])
+ *  - Enables zero-copy columnar reads when output is ColumnarBatch
+ *  - Uses off-heap memory via Arrow allocators during encode/decode
+ *  - Collects per-column statistics for partition pruning
+ *
+ * Configuration options:
+ *  - spark.sql.cache.serializer: Set to this class name to enable
+ *  - spark.sql.execution.arrow.maxRecordsPerBatch: Max rows per cached batch

Review Comment:
   Fixed. Added `spark.sql.execution.arrow.maxBytesPerBatch`, 
`spark.sql.execution.arrow.compression.zstd.level`, and 
`spark.sql.execution.arrow.cache.prefetch.enabled` to the class header.



##########
sql/core/src/main/scala/org/apache/spark/sql/execution/columnar/ArrowCachedBatchSerializer.scala:
##########
@@ -0,0 +1,1601 @@
+/*
+ * 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.spark.sql.execution.columnar
+
+import java.io.{ByteArrayInputStream, ByteArrayOutputStream}
+import java.nio.channels.Channels
+
+import scala.jdk.CollectionConverters._
+
+import org.apache.arrow.compression.{Lz4CompressionCodec, ZstdCompressionCodec}
+import org.apache.arrow.vector.{VectorLoader, VectorSchemaRoot, VectorUnloader}
+import org.apache.arrow.vector.compression.{CompressionCodec, 
NoCompressionCodec}
+import org.apache.arrow.vector.ipc.{ReadChannel, WriteChannel}
+import org.apache.arrow.vector.ipc.message.{ArrowRecordBatch, 
MessageSerializer}
+
+import org.apache.spark.{SparkException, TaskContext}
+import org.apache.spark.rdd.RDD
+import org.apache.spark.sql.catalyst.InternalRow
+import org.apache.spark.sql.catalyst.expressions.Attribute
+import org.apache.spark.sql.catalyst.expressions.codegen.UnsafeRowWriter
+import org.apache.spark.sql.catalyst.types.DataTypeUtils
+import org.apache.spark.sql.catalyst.util.DateTimeUtils
+import org.apache.spark.sql.columnar.{CachedBatch, 
SimpleMetricsCachedBatchSerializer}
+import org.apache.spark.sql.errors.ExecutionErrors
+import org.apache.spark.sql.execution.arrow.ArrowWriter
+import org.apache.spark.sql.internal.SQLConf
+import org.apache.spark.sql.types._
+import org.apache.spark.sql.util.ArrowUtils
+import org.apache.spark.sql.vectorized.{ArrowColumnVector, ColumnarBatch, 
ColumnVector}
+import org.apache.spark.storage.StorageLevel
+import org.apache.spark.unsafe.types.UTF8String
+import org.apache.spark.util.Utils
+
+/**
+ * A [[CachedBatchSerializer]] that uses Apache Arrow as the cache format.
+ *
+ * This serializer:
+ *  - Supports both row-based (InternalRow) and columnar (ColumnarBatch) input
+ *  - Stores each batch as an internal, schema-less encapsulated Arrow 
RecordBatch message with
+ *    optional compression (zstd/lz4); the schema is reconstructed from the 
relation's attributes
+ *    on read (see [[ArrowCachedBatch]])
+ *  - Enables zero-copy columnar reads when output is ColumnarBatch
+ *  - Uses off-heap memory via Arrow allocators during encode/decode
+ *  - Collects per-column statistics for partition pruning
+ *
+ * Configuration options:
+ *  - spark.sql.cache.serializer: Set to this class name to enable
+ *  - spark.sql.execution.arrow.maxRecordsPerBatch: Max rows per cached batch
+ *  - spark.sql.execution.arrow.compression.codec: Compression (none/zstd/lz4)
+ *  - spark.sql.inMemoryColumnarStorage.enableVectorizedReader: Enable 
columnar output
+ */
+class ArrowCachedBatchSerializer extends SimpleMetricsCachedBatchSerializer {
+
+  // supportsColumnarInput selects the columnar-vs-row input path; it does not 
gate which schemas
+  // this serializer accepts. The cache framework has no per-type fallback to 
another serializer
+  // (whatever spark.sql.cache.serializer selects handles every cached 
relation), so returning
+  // false here only routes input through convertInternalRowToCachedBatch, 
which is still this
+  // serializer. Type support is enforced once per partition by 
checkSupportedSchema below; the
+  // only real precondition for columnar input is that the plan can produce 
columnar output, which
+  // InMemoryRelation already checks via cachedPlan.supportsColumnar before 
calling this.
