python-peps/pep-0418.txt

PEP: 418
Title: Add monotonic and high-resolution time functions
Version: $Revision$
Last-Modified: $Date$
Author: Victor Stinner <victor.stinner@gmail.com>
Status: Draft
Type: Standards Track
Content-Type: text/x-rst
Created: 26-March-2012
Python-Version: 3.3


Abstract
========

Add time.monotonic(fallback=True) and time.highres() functions to Python 3.3.


Rationale
=========

Use cases:

 * Display the current time to a human (e.g. display a calendar or draw a wall
   clock): use system clock. time.time() or datetime.datetime.now()
 * Benchmark, profiling, timeout: time.highres()
 * Event scheduler: time.monotonic(), or time.monotonic(fallback=False)


Functions
=========

 * time.time(): system clock, "wall clock"
 * time.highres(): clock with the best accuracy
 * time.monotonic(fallback=True): monotonic clock. If no monotonic clock is
   available, falls back to system clock by default, or raises an OSError if
   *fallback* is False. time.monotonic(fallback=True) cannot go backward.


time.time()
-----------

The system time is the "wall clock". It can be set manually by the system
administrator or automatically by a NTP daemon.  It can jump backward and
forward. It is not monotonic.

It is available on all platforms and cannot fail.

Pseudo-code [#pseudo]_: ::

    if os.name == "nt":
        def time():
            return _time.GetSystemTimeAsFileTime()
    else:
        def time():
            if hasattr(time, "clock_gettime"):
                try:
                    # resolution = 1 nanosecond
                    return time.clock_gettime(time.CLOCK_REALTIME)
                except OSError:
                    # CLOCK_REALTIME is not supported (unlikely)
                    pass
            if hasattr(_time, "gettimeofday"):
                try:
                    # resolution = 1 microsecond
                    return _time.gettimeofday()
                except OSError:
                    # gettimeofday() should not fail
                    pass
            if hasattr(_time, "ftime"):
                # resolution = 1 millisecond
                return _time.ftime()
            else:
                # resolution = 1 second
                return _time.time()


time.monotonic(fallback=True)
-----------------------------

Clock that cannot go backward, its rate is as steady as possible. Its rate may
be adjusted by NTP. The reference point of the returned value is undefined so
only the difference of consecutive calls is valid.

It is not available on all platforms and may raise an OSError. It is not
available on GNU/Hurd for example.

The monotonic clock may stop while the system is suspended.

Pseudo-code [#pseudo]_: ::

    if os.name == 'nt':
        # GetTickCount64() requires Windows Vista, Server 2008 or later
        if hasattr(time, '_GetTickCount64'):
            def monotonic(fallback=True):
                return _time.GetTickCount64()
        else:
            def monotonic(fallback=True):
                ticks = _time.GetTickCount()
                if ticks < monotonic.last:
                    # Integer overflow detected
                    monotonic.delta += 2**32
                monotonic.last = ticks
                return ticks + monotonic.delta
            monotonic.last = 0
            monotonic.delta = 0

    elif os.name == 'mac':
        def monotonic(fallback=True):
            if monotonic.factor is None:
                factor = _time.mach_timebase_info()
                monotonic.factor = timebase[0] / timebase[1]
            return _time.mach_absolute_time() * monotonic.factor
        monotonic.factor = None

    elif os.name.startswith('sunos'):
        def monotonic(fallback=True):
            if monotonic.use_clock_highres:
                try:
                    time.clock_gettime(time.CLOCK_HIGHRES)
                except OSError:
                    monotonic.use_clock_highres = False
            if monotonic.use_gethrtime:
                try:
                    return time.gethrtime()
                except OSError:
                    if not fallback:
                        raise
                    monotonic.use_gethrtime = False
            return time.time()
        monotonic.use_clock_highres = (hasattr(time, 'clock_gettime')
                                       and hasattr(time, 'CLOCK_HIGHRES'))
        monotonic.use_gethrtime = True

    elif hasattr(time, "clock_gettime"):
        def monotonic(fallback=True):
            while monotonic.clocks:
                try:
                    clk_id = monotonic.clocks[0]
                    return time.clock_gettime(clk_id)
                except OSError:
                    # CLOCK_MONOTONIC_RAW requires a Linux kernel >= 2.6.28
                    if len(monotonic.clocks) == 1 and not fallback:
                        raise
                    del monotonic.clocks[0]
            return time.time()
        monotonic.clocks = []
        if hasattr(time, 'CLOCK_MONOTONIC_RAW'):
            monotonic.clocks.append(time.CLOCK_MONOTONIC_RAW)
        if hasattr(time, 'CLOCK_HIGHRES'):
            monotonic.clocks.append(time.CLOCK_HIGHRES)
        monotonic.clocks.append(time.CLOCK_MONOTONIC)

On Windows, QueryPerformanceCounter() is not used even if it has a better
resolution than GetTickCount(). It is not reliable and has too much issues.

