select_found.result, select_found.test:

  Added a test case for bug #7945.
sql_select.cc:
  Fixed bug #7945. If DISTINCT is used only with constants
  in a query with GROUP BY, we can apply an optimization
  that set LIMIT to 1 only in the case when there is 
  no SQL_CALC_FOUND_ROWS.

mysql-test/r/select_found.result

@@ -223,3 +223,11 @@ SELECT FOUND_ROWS();
 FOUND_ROWS()
 0
 DROP TABLE t1;
+CREATE TABLE t1 (a int, b int);
+INSERT INTO t1 VALUES (1,2), (1,3), (1,4), (1,5);
+SELECT SQL_CALC_FOUND_ROWS DISTINCT 'a' FROM t1 GROUP BY b LIMIT 2;
+a
+a
+SELECT FOUND_ROWS();
+FOUND_ROWS()
+1

mysql-test/t/select_found.test

@@ -146,3 +146,12 @@ INSERT INTO t1 VALUES (0), (0), (1), (2);
 SELECT SQL_CALC_FOUND_ROWS * FROM t1 WHERE a = 0 GROUP BY a HAVING a > 10;
 SELECT FOUND_ROWS();
 DROP TABLE t1;
+
+#
+# Bug #7945: group by + distinct with constant expression + limit 
+#
+
+CREATE TABLE t1 (a int, b int);
+INSERT INTO t1 VALUES (1,2), (1,3), (1,4), (1,5);
+SELECT SQL_CALC_FOUND_ROWS DISTINCT 'a' FROM t1 GROUP BY b LIMIT 2;
+SELECT FOUND_ROWS();

sql/sql_select.cc

@@ -2114,9 +2114,15 @@ find_best(JOIN *join,table_map rest_tables,uint idx,double record_count,
 		    x = used key parts (1 <= x <= c)
 		  */
 		  double rec_per_key;
+#if 0
 		  if (!(rec_per_key=(double)
 			keyinfo->rec_per_key[keyinfo->key_parts-1]))
 		    rec_per_key=(double) s->records/rec+1;
+#else
+                  rec_per_key= keyinfo->rec_per_key[keyinfo->key_parts-1] ?
+		    (double) keyinfo->rec_per_key[keyinfo->key_parts-1] :
+		    (double) s->records/rec+1;   
+#endif
 
 		  if (!s->records)
 		    tmp=0;
@@ -6276,13 +6282,14 @@ remove_duplicates(JOIN *join, TABLE *entry,List<Item> &fields, Item *having)
       field_count++;
   }
 
-  if (!field_count)
-  {						// only const items
+  if (!field_count && !(join->select_options & OPTION_FOUND_ROWS)) 
+  {                    // only const items with no OPTION_FOUND_ROWS
     join->thd->select_limit=1;	// Only send first row
     DBUG_RETURN(0);
   }
   Field **first_field=entry->field+entry->fields - field_count;
-  offset=entry->field[entry->fields - field_count]->offset();
+  offset= field_count ? 
+          entry->field[entry->fields - field_count]->offset() : 0;
   reclength=entry->reclength-offset;
 
   free_io_cache(entry);				// Safety