Postgresql – How to make postgresql SUM to be more accurate on large amount of floating point data

The usual approach is to return a rowset using returns table. The client calling the function can then print it. The function itself continues to run after the return. For example:

create or replace function script() 
RETURNS TABLE (col1 int)
language plpgsql
as $_$ begin
RETURN QUERY (VALUES (6), (7), (6*7));
RAISE NOTICE 'continuing after return';
end;
$_$;
select * from script();

This prints:

NOTICE:  continuing after return
 col1 
------
    6
    7
   42
(3 rows)

You can also store the result of the function in a (temporary) table:

create or replace function script2() 
returns table (col1 int)
language plpgsql
as $_$ 
begin
CREATE TEMPORARY TABLE temp_table (id int) ON COMMIT DROP;
INSERT INTO temp_table SELECT * FROM script();
return query (select * from temp_table);
end;
$_$;
select * from script2();

This prints:

NOTICE:  continuing after return
CONTEXT:  SQL statement "insert into temp_table select * from script() s where s.col1 < 42"
PL/pgSQL function script2() line 4 at SQL statement
 col1 
------
    6
    7
(2 rows)

pg_database_size() essentially queries the filesystem for the size of $PGDATA/base/oid-of-database (the per-database data directory), plus the size of every such directory in non-default tablespaces added with CREATE TABLESPACE.

If there are files in these directories that don't pertain to any relation , they will be counted too. Looking at a random database, I can see pg_internal.init, PG_VERSION, pg_filenode.map that are in that case. They add up to the directory size and will not be counted in any control query.

Stray data files may also exist. See How to reclaim space taken by an index that partially built and was terminated by a power outage for a concrete example. They also can't be found by querying against pg_class, by definition, and they're counted in the db size on disk.

Concerning the query, just for the purpose of getting the sum of objects sizes, I'd suggest a simpler version:

select sum(pg_total_relation_size(oid)) 
from pg_class
where relkind in ('r','m','S')
  and not relisshared

Note that shared relations are removed from this query (not relisshared). Shared objects are visible from all databases and don't belong to any database's directory, they're in $PGDATA/global. One of the shared tables that is expected to be significant in size is pg_shdepend. Overlooking this in your original query makes it overestimate (in addition to @jjanes comment about toast tables).