converting between infinity timestamp and float8 (epoch)

So first off some ground work:

postgres=# select 'infinity'::timestamp;
timestamp
-----------
infinity
(1 row)

postgres=# select 'infinity'::float8;
float8
----------
Infinity
(1 row)

Establishing that we do in fact have an infinity value for both the
timestamp type and the double precision type.

If I try to convert between them:

postgres=# select to_timestamp('infinity'::float8);
ERROR: timestamp out of range
CONTEXT: SQL function "to_timestamp" statement 1

Ok, so that didn't work. Maybe there is something in the SQL standard
stating that this should not be possible? At least it reports an
error.

However, if I try:

postgres=# select extract(epoch from 'infinity'::timestamp);
date_part
-----------
0
(1 row)

This seems busted. Even if we were to consider 0 to be a special
"error value" it would lead to things like this:

postgres=# select to_timestamp(extract(epoch from 'infinity'::timestamp));
to_timestamp
------------------------
1969-12-31 19:00:00-05
(1 row)

So I think the second form (extract) should return an error, or better
yet, they should both do the intuitive thing that is to return
'infinity' of the appropriate type.

Thoughts?