[SPARK-14163][CORE] SumEvaluator and countApprox cannot reliably handle RDDs of size 1

## What changes were proposed in this pull request?

This special cases 0 and 1 counts to avoid passing 0 degrees of freedom.

## How was this patch tested?

Tests run successfully. New test added.

## Note:
This recreates #11982 which was closed to due to non-updated diff. rxin srowen Commented there.
This also adds tests, reworks the code to perform the special casing (based on srowen's comments), and adds equality machinery for BoundedDouble, as well as changing how it is transformed to string.

Author: Marcin Tustin <mtustin@handybook.com>
Author: Marcin Tustin <mtustin@handy.com>

Closes #12016 from mtustin-handy/SPARK-14163.

core/src/main/scala/org/apache/spark/partial/BoundedDouble.scala

@@ -21,5 +21,23 @@ package org.apache.spark.partial
  * A Double value with error bars and associated confidence.
  */
 class BoundedDouble(val mean: Double, val confidence: Double, val low: Double, val high: Double) {
+
   override def toString(): String = "[%.3f, %.3f]".format(low, high)
+
+  override def hashCode: Int =
+    this.mean.hashCode ^ this.confidence.hashCode ^ this.low.hashCode ^ this.high.hashCode
+
+  /**
+    * Note that consistent with Double, any NaN value will make equality false
+    */
+  override def equals(that: Any): Boolean =
+    that match {
+      case that: BoundedDouble => {
+        this.mean == that.mean &&
+        this.confidence == that.confidence &&
+        this.low == that.low &&
+        this.high == that.high
+      }
+      case _ => false
+    }
 }

core/src/main/scala/org/apache/spark/partial/SumEvaluator.scala

@@ -29,8 +29,9 @@ import org.apache.spark.util.StatCounter
 private[spark] class SumEvaluator(totalOutputs: Int, confidence: Double)
   extends ApproximateEvaluator[StatCounter, BoundedDouble] {
 
+  // modified in merge
   var outputsMerged = 0
-  var counter = new StatCounter
+  val counter = new StatCounter
 
   override def merge(outputId: Int, taskResult: StatCounter) {
     outputsMerged += 1
@@ -40,30 +41,39 @@ private[spark] class SumEvaluator(totalOutputs: Int, confidence: Double)
   override def currentResult(): BoundedDouble = {
     if (outputsMerged == totalOutputs) {
       new BoundedDouble(counter.sum, 1.0, counter.sum, counter.sum)
-    } else if (outputsMerged == 0) {
+    } else if (outputsMerged == 0 || counter.count == 0) {
       new BoundedDouble(0, 0.0, Double.NegativeInfinity, Double.PositiveInfinity)
     } else {
       val p = outputsMerged.toDouble / totalOutputs
       val meanEstimate = counter.mean
-      val meanVar = counter.sampleVariance / counter.count
       val countEstimate = (counter.count + 1 - p) / p
-      val countVar = (counter.count + 1) * (1 - p) / (p * p)
       val sumEstimate = meanEstimate * countEstimate
-      val sumVar = (meanEstimate * meanEstimate * countVar) +
-                   (countEstimate * countEstimate * meanVar) +
-                   (meanVar * countVar)
-      val sumStdev = math.sqrt(sumVar)
-      val confFactor = {
-        if (counter.count > 100) {
+
+      val meanVar = counter.sampleVariance / counter.count
+
+      // branch at this point because counter.count == 1 implies counter.sampleVariance == Nan
+      // and we don't want to ever return a bound of NaN
+      if (meanVar.isNaN || counter.count == 1) {
+        new BoundedDouble(sumEstimate, confidence, Double.NegativeInfinity, Double.PositiveInfinity)
+      } else {
+        val countVar = (counter.count + 1) * (1 - p) / (p * p)
+        val sumVar = (meanEstimate * meanEstimate * countVar) +
+          (countEstimate * countEstimate * meanVar) +
+          (meanVar * countVar)
+        val sumStdev = math.sqrt(sumVar)
+        val confFactor = if (counter.count > 100) {
           new NormalDistribution().inverseCumulativeProbability(1 - (1 - confidence) / 2)
         } else {
+          // note that if this goes to 0, TDistribution will throw an exception.
+          // Hence special casing 1 above.
           val degreesOfFreedom = (counter.count - 1).toInt
           new TDistribution(degreesOfFreedom).inverseCumulativeProbability(1 - (1 - confidence) / 2)
         }
+
+        val low = sumEstimate - confFactor * sumStdev
+        val high = sumEstimate + confFactor * sumStdev
+        new BoundedDouble(sumEstimate, confidence, low, high)
       }
-      val low = sumEstimate - confFactor * sumStdev
-      val high = sumEstimate + confFactor * sumStdev
-      new BoundedDouble(sumEstimate, confidence, low, high)
     }
   }
 }

