Increasing a NUMERIC column precision doesn't cause a table rewrite. Why?

Hi everyone,

A numeric field is defined as: NUMERIC(precision, scale) [0].

After doing some playing around with different operations against a numeric
column, namely: increasing/decreasing the precision or increasing/decreasing
the scale, I noticed that the table is rewritten in all cases except when
increasing the precision number.

Take the following snippet as example (tested on postgres 15):

```sql
CREATE DATABASE test_precision_field;
-- \c test_precision_field

SET client_min_messages=debug1;

DROP TABLE IF EXISTS foo;
CREATE TABLE foo (id SERIAL PRIMARY KEY, bar NUMERIC(10, 2));

-- Only increase precision but keep the scale:
-- This does not rewrite the table
ALTER TABLE foo ALTER COLUMN bar TYPE numeric(20, 2);

-- Only decrease the precision but keep the scale:
-- This rewrites the table.
ALTER TABLE foo ALTER COLUMN bar TYPE numeric(10, 2);
-- DEBUG: rewriting table "foo"
-- DEBUG: building index "foo_pkey" on table "foo" serially
-- DEBUG: index "foo_pkey" can safely use deduplication

-- Only increase the scale, but keep the precision:
-- This rewrites the table.
ALTER TABLE foo ALTER COLUMN bar TYPE numeric(10, 4);
-- DEBUG: rewriting table "foo"
-- DEBUG: building index "foo_pkey" on table "foo" serially
-- DEBUG: index "foo_pkey" can safely use deduplication

-- Only decrease the scale, but keep the precision:
-- This rewrites the table.
ALTER TABLE foo ALTER COLUMN bar TYPE numeric(10, 2);
-- DEBUG: rewriting table "foo"
-- DEBUG: building index "foo_pkey" on table "foo" serially
-- DEBUG: index "foo_pkey" can safely use deduplication
```

My assumption is that once the precision is increased, Postgres can still
interpret the old values that were generated with a lower precision, whereas
this is not possible for any other types of changes on the numeric field.

Is that assumption correct? How can I verify it?

For example, is there a catalog table I can have a look to see how these values
are defined, along with some form of documentation to understand how they are
interpreted by Postgres?

Thank you,
Marcelo.

- [0] https://www.postgresql.org/docs/current/datatype-numeric.html#DATATYPE-NUMERIC-DECIMAL