diff --git a/core/src/main/scala/org/apache/spark/rdd/RDD.scala b/core/src/main/scala/org/apache/spark/rdd/RDD.scala
index 8baf199f215fb438f9c7bbfdde1c08ae05761602..7dad30ecbdd2f9a65144eba230539c44f9cbe1ef 100644
--- a/core/src/main/scala/org/apache/spark/rdd/RDD.scala
+++ b/core/src/main/scala/org/apache/spark/rdd/RDD.scala
@@ -1161,8 +1161,8 @@ abstract class RDD[T: ClassTag](
    */
   @Experimental
   def countApproxDistinct(p: Int, sp: Int): Long = withScope {
-    require(p >= 4, s"p ($p) must be at least 4")
-    require(sp <= 32, s"sp ($sp) cannot be greater than 32")
+    require(p >= 4, s"p ($p) must be >= 4")
+    require(sp <= 32, s"sp ($sp) must be <= 32")
     require(sp == 0 || p <= sp, s"p ($p) cannot be greater than sp ($sp)")
     val zeroCounter = new HyperLogLogPlus(p, sp)
     aggregate(zeroCounter)(
@@ -1187,8 +1187,9 @@ abstract class RDD[T: ClassTag](
    *                   It must be greater than 0.000017.
    */
   def countApproxDistinct(relativeSD: Double = 0.05): Long = withScope {
+    require(relativeSD > 0.000017, s"accuracy ($relativeSD) must be greater than 0.000017")
     val p = math.ceil(2.0 * math.log(1.054 / relativeSD) / math.log(2)).toInt
-    countApproxDistinct(p, 0)
+    countApproxDistinct(if (p < 4) 4 else p, 0)
   }
 
   /**
diff --git a/core/src/test/scala/org/apache/spark/rdd/RDDSuite.scala b/core/src/test/scala/org/apache/spark/rdd/RDDSuite.scala
index ef8c36a28655b174882869936f608ff333d8ab37..afc11bdc4d6aba7155baf81cb81ae4605bf35276 100644
--- a/core/src/test/scala/org/apache/spark/rdd/RDDSuite.scala
+++ b/core/src/test/scala/org/apache/spark/rdd/RDDSuite.scala
@@ -89,6 +89,8 @@ class RDDSuite extends FunSuite with SharedSparkContext {
     val simpleRdd = sc.makeRDD(uniformDistro, 10)
     assert(error(simpleRdd.countApproxDistinct(8, 0), size) < 0.2)
     assert(error(simpleRdd.countApproxDistinct(12, 0), size) < 0.1)
+    assert(error(simpleRdd.countApproxDistinct(0.02), size) < 0.1)
+    assert(error(simpleRdd.countApproxDistinct(0.5), size) < 0.22)
   }
 
   test("SparkContext.union") {
diff --git a/python/pyspark/rdd.py b/python/pyspark/rdd.py
index d254deb527d1052843ab16e515fb44f4604dfa88..545c5ad20cb96cbed06103522c40dea177e52b44 100644
--- a/python/pyspark/rdd.py
+++ b/python/pyspark/rdd.py
@@ -2239,8 +2239,6 @@ class RDD(object):
         """
         if relativeSD < 0.000017:
             raise ValueError("relativeSD should be greater than 0.000017")
-        if relativeSD > 0.37:
-            raise ValueError("relativeSD should be smaller than 0.37")
         # the hash space in Java is 2^32
         hashRDD = self.map(lambda x: portable_hash(x) & 0xFFFFFFFF)
         return hashRDD._to_java_object_rdd().countApproxDistinct(relativeSD)
diff --git a/python/pyspark/tests.py b/python/pyspark/tests.py
index ea63a396da5b8826f28a70cfca680d6350755e01..09de4d159fdcf4a65981b1a697ef3b9fdd1d9821 100644
--- a/python/pyspark/tests.py
+++ b/python/pyspark/tests.py
@@ -644,7 +644,6 @@ class RDDTests(ReusedPySparkTestCase):
         self.assertTrue(18 < rdd.map(lambda x: (x, -x)).countApproxDistinct() < 22)
 
         self.assertRaises(ValueError, lambda: rdd.countApproxDistinct(0.00000001))
-        self.assertRaises(ValueError, lambda: rdd.countApproxDistinct(0.5))
 
     def test_histogram(self):
         # empty