SPARK-6480 [CORE] histogram() bucket function is wrong in some simple edge cases

Fix fastBucketFunction for histogram() to handle edge conditions more correctly. Add a test, and fix existing one accordingly

Author: Sean Owen <sowen@cloudera.com>

Closes #5148 from srowen/SPARK-6480 and squashes the following commits:

974a0a0 [Sean Owen] Additional test of huge ranges, and a few more comments (and comment fixes)
23ec01e [Sean Owen] Fix fastBucketFunction for histogram() to handle edge conditions more correctly. Add a test, and fix existing one accordingly

core/src/main/scala/org/apache/spark/rdd/DoubleRDDFunctions.scala

@@ -191,25 +191,23 @@ class DoubleRDDFunctions(self: RDD[Double]) extends Logging with Serializable {
       }
     }
     // Determine the bucket function in constant time. Requires that buckets are evenly spaced
-    def fastBucketFunction(min: Double, increment: Double, count: Int)(e: Double): Option[Int] = {
+    def fastBucketFunction(min: Double, max: Double, count: Int)(e: Double): Option[Int] = {
       // If our input is not a number unless the increment is also NaN then we fail fast
-      if (e.isNaN()) {
-        return None
-      }
-      val bucketNumber = (e - min)/(increment)
-      // We do this rather than buckets.lengthCompare(bucketNumber)
-      // because Array[Double] fails to override it (for now).
-      if (bucketNumber > count || bucketNumber < 0) {
+      if (e.isNaN || e < min || e > max) {
         None
       } else {
-        Some(bucketNumber.toInt.min(count - 1))
+        // Compute ratio of e's distance along range to total range first, for better precision
+        val bucketNumber = (((e - min) / (max - min)) * count).toInt
+        // should be less than count, but will equal count if e == max, in which case
+        // it's part of the last end-range-inclusive bucket, so return count-1
+        Some(math.min(bucketNumber, count - 1))
       }
     }
     // Decide which bucket function to pass to histogramPartition. We decide here
-    // rather than having a general function so that the decission need only be made
+    // rather than having a general function so that the decision need only be made
     // once rather than once per shard
     val bucketFunction = if (evenBuckets) {
-      fastBucketFunction(buckets(0), buckets(1)-buckets(0), buckets.length-1) _
+      fastBucketFunction(buckets.head, buckets.last, buckets.length - 1) _
     } else {
       basicBucketFunction _
     }

core/src/test/scala/org/apache/spark/rdd/DoubleRDDSuite.scala

@@ -235,6 +235,12 @@ class DoubleRDDSuite extends FunSuite with SharedSparkContext {
     assert(histogramBuckets === expectedHistogramBuckets)
   }
 
+  test("WorksWithDoubleValuesAtMinMax") {
+    val rdd = sc.parallelize(Seq(1, 1, 1, 2, 3, 3))
+    assert(Array(3, 0, 1, 2) === rdd.map(_.toDouble).histogram(4)._2)
+    assert(Array(3, 1, 2) === rdd.map(_.toDouble).histogram(3)._2)
+  }
+
   test("WorksWithoutBucketsWithMoreRequestedThanElements") {
     // Verify the basic case of one bucket and all elements in that bucket works
     val rdd = sc.parallelize(Seq(1, 2))
@@ -248,7 +254,7 @@ class DoubleRDDSuite extends FunSuite with SharedSparkContext {
   }
 
   test("WorksWithoutBucketsForLargerDatasets") {
-    // Verify the case of slighly larger datasets
+    // Verify the case of slightly larger datasets
     val rdd = sc.parallelize(6 to 99)
     val (histogramBuckets, histogramResults) = rdd.histogram(8)
     val expectedHistogramResults =
@@ -259,17 +265,27 @@ class DoubleRDDSuite extends FunSuite with SharedSparkContext {
     assert(histogramBuckets === expectedHistogramBuckets)
   }
 
-  test("WorksWithoutBucketsWithIrrationalBucketEdges") {
-    // Verify the case of buckets with irrational edges. See #SPARK-2862.
+  test("WorksWithoutBucketsWithNonIntegralBucketEdges") {
+    // Verify the case of buckets with nonintegral edges. See #SPARK-2862.
     val rdd = sc.parallelize(6 to 99)
     val (histogramBuckets, histogramResults) = rdd.histogram(9)
+    // Buckets are 6.0, 16.333333333333336, 26.666666666666668, 37.0, 47.333333333333336 ...
     val expectedHistogramResults =
-      Array(11, 10, 11, 10, 10, 11, 10, 10, 11)
+      Array(11, 10, 10, 11, 10, 10, 11, 10, 11)
     assert(histogramResults === expectedHistogramResults)
     assert(histogramBuckets(0) === 6.0)
     assert(histogramBuckets(9) === 99.0)
   }
 
+  test("WorksWithHugeRange") {
+    val rdd = sc.parallelize(Array(0, 1.0e24, 1.0e30))
+    val histogramResults = rdd.histogram(1000000)._2
+    assert(histogramResults(0) === 1)
+    assert(histogramResults(1) === 1)
+    assert(histogramResults.last === 1)
+    assert((2 to histogramResults.length - 2).forall(i => histogramResults(i) == 0))
+  }
+
   // Test the failure mode with an invalid RDD
   test("ThrowsExceptionOnInvalidRDDs") {
     // infinity