.. note::

   time.monotonic() detects GetTickCount() integer overflow (32 bits, roll-over
   after 49.7 days): it increases a delta by 2\ :sup:`32` each time than an
   overflow is detected. The delta is stored in the process local state and so
   time.monotonic() value may be different in two Python processes.


time.highres()
--------------

Clock with the best available resolution.

It is available on all platforms and cannot fail.

Pseudo-code::

    def highres():
        if highres.use_performance_counter:
            try:
                return _time.QueryPerformanceCounter()
            except OSError:
                # QueryPerformanceFrequency() may fail, if the installed
                # hardware does not support a high-resolution performance
                # counter for example
                highres.use_performance_counter = False
        if highres.use_monotonic:
            # Monotonic clock is preferred over system clock
            try:
                return time.monotonic()
            except OSError:
                highres.use_monotonic = False
        return time.time()
    highres.use_performance_counter = (os.name == 'nt')
    highres.use_monotonic = hasattr(time, 'monotonic')


Clocks
======

Monotonic clocks
----------------

========================= =============== =============== ================ ====================
Name                      Resolution      Accuracy        Adjusted by NTP? Action on suspend
========================= =============== =============== ================ ====================
CLOCK_MONOTONIC_RAW       1 ns            (*)             No               Stopped
gethrtime                 1 ns            (*)             No               Not stopped
CLOCK_HIGHRES             1 ns            (*)             No               ?
CLOCK_MONOTONIC           1 ns            (*)             Yes on Linux     Stopped on Linux
mach_absolute_time()      1 ns            ?               No               ?
QueryPerformanceCounter() \-              0.3 ns - 5 ns   No               Accuracy issue
GetTickCount[64]()        1 ms            1 ms - 15 ms    No               Include suspend time
timeGetTime()             1 ms            1 ms - 15 ms    No               ?
========================= =============== =============== ================ ====================

(*) The accurary of monotonic clocks depends on the operating system and the
hardware clock.

The resolution is the smallest difference between two timestamps supported by
the format used by the clock. For example, clock_gettime() uses a timespec
structure which has two integer fileds, tv_sec and tv_nsec, so the resolution
is 1 nanosecond.

The accuracy is the effective smallest difference of two timestamps of the
clock. It does not reflect the stability the clock rate.  For example,
QueryPerformanceCounter() has a good accuracy but is known to not have a steady
rate.


mach_absolute_time
^^^^^^^^^^^^^^^^^^

Mac OS X provides a monotonic clock: mach_absolute_time(). It is based on
absolute elapsed time delta since system boot. It is not adjusted and cannot be
set.

mach_timebase_info() gives a fraction to convert the clock value to a number of
nanoseconds. According to the documentation (`Technical Q&A QA1398
<https://developer.apple.com/library/mac/#qa/qa1398/>`_), mach_timebase_info()
is always equals to one and does never fail, even if the function may fail
according to its prototype.

mach_absolute_time() stops during a sleep on PowerPC CPU, but not on Intel CPU:
`Different behaviour of mach_absolute_time() on i386 / ppc
<http://lists.apple.com/archives/PerfOptimization-dev/2006/Jul/msg00024.html>`_.

mach_absolute_time() has a resolution of 1 nanosecond.

CLOCK_MONOTONIC, CLOCK_MONOTONIC_RAW
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

CLOCK_MONOTONIC and CLOCK_MONOTONIC_RAW represents monotonic time since some
unspecified starting point. They cannot be set.

