How do I simultaneously update unique keys in PostgreSQL?

CREATE TABLE widget (
  id serial PRIMARY KEY,
  name text NOT NULL,
  ordinal int NOT NULL UNIQUE
);

I have the data

 id | name | ordinal 
----+------+---------
  1 | A    |       1
  2 | B    |       2
  3 | C    |       3

I would like to update it to

 id | name | ordinal 
----+------+---------
  1 | A    |       3
  2 | B    |       2
  3 | C    |       1

Touching records as little as possible (i.e. don’t rewrite the entire record set, don’t kick off unnecessary triggers), what’s the generally applicable approach to updating ordinal to be the target values?

A vanilla update just gives me constraint violations, even if it happens in a single statement.

And dropping and recreating the unique constraint is expensive and poor concurrency.

This seems like a common enough problem that there ought to be a good way to do this, that I just can’t think of.