If you call email.utils.make_msgid a number of times within the same
second, the uniqueness of the results depends on random.randint(100000)
returning different values each time.

A little mathematics proves that you don't have to call make_msgid
*that* often to get the same message id twice: if you call it 'n' times,
the probability of a collision is approximately "1 -
math.exp(-n*(n-1)/200000.0)", and for n == 100, that's about 5%.  For n
== 1000, it's over 99%.

These numbers are born out by experiment:

>>> def collisions(n):
...     msgids = [make_msgid() for i in range(n)]
...     return len(msgids) - len(set(msgids))
... 
>>> sum((collisions(100)>0) for i in range(1000))
49
>>> sum((collisions(1000)>0) for i in range(1000))
991

I think probably having a counter in addition to the randomness would be
a good fix for the problem, though I guess then you have to worry about
thread safety.

A higher resolution timer would also help, of course.

(Thanks to James Knight for the prod).

This patch replaces the random part with an increasing sequence (in a 
thread safe way).
Also, added a test case for make_msgid (there was none previously)

Is it ok if the message id is predictable?
Besides, _gen_next_number() can more efficiently be written as:

_gen_next_number = itertools.cycle(xrange(N))

--- El jue 6-ago-09, Antoine Pitrou <report@bugs.python.org> escribió:

> Antoine Pitrou <pitrou@free.fr>
> added the comment:
> 
> Is it ok if the message id is predictable?

I don't know of any use of message ids apart from uniquely identifying the message, but we could still keep a random part followed by the sequence.

> Besides, _gen_next_number() can more efficiently be written
> as:
> 
> _gen_next_number = itertools.cycle(xrange(N))

Written that way it will eventually hold a list with 100000 integers forever.

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An updated version of the make_msgid patch.
Includes a random part plus a sequential part. Testing takes at most 3 
seconds now (we're interested in those msgids generated in a whole 
second)

Can we have a patch review please.  If nothing else xrange will have to change for Python 3.

The probability of a collision when generated n numbers from 0 to m-1 is

    1 - factorial(m)/factorial(m-n)/m**n

When n << sqrt(m), it is approximately equal to n**2/(2*m). When m = 1000000, we have problems for n about 1000. When increase m to 2**32, the probability of collisions is decreased to 0.01%. When increase m to 2**64 as recommended in [1], it is decreased to 2.7e-14. I.e. when generate 1000 IDs per second, collisions happen one per a million years.

We could also take datetime with larger precision. E.g with 2 digits after the dot, as recommended in [1].

When apply both changes, we could generate 100000 IDs per second with one collision per 10000 years or 10000 IDs per second with one collision per 1000000 years.

[1] https://tools.ietf.org/html/draft-ietf-usefor-message-id-01

Here is a patch that changes the generating of message IDs:

1. The datetime is taken with higher precision, 2 decimal digits after dot.
2. The datetime is written as Unix time in 0.01 second units, not as YYYYmmddHHMMSS. This is more compact and faster.
3. The random part is taken as the random integer in the range 0 from to 2**64, not from 0 to 10**5.

This increases the length of generated part of the ID from 26 to 39 characters in average. Perhaps in new releases we can use non-decimal or even non-alphanumeric characters in ID for compactness.

Looking at my mail store, it looks like one more more mail clients use a GUID for the messageid, which is 36 characters.  So 39 doesn't seem so bad.  There's even one that is 74 characters long.  There are also shorter ones, though, so compactifying the result wouldn't be a bad thing.

An increase of 13 characters doesn't seem so bad.

Currently the maximal length of local part is

    14+1+len(str(2**16))+1+len(str(10**5-1)) == 26

With the patch it will be

    len(str(2**31*100))+1+len(str(2**16))+1+len(str(2**64)) = 39

If encode all three numbers with hexadecimal, it will be

    len('%x'%(2**31*100))+1+len('%x'%(2**16))+1+len('%x'%(2**64)) = 34

If encode their with base32:

    math.ceil((31+math.log(100)/math.log(2))/5)+1+math.ceil(16/5)+1+math.ceil(64/5) = 27

Using base64 or base85 can be not safe, because message ID can be used as file name in case-insensitive file system.

New changeset 6969bac411fa by Serhiy Storchaka in branch '2.7':
Issue #6598: Increased time precision and random number range in
https://hg.python.org/cpython/rev/6969bac411fa

New changeset ea878f847eee by Serhiy Storchaka in branch '3.4':
Issue #6598: Increased time precision and random number range in
https://hg.python.org/cpython/rev/ea878f847eee

New changeset 933addbc7041 by Serhiy Storchaka in branch 'default':
Issue #6598: Increased time precision and random number range in
https://hg.python.org/cpython/rev/933addbc7041

Now there is a question. Is it worth to use base16 (hexadecimal) to compact message id to 34 characters or base32 to compact it to 27 characters? Using base16 is pretty easy: just replace %d with %x. Using base32 is more complicated.

With base64 and base85 the length can be decreased to 23 and 21, but I doubt that this is safe.

On May 19, 2015, at 07:23 AM, Serhiy Storchaka wrote:

>Now there is a question. Is it worth to use base16 (hexadecimal) to compact
>message id to 34 characters or base32 to compact it to 27 characters? Using
>base16 is pretty easy: just replace %d with %x. Using base32 is more
>complicated.

It might not be relevant, but we're using base 32 in Message-ID-Hash:

http://wiki.list.org/DEV/Stable%20URLs

We settled on base 32 after consulting with the curators of mail-archive.com
and others.

http://buildbot.python.org/all/builders/x86%20Tiger%202.7/builds/3246/steps/test/logs/stdio
======================================================================
FAIL: test_make_msgid_collisions (email.test.test_email.TestMiscellaneous)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/Users/db3l/buildarea/2.7.bolen-tiger/build/Lib/email/test/test_email.py", line 2434, in test_make_msgid_collisions
    pass
  File "/Users/db3l/buildarea/2.7.bolen-tiger/build/Lib/contextlib.py", line 24, in __exit__
    self.gen.next()
  File "/Users/db3l/buildarea/2.7.bolen-tiger/build/Lib/test/test_support.py", line 1570, in start_threads
    raise AssertionError('Unable to join %d threads' % len(started))
AssertionError: Unable to join 5 threads

----------------------------------------------------------------------

Threads that should be finished for 3 seconds can't be finished for 15 minutes. It looks as clock() wrapped around. From clock (3) manpage:

    Note that the time can wrap around.  On a 32-bit system where CLOCKS_PER_SEC equals 1000000 this function will return the same value approximately every 72 minutes.

The solution is to use monotonic() (time() on older releases) instead of clock().

New changeset 3c0a817ab616 by Serhiy Storchaka in branch '3.4':
Issue #6598: Avoid clock wrapping around in test_make_msgid_collisions.
https://hg.python.org/cpython/rev/3c0a817ab616

New changeset e259c0ab7a69 by Serhiy Storchaka in branch '3.5':
Issue #6598: Avoid clock wrapping around in test_make_msgid_collisions.
https://hg.python.org/cpython/rev/e259c0ab7a69

New changeset d1c11a78b43a by Serhiy Storchaka in branch 'default':
Issue #6598: Avoid clock wrapping around in test_make_msgid_collisions.
https://hg.python.org/cpython/rev/d1c11a78b43a

New changeset bdd257d60da2 by Serhiy Storchaka in branch '2.7':
Issue #6598: Avoid clock wrapping around in test_make_msgid_collisions.
https://hg.python.org/cpython/rev/bdd257d60da2

Perhaps will open a separate issue for more compact non-decimal message ID.