Github user cloud-fan commented on a diff in the pull request:

    https://github.com/apache/spark/pull/19783#discussion_r154848428
  
    --- Diff: 
sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/logical/statsEstimation/EstimationUtils.scala
 ---
    @@ -114,4 +114,194 @@ object EstimationUtils {
         }
       }
     
    +  /**
    +   * Returns the number of the first bin into which a column values falls 
for a specified
    +   * numeric equi-height histogram.
    +   *
    +   * @param value a literal value of a column
    +   * @param bins an array of bins for a given numeric equi-height histogram
    +   * @return the number of the first bin into which a column values falls.
    +   */
    +  def findFirstBinForValue(value: Double, bins: Array[HistogramBin]): Int 
= {
    +    var binId = 0
    +    bins.foreach { bin =>
    +      if (value > bin.hi) binId += 1
    +    }
    +    binId
    +  }
    +
    +  /**
    +   * Returns the number of the last bin into which a column values falls 
for a specified
    +   * numeric equi-height histogram.
    +   *
    +   * @param value a literal value of a column
    +   * @param bins an array of bins for a given numeric equi-height histogram
    +   * @return the number of the last bin into which a column values falls.
    +   */
    +  def findLastBinForValue(value: Double, bins: Array[HistogramBin]): Int = 
{
    +    var binId = 0
    +    for (i <- bins.indices) {
    +      if (value > bins(i).hi) {
    +        // increment binId to point to next bin
    +        binId += 1
    +      }
    +      if ((value == bins(i).hi) && (i < bins.length - 1) && (value == 
bins(i + 1).lo)) {
    +        // We assume the above 3 conditions will be evaluated from left to 
right sequentially.
    +        // If the above 3 conditions are evaluated out-of-order, then 
out-of-bound error may happen.
    +        // At that time, we should split the third condition into another 
if statement.
    +        // increment binId since the value appears in this bin and next bin
    +        binId += 1
    +      }
    +    }
    +    binId
    +  }
    +
    +  /**
    +   * Returns a percentage of a bin holding values for column value in the 
range of
    +   * [lowerValue, higherValue]
    +   *
    +   * @param binId a given bin id in a specified histogram
    +   * @param higherValue a given upper bound value of a specified column 
value range
    +   * @param lowerValue a given lower bound value of a specified column 
value range
    +   * @param histogram a numeric equi-height histogram
    +   * @return the percentage of a single bin holding values in [lowerValue, 
higherValue].
    +   */
    +  private def getOccupation(
    +      binId: Int,
    +      higherValue: Double,
    +      lowerValue: Double,
    +      histogram: Histogram): Double = {
    +    val curBin = histogram.bins(binId)
    +    if (binId == 0 && curBin.hi == curBin.lo) {
    +      // the Min of the histogram occupies the whole first bin
    +      1.0
    +    } else if (binId == 0 && curBin.hi != curBin.lo) {
    +      if (higherValue == lowerValue) {
    +        // set percentage to 1/NDV
    +        1.0 / curBin.ndv.toDouble
    +      } else {
    +        // Use proration since the range falls inside this bin.
    +        (higherValue - lowerValue) / (curBin.hi - curBin.lo)
    --- End diff --
    
    this is the only branch we need to specialize for `binId=0`.


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