Implemented avg() window function.

It is based on the sum() function, thus much of the logic is shared.

Considering that there are 2 counters stored within the function, one
that handles the null value, while the other that handles the divisor
for the avg computation, it is possible to remove the counter from the
Item_sum_avg. I have not removed it in this patch as we may choose to
refactor the whole code into a separate class.
This remains to be dicussed.

mysql-test/r/win_avg.result

+create table t1 (
+pk int primary key,
+a int,
+b int,
+c real
+);
+insert into t1 values
+(101 , 0, 10, 1.1),
+(102 , 0, 10, 2.1),
+(103 , 1, 10, 3.1),
+(104 , 1, 10, 4.1),
+(108 , 2, 10, 5.1),
+(105 , 2, 20, 6.1),
+(106 , 2, 20, 7.1),
+(107 , 2, 20, 8.15),
+(109 , 4, 20, 9.15),
+(110 , 4, 20, 10.15),
+(111 , 5, NULL, 11.15),
+(112 , 5, 1, 12.25),
+(113 , 5, NULL, 13.35),
+(114 , 5, NULL, 14.50),
+(115 , 5, NULL, 15.65),
+(116 , 6, 1, NULL),
+(117 , 6, 1, 10),
+(118 , 6, 1, 1.1),
+(119 , 6, 1, NULL),
+(120 , 6, 1, NULL),
+(121 , 6, 1, NULL),
+(122 , 6, 1, 2.2),
+(123 , 6, 1, 20.1),
+(124 , 6, 1, -10.4),
+(125 , 6, 1, NULL),
+(126 , 6, 1, NULL),
+(127 , 6, 1, NULL);
+select pk, a, b, avg(b) over (partition by a order by pk ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING)
+from t1;
+pk	a	b	avg(b) over (partition by a order by pk ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING)
+101	0	10	10.0000
+102	0	10	10.0000
+103	1	10	10.0000
+104	1	10	10.0000
+105	2	20	20.0000
+106	2	20	20.0000
+107	2	20	16.6667
+108	2	10	15.0000
+109	4	20	20.0000
+110	4	20	20.0000
+111	5	NULL	1.0000
+112	5	1	1.0000
+113	5	NULL	1.0000
+114	5	NULL	NULL
+115	5	NULL	NULL
+116	6	1	1.0000
+117	6	1	1.0000
+118	6	1	1.0000
+119	6	1	1.0000
+120	6	1	1.0000
+121	6	1	1.0000
+122	6	1	1.0000
+123	6	1	1.0000
+124	6	1	1.0000
+125	6	1	1.0000
+126	6	1	1.0000
+127	6	1	1.0000
+select pk, a, c, avg(c) over (partition by a order by pk ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING)
+from t1;
+pk	a	c	avg(c) over (partition by a order by pk ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING)
+101	0	1.1	1.6
+102	0	2.1	1.6
+103	1	3.1	3.5999999999999996
+104	1	4.1	3.5999999999999996
+105	2	6.1	6.6
+106	2	7.1	7.116666666666667
+107	2	8.15	6.783333333333334
+108	2	5.1	6.625000000000001
+109	4	9.15	9.65
+110	4	10.15	9.65
+111	5	11.15	11.7
+112	5	12.25	12.25
+113	5	13.35	13.366666666666667
+114	5	14.5	14.5
+115	5	15.65	15.075
+116	6	NULL	10
+117	6	10	5.55
+118	6	1.1	5.55
+119	6	NULL	1.0999999999999996
+120	6	NULL	NULL
+121	6	NULL	2.1999999999999997
+122	6	2.2	11.15
+123	6	20.1	3.966666666666667
+124	6	-10.4	4.85
+125	6	NULL	-10.400000000000002
+126	6	NULL	NULL
+127	6	NULL	NULL
+drop table t1;

mysql-test/t/win_avg.test

+create table t1 (
+  pk int primary key,
+  a int,
+  b int,
+  c real
+);
+
+
+insert into t1 values
+(101 , 0, 10, 1.1),
+(102 , 0, 10, 2.1),
+(103 , 1, 10, 3.1),
+(104 , 1, 10, 4.1),
+(108 , 2, 10, 5.1),
+(105 , 2, 20, 6.1),
+(106 , 2, 20, 7.1),
+(107 , 2, 20, 8.15),
+(109 , 4, 20, 9.15),
+(110 , 4, 20, 10.15),
+(111 , 5, NULL, 11.15),
+(112 , 5, 1, 12.25),
+(113 , 5, NULL, 13.35),
+(114 , 5, NULL, 14.50),
+(115 , 5, NULL, 15.65),
+(116 , 6, 1, NULL),
+(117 , 6, 1, 10),
+(118 , 6, 1, 1.1),
+(119 , 6, 1, NULL),
+(120 , 6, 1, NULL),
+(121 , 6, 1, NULL),
+(122 , 6, 1, 2.2),
+(123 , 6, 1, 20.1),
+(124 , 6, 1, -10.4),
+(125 , 6, 1, NULL),
+(126 , 6, 1, NULL),
+(127 , 6, 1, NULL);
+
+
+--sorted_result
+select pk, a, b, avg(b) over (partition by a order by pk ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING)
+from t1;
+
+--sorted_result
+select pk, a, c, avg(c) over (partition by a order by pk ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING)
+from t1;
+
+drop table t1;

sql/item_sum.cc

@@ -1681,6 +1681,16 @@ bool Item_sum_avg::add()
   return FALSE;
 }
 
+void Item_sum_avg::remove()
+{
+  Item_sum_sum::remove();
+  if (!aggr->arg_is_null(true))
+  {
+    DBUG_ASSERT(count > 0);
+    count--;
+  }
+}
+
 double Item_sum_avg::val_real()
 {
   DBUG_ASSERT(fixed == 1);

sql/item_sum.h

@@ -837,6 +837,8 @@ class Item_sum_count :public Item_sum_int
 class Item_sum_avg :public Item_sum_sum
 {
 public:
+  // TODO-cvicentiu given that Item_sum_sum now uses a counter of its own, in
+  // order to implement remove(), it is possible to remove this member.
   ulonglong count;
   uint prec_increment;
   uint f_precision, f_scale, dec_bin_size;
@@ -855,6 +857,7 @@ class Item_sum_avg :public Item_sum_sum
   }
   void clear();
   bool add();
+  void remove();
   double val_real();
   // In SPs we might force the "wrong" type with select into a declare variable
   longlong val_int() { return val_int_from_real(); }

sql/sql_window.cc

@@ -1585,6 +1585,7 @@ bool JOIN::process_window_functions(List<Item> *curr_fields_list)
           case Item_sum::COUNT_FUNC:
           case Item_sum::SUM_BIT_FUNC:
           case Item_sum::SUM_FUNC:
+          case Item_sum::AVG_FUNC:
           {
             /*
               Frame-aware window function computation. It does one pass, but