+  override def supportsColumnarInput(schema: Seq[Attribute]): Boolean = true
+
+  override def convertInternalRowToCachedBatch(
+      input: RDD[InternalRow],
+      schema: Seq[Attribute],
+      storageLevel: StorageLevel,
+      conf: SQLConf): RDD[CachedBatch] = {
+    ArrowCachedBatchSerializer.checkSupportedSchema(schema)
+    // Capture config values on driver before RDD transformation
+    val sparkSchema = DataTypeUtils.fromAttributes(schema)
+    val maxRecordsPerBatch = conf.arrowMaxRecordsPerBatch
+    val maxBytesPerBatch = conf.arrowMaxBytesPerBatch
+    val timeZoneId = conf.sessionLocalTimeZone
+    val compressionCodecName = conf.arrowCompressionCodec
+    val compressionLevel = conf.arrowZstdCompressionLevel
+
+    input.mapPartitionsInternal { rowIterator =>
+      new InternalRowToArrowCachedBatchIterator(
+        rowIterator,
+        schema,
+        sparkSchema,
+        maxRecordsPerBatch,
+        maxBytesPerBatch,
+        timeZoneId,
+        compressionCodecName,
+        compressionLevel)
+    }
+  }
+
+  override def convertColumnarBatchToCachedBatch(
+      input: RDD[ColumnarBatch],
+      schema: Seq[Attribute],
+      storageLevel: StorageLevel,
+      conf: SQLConf): RDD[CachedBatch] = {
+    ArrowCachedBatchSerializer.checkSupportedSchema(schema)
+    // Capture config values on driver before RDD transformation
+    val sparkSchema = DataTypeUtils.fromAttributes(schema)
+    val timeZoneId = conf.sessionLocalTimeZone
+    val compressionCodecName = conf.arrowCompressionCodec
+    val compressionLevel = conf.arrowZstdCompressionLevel
+
+    input.mapPartitionsInternal { batchIterator =>
+      new ColumnarBatchToArrowCachedBatchIterator(
+        batchIterator,
+        schema,
+        sparkSchema,
+        timeZoneId,
+        compressionCodecName,
+        compressionLevel)
+    }
+  }
+
+  override def supportsColumnarOutput(schema: StructType): Boolean = {
+    // Always support columnar output with Arrow
+    true
+  }
+
+  override def vectorTypes(attributes: Seq[Attribute], conf: SQLConf): 
Option[Seq[String]] = {
+    Option(Seq.fill(attributes.length)(classOf[ArrowColumnVector].getName))
+  }
+
+  override def convertCachedBatchToColumnarBatch(
+      input: RDD[CachedBatch],
+      cacheAttributes: Seq[Attribute],
+      selectedAttributes: Seq[Attribute],
+      conf: SQLConf): RDD[ColumnarBatch] = {
+    val cacheSchema = DataTypeUtils.fromAttributes(cacheAttributes)
+    val selectedSchema = DataTypeUtils.fromAttributes(selectedAttributes)
+    val columnIndices =
+      selectedAttributes.map(a => cacheAttributes.map(o => 
o.exprId).indexOf(a.exprId)).toArray
+    // Capture config on driver
+    val timeZoneId = conf.sessionLocalTimeZone
+    val prefetchEnabled = conf.arrowCachePrefetchEnabled
+
+    input.mapPartitionsInternal { batchIterator =>
+      new ArrowCachedBatchToColumnarBatchIterator(
+        batchIterator,
+        cacheSchema,
+        selectedSchema,
+        columnIndices,
+        timeZoneId,
+        prefetchEnabled)
+    }
+  }
+
+  override def convertCachedBatchToInternalRow(
+      input: RDD[CachedBatch],
+      cacheAttributes: Seq[Attribute],
+      selectedAttributes: Seq[Attribute],
+      conf: SQLConf): RDD[InternalRow] = {
+    val cacheSchema = DataTypeUtils.fromAttributes(cacheAttributes)
+    val selectedSchema = DataTypeUtils.fromAttributes(selectedAttributes)
+    val timeZoneId = conf.sessionLocalTimeZone
+
+    // Calculate column indices for projection
+    val selectedIndices = selectedAttributes.map { attr =>
+      cacheAttributes.indexWhere(_.exprId == attr.exprId)
+    }.toArray
+
+    // Check if all selected types can use the fast path.
+    // Types not handled by ArrowColumnReader must use the fallback path.
+    val needsFallback = selectedSchema.fields.exists { f =>
+      f.dataType match {
+        case _: ArrayType | _: StructType | _: MapType => true
+        case CalendarIntervalType | VariantType | NullType => true
+        case _: UserDefinedType[_] => true
+        // Geometry/Geography are represented as an Arrow struct (srid + wkb); 
the fast-path
+        // ArrowColumnReader does not handle them, so route them through the 
fallback.
+        case _: GeometryType | _: GeographyType => true
+        // Nanosecond timestamps write a 16-byte TimestampNanosVal payload 
into the UnsafeRow;
+        // the fast-path typed readers only write fixed primitives, so use the 
fallback, which
+        // reads through 
ArrowColumnVector.getTimestampNTZNanos/getTimestampLTZNanos.
