Window sum, bit_* and bool_* don't return NULL after all non-NULL values leave the frame #27595

Problem

Once every non-NULL value has left a window frame, sum, bit_and, bit_or, bit_xor, bool_and and bool_or return 0, -1, false or true instead of NULL. It happens whether the frame is left with only NULLs or left empty, with ROWS and RANGE frames, in batch queries, streaming over window and EOWC over window.

Reproduced on main (a6100ed):

select ts, v, sum(v) over (order by ts rows between current row and current row) as s
from (values (0, 5), (10, null::int)) as t(ts, v)
order by ts;

 ts | v | s
----+---+---
  0 | 5 | 5
 10 |   | 0

PostgreSQL 14 returns NULL at ts = 10. The other functions on the same frame:

A frame left empty behaves the same, for example sum(v) over (order by ts rows between 1 following and 1 following) on the last row, or a RANGE frame between 1 preceding and 1 preceding over a gap. avg, var_pop, stddev_samp and count are correct, and so is a frame that never held a non-NULL value.

Streaming has the same results:

create table t (p int, ts int, v int);
create materialized view mv as select p, ts, v,
  sum(v) over (partition by p order by ts rows between current row and current row) as s
from t;
insert into t values (1, 0, 5), (1, 10, null);

mv has s = 0 at ts = 10, and so does the EMIT ON WINDOW CLOSE version on an append-only table with a watermark on ts.

Cause

For a retractable aggregate, AggImpl::Incremental in src/expr/impl/src/window_function/aggregate.rs keeps one state, and accumulates or retracts the values that enter or leave the frame. These states don't count their non-NULL inputs: sum keeps the sum, and the retractable bit_* and bool_* keep counts of set bits or of true or false values. Once every non-NULL value is retracted, the state looks like that of non-NULL values that cancel out, so the result is not NULL.

The GROUP BY form of this bug was fixed in the planner by #27429, which pairs these aggregates with a count. Window function calls don't go through that rewrite (see #27429 (comment)).

Possible fix: count the non-NULL inputs next to the incremental state, and output NULL when the count is 0. Aggregate window states are not persisted (WindowStateSnapshot only covers the numbering functions), so this changes no stored format.