[SPARK-43943][SQL][PYTHON][CONNECT] Add SQL math functions to Scala a…

…nd Python

### What changes were proposed in this pull request?
Add following functions:

* ceiling
* e
* pi
* ln
* negative
* positive
* power
* sign
* std
* width_bucket

to:

* Scala API
* Python API
* Spark Connect Scala Client
* Spark Connect Python Client

This PR also adds `negate` (which already exists in Scala API and SCSC) to Python API and SCPC.

### Why are the changes needed?
for parity

### Does this PR introduce _any_ user-facing change?
yes, new functions

### How was this patch tested?
added ut / doctest

Closes apache#41435 from zhengruifeng/sql_func_math.

Authored-by: Ruifeng Zheng <ruifengz@apache.org>
Signed-off-by: Ruifeng Zheng <ruifengz@apache.org>

connector/connect/client/jvm/src/main/scala/org/apache/spark/sql/functions.scala

@@ -873,6 +873,14 @@ object functions {
    */
   def skewness(columnName: String): Column = skewness(Column(columnName))
 
+  /**
+   * Aggregate function: alias for `stddev_samp`.
+   *
+   * @group agg_funcs
+   * @since 3.5.0
+   */
+  def std(e: Column): Column = stddev(e)
+
   /**
    * Aggregate function: alias for `stddev_samp`.
    *
@@ -1978,6 +1986,22 @@ object functions {
    */
   def ceil(columnName: String): Column = ceil(Column(columnName))
 
+  /**
+   * Computes the ceiling of the given value of `e` to `scale` decimal places.
+   *
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def ceiling(e: Column, scale: Column): Column = ceil(e, scale)
+
+  /**
+   * Computes the ceiling of the given value of `e` to 0 decimal places.
+   *
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def ceiling(e: Column): Column = ceil(e)
+
   /**
    * Convert a number in a string column from one base to another.
    *
@@ -2053,6 +2077,14 @@ object functions {
    */
   def csc(e: Column): Column = Column.fn("csc", e)
 
+  /**
+   * Returns Euler's number.
+   *
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def e(): Column = Column.fn("e")
+
   /**
    * Computes the exponential of the given value.
    *
@@ -2241,6 +2273,14 @@ object functions {
   def least(columnName: String, columnNames: String*): Column =
     least((columnName +: columnNames).map(Column.apply): _*)
 
+  /**
+   * Computes the natural logarithm of the given value.
+   *
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def ln(e: Column): Column = log(e)
+
   /**
    * Computes the natural logarithm of the given value.
    *
@@ -2321,6 +2361,30 @@ object functions {
    */
   def log2(columnName: String): Column = log2(Column(columnName))
 
+  /**
+   * Returns the negated value.
+   *
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def negative(e: Column): Column = Column.fn("negative", e)
+
+  /**
+   * Returns Pi.
+   *
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def pi(): Column = Column.fn("pi")
+
+  /**
+   * Returns the value.
+   *
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def positive(e: Column): Column = Column.fn("positive", e)
+
   /**
    * Returns the value of the first argument raised to the power of the second argument.
    *
@@ -2385,6 +2449,14 @@ object functions {
    */
   def pow(l: Double, rightName: String): Column = pow(l, Column(rightName))
 
+  /**
+   * Returns the value of the first argument raised to the power of the second argument.
+   *
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def power(l: Column, r: Column): Column = pow(l, r)
+
   /**
    * Returns the positive value of dividend mod divisor.
    *
@@ -2514,6 +2586,14 @@ object functions {
   def shiftrightunsigned(e: Column, numBits: Int): Column =
     Column.fn("shiftrightunsigned", e, lit(numBits))
 
+  /**
+   * Computes the signum of the given value.
+   *
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def sign(e: Column): Column = signum(e)
+
   /**
    * Computes the signum of the given value.
    *
@@ -2702,6 +2782,27 @@ object functions {
    */
   def radians(columnName: String): Column = radians(Column(columnName))
 