core/src/test/scala/org/apache/spark/partial/SumEvaluatorSuite.scala

+/*
+ * 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.partial
+
+import org.apache.spark._
+import org.apache.spark.util.StatCounter
+
+class SumEvaluatorSuite extends SparkFunSuite with SharedSparkContext {
+
+  test("correct handling of count 1") {
+
+    // setup
+    val counter = new StatCounter(List(2.0))
+    // count of 10 because it's larger than 1,
+    // and 0.95 because that's the default
+    val evaluator = new SumEvaluator(10, 0.95)
+    // arbitrarily assign id 1
+    evaluator.merge(1, counter)
+
+    // execute
+    val res = evaluator.currentResult()
+    // 38.0 - 7.1E-15 because that's how the maths shakes out
+    val targetMean = 38.0 - 7.1E-15
+
+    // Sanity check that equality works on BoundedDouble
+    assert(new BoundedDouble(2.0, 0.95, 1.1, 1.2) == new BoundedDouble(2.0, 0.95, 1.1, 1.2))
+
+    // actual test
+    assert(res ==
+      new BoundedDouble(targetMean, 0.950, Double.NegativeInfinity, Double.PositiveInfinity))
+  }
+
+  test("correct handling of count 0") {
+
+    // setup
+    val counter = new StatCounter(List())
+    // count of 10 because it's larger than 0,
+    // and 0.95 because that's the default
+    val evaluator = new SumEvaluator(10, 0.95)
+    // arbitrarily assign id 1
+    evaluator.merge(1, counter)
+
+    // execute
+    val res = evaluator.currentResult()
+    // assert
+    assert(res == new BoundedDouble(0, 0.0, Double.NegativeInfinity, Double.PositiveInfinity))
+  }
+
+  test("correct handling of NaN") {
+
+    // setup
+    val counter = new StatCounter(List(1, Double.NaN, 2))
+    // count of 10 because it's larger than 0,
+    // and 0.95 because that's the default
+    val evaluator = new SumEvaluator(10, 0.95)
+    // arbitrarily assign id 1
+    evaluator.merge(1, counter)
+
+    // execute
+    val res = evaluator.currentResult()
+    // assert - note semantics of == in face of NaN
+    assert(res.mean.isNaN)
+    assert(res.confidence == 0.95)
+    assert(res.low == Double.NegativeInfinity)
+    assert(res.high == Double.PositiveInfinity)
+  }
+
+  test("correct handling of > 1 values") {
+
+    // setup
+    val counter = new StatCounter(List(1, 3, 2))
+    // count of 10 because it's larger than 0,
+    // and 0.95 because that's the default
+    val evaluator = new SumEvaluator(10, 0.95)
+    // arbitrarily assign id 1
+    evaluator.merge(1, counter)
+
+    // execute
+    val res = evaluator.currentResult()
+
+    // These vals because that's how the maths shakes out
+    val targetMean = 78.0
+    val targetLow = -117.617 + 2.732357258139473E-5
+    val targetHigh = 273.617 - 2.7323572624027292E-5
+    val target = new BoundedDouble(targetMean, 0.95, targetLow, targetHigh)
+
+
+    // check that values are within expected tolerance of expectation
+    assert(res == target)
+  }
+
+}