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Python 3.5 now requires a monotonic clock to start and has the C function _PyTime_monotonic().
Python/condvar.h and Python/thread_pthread.h should use the monotonic clock CLOCK_MONOTONIC, not the system clock CLOCK_REALTIME. See the PEP 418 for the rationale.
Most platforms support pthread_condattr_setclock(CLOCK_MONOTONIC), except Mac OS X and old versions of Android.
The glib looks to use pthread_cond_timedwait_relative_np() for Mac OS X:
https://mail.gnome.org/archives/commits-list/2014-February/msg07782.html
Note: Android had non-standard pthread_cond_timedwait_monotonic() and pthread_cond_timedwait_monotonic_np() functions. Android is not a official supported platform, and newer Android version now support pthread_condattr_setclock(). I prefer to not support old Android versions (yet).
https://android-review.googlesource.com/#/c/83881/
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For Windows, SleepConditionVariableSRW() is used on Windows 7 and newer, otherwise WaitForSingleObjectEx() is used. By the way, the check looks to be done during the compilation. I should check which Windows version is used to build Python...
SleepConditionVariableSRW() and WaitForSingleObjectEx() both take a relative timeout, so they don't use (directly) the system clock. I don't see any required change for Windows.
According to the PEP 418: "WaitForSingleObject() uses the same timer as GetTickCount() with the same precision."
Hum, it is not possible to interrupt such wait() with CTRL+c? time.sleep() is implemented with WaitForSingleObjectEx() with _PyOS_SigintEvent(). It doesn't look to be the case here.

> Python/condvar.h and Python/thread_pthread.h should use the monotonic clock CLOCK_MONOTONIC
Oh, I forgot that Python/thread_pthread.h only uses pthread_cond_timedwait() if semaphores are emulated with mutexes+conditional variables.
On most platforms, PyThread_acquire_lock_timed() is implemented with sem_timedwait(). Problem: sem_timedwait() requires an absolute time using the CLOCK_REALTIME clock and the clock is not yet configurable on Linux :-(
See the feature request in the glibc: "Bug 14717 - Allow choice of clock source for calls to sem_timedwait() and pthread_mutex_timedwait()" opened in 2012:
https://sourceware.org/bugzilla/show_bug.cgi?id=14717
Note: QNX provides sem_timedwait_monotonic().

cond_timedwait_monotonic.patch: Work-in-progress patch. It doesn't change configure.ac yet to check if pthread_condattr_setclock() is supported (with CLOCK_MONOTONIC).

Oh, I missed the issue #12822 which looks to fix similar bugs.

Hello,
Is there any progress on the issue? Should someone take over?

I marked bpo-31267 "threading.Timer object is affected by changes to system time: Python locks should use a monotonic clock if available" as a duplicate of this issue.

I closed bpo-35747 "Python threading event wait influenced by date change" as a duplicate of the issue.

> Is there any progress on the issue? Should someone take over?
It's a limitation of the libc, not directly of Python.
The problem is that the sem_timedwait() function of the glibc doesn't allow to specify which clock is used:
https://sourceware.org/bugzilla/show_bug.cgi?id=14717
Someone has to contribute to the glibc to add an option to sem_init() or sem_timedwait() to allow to use a different clock than CLOCK_REALTIME.
One workaround is to use Python to use the mutex+cond implementation of pthread locks, since this one is already able to use CLOCK_MONOTONIC:
https://bugs.python.org/issue31267#msg302257 

See also bpo-12822: "NewGIL should use CLOCK_MONOTONIC if possible".

> One workaround is to use Python to use the mutex+cond implementation of pthread locks, since this one is already able to use CLOCK_MONOTONIC:
Does this have any drawbacks?

INADA-san fixed bpo-12822 with:
New changeset 001fee14e0f2ba5f41fb733adc69d5965925a094 by Inada Naoki in branch 'master':
bpo-12822: use monotonic clock for condvar if possible (GH-11723)
https://github.com/python/cpython/commit/001fee14e0f2ba5f41fb733adc69d5965925a094 

See bpo-41710 "Timeout is affected by jumps in system time".