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

    https://github.com/apache/spark/pull/19783#discussion_r155557934
  
    --- Diff: 
sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/logical/statsEstimation/EstimationUtils.scala
 ---
    @@ -114,4 +114,144 @@ object EstimationUtils {
         }
       }
     
    +  /**
    +   * Returns the number of the first bin into which a column value 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 id of the first bin into which a column value falls.
    +   */
    +  def findFirstBinForValue(value: Double, bins: Array[HistogramBin]): Int 
= {
    +    var i = 0
    +    while ((i < bins.length) && (value > bins(i).hi)) {
    +      i += 1
    +    }
    +    i
    +  }
    +
    +  /**
    +   * Returns the number of the last bin into which a column value 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 id of the last bin into which a column value falls.
    +   */
    +  def findLastBinForValue(value: Double, bins: Array[HistogramBin]): Int = 
{
    +    var i = bins.length - 1
    +    while ((i >= 0) && (value < bins(i).lo)) {
    +      i -= 1
    +    }
    +    i
    +  }
    +
    +  /**
    +   * Returns a percentage of a bin holding values for column value in the 
range of
    +   * [lowerValue, higherValue]
    +   *
    +   * @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 bin a single histogram bin
    +   * @return the percentage of a single bin holding values in [lowerValue, 
higherValue].
    +   */
    +  private def getOccupation(
    +      higherValue: Double,
    +      lowerValue: Double,
    +      bin: HistogramBin): Double = {
    +    assert(bin.lo <= lowerValue && lowerValue <= higherValue && 
higherValue <= bin.hi)
    +    if (bin.hi == bin.lo) {
    +      // the entire bin is covered in the range
    +      1.0
    +    } else if (higherValue == lowerValue) {
    +      // set percentage to 1/NDV
    +      1.0 / bin.ndv.toDouble
    +    } else {
    +      // Use proration since the range falls inside this bin.
    +      math.min((higherValue - lowerValue) / (bin.hi - bin.lo), 1.0)
    +    }
    +  }
    +
    +  /**
    +   * Returns the number of bins for column values in [lowerValue, 
higherValue].
    +   * This is an overloaded method. The column value distribution is saved 
in an
    +   * equi-height histogram.
    +   *
    +   * @param higherId id of the high end bin holding the high end value of 
a column range
    +   * @param lowerId id of the low end bin holding the low end value of a 
column range
    +   * @param higherEnd a given upper bound value of a specified column 
value range
    +   * @param lowerEnd a given lower bound value of a specified column value 
range
    --- End diff --
    
    do we have an assumption between `higherEnd`/`lowerEnd` and 
`higherId`/`lowerId`?


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