+        case _: TimestampNTZNanosType | _: TimestampLTZNanosType => true
+        case _ => false
+      }
+    }
+
+    if (needsFallback) {
+      // Fall back to columnar-to-row conversion via ColumnarBatch for complex 
types.
+      // Use UnsafeProjection to convert ColumnarBatchRow to UnsafeRow.
+      convertCachedBatchToColumnarBatch(input, cacheAttributes, 
selectedAttributes, conf)
+        .mapPartitionsInternal { batchIter =>
+          val toUnsafe = 
org.apache.spark.sql.catalyst.expressions.UnsafeProjection.create(
+            selectedSchema)
+          batchIter.flatMap { batch =>
+            val numRows = batch.numRows()
+            new Iterator[InternalRow] {
+              private var rowIdx = 0
+              override def hasNext: Boolean = rowIdx < numRows
+              override def next(): InternalRow = {
+                val row = batch.getRow(rowIdx)
+                rowIdx += 1
+                toUnsafe(row)
+              }
+            }
+          }
+        }
+    } else {
+      val prefetchEnabled = conf.arrowCachePrefetchEnabled
+      input.mapPartitionsInternal { batchIterator =>
+        new ArrowCachedBatchToInternalRowIterator(
+          batchIterator,
+          cacheSchema,
+          selectedSchema,
+          selectedIndices,
+          timeZoneId,
+          prefetchEnabled)
+      }
+    }
+  }
+}
+
+/**
+ * Companion object with shared utility methods for Arrow cache serialization.
+ */
+private object ArrowCachedBatchSerializer {
+
+  /**
+   * Run an Arrow write block, translating a CalendarInterval microsecond 
overflow into a clear
+   * error. Arrow's IntervalMonthDayNano representation is nanosecond-based, 
so writing a
+   * CalendarInterval multiplies its microseconds by 1000 with 
Math.multiplyExact; Spark allows the
+   * full Long microsecond domain, so values beyond Long.MaxValue/1000 
overflow and otherwise abort
+   * with an opaque "long overflow" ArithmeticException. The catch is only 
installed when the schema
+   * actually contains a CalendarInterval column (hasInterval), so there is no 
per-row cost and no
+   * effect on schemas without intervals; the try is entered once per batch, 
not per row.
+   */
+  def withIntervalOverflowTranslation[T](hasInterval: Boolean)(block: => T): T 
= {
+    if (!hasInterval) {
+      block
+    } else {
+      try {
+        block
+      } catch {
+        case e: ArithmeticException =>
+          throw SparkException.internalError(
+            "Arrow cache cannot represent a CalendarInterval whose 
microseconds exceed " +
+              "+/-(Long.MaxValue / 1000): Arrow stores intervals in 
nanoseconds and the " +
+              s"conversion overflows. Original error: ${e.getMessage}")
+      }
+    }
+  }
+
+  /**
+   * Whether the schema contains a CalendarInterval anywhere, including nested 
inside arrays,
+   * structs, maps, and UDT sql types (mirroring isSupportedByArrow's 
traversal): the nested Arrow
+   * writers reach the same nanosecond conversion, so a nested interval can 
overflow just like a
+   * top-level one. DataType.existsRecursively is not used because it does not 
descend into
+   * UserDefinedType.sqlType.
+   */
+  def hasCalendarInterval(schema: Seq[Attribute]): Boolean =
+    schema.exists(attr => typeContainsCalendarInterval(attr.dataType))
+
+  private def typeContainsCalendarInterval(dt: DataType): Boolean = dt match {
+    case CalendarIntervalType => true
+    case ArrayType(elementType, _) => typeContainsCalendarInterval(elementType)
+    case StructType(fields) => fields.exists(f => 
typeContainsCalendarInterval(f.dataType))
+    case MapType(keyType, valueType, _) =>
+      typeContainsCalendarInterval(keyType) || 
typeContainsCalendarInterval(valueType)
+    case udt: UserDefinedType[_] => typeContainsCalendarInterval(udt.sqlType)
+    case _ => false
+  }
+
+  /**
+   * Fail fast, once per partition on the driver-facing entry points, if any 
column type cannot be
+   * represented by the Arrow cache. This is the actual capability gate 
(supportsColumnarInput only
+   * chooses the input path). Without it, an unsupported type would otherwise 
surface as a less
+   * obvious failure deeper in schema conversion or statistics collection.
+   */
+  def checkSupportedSchema(schema: Seq[Attribute]): Unit = {
+    schema.find(attr => !ArrowUtils.isSupportedByArrow(attr.dataType)).foreach 
{ attr =>
+      // Use the structured user-facing condition (UNSUPPORTED_DATATYPE) 
rather than an internal
+      // error: an unsupported column type is a user-visible limitation, and 
the docs promise this
+      // condition. It is also the same condition toArrowSchema raises, so 
callers see one
+      // condition for the capability regardless of which layer detects it 
first.
