Issue #21718: cursor.description is now available for queries using CTEs

According to PEP 249, cursor.description must be
available for any SELECT statements, such as those
that use CTEs.

Backported from https://github.com/ghaering/pysqlite/commit/f67fa9c898a4713850e16934046f0fe2cba8c44c

Additional test cases added by me.
diff --git a/Lib/sqlite3/test/types.py b/Lib/sqlite3/test/types.py
index 6667bc8..0b5b3e7 100644
--- a/Lib/sqlite3/test/types.py
+++ b/Lib/sqlite3/test/types.py
@@ -274,6 +274,45 @@
         self.cur.execute("select * from test where 0 = 1")
         self.assertEqual(self.cur.description[0][0], "x")
 
+    def CheckCursorDescriptionInsert(self):
+        self.cur.execute("insert into test values (1)")
+        self.assertIsNone(self.cur.description)
+
+
+@unittest.skipIf(sqlite.sqlite_version_info < (3, 8, 3), "CTEs not supported")
+class CommonTableExpressionTests(unittest.TestCase):
+
+    def setUp(self):
+        self.con = sqlite.connect(":memory:")
+        self.cur = self.con.cursor()
+        self.cur.execute("create table test(x foo)")
+
+    def tearDown(self):
+        self.cur.close()
+        self.con.close()
+
+    def CheckCursorDescriptionCTESimple(self):
+        self.cur.execute("with one as (select 1) select * from one")
+        self.assertIsNotNone(self.cur.description)
+        self.assertEqual(self.cur.description[0][0], "1")
+
+    def CheckCursorDescriptionCTESMultipleColumns(self):
+        self.cur.execute("insert into test values(1)")
+        self.cur.execute("insert into test values(2)")
+        self.cur.execute("with testCTE as (select * from test) select * from testCTE")
+        self.assertIsNotNone(self.cur.description)
+        self.assertEqual(self.cur.description[0][0], "x")
+
+    def CheckCursorDescriptionCTE(self):
+        self.cur.execute("insert into test values (1)")
+        self.cur.execute("with bar as (select * from test) select * from test where x = 1")
+        self.assertIsNotNone(self.cur.description)
+        self.assertEqual(self.cur.description[0][0], "x")
+        self.cur.execute("with bar as (select * from test) select * from test where x = 2")
+        self.assertIsNotNone(self.cur.description)
+        self.assertEqual(self.cur.description[0][0], "x")
+
+
 class ObjectAdaptationTests(unittest.TestCase):
     def cast(obj):
         return float(obj)
@@ -372,7 +411,8 @@
     adaptation_suite = unittest.makeSuite(ObjectAdaptationTests, "Check")
     bin_suite = unittest.makeSuite(BinaryConverterTests, "Check")
     date_suite = unittest.makeSuite(DateTimeTests, "Check")
-    return unittest.TestSuite((sqlite_type_suite, decltypes_type_suite, colnames_type_suite, adaptation_suite, bin_suite, date_suite))
+    cte_suite = unittest.makeSuite(CommonTableExpressionTests, "Check")
+    return unittest.TestSuite((sqlite_type_suite, decltypes_type_suite, colnames_type_suite, adaptation_suite, bin_suite, date_suite, cte_suite))
 
 def test():
     runner = unittest.TextTestRunner()
diff --git a/Misc/NEWS b/Misc/NEWS
index 36af974..54cae1d 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -46,6 +46,8 @@
 Library
 -------
 
+- Issue #21718: cursor.description is now available for queries using CTEs.
+
 - Issue #2466: posixpath.ismount now correctly recognizes mount points which
   the user does not have permission to access.
 
diff --git a/Modules/_sqlite/cursor.c b/Modules/_sqlite/cursor.c
index 300da28..e1676de 100644
--- a/Modules/_sqlite/cursor.c
+++ b/Modules/_sqlite/cursor.c
@@ -646,12 +646,11 @@
             goto error;
         }
 
-        if (rc == SQLITE_ROW || (rc == SQLITE_DONE && statement_type == STATEMENT_SELECT)) {
-            if (self->description == Py_None) {
-                Py_BEGIN_ALLOW_THREADS
-                numcols = sqlite3_column_count(self->statement->st);
-                Py_END_ALLOW_THREADS
-
+        if (rc == SQLITE_ROW || rc == SQLITE_DONE) {
+            Py_BEGIN_ALLOW_THREADS
+            numcols = sqlite3_column_count(self->statement->st);
+            Py_END_ALLOW_THREADS
+            if (self->description == Py_None && numcols > 0) {
                 Py_SETREF(self->description, PyTuple_New(numcols));
                 if (!self->description) {
                     goto error;