[PATCH V8 3/3] irq: Compute the periodic interval for interrupts

[Daniel Lezcano]

An interrupt behaves with a burst of activity with periodic interval of time
followed by one or two peaks of longer interval.

As the time intervals are periodic, statistically speaking they follow a normal
distribution and each interrupts can be tracked individually.

This patch does statistics on all interrupts, except the timers which are
deterministic by essence. The goal is to extract the periodicity for each
interrupt, with the last timestamp and sum them, so we have the next event.

Taking the earliest prediction gives the expected wakeup on the system (assuming
a timer won't expire before).

As stated in the previous patch, this code is not enabled in the kernel by
default.

Signed-off-by: Daniel Lezcano <daniel.lezcano@xxxxxxxxxx>
---
 include/linux/interrupt.h |   1 +
 kernel/irq/internals.h    |  19 +++
 kernel/irq/timings.c      | 344 ++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 364 insertions(+)

diff --git a/include/linux/interrupt.h b/include/linux/interrupt.h
index c050333..62bb0c9 100644
--- a/include/linux/interrupt.h
+++ b/include/linux/interrupt.h
@@ -707,6 +707,7 @@ static inline void init_irq_proc(void)
 #ifdef CONFIG_IRQ_TIMINGS
 void irq_timings_enable(void);
 void irq_timings_disable(void);
+u64 irq_timings_next_event(u64 now);
 #endif
 
 struct seq_file;
diff --git a/kernel/irq/internals.h b/kernel/irq/internals.h
index abaadaa..677c1a2 100644
--- a/kernel/irq/internals.h
+++ b/kernel/irq/internals.h
@@ -247,13 +247,21 @@ struct irq_timings {
 
 DECLARE_PER_CPU(struct irq_timings, irq_timings);
 
+extern void irq_timings_free(int irq);
+extern int irq_timings_alloc(int irq);
+
 static inline void remove_timings(struct irq_desc *desc)
 {
 	desc->istate &= ~IRQS_TIMINGS;
+
+	irq_timings_free(irq_desc_get_irq(desc));
 }
 
 static inline void setup_timings(struct irq_desc *desc, struct irqaction *act)
 {
+	int irq = irq_desc_get_irq(desc);
+	int ret;
+
 	/*
 	 * We don't need the measurement because the idle code already
 	 * knows the next expiry event.
@@ -261,6 +269,17 @@ static inline void setup_timings(struct irq_desc *desc, struct irqaction *act)
 	if (act->flags & __IRQF_TIMER)
 		return;
 
+	/*
+	 * In case the timing allocation fails, we just want to warn,
+	 * not fail, so letting the system boot anyway.
+	 */
+	ret = irq_timings_alloc(irq);
+	if (ret) {
+		pr_warn("Failed to allocate irq timing stats for irq%d (%d)",
+			irq, ret);
+		return;
+	}
+
 	desc->istate |= IRQS_TIMINGS;
 }
 
diff --git a/kernel/irq/timings.c b/kernel/irq/timings.c
index 21ceca8..a3879cb 100644
--- a/kernel/irq/timings.c
+++ b/kernel/irq/timings.c
@@ -9,9 +9,14 @@
  *
  */
 #include <linux/percpu.h>
+#include <linux/slab.h>
 #include <linux/static_key.h>
 #include <linux/interrupt.h>
+#include <linux/idr.h>
 #include <linux/irq.h>
+#include <linux/math64.h>
+
+#include <trace/events/irq.h>
 
 #include "internals.h"
 
@@ -19,6 +24,18 @@
 
 DEFINE_PER_CPU(struct irq_timings, irq_timings);
 