+      throw ExecutionErrors.unsupportedDataTypeError(attr.dataType)
+    }
+  }
+
+  // scalastyle:off caselocale
+  def createCompressionCodec(
+      codecName: String,
+      compressionLevel: Int): CompressionCodec = {
+    codecName.toLowerCase match {
+      case "none" => NoCompressionCodec.INSTANCE
+      // The codec instance must be constructed directly so that 
compressionLevel is honored:
+      // CompressionCodec.Factory.createCodec(codecType) ignores the level and 
builds a codec at
+      // the default level. The level only matters on the write side; the read 
side looks up the
+      // codec by the type recorded in the IPC message.
+      case "zstd" => new ZstdCompressionCodec(compressionLevel)
+      case "lz4" => new Lz4CompressionCodec()
+      case other =>
+        throw SparkException.internalError(
+          s"Unsupported Arrow compression codec: $other. Supported values: 
none, zstd, lz4")
+    }
+  }
+  // scalastyle:on caselocale
+
+  def serializeBatch(batch: ArrowRecordBatch): Array[Byte] = {
+    val out = new ByteArrayOutputStream()
+    val writeChannel = new WriteChannel(Channels.newChannel(out))
+    MessageSerializer.serialize(writeChannel, batch)
+    out.toByteArray
+  }
+
+  /**
+   * Shut down a prefetch worker during task cleanup without leaking the root 
it may have produced.
+   *
+   * The prefetch worker deserializes the next batch into a fresh 
[[VectorSchemaRoot]] off-thread.
+   * If task completion runs while a result is in flight (e.g. a LIMIT 
consumer stops early),
+   * cancelling and discarding the future would drop a root that was already 
(or is about to be)
+   * produced, and the subsequent `allocator.close()` would fail with "Memory 
was leaked by query".
+   *
+   * This stops accepting new work, waits for the worker to finish so no root 
is produced after we
+   * stop looking, then closes any completed result. Always returns null so 
the caller can null out
+   * its future reference. Safe to call with a null executor or future.
+   */
+  def drainAndClosePrefetch(
+      executor: java.util.concurrent.ExecutorService,
+      future: java.util.concurrent.Future[VectorSchemaRoot]): 
java.util.concurrent.Future[
+        VectorSchemaRoot] = {
+    // Drain and join the worker uninterruptibly, then close any root it 
produced, before the
+    // caller closes the allocator. This runs from a task-completion listener, 
which can fire with
+    // the task thread already interrupted (e.g. a killed task). If we let 
awaitTermination or
+    // future.get observe the interrupt and bail early, the worker could still 
be allocating into,
+    // or have already returned, a root that we then neither join nor close -- 
and the subsequent
+    // allocator.close() would race the worker or fail with "Memory was leaked 
by query". So we
+    // defer every interruption -- whether present on entry or delivered while 
blocked (throwing
+    // InterruptedException clears the status, so it must be recorded here or 
it is lost) -- and
+    // restore the flag once draining is done.
+    var wasInterrupted = Thread.interrupted()
+    try {
+      if (executor != null) {
+        executor.shutdown()
+        var terminated = false
+        while (!terminated) {
+          try {
+            terminated =
+              executor.awaitTermination(Long.MaxValue, 
java.util.concurrent.TimeUnit.NANOSECONDS)
+          } catch {
+            // Record the interruption and keep waiting: we must not leave the 
worker running.
+            case _: InterruptedException => wasInterrupted = true
+          }
+        }
+      }
+      if (future != null) {
+        try {
+          // The worker has terminated, so this does not block; close the root 
it produced.
+          val root = future.get()
+          if (root != null) {
+            root.close()
+          }
+        } catch {
+          // The batch was never produced (cancelled/failed); nothing to close.
+          case _: java.util.concurrent.CancellationException =>
+          case _: java.util.concurrent.ExecutionException =>
+          case _: InterruptedException => wasInterrupted = true
+        }
+      }
+    } finally {
+      if (wasInterrupted) {
+        Thread.currentThread().interrupt()
+      }
+    }
+    null
+  }
+
+  def createColumnStats(dataType: DataType): ColumnStats = {
+    dataType match {
+      case BooleanType => new BooleanColumnStats
+      case ByteType => new ByteColumnStats
+      case ShortType => new ShortColumnStats
+      case IntegerType => new IntColumnStats
+      case DateType => new IntColumnStats  // Date is stored as Int
+      case LongType => new LongColumnStats
+      case TimestampType => new LongColumnStats  // Timestamp is stored as Long
+      case TimestampNTZType => new LongColumnStats  // TimestampNTZ is stored 
as Long
+      // Nanosecond timestamps use the TimestampNanosVal-aware collector 
(min/max bounds), the
+      // same one the default cache serializer uses for these types.
