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Since Linux 2.5 stat() has supported reading nanosecond resolution (1b/sec) for atime and mtime. However, the utime() family of functions could only write atime and mtime with microsecond resolution (1m/sec) until relatively recently.
On POSIX platforms Python reads atime and mtime at nanosecond resolution but only writes them at microsecond resolution. This impedance mismatch can cause undesirable behavior. Consider the following code:
 import os
 import shutil
 import sys
 def mtime(path):
 return os.stat(path).st_mtime
 src = sys.argv[0]
 dest = src + ".new"
 shutil.copy2(src, dest)
 assert mtime(src) == mtime(dest)
When run under Python on any modern Linux system, the assert fails. (I think any Python since 2.5 will do; I tested with 2.7.1 and a fresh 3.3 trunk.)
The accompanying patch modifies Modules/posixmodule.c so all functions that write atime and mtime use nanosecond resolution when possible. With this patch applied, all the regression tests pass (except the ones for extension modules I didn't compile), and the above code runs to completion.
Happy to hoist the patch up on Rietveld if there's interest.
p.s. I have the commit bit set, so I'd like to be the one to check this in if we get that far.

A small aside:
An IEEE 754 double is insufficient to store a modern timestamp with nanosecond accuracy. We're currently at just over 1.3 billion seconds since the epoch. This eats 28 bits of the mantissa. (The value is actually 31 bits to the left of the decimal point, but you get the leading 1 and the subsequent two 0s for free.) Precisely storing a billion values to the right of the decimal point would require another 30 bits. The mantissa of a double is sadly only 52 bits. So we're shy by 6 bits, give or take.
So this patch doesn't make Python 100% accurate with respect to atime/mtime. What it *does* do is makes Python's loss of accuracy consistent. I claim that's a definite improvement.

It's a duplicate of issue #11457.
(Python >=3.3 has os.utimensat() and os.futimens().)

> It's a duplicate of issue #11457.
No. #11457 is a how-many-angels-on-the-head-of-a-pin discussion proposing new representations of ctime/mtime/atime to preserve nanosecond accuracy. This patch changes the behavior of os.utime, os.futimes, os.lutimes, and os.futimesat so they conserve all of the existing representation's accuracy, making them consistent with os.stat.
> (Python >=3.3 has os.utimensat() and os.futimens().)
How is that relevant?
I mean, sure, I leveraged some of the work from that support in my patch--it's heavily reliant on the preprocessor macros HAVE_UTIMENSAT and HAVE_FUTIMENS now generated by configure. (Thanks, Ross!) But the presence of those functions does not mitigate the loss of accuracy inside os.utime &c.

The patch looks fine to me.

New changeset 1de6619733d9 by Larry Hastings in branch 'default':
Issue #12904: os.utime, os.futimes, os.lutimes, and os.futimesat now write
http://hg.python.org/cpython/rev/1de6619733d9 

This was committed last September; I should have marked it closed then.