+struct irq_stat {
+	u64 ne;         /* next event                               */
+	u64 lts;	/* last timestamp                           */
+	u64 variance;	/* variance                                 */
+	u32 avg;	/* mean value                               */
+	u32 count;      /* number of samples                        */
+	int anomalies;  /* number of consecutives anomalies         */
+	int valid;      /* behaviour of the interrupt               */
+};
+
+static DEFINE_IDR(irq_stats);
+
 void irq_timings_enable(void)
 {
 	static_branch_inc(&irq_timing_enabled);
@@ -28,3 +45,330 @@ void irq_timings_disable(void)
 {
 	static_branch_dec(&irq_timing_enabled);
 }
+
+/**
+ * irqs_update - update the irq timing statistics with a new timestamp
+ *
+ * @irqs: an irq_stat struct pointer
+ * @ts: the new timestamp
+ *
+ * ** This function must be called with the local irq disabled **
+ *
+ * The statistics are computed online, in other words, the code is
+ * designed to compute the statistics on a stream of values rather
+ * than doing multiple passes on the values to compute the average,
+ * then the variance. The integer division introduces a loss of
+ * precision but with an acceptable error margin regarding the results
+ * we would have with the double floating precision: we are dealing
+ * with nanosec, so big numbers, consequently the mantisse is
+ * negligeable, especially when converting the time in usec
+ * afterwards.
+ *
+ * The computation happens at idle time. When the CPU is not idle, the
+ * interrupts' timestamps are stored in the circular buffer, when the
+ * CPU goes idle and this routine is called, all the buffer's values
+ * are injected in the statistical model continuying to extend the
+ * statistics from the previous busy-idle cycle.
+ *
+ * The observations showed a device will trigger a burst of periodic
+ * interrupts followed by one or two peaks of longer time, for
+ * instance when a SD card device flushes its cache, then the periodic
+ * intervals occur again. A one second inactivity period resets the
+ * stats, that gives us the certitude the statistical values won't
+ * exceed 1x10^9, thus the computation won't overflow.
+ *
+ * Basically, the purpose of the algorithm is to watch the periodic
+ * interrupts and eliminate the peaks.
+ *
+ * An interrupt is considered periodically stable if the interval of
+ * its occurences follow the normal distribution, thus the values
+ * comply with:
+ *
+ *      avg - 3 x stddev < value < avg + 3 x stddev
+ *
+ * Which can be simplified to:
+ *
+ *      -3 x stddev < value - avg < 3 x stddev
+ *
+ *      abs(value - avg) < 3 x stddev
+ *
+ * In order to save a costly square root computation, we use the
+ * variance. For the record, stddev = sqrt(variance). The equation
+ * above becomes:
+ *
+ *      abs(value - avg) < 3 x sqrt(variance)
+ *
+ * And finally we square it:
+ *
+ *      (value - avg) ^ 2 < (3 x sqrt(variance)) ^ 2
+ *
+ *      (value - avg) x (value - avg) < 9 x variance
+ *
+ * Statistically speaking, any values out of this interval is
+ * considered as an anomaly and is discarded. However, a normal
+ * distribution appears when the number of samples is 30 (it is the
+ * rule of thumb in statistics, cf. "30 samples" on Internet). When
+ * there are three consecutive anomalies, the statistics are resetted.
+ *
+ */
+static void irqs_update(struct irq_stat *irqs, u64 ts)
+{
+	u64 old_ts = irqs->lts;
+	u64 variance = 0;
+	u64 interval;
+	s64 diff;
+
+	/*
+	 * The timestamps are absolute time values, we need to compute
+	 * the timing interval between two interrupts.
+	 */
+	irqs->lts = ts;
+
+	/*
+	 * The interval type is u64 in order to deal with the same
+	 * type in our computation, that prevent mindfuck issues with
+	 * overflow, sign and do_div.
+	 */
+	interval = ts - old_ts;
+
+	/*
+	 * The interrupt triggered more than one second apart, that
+	 * ends the sequence as predictible for our purpose. In this