+  /**
+   * Returns the bucket number into which the value of this expression would fall after being
+   * evaluated. Note that input arguments must follow conditions listed below; otherwise, the
+   * method will return null.
+   *
+   * @param v
+   *   value to compute a bucket number in the histogram
+   * @param min
+   *   minimum value of the histogram
+   * @param max
+   *   maximum value of the histogram
+   * @param numBucket
+   *   the number of buckets
+   * @return
+   *   the bucket number into which the value would fall after being evaluated
+   * @group math_funcs
+   * @since 3.5.0
+   */
+  def width_bucket(v: Column, min: Column, max: Column, numBucket: Column): Column =
+    Column.fn("width_bucket", v, min, max, numBucket)
+
   //////////////////////////////////////////////////////////////////////////////////////////////
   // Misc functions
   //////////////////////////////////////////////////////////////////////////////////////////////

connector/connect/client/jvm/src/test/scala/org/apache/spark/sql/PlanGenerationTestSuite.scala

@@ -1006,6 +1006,10 @@ class PlanGenerationTestSuite
     fn.stddev("a")
   }
 
+  functionTest("std") {
+    fn.std(fn.col("a"))
+  }
+
   functionTest("stddev_samp") {
     fn.stddev_samp("a")
   }
@@ -1182,6 +1186,14 @@ class PlanGenerationTestSuite
     fn.ceil(fn.col("b"), lit(2))
   }
 
+  functionTest("ceiling") {
+    fn.ceiling(fn.col("b"))
+  }
+
+  functionTest("ceiling scale") {
+    fn.ceiling(fn.col("b"), lit(2))
+  }
+
   functionTest("conv") {
     fn.conv(fn.col("b"), 10, 16)
   }
@@ -1202,6 +1214,10 @@ class PlanGenerationTestSuite
     fn.csc(fn.col("b"))
   }
 
+  functionTest("e") {
+    fn.e()
+  }
+
   functionTest("exp") {
     fn.exp("b")
   }
@@ -1246,6 +1262,10 @@ class PlanGenerationTestSuite
     fn.log("b")
   }
 
+  functionTest("ln") {
+    fn.ln(fn.col("b"))
+  }
+
   functionTest("log with base") {
     fn.log(2, "b")
   }
@@ -1262,10 +1282,26 @@ class PlanGenerationTestSuite
     fn.log2("a")
   }
 
+  functionTest("negative") {
+    fn.negative(fn.col("a"))
+  }
+
+  functionTest("pi") {
+    fn.pi()
+  }
+
+  functionTest("positive") {
+    fn.positive(fn.col("a"))
+  }
+
   functionTest("pow") {
     fn.pow("a", "b")
   }
 
+  functionTest("power") {
+    fn.power(fn.col("a"), fn.col("b"))
+  }
+
   functionTest("pmod") {
     fn.pmod(fn.col("a"), fn.lit(10))
   }
@@ -1302,6 +1338,10 @@ class PlanGenerationTestSuite
     fn.signum("b")
   }
 
+  functionTest("sign") {
+    fn.sign(fn.col("b"))
+  }
+
   functionTest("sin") {
     fn.sin("b")
   }
@@ -2132,6 +2172,10 @@ class PlanGenerationTestSuite
     simple.groupBy(Column("id")).pivot("a").agg(functions.count(Column("b")))
   }
 
+  test("width_bucket") {
+    simple.select(fn.width_bucket(fn.col("b"), fn.col("b"), fn.col("b"), fn.col("a")))
+  }
+
   test("test broadcast") {
     left.join(fn.broadcast(right), "id")
   }

connector/connect/common/src/test/resources/query-tests/explain-results/function_ceiling.explain

@@ -0,0 +1,2 @@
+Project [CEIL(b#0) AS CEIL(b)#0L]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/function_ceiling_scale.explain

@@ -0,0 +1,2 @@
+Project [ceil(cast(b#0 as decimal(30,15)), 2) AS ceil(b, 2)#0]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/function_e.explain

@@ -0,0 +1,2 @@
+Project [E() AS E()#0]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/function_ln.explain

@@ -0,0 +1,2 @@
+Project [LOG(E(), b#0) AS LOG(E(), b)#0]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/function_negative.explain

@@ -0,0 +1,2 @@
+Project [-a#0 AS negative(a)#0]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/function_pi.explain

@@ -0,0 +1,2 @@
+Project [PI() AS PI()#0]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/function_positive.explain

@@ -0,0 +1,2 @@
+Project [positive(a#0) AS (+ a)#0]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/function_power.explain

