time: Improve documentation of timekeeeping_adjust()

After getting a number of questions in private emails about the
math around admittedly very complex timekeeping_adjust() and
timekeeping_big_adjust(), I figure the code needs some better
comments.

Hopefully the explanations are clear enough and don't muddy the
water any worse.

Still needs documentation for ntp_error, but I couldn't recall
exactly the full explanation behind the code that's there
(although I do recall once working it out when Roman first
proposed it). Given a bit more time I can probably work it out,
but I don't want to hold back this documentation until then.

Signed-off-by: John Stultz <john.stultz@linaro.org>
Cc: Chen Jie <chenj@lemote.com>
Cc: Steven Rostedt <rostedt@goodmis.org>
Link: http://lkml.kernel.org/r/1319764362-32367-1-git-send-email-john.stultz@linaro.org
Signed-off-by: Ingo Molnar <mingo@elte.hu>

1 files changed, 80 insertions, 1 deletions

diff --git a/kernel/time/timekeeping.c b/kernel/time/timekeeping.c
index 2b021b0e850..025e136f388 100644
--- a/kernel/time/timekeeping.c
+++ b/kernel/time/timekeeping.c
@@ -802,14 +802,44 @@ static void timekeeping_adjust(s64 offset)
         s64 error, interval = timekeeper.cycle_interval;
         int adj;
 
+        /*
+         * The point of this is to check if the error is greater then half
+         * an interval.
+         *
+         * First we shift it down from NTP_SHIFT to clocksource->shifted nsecs.
+         *
+         * Note we subtract one in the shift, so that error is really error*2.
+         * This "saves" dividing(shifting) intererval twice, but keeps the
+         * (error > interval) comparision as still measuring if error is
+         * larger then half an interval.
+         *
+         * Note: It does not "save" on aggrivation when reading the code.
+         */
         error = timekeeper.ntp_error >> (timekeeper.ntp_error_shift - 1);
         if (error > interval) {
+                /*
+                 * We now divide error by 4(via shift), which checks if
+                 * the error is greater then twice the interval.
+                 * If it is greater, we need a bigadjust, if its smaller,
+                 * we can adjust by 1.
+                 */
                 error >>= 2;
+                /*
+                 * XXX - In update_wall_time, we round up to the next
+                 * nanosecond, and store the amount rounded up into
+                 * the error. This causes the likely below to be unlikely.
+                 *
+                 * The properfix is to avoid rounding up by using
+                 * the high precision timekeeper.xtime_nsec instead of
+                 * xtime.tv_nsec everywhere. Fixing this will take some
+                 * time.
+                 */
                 if (likely(error <= interval))
                         adj = 1;
                 else
                         adj = timekeeping_bigadjust(error, &interval, &offset);
         } else if (error < -interval) {
+                /* See comment above, this is just switched for the negative */
                 error >>= 2;
                 if (likely(error >= -interval)) {
                         adj = -1;
@@ -817,9 +847,58 @@ static void timekeeping_adjust(s64 offset)
                         offset = -offset;
                 } else
                         adj = timekeeping_bigadjust(error, &interval, &offset);
-        } else
+        } else /* No adjustment needed */
                 return;
 
+        /*
+         * So the following can be confusing.
+         *
+         * To keep things simple, lets assume adj == 1 for now.
+         *
+         * When adj != 1, remember that the interval and offset values
+         * have been appropriately scaled so the math is the same.
+         *
+         * The basic idea here is that we're increasing the multiplier
+         * by one, this causes the xtime_interval to be incremented by
+         * one cycle_interval. This is because:
+         *      xtime_interval = cycle_interval * mult
+         * So if mult is being incremented by one:
+         *      xtime_interval = cycle_interval * (mult + 1)
+         * Its the same as:
+         *      xtime_interval = (cycle_interval * mult) + cycle_interval
+         * Which can be shortened to:
+         *      xtime_interval += cycle_interval
+         *
+         * So offset stores the non-accumulated cycles. Thus the current
+         * time (in shifted nanoseconds) is:
+         *      now = (offset * adj) + xtime_nsec
+         * Now, even though we're adjusting the clock frequency, we have
+         * to keep time consistent. In other words, we can't jump back
+         * in time, and we also want to avoid jumping forward in time.
+         *
+         * So given the same offset value, we need the time to be the same
+         * both before and after the freq adjustment.
+         *      now = (offset * adj_1) + xtime_nsec_1
+         *      now = (offset * adj_2) + xtime_nsec_2
+         * So:
+         *      (offset * adj_1) + xtime_nsec_1 =
+         *              (offset * adj_2) + xtime_nsec_2
+         * And we know:
+         *      adj_2 = adj_1 + 1
+         * So:
+         *      (offset * adj_1) + xtime_nsec_1 =
+         *              (offset * (adj_1+1)) + xtime_nsec_2
+         *      (offset * adj_1) + xtime_nsec_1 =
+         *              (offset * adj_1) + offset + xtime_nsec_2
+         * Canceling the sides:
+         *      xtime_nsec_1 = offset + xtime_nsec_2
+         * Which gives us:
+         *      xtime_nsec_2 = xtime_nsec_1 - offset
+         * Which simplfies to:
+         *      xtime_nsec -= offset
+         *
+         * XXX - TODO: Doc ntp_error calculation.
+         */
         timekeeper.mult += adj;
         timekeeper.xtime_interval += interval;
         timekeeper.xtime_nsec -= offset;