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test_mmap fails on an android emulator running an x86 system image at API level 21.
======================================================================
ERROR: test_large_filesize (test.test_mmap.LargeMmapTests)
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Traceback (most recent call last):
 File "/sdcard/org.bitbucket.pyona/lib/python3.6/test/test_mmap.py", line 755, in test_large_filesize
 with self._make_test_file(0x17FFFFFFF, b" ") as f:
 File "/sdcard/org.bitbucket.pyona/lib/python3.6/test/test_mmap.py", line 738, in _make_test_file
 f.seek(num_zeroes)
ValueError: cannot fit 'int' into an offset-sized integer
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ERROR: test_large_offset (test.test_mmap.LargeMmapTests)
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Traceback (most recent call last):
 File "/sdcard/org.bitbucket.pyona/lib/python3.6/test/test_mmap.py", line 750, in test_large_offset
 with self._make_test_file(0x14FFFFFFF, b" ") as f:
 File "/sdcard/org.bitbucket.pyona/lib/python3.6/test/test_mmap.py", line 738, in _make_test_file
 f.seek(num_zeroes)
ValueError: cannot fit 'int' into an offset-sized integer
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Ran 35 tests in 0.134s
FAILED (errors=2, skipped=6)
test test_mmap failed
1 test failed:
 test_mmap
Total duration: 0:00:01

This is other manifestation of issue26926.

f.seek(number) raises ValueError (ValueError: cannot fit 'int' into an offset-sized integer) when 'number' is greater than the size allowed by off_t. ValueError is not handled in test_mmap to detect that large file is not supported.
With this patch, test_large_filesize and test_large_offset are skipped as expected on an Android emulator.

I'm wondering in what cases other exceptions (OSError, OverflowError) can be raised? Initial test was added in issue4681.

On linux with large file support, OSError is raised when the file system limit is exceeded, here with ext4:
>>> f.seek(2**44 - 2**11)
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
OSError: [Errno 22] Invalid argument
>>> f.seek(2**44 - 2**12)
17592186040320
>>> f.write(b'A' * 2**11)
2048
>>> f.write(b'A' * 2**11)
2048
>>> f.tell()
17592186044416
>>> f.write(b'A' * 2**11)
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
OSError: [Errno 27] File too large
On the Android emulator (no large file support):
>>> f.seek(2**31)
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
ValueError: cannot fit 'int' into an offset-sized integer
>>> f.seek(2**31 - 1)
2147483647
>>> f.write(b'A')
1
>>> f.tell()
-2147483648
>>> f.flush()
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
OSError: [Errno 75] Value too large for defined data type
Surprisingly f.write(b'A') does not raise an exception.

When OverflowError is raised? Shouldn't it be replaced with ValueError?

New changeset bca81ea8f898 by Serhiy Storchaka in branch '3.5':
Issue #26927: Fixed test_mmap on platforms with 32-bit off_t (like Android).
https://hg.python.org/cpython/rev/bca81ea8f898
New changeset 6147a2c99db0 by Serhiy Storchaka in branch 'default':
Issue #26927: Fixed test_mmap on platforms with 32-bit off_t (like Android).
https://hg.python.org/cpython/rev/6147a2c99db0 

> When OverflowError is raised? Shouldn't it be replaced with ValueError?
At least Python implementation of io.FileIO can raise OverflowError (from os.lseek()). Thus OverflowError should be kept.