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There are a number of issues dealing with the offset and length checks in offset, such as issue12556.
I'm running into this issue as well, but with a normal file that happens to be empty. I'm trying to access it with:
mmap.mmap(f.fileno(), length=0, access=mmap.ACCESS_READ)
So the length and offset should be calculated automatically. The man page for mmap says:
"SUSv3 specifies that mmap() should fail if length is 0. However, in kernels before 2.6.12, mmap() succeeded in this case: no mapping was created and the call returned addr. Since kernel 2.6.12, mmap() fails with the error EINVAL for this case."
So alright, mmapping an empty file is now allowed. But, could the check for an empty file be done prior to the check for the offset exceeding the size of the file? It would be much clearer in the cases where an empty (regular or otherwise) file was mmapped if the error message were something like "empty files cannot be mapped" insted of "offset is greater than file size" since I didn't even set the offset.

I do agree. Solaris also returns an error if len=0.
Could you please, provide patches for 2.7, 3.2 and 3.3?

Here's a patch for 2.7. I don't know if it cleanly applies to the rest.

Here's a patch for 3.1

Here's a patch for 3.2

Here's a branch against the default branch in mercurial. I couldn't find a branch for 3.3 or 3.4.

Thanks for the patches.
Note that you don't have to provide a patch for each branch, it's usually the committer's job.
The patch looks good, but the test could be rewritten with assertRaisesRegex():
http://docs.python.org/dev/library/unittest.html#unittest.TestCase.assertRaisesRegex 

Sorry, I thought that's what jcea was asking for. Here's an updated patch for the default branch in mercurial that uses assertRaisesRegex in the test.

Having separate patches is useful if the patch can not be applied cleanly to different python branches. This is specially true with 2.7/3.x.
Checking the fix and committing it to 2.7, 3.2 and 3.3 (probably available in 3.3.1, not 3.3.0, already in release candidate).

New changeset d85f80b31b54 by Jesus Cea in branch '3.2':
Closes #15676: mmap: add empty file check prior to offset check
http://hg.python.org/cpython/rev/d85f80b31b54
New changeset f962ec8e47a1 by Jesus Cea in branch 'default':
Closes #15676: mmap: add empty file check prior to offset check
http://hg.python.org/cpython/rev/f962ec8e47a1
New changeset 27837a33790d by Jesus Cea in branch '2.7':
Closes #15676: mmap: add empty file check prior to offset check
http://hg.python.org/cpython/rev/27837a33790d 

You forgot to add an entry in Misc/ACKS.

New changeset 9ed2e8307e60 by Jesus Cea in branch '2.7':
#15676: Proper attribution in Misc/ACKS
http://hg.python.org/cpython/rev/9ed2e8307e60
New changeset 4f21f7532038 by Jesus Cea in branch '3.2':
#15676: Proper attribution in Misc/ACKS
http://hg.python.org/cpython/rev/4f21f7532038
New changeset 4fdc6c501e63 by Jesus Cea in branch 'default':
MERGE: #15676: Proper attribution in Misc/ACKS
http://hg.python.org/cpython/rev/4fdc6c501e63 

For some reason all Windows buildbots are failing since f962ec8e47a1:
======================================================================
ERROR: test_entire_file (test.test_mmap.MmapTests)
----------------------------------------------------------------------
Traceback (most recent call last):
 File "D:\Buildslave3円.x.moore-windows\build\lib\test\test_mmap.py", line 19, in setUp
 os.unlink(TESTFN)
PermissionError: [WinError 32] The process cannot access the file because it is being used by another process: '@test_2636_tmp'
======================================================================
ERROR: test_error (test.test_mmap.MmapTests)
----------------------------------------------------------------------
Traceback (most recent call last):
 File "D:\Buildslave3円.x.moore-windows\build\lib\test\test_mmap.py", line 19, in setUp
 os.unlink(TESTFN)
PermissionError: [WinError 32] The process cannot access the file because it is being used by another process: '@test_2636_tmp'
======================================================================
[...]

This gets rid of the permission error:
diff -r f962ec8e47a1 Lib/test/test_mmap.py 
--- a/Lib/test/test_mmap.py Mon Sep 10 01:23:05 2012 +0200 
+++ b/Lib/test/test_mmap.py Mon Sep 10 22:22:38 2012 +0200 
@@ -491,11 +491,11 @@ 
 def test_empty_file (self): 
 f = open (TESTFN, 'w+b') 
 f.close() 
- f = open(TESTFN, "rb") 
- self.assertRaisesRegex(ValueError, 
- "cannot mmap an empty file", 
- mmap.mmap, f.fileno(), 0, access=mmap.ACCESS_READ) 
- f.close() 
+ with open(TESTFN, "rb") as f: 
+ self.assertRaisesRegex(ValueError, 
+ "cannot mmap an empty file", 
+ mmap.mmap, f.fileno(), 0, 
+ access=mmap.ACCESS_READ) 
 
 def test_offset (self): 
 f = open (TESTFN, 'w+b') 
 
But the test still fails:
== CPython 3.3.0rc2+ (default, Sep 10 2012, 22:01:26) [MSC v.1600 64 bit (AMD64)] 
== Windows-7-6.1.7601-SP1 little-endian 
== C:\Users\stefan\pydev\cpython\build\test_python_2908 
Testing with flags: sys.flags(debug=0, inspect=0, interactive=0, optimize=0, dont_write_bytecode=0, no_use
r_site=0, no_site=0, ignore_environment=0, verbose=0, bytes_warning=0, quiet=0, hash_randomization=1) 
[1/1] test_mmap 
test_empty_file (test.test_mmap.MmapTests) ... FAIL 
 
====================================================================== 
FAIL: test_empty_file (test.test_mmap.MmapTests) 
---------------------------------------------------------------------- 
ValueError: mmap offset is greater than file size 
 
During handling of the above exception, another exception occurred: 
 
Traceback (most recent call last): 
 File "C:\Users\stefan\pydev\cpython\lib\test\test_mmap.py", line 498, in test_empty_file 
 access=mmap.ACCESS_READ) 
AssertionError: "cannot mmap an empty file" does not match "mmap offset is greater than file size"

New changeset 25d477647a2d by Jesus Cea in branch '2.7':
#15676: mmap: add empty file check prior to offset check <- Previous patch was incomplete
http://hg.python.org/cpython/rev/25d477647a2d 

New changeset 88a88c32661e by Jesus Cea in branch '3.2':
#15676: mmap: add empty file check prior to offset check <- Previous patch was incomplete
http://hg.python.org/cpython/rev/88a88c32661e
New changeset 0ac94ae29abe by Jesus Cea in branch 'default':
#15676: mmap: add empty file check prior to offset check <- Previous patch was incomplete
http://hg.python.org/cpython/rev/0ac94ae29abe 

I think Py_DECREF(m_obj) is missing (at least in 3.3, I didn't
look at the other versions).

New changeset 39efccf7a167 by Jesus Cea in branch '2.7':
#15676: mmap: add empty file check prior to offset check <- Previous patch was incomplete (fix 2)
http://hg.python.org/cpython/rev/39efccf7a167
New changeset 56a2e862561c by Jesus Cea in branch '3.2':
#15676: mmap: add empty file check prior to offset check <- Previous patch was incomplete (fix 2)
http://hg.python.org/cpython/rev/56a2e862561c
New changeset 306b2ecb1a3e by Jesus Cea in branch 'default':
MERGE: #15676: mmap: add empty file check prior to offset check <- Previous patch was incomplete (fix 2)
http://hg.python.org/cpython/rev/306b2ecb1a3e 

Thanks for the heads-up, Stefan.