+      case _: TimestampNTZNanosType | _: TimestampLTZNanosType => new 
TimestampNanosColumnStats
+      case FloatType => new FloatColumnStats
+      case DoubleType => new DoubleColumnStats
+      case st: StringType => new StringColumnStats(st)
+      case BinaryType => new BinaryColumnStats
+      case dt: DecimalType => new DecimalColumnStats(dt)
+      case CalendarIntervalType => new IntervalColumnStats
+      case _: YearMonthIntervalType => new IntColumnStats   // stored as Int
+      case _: DayTimeIntervalType => new LongColumnStats  // stored as Long
+      case _: TimeType => new LongColumnStats  // Time is stored as Long 
(nanoseconds)
+      case VariantType => new VariantColumnStats
+      // Geometry/Geography collect size/count without min/max bounds. Their 
physical value is a
+      // BinaryView (not Array[Byte]), so GeoColumnStats reads it via 
getBinaryView rather than
+      // BinaryColumnStats' getBinary, which would throw ClassCastException on 
a row that stores a
+      // BinaryView. They are also AtomicTypes that ColumnType (used by 
ObjectColumnStats) does not
+      // handle, so they must be matched explicitly here.
+      case _: GeometryType | _: GeographyType => new GeoColumnStats
+      // Unwrap UDTs to the same collector their underlying type would use. 
isSupportedByArrow
+      // accepts a UDT whenever its sqlType is supported (including 
Variant/Geometry/Geography),
+      // but ObjectColumnStats -> ColumnType(udt.sqlType) only unwraps one 
level and has no case
+      // for those types, so it would throw UNSUPPORTED_DATATYPE during 
materialization. Recursing
+      // here keeps the capability check and the statistics path in agreement.
+      case udt: UserDefinedType[_] => createColumnStats(udt.sqlType)
+      case _ => new ObjectColumnStats(dataType)
+    }
+  }
+
+  def buildStatisticsFromCollectors(
+      collectors: Array[ColumnStats],
+      schema: Seq[Attribute]): InternalRow = {
+    val stats = collectors.flatMap { collector =>
+      val collected = collector.collectedStatistics
+      // ColumnStats returns: [lowerBound, upperBound, nullCount, count, 
sizeInBytes]
+      Seq(collected(0), collected(1), collected(2), collected(3), collected(4))
+    }
+    InternalRow.fromSeq(stats.toSeq)
+  }
+
+  def collectStatistics(
+      root: VectorSchemaRoot,
+      schema: Seq[Attribute]): InternalRow = {
+    val rowCount = root.getRowCount
+    val vectors = root.getFieldVectors.asScala.toSeq
+
+    // Collect stats for each column: lowerBound, upperBound, nullCount, 
rowCount, sizeInBytes
+    val stats = schema.zip(vectors).flatMap { case (attr, vector) =>
+      val nullCount = (0 until rowCount).count(i => vector.isNull(i))
+      val sizeInBytes = vector.getBufferSize.toLong
+
+      val (lower, upper) = attr.dataType match {
+        case BooleanType => calculateMinMaxBoolean(vector, rowCount)
+        case ByteType => calculateMinMaxByte(vector, rowCount)
+        case ShortType => calculateMinMaxShort(vector, rowCount)
+        case IntegerType => calculateMinMaxInt(vector, rowCount)
+        case DateType => calculateMinMaxDate(vector, rowCount)
+        case LongType => calculateMinMaxLong(vector, rowCount)
+        case TimestampType => calculateMinMaxTimestamp(vector, rowCount)
+        case TimestampNTZType => calculateMinMaxTimestampNTZ(vector, rowCount)
+        case t: TimestampNTZNanosType =>
+          calculateMinMaxTimestampNanos(vector, rowCount, t.precision)
+        case t: TimestampLTZNanosType =>
+          calculateMinMaxTimestampNanos(vector, rowCount, t.precision)
+        case FloatType => calculateMinMaxFloat(vector, rowCount)
+        case DoubleType => calculateMinMaxDouble(vector, rowCount)
+        case st: StringType => calculateMinMaxString(vector, rowCount, 
st.collationId)
+        case _: DecimalType => calculateMinMaxDecimal(vector, rowCount, 
attr.dataType)
+        case _: YearMonthIntervalType => 
calculateMinMaxYearMonthInterval(vector, rowCount)
+        case _: DayTimeIntervalType => calculateMinMaxDayTimeInterval(vector, 
rowCount)
+        case _: TimeType => calculateMinMaxTime(vector, rowCount)
+        case _ => (null, null) // Skip for binary, complex, and other 
unsupported types
+      }
+
+      Seq(lower, upper, nullCount, rowCount, sizeInBytes)
+    }
+
+    new 
org.apache.spark.sql.catalyst.expressions.GenericInternalRow(stats.toArray)
+  }
+
+  def calculateMinMaxBoolean(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = true
+    var max = false
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.BitVector].get(i) != 0
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxByte(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Byte.MaxValue
+    var max = Byte.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.TinyIntVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxShort(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Short.MaxValue
+    var max = Short.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.SmallIntVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxInt(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Int.MaxValue
+    var max = Int.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.IntVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxDate(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Int.MaxValue
+    var max = Int.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.DateDayVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxLong(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Long.MaxValue
+    var max = Long.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.BigIntVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxTimestamp(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Long.MaxValue
+    var max = Long.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value =
+          
vector.asInstanceOf[org.apache.arrow.vector.TimeStampMicroTZVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxTimestampNTZ(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Long.MaxValue
+    var max = Long.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value =
+          
vector.asInstanceOf[org.apache.arrow.vector.TimeStampMicroVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxTimestampNanos(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int,
+      precision: Int): (Any, Any) = {
+    // Both TimeStampNanoVector (NTZ) and TimeStampNanoTZVector (LTZ) extend 
TimeStampVector and
+    // store epoch nanoseconds as a long; min/max over the longs matches 
TimestampNanosVal's
+    // calendar order. Convert the bounds back to TimestampNanosVal since that 
is the stat schema's
+    // bound type for these columns.
