Hi,
I have tested on OpenBSD -current, and it seems to work fine:

$ ./python -E -bb Lib/test/test_mmap.py          
test_access_parameter (__main__.MmapTests) ... ok
test_anonymous (__main__.MmapTests) ... ok
test_bad_file_desc (__main__.MmapTests) ... ok
test_basic (__main__.MmapTests) ... ok
test_context_manager (__main__.MmapTests) ... ok
test_context_manager_exception (__main__.MmapTests) ... ok
test_double_close (__main__.MmapTests) ... ok
test_entire_file (__main__.MmapTests) ... ok
test_error (__main__.MmapTests) ... ok
test_extended_getslice (__main__.MmapTests) ... ok
test_extended_set_del_slice (__main__.MmapTests) ... ok
test_find_end (__main__.MmapTests) ... ok
test_io_methods (__main__.MmapTests) ... ok
test_length_0_large_offset (__main__.MmapTests) ... ok
test_length_0_offset (__main__.MmapTests) ... ok
test_move (__main__.MmapTests) ... ok
test_non_ascii_byte (__main__.MmapTests) ... ok
test_offset (__main__.MmapTests) ... ok
test_prot_readonly (__main__.MmapTests) ... ok
test_read_all (__main__.MmapTests) ... ok
test_read_invalid_arg (__main__.MmapTests) ... ok
test_rfind (__main__.MmapTests) ... ok
test_subclass (__main__.MmapTests) ... ok
test_tougher_find (__main__.MmapTests) ... ok
test_around_2GB (__main__.LargeMmapTests) ... ok
test_around_4GB (__main__.LargeMmapTests) ... ok
test_large_filesize (__main__.LargeMmapTests) ... ok
test_large_offset (__main__.LargeMmapTests) ... ok

----------------------------------------------------------------------
Ran 28 tests in 0.141s

OK
$ ./python -E -bb Lib/test/test_exceptions.py
...........................
----------------------------------------------------------------------
Ran 27 tests in 0.026s

OK
$ ./python -E -bb Lib/test/test_pep3151.py
test_blockingioerror (__main__.AttributesTest) ... ok
test_errno_translation (__main__.AttributesTest) ... skipped 'Windows-specific test'
test_posix_error (__main__.AttributesTest) ... ok
test_windows_error (__main__.AttributesTest) ... ok
test_builtin_errors (__main__.HierarchyTest) ... ok
test_errno_mapping (__main__.HierarchyTest) ... ok
test_ioerror_subclass_mapping (__main__.HierarchyTest) ... ok
test_select_error (__main__.HierarchyTest) ... ok
test_socket_errors (__main__.HierarchyTest) ... ok

----------------------------------------------------------------------
Ran 9 tests in 0.001s

OK (skipped=1)


Don't hesitate to indicate me if you need more tests, or if I did something wrong.

Cheers,
Remi.