Yeah, the other way is more general: create, then join to a temporary table. (that floor() was just a first try, I should have removed it)

insert into $t values (394, 2, '*Inserted 1st*', :insert_location);

-- update $t set f_sort = floor(f_sort)+1 where f_sort >= :insert_loca
+tion;  -- meh

-- instead:

-- create temporary table
create temp table _t as 
   select f_node_id, f_sort, row_number() over () as new_number
   from (
      select f_node_id, f_sort
      from $t
      order by f_sort
   ) as f
   order by new_number ;

-- update table
update $t t  set f_sort = _t.new_number
from _t 
where _t.f_node_id = t.f_node_id --> join expression
  and _t.new_number <> t.f_sort  --> avoid unnecessary writes
;

drop table _t; --> remove temp table
[download]

It's verbose-ugly but it works without repeating the values.

>   and _t.new_number <> t.f_sort  --> avoid unnecessary writes

see "If you set a column to the value it currently has, MySQL notices this and does not update it."

Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Wikisyntax for the Monastery}

I haven't tested it yet, but why does an UPDATE from a temp table have no conflict with the UNIQUEness of f_sort (see the UPDATE in the OP)?

Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Wikisyntax for the Monastery}

Ah, you were looking for a DEFERRABLE CONSTRAINT, which postpones the constraint-validation to the end of a transaction.

So, you'd do (again, postgres):

create table         tree (
   f_node_id   int primary key
 , f_parent_id int
 , f_name      text
 , f_sort      float
 , constraint tree_parent_sort_uniq_idx unique (f_parent_id, f_sort) d
+eferrable
);
[download]

This lets you mess about with non-unique states for the duration of a transaction. The constraint (here: uniqueness) is only then enforced.

I can't imagine MariaDB does not have this functionality but I can't find it in the documentation. (I looked for DEFERRED or DEFERRABLE. The MariaDB docs list 'DEFERRED' as a reserved word but I see no functionality associated with it.)