Github user gatorsmile commented on a diff in the pull request:

    https://github.com/apache/spark/pull/21288#discussion_r189635143
  
    --- Diff: 
sql/core/src/test/scala/org/apache/spark/sql/execution/benchmark/FilterPushdownBenchmark.scala
 ---
    @@ -0,0 +1,437 @@
    +/*
    + * 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.benchmark
    +
    +import java.io.File
    +
    +import scala.util.{Random, Try}
    +
    +import org.apache.spark.SparkConf
    +import org.apache.spark.sql.{DataFrame, SparkSession}
    +import org.apache.spark.sql.functions.monotonically_increasing_id
    +import org.apache.spark.sql.internal.SQLConf
    +import org.apache.spark.util.{Benchmark, Utils}
    +
    +
    +/**
    + * Benchmark to measure read performance with Filter pushdown.
    + * To run this:
    + *  spark-submit --class <this class> <spark sql test jar>
    + */
    +object FilterPushdownBenchmark {
    +  val conf = new SparkConf()
    +    .setAppName("FilterPushdownBenchmark")
    +    .setIfMissing("spark.master", "local[1]")
    +    .setIfMissing("spark.driver.memory", "3g")
    +    .setIfMissing("spark.executor.memory", "3g")
    +    .setIfMissing("orc.compression", "snappy")
    +    .setIfMissing("spark.sql.parquet.compression.codec", "snappy")
    +
    +  private val spark = SparkSession.builder().config(conf).getOrCreate()
    +
    +  def withTempPath(f: File => Unit): Unit = {
    +    val path = Utils.createTempDir()
    +    path.delete()
    +    try f(path) finally Utils.deleteRecursively(path)
    +  }
    +
    +  def withTempTable(tableNames: String*)(f: => Unit): Unit = {
    +    try f finally tableNames.foreach(spark.catalog.dropTempView)
    +  }
    +
    +  def withSQLConf(pairs: (String, String)*)(f: => Unit): Unit = {
    +    val (keys, values) = pairs.unzip
    +    val currentValues = keys.map(key => Try(spark.conf.get(key)).toOption)
    +    (keys, values).zipped.foreach(spark.conf.set)
    +    try f finally {
    +      keys.zip(currentValues).foreach {
    +        case (key, Some(value)) => spark.conf.set(key, value)
    +        case (key, None) => spark.conf.unset(key)
    +      }
    +    }
    +  }
    +
    +  private def prepareTable(
    +      dir: File, numRows: Int, width: Int, useStringForValue: Boolean): 
Unit = {
    +    import spark.implicits._
    +    val selectExpr = (1 to width).map(i => s"CAST(value AS STRING) c$i")
    +    val valueCol = if (useStringForValue) {
    +      monotonically_increasing_id().cast("string")
    +    } else {
    +      monotonically_increasing_id()
    +    }
    +    val df = spark.range(numRows).map(_ => 
Random.nextLong).selectExpr(selectExpr: _*)
    +      .withColumn("value", valueCol)
    +      .sort("value")
    +
    +    saveAsOrcTable(df, dir.getCanonicalPath + "/orc")
    +    saveAsParquetTable(df, dir.getCanonicalPath + "/parquet")
    +  }
    +
    +  private def prepareStringDictTable(
    +      dir: File, numRows: Int, numDistinctValues: Int, width: Int): Unit = 
{
    +    val selectExpr = (0 to width).map {
    +      case 0 => s"CAST(id % $numDistinctValues AS STRING) AS value"
    +      case i => s"CAST(rand() AS STRING) c$i"
    +    }
    +    val df = spark.range(numRows).selectExpr(selectExpr: _*).sort("value")
    +
    +    saveAsOrcTable(df, dir.getCanonicalPath + "/orc")
    +    saveAsParquetTable(df, dir.getCanonicalPath + "/parquet")
    +  }
    +
    +  private def saveAsOrcTable(df: DataFrame, dir: String): Unit = {
    +    df.write.mode("overwrite").orc(dir)
    +    spark.read.orc(dir).createOrReplaceTempView("orcTable")
    +  }
    +
    +  private def saveAsParquetTable(df: DataFrame, dir: String): Unit = {
    +    df.write.mode("overwrite").parquet(dir)
    +    spark.read.parquet(dir).createOrReplaceTempView("parquetTable")
    +  }
    +
    +  def filterPushDownBenchmark(
    +      values: Int,
    +      title: String,
    +      whereExpr: String,
    +      selectExpr: String = "*"): Unit = {
    +    val benchmark = new Benchmark(title, values, minNumIters = 5)
    +
    +    Seq(false, true).foreach { pushDownEnabled =>
    +      val name = s"Parquet Vectorized ${if (pushDownEnabled) s"(Pushdown)" 
else ""}"
    +      benchmark.addCase(name) { _ =>