+    var min = Long.MaxValue
+    var max = Long.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.TimeStampVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) {
+      (DateTimeUtils.epochNanosToTimestampNanos(min, precision),
+        DateTimeUtils.epochNanosToTimestampNanos(max, precision))
+    } else {
+      (null, null)
+    }
+  }
+
+  def calculateMinMaxFloat(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Float.MaxValue
+    var max = Float.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.Float4Vector].get(i)
+        // Skip NaN: IEEE 754 comparisons with NaN are always false, so NaN 
never
+        // updates min/max in the row-based path 
(FloatColumnStats.gatherValueStats).
+        if (!value.isNaN) {
+          if (!hasValue) {
+            min = value
+            max = value
+            hasValue = true
+          } else {
+            if (value < min) min = value
+            if (value > max) max = value
+          }
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxDouble(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Double.MaxValue
+    var max = Double.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.Float8Vector].get(i)
+        // Skip NaN to match DoubleColumnStats.gatherValueStats.
+        if (!value.isNaN) {
+          if (!hasValue) {
+            min = value
+            max = value
+            hasValue = true
+          } else {
+            if (value < min) min = value
+            if (value > max) max = value
+          }
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxString(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int,
+      collationId: Int = StringType.collationId): (Any, Any) = {
+    var min: org.apache.spark.unsafe.types.UTF8String = null
+    var max: org.apache.spark.unsafe.types.UTF8String = null
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val bytes = 
vector.asInstanceOf[org.apache.arrow.vector.VarCharVector].get(i)
+        val value = org.apache.spark.unsafe.types.UTF8String.fromBytes(bytes)
+        if (!hasValue) {
+          min = value.clone()
+          max = value.clone()
+          hasValue = true
+        } else {
+          if (value.semanticCompare(min, collationId) < 0) min = value.clone()
+          if (value.semanticCompare(max, collationId) > 0) max = value.clone()
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxDecimal(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int,
+      dataType: org.apache.spark.sql.types.DataType): (Any, Any) = {
+    val decimalType = dataType.asInstanceOf[DecimalType]
+    var min: org.apache.spark.sql.types.Decimal = null
+    var max: org.apache.spark.sql.types.Decimal = null
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val bigDecimal = vector.asInstanceOf[
+          org.apache.arrow.vector.DecimalVector].getObject(i)
+        val value = org.apache.spark.sql.types.Decimal(
+          bigDecimal, decimalType.precision, decimalType.scale)
+
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value.compareTo(min) < 0) min = value
+          if (value.compareTo(max) > 0) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxYearMonthInterval(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Int.MaxValue
+    var max = Int.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.IntervalYearVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxDayTimeInterval(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Long.MaxValue
+    var max = Long.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = org.apache.arrow.vector.DurationVector.get(
+          
vector.asInstanceOf[org.apache.arrow.vector.DurationVector].getDataBuffer, i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+
+  def calculateMinMaxTime(
+      vector: org.apache.arrow.vector.FieldVector,
+      rowCount: Int): (Any, Any) = {
+    var min = Long.MaxValue
+    var max = Long.MinValue
+    var hasValue = false
+
+    (0 until rowCount).foreach { i =>
+      if (!vector.isNull(i)) {
+        val value = 
vector.asInstanceOf[org.apache.arrow.vector.TimeNanoVector].get(i)
+        if (!hasValue) {
+          min = value
+          max = value
+          hasValue = true
+        } else {
+          if (value < min) min = value
+          if (value > max) max = value
+        }
+      }
+    }
+
+    if (hasValue) (min, max) else (null, null)
+  }
+}
+
+/**
+ * Iterator that converts InternalRow to ArrowCachedBatch.