@@ -0,0 +1,2 @@
+Project [POWER(cast(a#0 as double), b#0) AS POWER(a, b)#0]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/function_sign.explain

@@ -0,0 +1,2 @@
+Project [SIGNUM(b#0) AS SIGNUM(b)#0]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/function_std.explain

@@ -0,0 +1,2 @@
+Aggregate [stddev(cast(a#0 as double)) AS stddev(a)#0]
++- LocalRelation <empty>, [id#0L, a#0, b#0, d#0, e#0, f#0, g#0]

connector/connect/common/src/test/resources/query-tests/explain-results/width_bucket.explain

@@ -0,0 +1,2 @@
+Project [width_bucket(b#0, b#0, b#0, cast(a#0 as bigint)) AS width_bucket(b, b, b, a)#0L]
++- LocalRelation <empty>, [id#0L, a#0, b#0]

connector/connect/common/src/test/resources/query-tests/queries/function_ceiling.json

@@ -0,0 +1,25 @@
+{
+  "common": {
+    "planId": "1"
+  },
+  "project": {
+    "input": {
+      "common": {
+        "planId": "0"
+      },
+      "localRelation": {
+        "schema": "struct\u003cid:bigint,a:int,b:double,d:struct\u003cid:bigint,a:int,b:double\u003e,e:array\u003cint\u003e,f:map\u003cstring,struct\u003cid:bigint,a:int,b:double\u003e\u003e,g:string\u003e"
+      }
+    },
+    "expressions": [{
+      "unresolvedFunction": {
+        "functionName": "ceil",
+        "arguments": [{
+          "unresolvedAttribute": {
+            "unparsedIdentifier": "b"
+          }
+        }]
+      }
+    }]
+  }
+}

connector/connect/common/src/test/resources/query-tests/queries/function_ceiling_scale.json

@@ -0,0 +1,29 @@
+{
+  "common": {
+    "planId": "1"
+  },
+  "project": {
+    "input": {
+      "common": {
+        "planId": "0"
+      },
+      "localRelation": {
+        "schema": "struct\u003cid:bigint,a:int,b:double,d:struct\u003cid:bigint,a:int,b:double\u003e,e:array\u003cint\u003e,f:map\u003cstring,struct\u003cid:bigint,a:int,b:double\u003e\u003e,g:string\u003e"
+      }
+    },
+    "expressions": [{
+      "unresolvedFunction": {
+        "functionName": "ceil",
+        "arguments": [{
+          "unresolvedAttribute": {
+            "unparsedIdentifier": "b"
+          }
+        }, {
+          "literal": {
+            "integer": 2
+          }
+        }]
+      }
+    }]
+  }
+}

connector/connect/common/src/test/resources/query-tests/queries/function_e.json

@@ -0,0 +1,20 @@
+{
+  "common": {
+    "planId": "1"
+  },
+  "project": {
+    "input": {
+      "common": {
+        "planId": "0"
+      },
+      "localRelation": {
+        "schema": "struct\u003cid:bigint,a:int,b:double,d:struct\u003cid:bigint,a:int,b:double\u003e,e:array\u003cint\u003e,f:map\u003cstring,struct\u003cid:bigint,a:int,b:double\u003e\u003e,g:string\u003e"
+      }
+    },
+    "expressions": [{
+      "unresolvedFunction": {
+        "functionName": "e"
+      }
+    }]
+  }
+}

connector/connect/common/src/test/resources/query-tests/queries/function_ln.json

@@ -0,0 +1,25 @@
+{
+  "common": {
+    "planId": "1"
+  },
+  "project": {
+    "input": {
+      "common": {
+        "planId": "0"
+      },
+      "localRelation": {
+        "schema": "struct\u003cid:bigint,a:int,b:double,d:struct\u003cid:bigint,a:int,b:double\u003e,e:array\u003cint\u003e,f:map\u003cstring,struct\u003cid:bigint,a:int,b:double\u003e\u003e,g:string\u003e"
+      }
+    },
+    "expressions": [{
+      "unresolvedFunction": {
+        "functionName": "log",
+        "arguments": [{
+          "unresolvedAttribute": {
+            "unparsedIdentifier": "b"
+          }
+        }]
+      }
+    }]
+  }
+}