    +        withSQLConf(SQLConf.PARQUET_FILTER_PUSHDOWN_ENABLED.key -> 
s"$pushDownEnabled") {
    +          spark.sql(s"SELECT $selectExpr FROM parquetTable WHERE 
$whereExpr").collect()
    +        }
    +      }
    +    }
    +
    +    Seq(false, true).foreach { pushDownEnabled =>
    +      val name = s"Native ORC Vectorized ${if (pushDownEnabled) 
s"(Pushdown)" else ""}"
    +      benchmark.addCase(name) { _ =>
    +        withSQLConf(SQLConf.ORC_FILTER_PUSHDOWN_ENABLED.key -> 
s"$pushDownEnabled") {
    +          spark.sql(s"SELECT $selectExpr FROM orcTable WHERE 
$whereExpr").collect()
    +        }
    +      }
    +    }
    +
    +    /*
    +    Intel(R) Xeon(R) CPU E5-2686 v4 @ 2.30GHz
    +    Select 0 string row (value IS NULL):     Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            8452 / 8504          1.9 
        537.3       1.0X
    +    Parquet Vectorized (Pushdown)                  274 /  281         57.3 
         17.4      30.8X
    +    Native ORC Vectorized                         8167 / 8185          1.9 
        519.3       1.0X
    +    Native ORC Vectorized (Pushdown)               365 /  379         43.1 
         23.2      23.1X
    +
    +
    +    Select 0 string row
    +    ('7864320' < value < '7864320'):         Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            8532 / 8564          1.8 
        542.4       1.0X
    +    Parquet Vectorized (Pushdown)                  366 /  386         43.0 
         23.3      23.3X
    +    Native ORC Vectorized                         8289 / 8300          1.9 
        527.0       1.0X
    +    Native ORC Vectorized (Pushdown)               378 /  385         41.6 
         24.0      22.6X
    +
    +
    +    Select 1 string row (value = '7864320'): Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            8547 / 8564          1.8 
        543.4       1.0X
    +    Parquet Vectorized (Pushdown)                  351 /  356         44.9 
         22.3      24.4X
    +    Native ORC Vectorized                         8310 / 8323          1.9 
        528.3       1.0X
    +    Native ORC Vectorized (Pushdown)               370 /  375         42.5 
         23.5      23.1X
    +
    +
    +    Select 1 string row
    +    (value <=> '7864320'):                   Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            8537 / 8563          1.8 
        542.8       1.0X
    +    Parquet Vectorized (Pushdown)                  310 /  319         50.7 
         19.7      27.5X
    +    Native ORC Vectorized                         8316 / 8335          1.9 
        528.7       1.0X
    +    Native ORC Vectorized (Pushdown)               364 /  367         43.2 
         23.1      23.5X
    +
    +
    +    Select 1 string row
    +    ('7864320' <= value <= '7864320'):       Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            8594 / 8607          1.8 
        546.4       1.0X
    +    Parquet Vectorized (Pushdown)                  370 /  374         42.5 
         23.5      23.2X
    +    Native ORC Vectorized                         8350 / 8358          1.9 
        530.9       1.0X
    +    Native ORC Vectorized (Pushdown)               371 /  374         42.4 
         23.6      23.2X
    +
    +
    +    Select all string rows
    +    (value IS NOT NULL):                     Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                          19601 / 19625          0.8 
       1246.2       1.0X
    +    Parquet Vectorized (Pushdown)               19698 / 19703          0.8 
       1252.3       1.0X
    +    Native ORC Vectorized                       19435 / 19470          0.8 
       1235.6       1.0X
    +    Native ORC Vectorized (Pushdown)            19568 / 19590          0.8 
       1244.1       1.0X
    +
    +
    +    Select 0 int row (value IS NULL):        Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7815 / 7824          2.0 
        496.9       1.0X
    +    Parquet Vectorized (Pushdown)                  245 /  251         64.2 
         15.6      31.9X
    +    Native ORC Vectorized                         7436 / 7460          2.1 
        472.8       1.1X
    +    Native ORC Vectorized (Pushdown)               344 /  351         45.7 
