What's the complexity of renaming a column in MySql? We want to rename a column in our MySql (version 5.5) database with something like this:

ALTER TABLE t1 CHANGE a b INTEGER;


Is this an O(N) (N=number of rows in the table) or an O(1) operation? I can't seem to find an answer in the manual nor on Google. The table has millions of records, and it wouldn't be feasible directly if it's O(N).
It can be an O(1) operation if only the name is changing, see:

https://dev.mysql.com/doc/refman/8.0/en/alter-table.html

and search for: 


  Renaming, Redefining, and Reordering Columns


That is in a section that explains that the operation only modifies table metadata.

Back in MySQL 5.5 the manual says it works there too, except for InnoDB tables.