timers: Switch to a non-cascading wheel

The current timer wheel has some drawbacks:

1) Cascading:

   Cascading can be an unbound operation and is completely pointless in most
   cases because the vast majority of the timer wheel timers are canceled or
   rearmed before expiration. (They are used as timeout safeguards, not as
   real timers to measure time.)

2) No fast lookup of the next expiring timer:

   In NOHZ scenarios the first timer soft interrupt after a long NOHZ period
   must fast forward the base time to the current value of jiffies. As we
   have no way to find the next expiring timer fast, the code loops linearly
   and increments the base time one by one and checks for expired timers
   in each step. This causes unbound overhead spikes exactly in the moment
   when we should wake up as fast as possible.

After a thorough analysis of real world data gathered on laptops,
workstations, webservers and other machines (thanks Chris!) I came to the
conclusion that the current 'classic' timer wheel implementation can be
modified to address the above issues.

The vast majority of timer wheel timers is canceled or rearmed before
expiry. Most of them are timeouts for networking and other I/O tasks. The
nature of timeouts is to catch the exception from normal operation (TCP ack
timed out, disk does not respond, etc.). For these kinds of timeouts the
accuracy of the timeout is not really a concern. Timeouts are very often
approximate worst-case values and in case the timeout fires, we already
waited for a long time and performance is down the drain already.

The few timers which actually expire can be split into two categories:

 1) Short expiry times which expect halfways accurate expiry

 2) Long term expiry times are inaccurate today already due to the
    batching which is done for NOHZ automatically and also via the
    set_timer_slack() API.

So for long term expiry timers we can avoid the cascading property and just
leave them in the less granular outer wheels until expiry or
cancelation. Timers which are armed with a timeout larger than the wheel
capacity are no longer cascaded. We expire them with the longest possible
timeout (6+ days). We have not observed such timeouts in our data collection,
but at least we handle them, applying the rule of the least surprise.

To avoid extending the wheel levels for HZ=1000 so we can accomodate the
longest observed timeouts (5 days in the network conntrack code) we reduce the
first level granularity on HZ=1000 to 4ms, which effectively is the same as
the HZ=250 behaviour. From our data analysis there is nothing which relies on
that 1ms granularity and as a side effect we get better batching and timer
locality for the networking code as well.

Contrary to the classic wheel the granularity of the next wheel is not the
capacity of the first wheel. The granularities of the wheels are in the
currently chosen setting 8 times the granularity of the previous wheel.

So for HZ=250 we end up with the following granularity levels:

 Level Offset   Granularity                  Range
     0      0          4 ms                 0 ms -        252 ms
     1     64         32 ms               256 ms -       2044 ms (256ms - ~2s)
     2    128        256 ms              2048 ms -      16380 ms (~2s   - ~16s)
     3    192       2048 ms (~2s)       16384 ms -     131068 ms (~16s  - ~2m)
     4    256      16384 ms (~16s)     131072 ms -    1048572 ms (~2m   - ~17m)
     5    320     131072 ms (~2m)     1048576 ms -    8388604 ms (~17m  - ~2h)
     6    384    1048576 ms (~17m)    8388608 ms -   67108863 ms (~2h   - ~18h)
     7    448    8388608 ms (~2h)    67108864 ms -  536870911 ms (~18h  - ~6d)

That's a worst case inaccuracy of 12.5% for the timers which are queued at the
beginning of a level.

So the new wheel concept addresses the old issues:

1) Cascading is avoided completely

2) By keeping the timers in the bucket until expiry/cancelation we can track
   the buckets which have timers enqueued in a bucket bitmap and therefore can
   look up the next expiring timer very fast and O(1).

A further benefit of the concept is that the slack calculation which is done
on every timer start is no longer necessary because the granularity levels
provide natural batching already.

Our extensive testing with various loads did not show any performance
degradation vs. the current wheel implementation.

This patch does not address the 'fast lookup' issue as we wanted to make sure
that there is no regression introduced by the wheel redesign. The
optimizations are in follow up patches.

This patch contains fixes from Anna-Maria Gleixner and Richard Cochran.
Signed-off-by: NThomas Gleixner <tglx@linutronix.de>
Cc: Arjan van de Ven <arjan@infradead.org>
Cc: Chris Mason <clm@fb.com>
Cc: Eric Dumazet <edumazet@google.com>
Cc: Frederic Weisbecker <fweisbec@gmail.com>
Cc: George Spelvin <linux@sciencehorizons.net>
Cc: Josh Triplett <josh@joshtriplett.org>
Cc: Len Brown <lenb@kernel.org>
Cc: Linus Torvalds <torvalds@linux-foundation.org>
Cc: Paul E. McKenney <paulmck@linux.vnet.ibm.com>
Cc: Peter Zijlstra <peterz@infradead.org>
Cc: Rik van Riel <riel@redhat.com>
Cc: rt@linutronix.de
Link: http://lkml.kernel.org/r/20160704094342.108621834@linutronix.deSigned-off-by: NIngo Molnar <mingo@kernel.org>

include/linux/timer.h

@@ -64,6 +64,8 @@ struct timer_list {
 #define TIMER_DEFERRABLE	0x00080000
 #define TIMER_PINNED		0x00100000
 #define TIMER_IRQSAFE		0x00200000
+#define TIMER_ARRAYSHIFT	22
+#define TIMER_ARRAYMASK		0xFFC00000
 
 #define __TIMER_INITIALIZER(_function, _expires, _data, _flags) { \
 		.entry = { .next = TIMER_ENTRY_STATIC },	\