diff --git a/core/src/main/scala/org/apache/spark/util/collection/OpenHashSet.scala b/core/src/main/scala/org/apache/spark/util/collection/OpenHashSet.scala
index 1501111a06655..60deb91aa8fc6 100644
--- a/core/src/main/scala/org/apache/spark/util/collection/OpenHashSet.scala
+++ b/core/src/main/scala/org/apache/spark/util/collection/OpenHashSet.scala
@@ -43,7 +43,8 @@ class OpenHashSet[@specialized(Long, Int) T: ClassTag](
     loadFactor: Double)
   extends Serializable {
 
-  require(initialCapacity <= (1 << 29), "Can't make capacity bigger than 2^29 elements")
+  require(initialCapacity <= OpenHashSet.MAX_CAPACITY,
+    s"Can't make capacity bigger than ${OpenHashSet.MAX_CAPACITY} elements")
   require(initialCapacity >= 1, "Invalid initial capacity")
   require(loadFactor < 1.0, "Load factor must be less than 1.0")
   require(loadFactor > 0.0, "Load factor must be greater than 0.0")
@@ -213,6 +214,8 @@ class OpenHashSet[@specialized(Long, Int) T: ClassTag](
    */
   private def rehash(k: T, allocateFunc: (Int) => Unit, moveFunc: (Int, Int) => Unit) {
     val newCapacity = _capacity * 2
+    require(newCapacity > 0 && newCapacity <= OpenHashSet.MAX_CAPACITY,
+      s"Can't contain more than ${(loadFactor * OpenHashSet.MAX_CAPACITY).toInt} elements")
     allocateFunc(newCapacity)
     val newBitset = new BitSet(newCapacity)
     val newData = new Array[T](newCapacity)
@@ -266,9 +269,10 @@ class OpenHashSet[@specialized(Long, Int) T: ClassTag](
 private[spark]
 object OpenHashSet {
 
+  val MAX_CAPACITY = 1 << 30
   val INVALID_POS = -1
-  val NONEXISTENCE_MASK = 0x80000000
-  val POSITION_MASK = 0xEFFFFFF
+  val NONEXISTENCE_MASK = 1 << 31
+  val POSITION_MASK = (1 << 31) - 1
 
   /**
    * A set of specialized hash function implementation to avoid boxing hash code computation
diff --git a/core/src/test/scala/org/apache/spark/util/collection/OpenHashMapSuite.scala b/core/src/test/scala/org/apache/spark/util/collection/OpenHashMapSuite.scala
index 94e011799921b..3066e9996abda 100644
--- a/core/src/test/scala/org/apache/spark/util/collection/OpenHashMapSuite.scala
+++ b/core/src/test/scala/org/apache/spark/util/collection/OpenHashMapSuite.scala
@@ -44,7 +44,7 @@ class OpenHashMapSuite extends SparkFunSuite with Matchers {
     val goodMap3 = new OpenHashMap[String, String](256)
     assert(goodMap3.size === 0)
     intercept[IllegalArgumentException] {
-      new OpenHashMap[String, Int](1 << 30) // Invalid map size: bigger than 2^29
+      new OpenHashMap[String, Int](1 << 30 + 1) // Invalid map size: bigger than 2^30
     }
     intercept[IllegalArgumentException] {
       new OpenHashMap[String, Int](-1)
@@ -186,4 +186,14 @@ class OpenHashMapSuite extends SparkFunSuite with Matchers {
     map(null) = 0
     assert(map.contains(null))
   }
+
+  test("support for more than 12M items") {
+    val cnt = 12000000 // 12M
+    val map = new OpenHashMap[Int, Int](cnt)
+    for (i <- 0 until cnt) {
+      map(i) = 1
+    }
+    val numInvalidValues = map.iterator.count(_._2 == 0)
+    assertResult(0)(numInvalidValues)
+  }
 }
diff --git a/core/src/test/scala/org/apache/spark/util/collection/PrimitiveKeyOpenHashMapSuite.scala b/core/src/test/scala/org/apache/spark/util/collection/PrimitiveKeyOpenHashMapSuite.scala
index 462bc2f29f9f8..508e737b725bc 100644
--- a/core/src/test/scala/org/apache/spark/util/collection/PrimitiveKeyOpenHashMapSuite.scala
+++ b/core/src/test/scala/org/apache/spark/util/collection/PrimitiveKeyOpenHashMapSuite.scala
@@ -44,7 +44,7 @@ class PrimitiveKeyOpenHashMapSuite extends SparkFunSuite with Matchers {
     val goodMap3 = new PrimitiveKeyOpenHashMap[Int, Int](256)
     assert(goodMap3.size === 0)
     intercept[IllegalArgumentException] {
-      new PrimitiveKeyOpenHashMap[Int, Int](1 << 30) // Invalid map size: bigger than 2^29
+      new PrimitiveKeyOpenHashMap[Int, Int](1 << 30 + 1) // Invalid map size: bigger than 2^30
     }
     intercept[IllegalArgumentException] {
       new PrimitiveKeyOpenHashMap[Int, Int](-1)