Documentation: refer to the manual page of your operating system. Examples:

 * `FreeBSD clock_gettime() manual page
   <http://www.freebsd.org/cgi/man.cgi?query=clock_gettime>`_
 * `Linux clock_gettime() manual page
   <http://linux.die.net/man/3/clock_gettime>`_

CLOCK_MONOTONIC is available at least on the following operating systems:

 * DragonFly BSD, FreeBSD >= 5.0, OpenBSD, NetBSD
 * Linux
 * Solaris

The following operating systems don't support CLOCK_MONOTONIC:


 * GNU/Hurd (see `open issues/ clock_gettime <http://www.gnu.org/software/hurd/open_issues/clock_gettime.html>`_)
 * Mac OS X
 * Windows

CLOCK_MONOTONIC_RAW is specific to Linux. It is similar to CLOCK_MONOTONIC, but
provides access to a raw hardware-based time that is not subject to NTP
adjustments. CLOCK_MONOTONIC_RAW requires Linux 2.6.28 or later.

On Linux, NTP may adjust CLOCK_MONOTONIC rate, but not jump backward.  If
available, CLOCK_MONOTONIC_RAW should be used instead of CLOCK_MONOTONIC to
avoid the NTP adjustement.

CLOCK_MONOTONIC stops while the machine is suspended.

clock_gettime() fails if the system does not support the specified clock,
whereas the standard C library supports it. For example, CLOCK_MONOTONIC_RAW
requires a kernel version 2.6.28 or later.

clock_getres() gives the clock resolution. It is 1 nanosecond on Linux.

.. note::
   clock_gettime() requires to link the program to the rt (real-time) library.

Windows: QueryPerformanceCounter
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

High-resolution performance counter. It is monotonic.
QueryPerformanceFrequency() gives its frequency.

It has much higher resolution, but has lower long term accuracy than
GetTickCount() and timeGetTime() clocks. For example, it will drift compared to
the low precision clocks.

Documentation:

 * `MSDN: QueryPerformanceCounter() documentation
   <http://msdn.microsoft.com/en-us/library/windows/desktop/ms644904%28v=vs.85%29.aspx>`_
 * `MSDN: QueryPerformanceFrequency() documentation
   <http://msdn.microsoft.com/en-us/library/windows/desktop/ms644905%28v=vs.85%29.aspx>`_

Hardware clocks used by QueryPerformanceCounter:

 * Windows XP: RDTSC instruction of Intel processors, the clock frequency is
   the frequency of the processor (between 200 MHz and 3 GHz, usually greater
   than 1 GHz nowadays)
 * Windows 2000: ACPI power management timer, frequency = 3,549,545 Hz. It can
   be forced through the "/usepmtimer" flag in boot.ini
 * Windows 95/98: 8245 PIT chipset, frequency = 1,193,181 Hz

QueryPerformanceFrequency() should only be called once:  the frequency will not
change while the system is running. It fails if the installed hardware does not
support a high-resolution performance counter.

QueryPerformanceCounter() cannot be adjusted: `SetSystemTimeAdjustment()
<http://msdn.microsoft.com/en-us/library/windows/desktop/ms724943(v=vs.85).aspx>`_
does only adjust the system time.

Bugs:

 * The performance counter value may unexpectedly leap forward because of a
   hardware bug, see the `KB274323`_.
 * On VirtualBox, QueryPerformanceCounter() does not increment the high part
   every time the low part overflows, see `Monotonic timers
   <http://code-factor.blogspot.fr/2009/11/monotonic-timers.html>`_ (2009).
 * VirtualBox had a bug in its HPET virtualized device:
   QueryPerformanceCounter() did jump forward by approx. 42 seconds (`issue
   #8707 <https://www.virtualbox.org/ticket/8707>`_).
 * Windows XP had a bug (see `KB896256`_): on a multiprocessor computer,
   QueryPerformanceCounter() returned a different value for each processor.
   The bug was fixed in Windows XP SP2.

.. _KB896256: http://support.microsoft.com/?id=896256
.. _KB274323: http://support.microsoft.com/?id=274323


Windows: GetTickCount(), GetTickCount64()
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

GetTickCount() and GetTickCount64() are monotonic, cannot fail and are not
adjusted by SetSystemTimeAdjustment().  MSDN documentation:
`GetTickCount() <http://msdn.microsoft.com/en-us/library/windows/desktop/ms724408(v=vs.85).aspx>`_,
`GetTickCount64() <http://msdn.microsoft.com/en-us/library/windows/desktop/ms724411(v=vs.85).aspx>`_.

The elapsed time retrieved by GetTickCount or GetTickCount64 includes time the
system spends in sleep or hibernation.

GetTickCount64() was added to Windows Vista and Windows Server 2008.