+ */
+private class InternalRowToArrowCachedBatchIterator(
+    rowIter: Iterator[InternalRow],
+    schema: Seq[Attribute],
+    sparkSchema: StructType,
+    maxRecordsPerBatch: Long,
+    maxBytesPerBatch: Long,
+    timeZoneId: String,
+    compressionCodecName: String,
+    compressionLevel: Int) extends Iterator[ArrowCachedBatch] {
+
+  private val compressionCodec = 
ArrowCachedBatchSerializer.createCompressionCodec(
+    compressionCodecName,
+    compressionLevel)
+
+  private val allocator = ArrowUtils.rootAllocator.newChildAllocator(
+    
s"InternalRowToArrowCachedBatchIterator-${TaskContext.get().taskAttemptId()}",
+    0,
+    Long.MaxValue)
+
+  private val arrowSchema = ArrowUtils.toArrowSchema(sparkSchema, timeZoneId, 
false, false)
+  private val root = VectorSchemaRoot.create(arrowSchema, allocator)
+  private val arrowWriter = ArrowWriter.create(root)
+  private val unloader = new VectorUnloader(root, true, compressionCodec, true)
+
+  // Create statistics collectors for each column
+  private val statsCollectors: Array[ColumnStats] = schema.map { attr =>
+    ArrowCachedBatchSerializer.createColumnStats(attr.dataType)
+  }.toArray
+
+  // Computed once: only CalendarInterval columns can overflow when written to 
Arrow nanoseconds.
+  private val hasCalendarInterval = 
ArrowCachedBatchSerializer.hasCalendarInterval(schema)
+
+  // Register cleanup
+  Option(TaskContext.get()).foreach { tc =>
+    tc.addTaskCompletionListener[Unit] { _ =>
+      close()
+    }
+  }
+
+  override def hasNext: Boolean = rowIter.hasNext || {
+    close()
+    false
+  }
+
+  override def next(): ArrowCachedBatch = {
+    var rowCount = 0
+
+    // Reset statistics collectors for new batch
+    var idx = 0
+    while (idx < statsCollectors.length) {
+      statsCollectors(idx) = 
ArrowCachedBatchSerializer.createColumnStats(schema(idx).dataType)
+      idx += 1
+    }
+
+    Utils.tryWithSafeFinally {
+      // Write rows to Arrow vectors and collect statistics incrementally, 
stopping when either the
+      // record-count or byte limit is reached (whichever is hit first), so 
wide rows cannot form
+      // multi-gigabyte batches that exhaust memory or overflow Arrow's 32-bit 
variable-width
+      // offsets. A nonpositive limit means that limit is unlimited; the `<= 
0` guards also keep the
+      // loop from emitting empty batches forever. At least one row is always 
written so a single
+      // oversized row still makes progress. The byte limit is measured from 
the actual bytes
+      // already written to the Arrow vectors (arrowWriter.sizeInBytes), which 
is accurate for every
+      // row type -- a row-size estimate would undercount large values in a 
GenericInternalRow (e.g.
+      // a multi-megabyte string) and let the batch grow past the limit.
+      def recordLimitReached: Boolean = maxRecordsPerBatch > 0 && rowCount >= 
maxRecordsPerBatch
+      def byteLimitReached: Boolean =
+        maxBytesPerBatch > 0 && arrowWriter.sizeInBytes() >= maxBytesPerBatch
+      
ArrowCachedBatchSerializer.withIntervalOverflowTranslation(hasCalendarInterval) 
{
+        while (rowIter.hasNext && (rowCount == 0 || (!recordLimitReached && 
!byteLimitReached))) {
+          val row = rowIter.next()
+          arrowWriter.write(row)
+
+          // Collect statistics for this row
+          var i = 0
+          while (i < statsCollectors.length) {
+            statsCollectors(i).gatherStats(row, i)
+            i += 1
+          }
+
+          rowCount += 1
+        }
+        arrowWriter.finish()
+      }
+
+      // Get the Arrow RecordBatch with compression
+      val recordBatch = unloader.getRecordBatch()
+
+      Utils.tryWithSafeFinally {
+        // Serialize to Arrow IPC format
+        val arrowData = ArrowCachedBatchSerializer.serializeBatch(recordBatch)
+
+        // Build statistics InternalRow from collected stats
+        val stats = ArrowCachedBatchSerializer.buildStatisticsFromCollectors(
+          statsCollectors, schema)
+
+        ArrowCachedBatch(rowCount, arrowData, stats)
+      } {
+        recordBatch.close()
+      }
+    } {
+      arrowWriter.reset()
+    }
+  }
+
+  private def close(): Unit = {
+    root.close()
+    allocator.close()
+  }
+}
+
+/**
+ * Iterator that converts ColumnarBatch to ArrowCachedBatch.
