+/*
+ * Maintain bdi->dirty_ratelimit, the base dirty throttle rate.
+ *
+ * Normal bdi tasks will be curbed at or below it in long term.
+ * Obviously it should be around (write_bw / N) when there are N dd tasks.
+ */
+static void bdi_update_dirty_ratelimit(struct backing_dev_info *bdi,
+ unsigned long thresh,
+ unsigned long bg_thresh,
+ unsigned long dirty,
+ unsigned long bdi_thresh,
+ unsigned long bdi_dirty,
+ unsigned long dirtied,
+ unsigned long elapsed)
+{
+ unsigned long freerun = dirty_freerun_ceiling(thresh, bg_thresh);
+ unsigned long limit = hard_dirty_limit(thresh);
+ unsigned long setpoint = (freerun + limit) / 2;
+ unsigned long write_bw = bdi->avg_write_bandwidth;
+ unsigned long dirty_ratelimit = bdi->dirty_ratelimit;
+ unsigned long dirty_rate;
+ unsigned long task_ratelimit;
+ unsigned long balanced_dirty_ratelimit;
+ unsigned long pos_ratio;
+ unsigned long step;
+ unsigned long x;
+
+ /*
+ * The dirty rate will match the writeout rate in long term, except
+ * when dirty pages are truncated by userspace or re-dirtied by FS.
+ */
+ dirty_rate = (dirtied - bdi->dirtied_stamp) * HZ / elapsed;
+
+ pos_ratio = bdi_position_ratio(bdi, thresh, bg_thresh, dirty,
+ bdi_thresh, bdi_dirty);
+ /*
+ * task_ratelimit reflects each dd's dirty rate for the past 200ms.
+ */
+ task_ratelimit = (u64)dirty_ratelimit *
+ pos_ratio >> RATELIMIT_CALC_SHIFT;
+ task_ratelimit++; /* it helps rampup dirty_ratelimit from tiny values */
+
+ /*
+ * A linear estimation of the "balanced" throttle rate. The theory is,
+ * if there are N dd tasks, each throttled at task_ratelimit, the bdi's
+ * dirty_rate will be measured to be (N * task_ratelimit). So the below
+ * formula will yield the balanced rate limit (write_bw / N).
+ *
+ * Note that the expanded form is not a pure rate feedback:
+ * rate_(i+1) = rate_(i) * (write_bw / dirty_rate) (1)
+ * but also takes pos_ratio into account:
+ * rate_(i+1) = rate_(i) * (write_bw / dirty_rate) * pos_ratio (2)
+ *
+ * (1) is not realistic because pos_ratio also takes part in balancing
+ * the dirty rate. Consider the state
+ * pos_ratio = 0.5 (3)
+ * rate = 2 * (write_bw / N) (4)
+ * If (1) is used, it will stuck in that state! Because each dd will
+ * be throttled at
+ * task_ratelimit = pos_ratio * rate = (write_bw / N) (5)
+ * yielding
+ * dirty_rate = N * task_ratelimit = write_bw (6)
+ * put (6) into (1) we get
+ * rate_(i+1) = rate_(i) (7)
+ *
+ * So we end up using (2) to always keep
+ * rate_(i+1) ~= (write_bw / N) (8)
+ * regardless of the value of pos_ratio. As long as (8) is satisfied,
+ * pos_ratio is able to drive itself to 1.0, which is not only where
+ * the dirty count meet the setpoint, but also where the slope of
+ * pos_ratio is most flat and hence task_ratelimit is least fluctuated.
+ */
+ balanced_dirty_ratelimit = div_u64((u64)task_ratelimit * write_bw,
+ dirty_rate | 1);
+
+ /*
+ * We could safely do this and return immediately:
+ *
+ * bdi->dirty_ratelimit = balanced_dirty_ratelimit;
+ *
+ * However to get a more stable dirty_ratelimit, the below elaborated
+ * code makes use of task_ratelimit to filter out sigular points and
+ * limit the step size.
+ *
+ * The below code essentially only uses the relative value of
+ *
+ * task_ratelimit - dirty_ratelimit
+ * = (pos_ratio - 1) * dirty_ratelimit
+ *
+ * which reflects the direction and size of dirty position error.
+ */
+
+ /*
+ * dirty_ratelimit will follow balanced_dirty_ratelimit iff
+ * task_ratelimit is on the same side of dirty_ratelimit, too.
+ * For example, when
+ * - dirty_ratelimit > balanced_dirty_ratelimit
+ * - dirty_ratelimit > task_ratelimit (dirty pages are above setpoint)
+ * lowering dirty_ratelimit will help meet both the position and rate
+ * control targets. Otherwise, don't update dirty_ratelimit if it will
+ * only help meet the rate target. After all, what the users ultimately
+ * feel and care are stable dirty rate and small position error.
+ *
+ * |task_ratelimit - dirty_ratelimit| is used to limit the step size
+ * and filter out the sigular points of balanced_dirty_ratelimit. Which
+ * keeps jumping around randomly and can even leap far away at times
+ * due to the small 200ms estimation period of dirty_rate (we want to
+ * keep that period small to reduce time lags).
+ */
+ step = 0;
+ if (dirty < setpoint) {
+ x = min(bdi->balanced_dirty_ratelimit,
+ min(balanced_dirty_ratelimit, task_ratelimit));
+ if (dirty_ratelimit < x)
+ step = x - dirty_ratelimit;
+ } else {
+ x = max(bdi->balanced_dirty_ratelimit,
+ max(balanced_dirty_ratelimit, task_ratelimit));
+ if (dirty_ratelimit > x)
+ step = dirty_ratelimit - x;
+ }
+
+ /*
+ * Don't pursue 100% rate matching. It's impossible since the balanced
+ * rate itself is constantly fluctuating. So decrease the track speed
+ * when it gets close to the target. Helps eliminate pointless tremors.
+ */
+ step >>= dirty_ratelimit / (2 * step + 1);
+ /*
+ * Limit the tracking speed to avoid overshooting.
+ */
+ step = (step + 7) / 8;
+
+ if (dirty_ratelimit < balanced_dirty_ratelimit)
+ dirty_ratelimit += step;
+ else
+ dirty_ratelimit -= step;
+
+ bdi->dirty_ratelimit = max(dirty_ratelimit, 1UL);
+ bdi->balanced_dirty_ratelimit = balanced_dirty_ratelimit;
+
+ trace_bdi_dirty_ratelimit(bdi, dirty_rate, task_ratelimit);
+}
+