         21.9      22.7X
    +
    +
    +    Select 0 int row
    +    (7864320 < value < 7864320):             Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7792 / 7807          2.0 
        495.4       1.0X
    +    Parquet Vectorized (Pushdown)                  349 /  353         45.1 
         22.2      22.3X
    +    Native ORC Vectorized                         7451 / 7465          2.1 
        473.7       1.0X
    +    Native ORC Vectorized (Pushdown)               365 /  368         43.0 
         23.2      21.3X
    +
    +
    +    Select 1 int row (value = 7864320):      Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7836 / 7872          2.0 
        498.2       1.0X
    +    Parquet Vectorized (Pushdown)                  322 /  327         48.8 
         20.5      24.3X
    +    Native ORC Vectorized                         7533 / 7540          2.1 
        478.9       1.0X
    +    Native ORC Vectorized (Pushdown)               358 /  363         43.9 
         22.8      21.9X
    +
    +
    +    Select 1 int row (value <=> 7864320):    Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7855 / 7870          2.0 
        499.4       1.0X
    +    Parquet Vectorized (Pushdown)                  286 /  297         54.9 
         18.2      27.4X
    +    Native ORC Vectorized                         7511 / 7557          2.1 
        477.5       1.0X
    +    Native ORC Vectorized (Pushdown)               358 /  361         43.9 
         22.8      21.9X
    +
    +
    +    Select 1 int row
    +    (7864320 <= value <= 7864320):           Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7851 / 7870          2.0 
        499.2       1.0X
    +    Parquet Vectorized (Pushdown)                  345 /  347         45.6 
         21.9      22.8X
    +    Native ORC Vectorized                         7543 / 7554          2.1 
        479.6       1.0X
    +    Native ORC Vectorized (Pushdown)               364 /  374         43.2 
         23.1      21.6X
    +
    +
    +    Select 1 int row
    +    (7864319 < value < 7864321):             Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7837 / 7840          2.0 
        498.2       1.0X
    +    Parquet Vectorized (Pushdown)                  338 /  339         46.6 
         21.5      23.2X
    +    Native ORC Vectorized                         7524 / 7541          2.1 
        478.3       1.0X
    +    Native ORC Vectorized (Pushdown)               361 /  364         43.6 
         22.9      21.7X
    +
    +
    +    Select 10% int rows (value < 1572864):   Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            8864 / 8900          1.8 
        563.5       1.0X
    +    Parquet Vectorized (Pushdown)                 2088 / 2095          7.5 
        132.7       4.2X
    +    Native ORC Vectorized                         8562 / 8579          1.8 
        544.3       1.0X
    +    Native ORC Vectorized (Pushdown)              2127 / 2131          7.4 
        135.2       4.2X
    +
    +
    +    Select 50% int rows (value < 7864320):   Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                          12671 / 12684          1.2 
        805.6       1.0X
    +    Parquet Vectorized (Pushdown)                 9032 / 9041          1.7 
        574.2       1.4X
    +    Native ORC Vectorized                       12388 / 12411          1.3 
        787.6       1.0X
    +    Native ORC Vectorized (Pushdown)              8873 / 8884          1.8 
        564.1       1.4X
    +
    +
    +    Select 90% int rows (value < 14155776):  Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                          16481 / 16495          1.0 
       1047.8       1.0X
    +    Parquet Vectorized (Pushdown)               15906 / 15919          1.0 
       1011.3       1.0X
    +    Native ORC Vectorized                       16224 / 16254          1.0 
       1031.5       1.0X
    +    Native ORC Vectorized (Pushdown)            15632 / 15661          1.0 
        993.9       1.1X
    +
    +
    +    Select all int rows (value IS NOT NULL): Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                          17341 / 17354          0.9 
       1102.5       1.0X
    +    Parquet Vectorized (Pushdown)               17463 / 17481          0.9 