The clock resolution is 1 millisecond. Its accuracy is usually around 15 ms. It
is possible to improve the accuracy using the `undocumented
NtSetTimerResolution() function
<http://undocumented.ntinternals.net/UserMode/Undocumented%20Functions/Time/NtSetTimerResolution.html>`_.
There are applications using this undocumented function, example:
`Timer Resolution <http://www.lucashale.com/timer-resolution/>`_.


Windows: timeGetTime
^^^^^^^^^^^^^^^^^^^^

The timeGetTime function retrieves the system time, in milliseconds. The system
time is the time elapsed since Windows was started. Read the `timeGetTime()
documentation
<http://msdn.microsoft.com/en-us/library/windows/desktop/dd757629(v=vs.85).aspx>`_.

The return type of timeGetTime() is a 32-bit unsigned integer. As
GetTickCount(), timeGetTime() rolls over after 2^32 milliseconds (49.7 days).

The default precision of the timeGetTime function can be five milliseconds or
more, depending on the machine.

timeBeginPeriod() can be used to increase the precision of timeGetTime() up to
1 millisecond, but it negatively affects power consumption.

.. note::
   timeGetTime() and timeBeginPeriod() are part the Windows multimedia library
   and so require to link the program with winmm or to load dynamically the
   library.


Solaris: CLOCK_HIGHRES
^^^^^^^^^^^^^^^^^^^^^^

The Solaris OS has an CLOCK_HIGHRES timer that attempts to use an optimal
hardware source, and may give close to nanosecond resolution. CLOCK_HIGHRES is
the nonadjustable, high-resolution clock. For timers created with a clockid_t
value of CLOCK_HIGHRES, the system will attempt to use an optimal hardware
source.

Solaris: gethrtime
^^^^^^^^^^^^^^^^^^

The gethrtime() function returns the current high-resolution real time. Time is
expressed as nanoseconds since some arbitrary time in the past; it is not
correlated in any  way  to the  time  of  day,  and thus is not subject to
resetting or drifting by way of adjtime() or settimeofday(). The  hires timer
is  ideally  suited  to  performance measurement tasks, where cheap, accurate
interval timing is required.

The linearity of gethrtime() is not preserved accross cpr suspend-resume cycle
(`Bug 4272663 <http://wesunsolve.net/bugid/id/4272663>`_).

Read the `gethrtime() manual page of Solaris 11
<http://docs.oracle.com/cd/E23824_01/html/821-1465/gethrtime-3c.html#scrolltoc>`_.

On Solaris, gethrtime() is the same as clock_gettime(CLOCK_MONOTONIC).


System time clocks
------------------

========================= =============== ===============
Name                      Resolution      Accuracy
========================= =============== ===============
CLOCK_REALTIME            1 ns            (*)
GetSystemTimeAsFileTime   100 ns          1 ms - 15 ms
gettimeofday()            1 µs            (*)
ftime()                   1 ms            (*)
time()                    1 sec           1 sec
========================= =============== ===============

(*) The accurary of system clocks depends on the operating system and the
hardware clock. On Windows, the accuracy is in the range 1 ms - 15 ms.


Windows: GetSystemTimeAsFileTime
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The system time can be read using GetSystemTimeAsFileTime(), ftime() and
time().

The system time resolution can be read using GetSystemTimeAdjustment(). The
accurary is usually between 1 millisecond and 15 milliseconds. Resolution:

 * GetSystemTimeAsFileTime(): 100 nanoseconds
 * ftime(): 1 millisecond
 * time(): 1 second

The system time can be set using SetSystemTime().

System time on UNIX
^^^^^^^^^^^^^^^^^^^

gettimeofday(), ftime(), time() and clock_gettime(CLOCK_REALTIME) return the
system clock.

Resolution:

 * clock_gettime(): clock_getres(CLOCK_REALTIME), 1 nanosecond on Linux
 * gettimeofday(): 1 microsecond
 * ftime(): 1 millisecond
 * time(): 1 second

The system time can be set using settimeofday() or clock_settime(CLOCK_REALTIME).


Process and thread time
-----------------------

The process and thread time cannot be set. They are not monotonic: the clocks
stop while the process/thread is idle.

Process
^^^^^^^

 * Windows: GetProcessTimes()
 * clock_gettime(CLOCK_PROCESS_CPUTIME_ID): High-resolution per-process timer
   from the CPU.
 * clock():

   * Windows:  The elapsed wall-clock time since the start of the process
     (elapsed time in seconds times CLOCKS_PER_SEC). It can fail.
   * UNIX: returns an approximation of processor time used by the program.

