[SPARK-44891][PYTHON][CONNECT] Enable Doctests of rand, randn and…

… `log`

### What changes were proposed in this pull request?

I roughly went thought all the skipped doctests in `pyspark.sql.functions`, and find we can enabled doctests of `rand`, `randn` and `log`, by making them deterministic:

- specify the `numPartitions` in `spark.range` for `rand` `randn`;
- changes the input values for `log`

### Why are the changes needed?
Enable Doctests of `rand`, `randn` and `log`, improve test coverage

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

### How was this patch tested?
enabled doctests

### Was this patch authored or co-authored using generative AI tooling?
No

Closes #42584 from zhengruifeng/make_doctest_deterministic.

Authored-by: Ruifeng Zheng <[email protected]>
Signed-off-by: Ruifeng Zheng <[email protected]>

python/pyspark/sql/functions.py

@@ -4616,13 +4616,13 @@ def rand(seed: Optional[int] = None) -> Column:
 
     Examples
     --------
-    >>> df = spark.range(2)
-    >>> df.withColumn('rand', rand(seed=42) * 3).show() # doctest: +SKIP
+    >>> from pyspark.sql import functions as F
+    >>> spark.range(0, 2, 1, 1).withColumn('rand', F.rand(seed=42) * 3).show()
     +---+------------------+
     | id|              rand|
     +---+------------------+
-    |  0|1.4385751892400076|
-    |  1|1.7082186019706387|
+    |  0|1.8575681106759028|
+    |  1|1.5288056527339444|
     +---+------------------+
     """
     if seed is not None:
@@ -4657,14 +4657,14 @@ def randn(seed: Optional[int] = None) -> Column:
 
     Examples
     --------
-    >>> df = spark.range(2)
-    >>> df.withColumn('randn', randn(seed=42)).show() # doctest: +SKIP
-    +---+--------------------+
-    | id|               randn|
-    +---+--------------------+
-    |  0|-0.04167221574820542|
-    |  1| 0.15241403986452778|
-    +---+--------------------+
+    >>> from pyspark.sql import functions as F
+    >>> spark.range(0, 2, 1, 1).withColumn('randn', F.randn(seed=42)).show()
+    +---+------------------+
+    | id|             randn|
+    +---+------------------+
+    |  0| 2.384479054241165|
+    |  1|0.1920934041293524|
+    +---+------------------+
     """
     if seed is not None:
         return _invoke_function("randn", seed)
@@ -5159,26 +5159,27 @@ def log(arg1: Union["ColumnOrName", float], arg2: Optional["ColumnOrName"] = Non
 
     Examples
     --------
-    >>> df = spark.createDataFrame([10, 100, 1000], "INT")
-    >>> df.select(log(10.0, df.value).alias('ten')).show() # doctest: +SKIP
-    +---+
-    |ten|
-    +---+
-    |1.0|
-    |2.0|
-    |3.0|
-    +---+
+    >>> from pyspark.sql import functions as F
+    >>> df = spark.sql("SELECT * FROM VALUES (1), (2), (4) AS t(value)")
+    >>> df.select(F.log(2.0, df.value).alias('log2_value')).show()
+    +----------+
+    |log2_value|
+    +----------+
+    |       0.0|
+    |       1.0|
+    |       2.0|
+    +----------+
 
     And Natural logarithm
 
-    >>> df.select(log(df.value)).show() # doctest: +SKIP
-    +-----------------+
-    |        ln(value)|
-    +-----------------+
-    |2.302585092994046|
-    |4.605170185988092|
-    |4.605170185988092|
-    +-----------------+
+    >>> df.select(F.log(df.value).alias('ln_value')).show()
+    +------------------+
+    |          ln_value|
+    +------------------+
+    |               0.0|
+    |0.6931471805599453|
+    |1.3862943611198906|
+    +------------------+
     """
     if arg2 is None:
         return _invoke_function_over_columns("log", cast("ColumnOrName", arg1))