       1110.2       1.0X
    +    Native ORC Vectorized                       17073 / 17089          0.9 
       1085.4       1.0X
    +    Native ORC Vectorized (Pushdown)            17194 / 17232          0.9 
       1093.2       1.0X
    +
    +
    +    Select all int rows (value > -1):        Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                          17452 / 17467          0.9 
       1109.6       1.0X
    +    Parquet Vectorized (Pushdown)               17613 / 17630          0.9 
       1119.8       1.0X
    +    Native ORC Vectorized                       17259 / 17271          0.9 
       1097.3       1.0X
    +    Native ORC Vectorized (Pushdown)            17385 / 17429          0.9 
       1105.3       1.0X
    +
    +
    +    Select all int rows (value != -1):       Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                          17363 / 17372          0.9 
       1103.9       1.0X
    +    Parquet Vectorized (Pushdown)               17526 / 17535          0.9 
       1114.2       1.0X
    +    Native ORC Vectorized                       17052 / 17089          0.9 
       1084.2       1.0X
    +    Native ORC Vectorized (Pushdown)            17209 / 17229          0.9 
       1094.1       1.0X
    +
    +
    +    Select 0 distinct string row
    +    (value IS NULL):                         Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7697 / 7751          2.0 
        489.4       1.0X
    +    Parquet Vectorized (Pushdown)                  264 /  284         59.5 
         16.8      29.1X
    +    Native ORC Vectorized                         6942 / 6970          2.3 
        441.4       1.1X
    +    Native ORC Vectorized (Pushdown)               372 /  381         42.3 
         23.7      20.7X
    +
    +
    +    Select 0 distinct string row
    +    ('100' < value < '100'):                 Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7983 / 8018          2.0 
        507.5       1.0X
    +    Parquet Vectorized (Pushdown)                  334 /  337         47.0 
         21.3      23.9X
    +    Native ORC Vectorized                         7307 / 7313          2.2 
        464.5       1.1X
    +    Native ORC Vectorized (Pushdown)               363 /  371         43.3 
         23.1      22.0X
    +
    +
    +    Select 1 distinct string row
    +    (value = '100'):                         Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7882 / 7915          2.0 
        501.1       1.0X
    +    Parquet Vectorized (Pushdown)                  504 /  522         31.2 
         32.1      15.6X
    +    Native ORC Vectorized                         7143 / 7155          2.2 
        454.1       1.1X
    +    Native ORC Vectorized (Pushdown)               555 /  573         28.4 
         35.3      14.2X
    +
    +
    +    Select 1 distinct string row
    +    (value <=> '100'):                       Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            7898 / 7912          2.0 
        502.1       1.0X
    +    Parquet Vectorized (Pushdown)                  470 /  481         33.5 
         29.9      16.8X
    +    Native ORC Vectorized                         7135 / 7149          2.2 
        453.6       1.1X
    +    Native ORC Vectorized (Pushdown)               552 /  557         28.5 
         35.1      14.3X
    +
    +
    +    Select 1 distinct string row
    +    ('100' <= value <= '100'):               Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                            8189 / 8213          1.9 
        520.7       1.0X
    +    Parquet Vectorized (Pushdown)                  527 /  534         29.9 
         33.5      15.5X
    +    Native ORC Vectorized                         7477 / 7498          2.1 
        475.3       1.1X
    +    Native ORC Vectorized (Pushdown)               558 /  566         28.2 
         35.5      14.7X
    +
    +
    +    Select all distinct string rows
    +    (value IS NOT NULL):                     Best/Avg Time(ms)    
Rate(M/s)   Per Row(ns)   Relative
    +    
------------------------------------------------------------------------------------------------
    +    Parquet Vectorized                          19462 / 19476          0.8 