 * times()
 * getrusage(): ru_utime and ru_stime fields

Resolution:

 * clock() rate is CLOCKS_PER_SEC. It was called CLK_TCK in Microsoft C before
   6.0. On Linux 3, clock() has a resolution of 1 microsecond
 * The clock resolution can be read using clock_getres().
   clock_getres(CLOCK_REALTIME) is 1 nanosecond on Linux
 * GetProcessTimes(): call GetSystemTimeAdjustment()

Thread
^^^^^^

 * Windows: GetThreadTimes()
 * clock_gettime(CLOCK_THREAD_CPUTIME_ID): Thread-specific CPU-time clock.

Resolution:

 * CLOCK_THREAD_CPUTIME_ID: call clock_getres(). 1 nanosecond on Linux.
 * GetThreadTimes(): call GetSystemTimeAdjustment()

See also pthread_getcpuclockid().


Windows: QueryUnbiasedInterruptTime
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Gets the current unbiased interrupt time from the biased interrupt time and the
current sleep bias amount. This time is not affected by power management sleep
transitions.

The elapsed time retrieved by the QueryUnbiasedInterruptTime function includes
only time that the system spends in the working state.
QueryUnbiasedInterruptTime() is not monotonic.

QueryUnbiasedInterruptTime() was introduced in Windows 7.

Linux timers
------------

There were 4 implementations of the time in the Linux kernel: UTIME (1996),
timer wheel (1997), HRT (2001) and hrtimers (2007). The later is the result of
the "high-res-timers" project started by George Anzinger in 2001, contributed
by Thomas Gleixner and Douglas Niehaus. hrtimers implementation was merged into
Linux 2.6.21 released in 2007.

hrtimers supports various clock sources. It sets a priority to each source to
decide which one will be used.

 * TSC (Time Stamp Counter): Internal processor clock incremented at each
   processor cycle. Its frequency is the processor frequency and so usually
   higher than 1 GHz. Its priority is 300 by default, but falls to 0 if the
   processor frequency changes and the counter becomes unstable.
 * HPET: An HPET chip consists of a 64-bit up-counter (main counter) counting
   at least at 10 MHz and a set of up to 256 comparators (at least 3). Each
   HPET can have up to 32 timers.
 * PIT (programmable interrupt timer): Intel 8253/8254 chipsets with a
   configurable frequecency in range 18.2 Hz - 1.2 MHz. Linux uses the
   frequency: 1,193,181.8 Hz. It is a 16-bit counter.
 * PMTMR (power management timer): ACPI 24-bit timer with a frequency of 3.5
   MHz (3,579,545 Hz). Its priority is 200 by default, but changes to 110 if
   the chipset is broken and need a software workaround. HPET can cause around
   3 seconds of drift per day.
 * Cyclone: The Cyclone timer uses a 32-bit counter on IBM Extended
   X-Architecture (EXA) chipsets which include computers that use the IBM
   "Summit" series chipsets (ex: x440). This is available in IA32 and IA64
   architectures.

High-resolution timers are not supported on all hardware architectures. They
are at least provided on x86/x86_64, ARM and PowerPC.

The list of available clock sources can be read in
/sys/devices/system/clocksource/clocksource0/available_clocksource. It is
possible to force a clocksource at runtime by writing its name into
/sys/devices/system/clocksource/clocksource0/current_clocksource.
/proc/timer_list contains the list of all hardware timers.

Read also the `time(7) manual page
<http://www.kernel.org/doc/man-pages/online/pages/man7/time.7.html>`_:
"overview of time and timers".


Alternatives: API design
========================

time.highres() function name
----------------------------

Other names were proposed:

 * time.hires(): "hires" can be read as "to hire" as in "he hires a car to go
   on holiday", rather than a "HIgh-RESolution clock".
 * time.steady(): no OS provides a clock advancing at a steady rate, so
   "steady" should be avoided.
 * time.try_monotonic(): it is a clear and obvious solution for the use-case of
   "I prefer the monotonic clock, if it is available, otherwise I'll take my
   chances with a best-effect clock."
 * time.wallclock()

One function with a flag: time.monotonic(strict=False)
------------------------------------------------------

 * time.monotonic(strict=False) falls back to the system clock if no monotonic
   clock is available or if the monotonic clock failed.
 * time.monotonic(strict=True) raises OSError if monotonic clock fails and
   NotImplementedError if the system does not provide a monotonic clock

"A keyword argument that gets passed as a constant in the caller is usually
poor API."

