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On old FreeBSD versions, concurrent.futures cannot be used. I don't remember why, it's probably related to semaphores (something like a low hardcoded limit). See for example first lines of Lib/test/test_concurrent_futures.py:
---
# Skip tests if _multiprocessing wasn't built. 
test.support.import_module('_multiprocessing') 
# Skip tests if sem_open implementation is broken. 
test.support.import_module('multiprocessing.synchronize')
# import threading after _multiprocessing to raise a more revelant error 
# message: "No module named _multiprocessing". _multiprocessing is not compiled
# without thread support.
test.support.import_module('threading')
---
The problem is that asyncio always try to import concurrent.futures. Example: 
http://buildbot.python.org/all/builders/x86%20FreeBSD%206.4%203.x/builds/4213/steps/test/logs/stdio
test test_asyncio crashed -- Traceback (most recent call last):
 File "/usr/home/db3l/buildarea/3.x.bolen-freebsd/build/Lib/test/regrtest.py", line 1276, in runtest_inner
 test_runner()
 File "/usr/home/db3l/buildarea/3.x.bolen-freebsd/build/Lib/test/test_asyncio/__init__.py", line 31, in test_main
 run_unittest(suite())
 File "/usr/home/db3l/buildarea/3.x.bolen-freebsd/build/Lib/test/test_asyncio/__init__.py", line 21, in suite
 __import__(mod_name)
 File "/usr/home/db3l/buildarea/3.x.bolen-freebsd/build/Lib/test/test_asyncio/test_base_events.py", line 11, in <module>
 from asyncio import base_events
 File "/usr/home/db3l/buildarea/3.x.bolen-freebsd/build/Lib/asyncio/__init__.py", line 21, in <module>
 from .futures import *
 File "/usr/home/db3l/buildarea/3.x.bolen-freebsd/build/Lib/asyncio/futures.py", line 21, in <module>
 Error = concurrent.futures._base.Error
AttributeError: 'module' object has no attribute 'futures'

I don't think it's worth complicating the code for this (except perhaps by making the tests fail more gracefully).
The tasks and futures modules import various things from concurrent.futures (some exceptions, and some constants for wait()).
If a platform doesn't have threads, asyncio is not very useful anyway -- you can't create network connections or servers because of the way getaddrinfo() is called.
I recall that this was reported before and I decided I just didn't care.
Who would be using such an old FreeBSD version anyway (while wanting to use a bleeding edge Python version and the bleeding edge asyncio package)?

> Who would be using such an old FreeBSD version anyway (while wanting to use a bleeding edge Python version and the bleeding edge asyncio package)?
If we want to drop support of old FreeBSD versions, something can be done using the PEP 11. We have FreeBSD 6.4 and 7.2 buildbots. I'm trying to fix all buildbots.

Well, what would be the incantation to just skip the tests if concurrent.futures can't be imported?
(Although it seems that there's a problem with concurrent.futures if the whole thing refuses to import just because multiprocessing isn't supported -- couldn't the threadpool executor still work? Asyncio doesn't use any of the multiprocessing stuff.)

Can you try this patch? It tweaks the test to skip everything if it can't import concurrent.futures.

> Can you try this patch?
I don't have access to the buildbot. You may try the custom buildbot if you don't want to commit directly:
http://buildbot.python.org/all/builders/x86%20FreeBSD%206.4%20custom 

I'll just commit it and pray.

@Guido: If you write "issue #xxx" in your commit message, the changeset will be mentionned in the related issue.
---
changeset: 87237:0031ac40806a
user: Guido van Rossum <guido@dropbox.com>
date: Sun Nov 17 17:00:21 2013 -0800
files: Lib/test/test_asyncio/__init__.py
description:
Skip test_asyncio if concurrent.futures can't be imported. Hopeful fix for issue 19645.
---
The changeset fixed the issue: the test is now skipped on "x86 FreeBSD 6.4 3.x" buildbot.