       1237.4       1.0X
    +    Parquet Vectorized (Pushdown)               19570 / 19582          0.8 
       1244.2       1.0X
    +    Native ORC Vectorized                       18577 / 18604          0.8 
       1181.1       1.0X
    +    Native ORC Vectorized (Pushdown)            18701 / 18742          0.8 
       1189.0       1.0X
    +    */
    +    benchmark.run()
    +  }
    +
    +  private def runIntBenchmark(numRows: Int, width: Int, mid: Int): Unit = {
    +    Seq("value IS NULL", s"$mid < value AND value < $mid").foreach { 
whereExpr =>
    +      val title = s"Select 0 int row ($whereExpr)".replace("value AND 
value", "value")
    +      filterPushDownBenchmark(numRows, title, whereExpr)
    +    }
    +
    +    Seq(
    +      s"value = $mid",
    +      s"value <=> $mid",
    +      s"$mid <= value AND value <= $mid",
    +      s"${mid - 1} < value AND value < ${mid + 1}"
    +    ).foreach { whereExpr =>
    +      val title = s"Select 1 int row ($whereExpr)".replace("value AND 
value", "value")
    +      filterPushDownBenchmark(numRows, title, whereExpr)
    +    }
    +
    +    val selectExpr = (1 to width).map(i => s"MAX(c$i)").mkString("", ",", 
", MAX(value)")
    +
    +    Seq(10, 50, 90).foreach { percent =>
    +      filterPushDownBenchmark(
    +        numRows,
    +        s"Select $percent% int rows (value < ${numRows * percent / 100})",
    +        s"value < ${numRows * percent / 100}",
    +        selectExpr
    +      )
    +    }
    +
    +    Seq("value IS NOT NULL", "value > -1", "value != -1").foreach { 
whereExpr =>
    +      filterPushDownBenchmark(
    +        numRows,
    +        s"Select all int rows ($whereExpr)",
    +        whereExpr,
    +        selectExpr)
    +    }
    +  }
    +
    +  private def runStringBenchmark(
    +      numRows: Int, width: Int, searchValue: Int, colType: String): Unit = 
{
    +    Seq("value IS NULL", s"'$searchValue' < value AND value < 
'$searchValue'")
    +        .foreach { whereExpr =>
    +      val title = s"Select 0 $colType row ($whereExpr)".replace("value AND 
value", "value")
    +      filterPushDownBenchmark(numRows, title, whereExpr)
    +    }
    +
    +    Seq(
    +      s"value = '$searchValue'",
    +      s"value <=> '$searchValue'",
    +      s"'$searchValue' <= value AND value <= '$searchValue'"
    +    ).foreach { whereExpr =>
    +      val title = s"Select 1 $colType row ($whereExpr)".replace("value AND 
value", "value")
    +      filterPushDownBenchmark(numRows, title, whereExpr)
    +    }
    +
    +    val selectExpr = (1 to width).map(i => s"MAX(c$i)").mkString("", ",", 
", MAX(value)")
    +
    +    Seq("value IS NOT NULL").foreach { whereExpr =>
    +      filterPushDownBenchmark(
    +        numRows,
    +        s"Select all $colType rows ($whereExpr)",
    +        whereExpr,
    +        selectExpr)
    +    }
    +  }
    +
    +  def main(args: Array[String]): Unit = {
    +    val numRows = 1024 * 1024 * 15
    +    val width = 5
    +
    +    // Pushdown for many distinct value case
    +    withTempPath { dir =>
    +      val mid = numRows / 2
    +
    +      withTempTable("orcTable", "patquetTable") {
    +        Seq(true, false).foreach { useStringForValue =>
    +          prepareTable(dir, numRows, width, useStringForValue)
    +          if (useStringForValue) {
    +            runStringBenchmark(numRows, width, mid, "string")
    +          } else {
    +            runIntBenchmark(numRows, width, mid)
    +          }
    +        }
    +      }
    +    }
    +
    +    // Pushdown for few distinct value case (use dictionary encoding)
    --- End diff --
    
    For ORC, the ORC has the conf called `orc.dictionary.key.threshold`. Do we 
need to set the conf here? cc @dongjoon-hyun 
    ```
      DICTIONARY_KEY_SIZE_THRESHOLD("orc.dictionary.key.threshold",
          "hive.exec.orc.dictionary.key.size.threshold",
          0.8,
          "If the number of distinct keys in a dictionary is greater than 
this\n" +
              "fraction of the total number of non-null rows, turn off \n" +
              "dictionary encoding.  Use 1 to always use dictionary encoding.")
    ```


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