+ */
+private class ColumnarBatchToArrowCachedBatchIterator(
+    batchIter: Iterator[ColumnarBatch],
+    schema: Seq[Attribute],
+    sparkSchema: StructType,
+    timeZoneId: String,
+    compressionCodecName: String,
+    compressionLevel: Int) extends Iterator[ArrowCachedBatch] {
+
+  private val compressionCodec = 
ArrowCachedBatchSerializer.createCompressionCodec(
+    compressionCodecName,
+    compressionLevel)
+
+  private val allocator = ArrowUtils.rootAllocator.newChildAllocator(
+    
s"ColumnarBatchToArrowCachedBatchIterator-${TaskContext.get().taskAttemptId()}",
+    0,
+    Long.MaxValue)
+
+  private val arrowSchema = ArrowUtils.toArrowSchema(sparkSchema, timeZoneId, 
false, false)
+
+  // Computed once: only CalendarInterval columns can overflow when written to 
Arrow nanoseconds.
+  private val hasCalendarInterval = 
ArrowCachedBatchSerializer.hasCalendarInterval(schema)
+
+  // Register cleanup
+  Option(TaskContext.get()).foreach { tc =>
+    tc.addTaskCompletionListener[Unit] { _ =>
+      allocator.close()
+    }
+  }
+
+  override def hasNext: Boolean = batchIter.hasNext
+
+  override def next(): ArrowCachedBatch = {
+    val batch = batchIter.next()
+    // Release the consumed input batch once converted. This iterator replaces 
the normal
+    // ColumnarToRow consumer (which calls closeIfFreeable() after each 
batch), so without this
+    // an Arrow-backed source's fresh off-heap vectors would stay live for 
every cached batch and
+    // grow executor memory until OOM. Both conversion branches finish 
synchronously and copy the
+    // data out (VectorUnloader / row conversion), so the input is safe to 
free here on success or
+    // failure; closeIfFreeable() is a no-op for reusable writable/constant 
vectors.
+    // One input ColumnarBatch maps to one cached batch: the upstream batch's 
row count is already
+    // bounded by the source's batch-size config (e.g. 
spark.sql.parquet.columnarReaderBatchSize),
+    // so no further record/byte splitting is needed here.
+    Utils.tryWithSafeFinally {
+      val rowCount = batch.numRows()
+
+      // Check if batch is already Arrow-based for zero-copy path. The 
zero-copy path reuses the
+      // input vectors but serializes them under a schema built with 
largeVarTypes=false, and the
+      // read path reconstructs that same non-large schema. Large var-width 
vectors use 64-bit
+      // offsets, so reading them back under a 32-bit-offset schema would 
silently corrupt data.
+      // Fall back to the row-based conversion (which always produces standard 
var-width vectors)
+      // whenever any input vector is, or nests, a large var-width vector.
+      val vectors = (0 until batch.numCols()).map(batch.column)
+      val zeroCopyEligible = vectors.forall {
+        case acv: ArrowColumnVector =>
+          
!ColumnarBatchToArrowCachedBatchIterator.containsLargeVarType(acv.getValueVector)
+        case _ => false
+      }
+      if (zeroCopyEligible) {
+        // Fast path: zero-copy extraction of Arrow RecordBatch
+        convertArrowBatchZeroCopy(batch, rowCount, schema, vectors)
+      } else {
+        // Slow path: convert to Arrow via rows
+        convertToArrowBatch(batch, rowCount, schema)
+      }
+    } {
+      batch.closeIfFreeable()
+    }
+  }
+
+  private def convertArrowBatchZeroCopy(
+      batch: ColumnarBatch,
+      rowCount: Int,
+      schema: Seq[Attribute],
+      vectors: Seq[ColumnVector]): ArrowCachedBatch = {
+    // Zero-copy path: extract Arrow vectors directly from ArrowColumnVector
+    val arrowVectors = vectors.map(
+      _.asInstanceOf[ArrowColumnVector].getValueVector.asInstanceOf[
+        org.apache.arrow.vector.FieldVector])
+
+    // Create a VectorSchemaRoot from the existing vectors
+    val root = new VectorSchemaRoot(arrowSchema, arrowVectors.asJava, rowCount)
+
+    Utils.tryWithSafeFinally {
+      // Use VectorUnloader to create compressed RecordBatch
+      val unloader = new VectorUnloader(root, true, compressionCodec, true)
+      val recordBatch = unloader.getRecordBatch()
+
+      Utils.tryWithSafeFinally {
+        val arrowData = ArrowCachedBatchSerializer.serializeBatch(recordBatch)
+        val stats = ArrowCachedBatchSerializer.collectStatistics(root, schema)
+        ArrowCachedBatch(rowCount, arrowData, stats)
+      } {
+        recordBatch.close()
+      }
+    } {
+      // Note: We don't close the root here because we don't own the vectors

Review Comment:
   Fixed. Clarified that this isn't a use-after-free: 
`serializeBatch`/`collectStatistics` fully materialize their outputs (a copied 
`Array[Byte]` and plain stat values) before this method returns, so nothing 
here still references the input `ColumnarBatch`'s buffers once the caller frees 
them via `closeIfFreeable()`.



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