"reviewer comment addressed"

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

@@ -391,6 +391,7 @@ abstract class RDD[T: ClassTag](
       seed: Long = Utils.random.nextLong): Array[T] = {
     var fraction = 0.0
     var total = 0
+    val numStDev =  10.0
     val initialCount = this.count()
 
     if (num < 0) {
@@ -406,15 +407,15 @@ abstract class RDD[T: ClassTag](
         "sampling without replacement")
     }
 
-    if (initialCount > Integer.MAX_VALUE - 1) {
-      val maxSelected = Integer.MAX_VALUE - (5.0 * math.sqrt(Integer.MAX_VALUE)).toInt
+    if (initialCount > Int.MaxValue - 1) {
+      val maxSelected = Int.MaxValue - (numStDev * math.sqrt(Int.MaxValue)).toInt
       if (num > maxSelected) {
-        throw new IllegalArgumentException("Cannot support a sample size > Integer.MAX_VALUE - " +
-          "5.0 * math.sqrt(Integer.MAX_VALUE)")
+        throw new IllegalArgumentException("Cannot support a sample size > Int.MaxValue - " +
+          s"$numStDev * math.sqrt(Int.MaxValue)")
       }
     }
 
-    fraction = SamplingUtils.computeFraction(num, initialCount, withReplacement)
+    fraction = SamplingUtils.computeFractionForSampleSize(num, initialCount, withReplacement)
     total = num
 
     val rand = new Random(seed)

core/src/main/scala/org/apache/spark/util/random/SamplingUtils.scala

@@ -31,15 +31,15 @@ private[spark] object SamplingUtils {
    *     ~ Binomial(total, fraction) and our choice of q guarantees 1-delta, or 0.9999 success
    *     rate, where success rate is defined the same as in sampling with replacement.
    *
-   * @param num sample size
+   * @param sampleSizeLowerBound sample size
    * @param total size of RDD
    * @param withReplacement whether sampling with replacement
    * @return a sampling rate that guarantees sufficient sample size with 99.99% success rate
    */
-  def computeFraction(num: Int, total: Long, withReplacement: Boolean): Double = {
-    val fraction = num.toDouble / total
+  def computeFractionForSampleSize(sampleSizeLowerBound: Int, total: Long, withReplacement: Boolean): Double = {
+    val fraction = sampleSizeLowerBound.toDouble / total
     if (withReplacement) {
-      val numStDev = if (num < 12) 9 else 5
+      val numStDev = if (sampleSizeLowerBound < 12) 9 else 5
       fraction + numStDev * math.sqrt(fraction / total)
     } else {
       val delta = 1e-4

core/src/test/scala/org/apache/spark/util/random/SamplingUtilsSuite.scala

@@ -28,17 +28,17 @@ class SamplingUtilsSuite extends FunSuite{
     val n = 100000
 
     for (s <- 1 to 15) {
-      val frac = SamplingUtils.computeFraction(s, n, true)
+      val frac = SamplingUtils.computeFractionForSampleSize(s, n, true)
       val poisson = new PoissonDistribution(frac * n)
       assert(poisson.inverseCumulativeProbability(0.0001) >= s, "Computed fraction is too low")
     }
     for (s <- List(20, 100, 1000)) {
-      val frac = SamplingUtils.computeFraction(s, n, true)
+      val frac = SamplingUtils.computeFractionForSampleSize(s, n, true)
       val poisson = new PoissonDistribution(frac * n)
       assert(poisson.inverseCumulativeProbability(0.0001) >= s, "Computed fraction is too low")
     }
     for (s <- List(1, 10, 100, 1000)) {
-      val frac = SamplingUtils.computeFraction(s, n, false)
+      val frac = SamplingUtils.computeFractionForSampleSize(s, n, false)
       val binomial = new BinomialDistribution(n, frac)
       assert(binomial.inverseCumulativeProbability(0.0001)*n >= s, "Computed fraction is too low")
     }

pom.xml

@@ -256,11 +256,6 @@
 	    <artifactId>commons-codec</artifactId>
 	    <version>1.5</version>
       </dependency>
-      <dependency>
-        <groupId>org.apache.commons</groupId>
-        <artifactId>commons-math3</artifactId>
-        <version>3.3</version>
-      </dependency>
       <dependency>
         <groupId>com.google.code.findbugs</groupId>
         <artifactId>jsr305</artifactId>

python/pyspark/rdd.py

@@ -366,27 +366,25 @@ def takeSample(self, withReplacement, num, seed=None):
 
         fraction = 0.0
         total = 0
-        multiplier = 3.0
+        numStDev = 10.0
         initialCount = self.count()
-        maxSelected = 0
 
-        if (num < 0):
+        if num < 0:
             raise ValueError
 
-        if (initialCount == 0):
+        if initialCount == 0:
             return list()
 
+        if (not withReplacement) and num > initialCount:
+            raise ValueError
+
         if initialCount > sys.maxint - 1:
-            maxSelected = sys.maxint - 1
-        else:
-            maxSelected = initialCount
+            maxSelected = sys.maxint  - int(numStDev * sqrt(sys.maxint))
+            if num > maxSelected:
+                raise ValueError
 
-        if num > initialCount and not withReplacement:
-            total = maxSelected
-            fraction = multiplier * (maxSelected + 1) / initialCount
-        else:
-            fraction = self._computeFraction(num, initialCount, withReplacement)
-            total = num
+        fraction = self._computeFraction(num, initialCount, withReplacement)
+        total = num
 
         samples = self.sample(withReplacement, fraction, seed).collect()