[SPARK-8215] [SPARK-8212] [SQL] add leaf math expression for e and pi

Author: Daoyuan Wang <daoyuan.wang@intel.com>

Closes #6716 from adrian-wang/epi and squashes the following commits:

e2e8dbd [Daoyuan Wang] move tests
11b351c [Daoyuan Wang] add tests and remove pu
db331c9 [Daoyuan Wang] py style
599ddd8 [Daoyuan Wang] add py
e6783ef [Daoyuan Wang] register function
82d426e [Daoyuan Wang] add function entry
dbf3ab5 [Daoyuan Wang] add PI and E

sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/analysis/FunctionRegistry.scala

@@ -106,6 +106,7 @@ object FunctionRegistry {
     expression[Cbrt]("cbrt"),
     expression[Ceil]("ceil"),
     expression[Cos]("cos"),
+    expression[EulerNumber]("e"),
     expression[Exp]("exp"),
     expression[Expm1]("expm1"),
     expression[Floor]("floor"),
@@ -113,6 +114,7 @@ object FunctionRegistry {
     expression[Log]("log"),
     expression[Log10]("log10"),
     expression[Log1p]("log1p"),
+    expression[Pi]("pi"),
     expression[Pow]("pow"),
     expression[Rint]("rint"),
     expression[Signum]("signum"),

sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/math.scala

@@ -20,9 +20,34 @@ package org.apache.spark.sql.catalyst.expressions
 import org.apache.spark.sql.catalyst.expressions.codegen._
 import org.apache.spark.sql.types.{DataType, DoubleType}
 
+/**
+ * A leaf expression specifically for math constants. Math constants expect no input.
+ * @param c The math constant.
+ * @param name The short name of the function
+ */
+abstract class LeafMathExpression(c: Double, name: String)
+  extends LeafExpression with Serializable {
+  self: Product =>
+
+  override def dataType: DataType = DoubleType
+  override def foldable: Boolean = true
+  override def nullable: Boolean = false
+  override def toString: String = s"$name()"
+
+  override def eval(input: Row): Any = c
+
+  override def genCode(ctx: CodeGenContext, ev: GeneratedExpressionCode): String = {
+    s"""
+      boolean ${ev.isNull} = false;
+      ${ctx.javaType(dataType)} ${ev.primitive} = java.lang.Math.$name;
+    """
+  }
+}
+
 /**
  * A unary expression specifically for math functions. Math Functions expect a specific type of
  * input format, therefore these functions extend `ExpectsInputTypes`.
+ * @param f The math function.
  * @param name The short name of the function
  */
 abstract class UnaryMathExpression(f: Double => Double, name: String)
@@ -98,6 +123,16 @@ abstract class BinaryMathExpression(f: (Double, Double) => Double, name: String)
   }
 }
 
+////////////////////////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Leaf math functions
+////////////////////////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+case class EulerNumber() extends LeafMathExpression(math.E, "E")
+
+case class Pi() extends LeafMathExpression(math.Pi, "PI")
+
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 // Unary math functions

sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/MathFunctionsSuite.scala

@@ -22,6 +22,20 @@ import org.apache.spark.sql.types.DoubleType
 
 class MathFunctionsSuite extends SparkFunSuite with ExpressionEvalHelper {
 
+  /**
+   * Used for testing leaf math expressions.
+   *
+   * @param e expression
+   * @param c The constants in scala.math
+   * @tparam T Generic type for primitives
+   */
+  private def testLeaf[T](
+      e: () => Expression,
+      c: T): Unit = {
+    checkEvaluation(e(), c, EmptyRow)
+    checkEvaluation(e(), c, create_row(null))
+  }
+
   /**
    * Used for testing unary math expressions.
    *
@@ -74,6 +88,14 @@ class MathFunctionsSuite extends SparkFunSuite with ExpressionEvalHelper {
     checkEvaluation(c(Literal(1.0), Literal.create(null, DoubleType)), null, create_row(null))
   }
 
+  test("e") {
+    testLeaf(EulerNumber, math.E)
+  }
+
+  test("pi") {
+    testLeaf(Pi, math.Pi)
+  }
+
   test("sin") {
     testUnary(Sin, math.sin)
   }

sql/core/src/main/scala/org/apache/spark/sql/functions.scala

@@ -944,6 +944,15 @@ object functions {
    */
   def cosh(columnName: String): Column = cosh(Column(columnName))
 
+  /**
+   * Returns the double value that is closer than any other to e, the base of the natural
+   * logarithms.
+   *
+   * @group math_funcs
+   * @since 1.5.0
+   */
+  def e(): Column = EulerNumber()
+
   /**
    * Computes the exponential of the given value.
    *
@@ -1105,6 +1114,15 @@ object functions {
    */
   def log1p(columnName: String): Column = log1p(Column(columnName))
 
+  /**
+   * Returns the double value that is closer than any other to pi, the ratio of the circumference
+   * of a circle to its diameter.
+   *
+   * @group math_funcs
+   * @since 1.5.0
+   */
+  def pi(): Column = Pi()
+
   /**
    * Returns the value of the first argument raised to the power of the second argument.
    *

sql/core/src/test/scala/org/apache/spark/sql/DataFrameFunctionsSuite.scala

@@ -85,6 +85,25 @@ class DataFrameFunctionsSuite extends QueryTest {
     }
   }
 
+  test("constant functions") {
+    checkAnswer(
+      testData2.select(e()).limit(1),
+      Row(scala.math.E)
+    )
+    checkAnswer(
+      testData2.select(pi()).limit(1),
+      Row(scala.math.Pi)
+    )
+    checkAnswer(
+      ctx.sql("SELECT E()"),
+      Row(scala.math.E)
+    )
+    checkAnswer(
+      ctx.sql("SELECT PI()"),
+      Row(scala.math.Pi)
+    )
+  }
+
   test("bitwiseNOT") {
     checkAnswer(
       testData2.select(bitwiseNOT($"a")),