Hashing Algorithm in MySQL PASSWORD()

Recently we had a question from a Customer: what is the hashing algorithm implemented in PASSWORD() ?

The manual doesn't give a straight answer in none of these two pages:

http://dev.mysql.com/doc/refman/5.1/en/encryption-functions.html#function_password

http://dev.mysql.com/doc/refman/5.1/en/password-hashing.html

It is enough to dig a bit more to find the solution in http://forge.mysql.com/wiki/MySQL_Internals_ClientServer_Protocol#4.1_and_later that specifies "mysql.user.Password stores SHA1(SHA1(password))" .

Instead of blindly trust the documentation (even if I believe it is correct), I did some test and was confused by the first result:

mysql> SELECT PASSWORD("this_is_a_random_string") `pass`\G 

pass: *12E76A751EFA43A177049262A2EE36DA327D8E50

mysql> SELECT SHA1(SHA1("this_is_a_random_string")) `pass`\G 

pass: 9b653fd9fb63e1655786bfa3b3e00b0913dfc177

Looked like SHA1(SHA1(password)) wasn't PASSWORD(password)), at least in this test.

The best documentation ever is the source code, so I went to read the source code and I understood why my previous test was incorrect: the second SHA1() is applied to the binary data returned by the first SHA1() and not to its hex representation. Therefore in in SQL I have to UNHEX() it before applying the second SHA1. In fact: 

mysql> SELECT SHA1(UNHEX(SHA1("this_is_a_random_string"))) `pass`\G 

pass: 12e76a751efa43a177049262a2ee36da327d8e50

So yes, I confirm that mysql.user.password stores SHA1(SHA1(password)) . I also hope this post is useful to understand how MySQL implements PASSWORD().