Raising NotImplementedError for a function is something uncommon in Python and
should be avoided.


One function, no flag
---------------------

time.monotonic() returns (time: float, is_monotonic: bool).

An alternative is to use a function attribute: time.monotonic.is_monotonic. The
attribute value would be None before the first call to time.monotonic().


Working around operating system bugs?
=====================================

Should Python ensure manually that a monotonic clock is truly monotonic by
computing the maximum with the clock value and the previous value?

Since it's relatively straightforward to cache the last value returned using a
static variable, it might be interesting to use this to make sure that the
values returned are indeed monotonic.

 * Virtual machines provide less reliable clocks.
 * QueryPerformanceCounter() has known bugs (only one is not fixed yet)

Python may only workaround a specific known operating system bug: `KB274323`_
contains a code example to workaround the bug (use GetTickCount() to detect
QueryPerformanceCounter() leap).


Footnotes
=========

.. [#pseudo] "_time" is an hypothetical module only used for the example.
   The time module is implemented in C and so there is no need for such module.


Links
=====

Related Python issues:

 * `Issue #12822: NewGIL should use CLOCK_MONOTONIC if possible.
   <http://bugs.python.org/issue12822>`_
 * `Issue #14222: Use time.steady() to implement timeout
   <http://bugs.python.org/issue14222>`_
 * `Issue #14397: Use GetTickCount/GetTickCount64 instead of QueryPerformanceCounter for monotonic clock
   <http://bugs.python.org/issue14397>`_
 * `Issue #14428: Implementation of the PEP 418
   <http://bugs.python.org/issue14428>`_

Librairies exposing monotonic clocks:

 * `Java: System.nanoTime
   <http://docs.oracle.com/javase/1.5.0/docs/api/java/lang/System.html#nanoTime()>`_
 * `Qt library: QElapsedTimer
   <http://qt-project.org/doc/qt-4.8/qelapsedtimer.html>`_
 * `glib library: g_get_monotonic_time ()
   <http://developer.gnome.org/glib/2.30/glib-Date-and-Time-Functions.html#g-get-monotonic-time>`_
   uses GetTickCount64()/GetTickCount() on Windows,
   clock_gettime(CLOCK_MONOTONIC) on UNIX or falls back to the system clock
 * `python-monotonic-time
   <http://code.google.com/p/python-monotonic-time/>`_
   (`github <https://github.com/gavinbeatty/python-monotonic-time>`_)
 * `monotonic_clock
   <https://github.com/ThomasHabets/monotonic_clock>`_
 * `Perl: Time::HiRes
   <http://perldoc.perl.org/Time/HiRes.html>`_ exposes
   clock_gettime(CLOCK_MONOTONIC)
 * `Ruby: AbsoluteTime.now
   <https://github.com/bwbuchanan/absolute_time/>`_: use
   clock_gettime(CLOCK_MONOTONIC), mach_absolute_time() or gettimeofday().
   "AbsoluteTime.monotonic?" method indicates if AbsoluteTime.now is monotonic
   or not.

Time:

 * `hrtimers - subsystem for high-resolution kernel timers
   <http://www.kernel.org/doc/Documentation/timers/hrtimers.txt>`_
 * `C++ Timeout Specification
   <http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2010/n3128.html>`_
 * `Windows: Game Timing and Multicore Processors
   <http://msdn.microsoft.com/en-us/library/ee417693.aspx>`_
 * `Implement a Continuously Updating, High-Resolution Time Provider for Windows
   <http://msdn.microsoft.com/en-us/magazine/cc163996.aspx>`_
 * `clockspeed <http://cr.yp.to/clockspeed.html>`_ uses a hardware tick counter
   to compensate for a persistently fast or slow system clock
 * `Retrieving system time
   <http://en.wikipedia.org/wiki/System_time#Retrieving_system_time>`_
   lists hardware clocks and time functions with their resolution
   and epoch or range
 * On Windows, the JavaScript runtime of Firefox interpolates
   GetSystemTimeAsFileTime() with QueryPerformanceCounter() to get
   an higher resolution. See the `Bug 363258 - bad millisecond resolution for
   (new Date).getTime() / Date.now() on Windows
   <https://bugzilla.mozilla.org/show_bug.cgi?id=363258>`_.
 * `When microseconds matter
   <http://www.ibm.com/developerworks/library/i-seconds/>`_: How the IBM High
   Resolution Time Stamp Facility accurately measures itty bits of time