+	 * case, assume we have the beginning of a sequence and the
+	 * timestamp is the first value. As it is impossible to
+	 * predict anything at this point, return.
+	 *
+	 * Note the first timestamp of the sequence will always fall
+	 * in this test because the old_ts is zero. That is what we
+	 * want as we need another timestamp to compute an interval.
+	 */
+	if (interval >= NSEC_PER_SEC) {
+		memset(irqs, 0, sizeof(*irqs));
+		irqs->lts = ts;
+		return;
+	}
+
+	/*
+	 * Pre-compute the delta with the average as the result is
+	 * used several times in this function.
+	 */
+	diff = interval - irqs->avg;
+
+	/*
+	 * Increment the number of samples.
+	 */
+	irqs->count++;
+
+	/*
+	 * Online variance divided by the number of elements if there
+	 * is more than one sample.
+	 */
+	if (likely(irqs->count > 1))
+		variance = div_u64(irqs->variance, irqs->count - 1);
+
+	/*
+	 * The rule of thumb in statistics for the normal distribution
+	 * is having at least 30 samples in order to have the model to
+	 * apply. Values outside the interval are considered as an
+	 * anomaly.
+	 */
+	if ((irqs->count >= 30) && ((diff * diff) > (9 * variance))) {
+		/*
+		 * After three consecutive anomalies, we reset the
+		 * stats as it is no longer stable enough.
+		 */
+		if (irqs->anomalies++ >= 3) {
+			memset(irqs, 0, sizeof(*irqs));
+			irqs->lts = ts;
+			return;
+		}
+	} else {
+		/*
+		 * The anomalies must be consecutives, so at this
+		 * point, we reset the anomalies counter.
+		 */
+		irqs->anomalies = 0;
+	}
+
+	/*
+	 * The interrupt is considered stable enough to try to predict
+	 * the next event on it.
+	 */
+	irqs->valid = 1;
+
+	/*
+	 * Online average algorithm:
+	 *
+	 *  new_average = average + ((value - average) / count)
+	 *
+	 * The variance computation depends on the new average
+	 * to be computed here first.
+	 *
+	 */
+	irqs->avg = irqs->avg + div_s64(diff, irqs->count);
+
+	/*
+	 * Online variance algorithm:
+	 *
+	 *  new_variance = variance + (value - average) x (value - new_average)
+	 *
+	 * Warning: irqs->avg is updated with the line above, hence
+	 * 'interval - irqs->avg' is no longer equal to 'diff'
+	 */
+	irqs->variance = irqs->variance + (diff * (interval - irqs->avg));
+
+	/*
+	 * Update the next event
+	 */
+	irqs->ne = ts + irqs->avg;
+}
+
+/**
+ * irq_timings_next_event - Return when the next event is supposed to arrive
+ *
+ * *** This function must be called with the local irq disabled ***
+ *
+ * During the last busy cycle, the number of interrupts is incremented
+ * and stored in the irq_timings structure. This information is
+ * necessary to:
+ *
+ * - know if the index in the table wrapped up:
+ *
+ *      If more than the array size interrupts happened during the
+ *      last busy/idle cycle, the index wrapped up and we have to
+ *      begin with the next element in the array which is the last one
+ *      in the sequence, otherwise it is a the index 0.
+ *
+ * - have an indication of the interrupts activity on this CPU
+ *   (eg. irq/sec)
+ *
+ * The values are 'consumed' after inserting in the statistical model,
+ * thus the count is reinitialized.
+ *
+ * The array of values **must** be browsed in the time direction, the
+ * timestamp must increase between an element and the next one.
+ *
+ * Returns a nanosec time based estimation of the earliest interrupt,
+ * U64_MAX otherwise.
+ */
+u64 irq_timings_next_event(u64 now)
+{
+	struct irq_timings *irqts = this_cpu_ptr(&irq_timings);
+	struct irq_timing *irqt;
+	struct irq_stat *irqs;
+	struct irq_stat __percpu *s;
+	u64 ne = U64_MAX;
+	int index, count, i, irq = 0;
+
+	/*
+	 * Number of elements in the circular buffer. If it happens it
+	 * was flushed before, then the number of elements could be
+	 * smaller than IRQ_TIMINGS_SIZE, so the count is used,
+	 * otherwise the array size is used as we wrapped. The index
+	 * begins from zero when we did not wrap. That could be done
+	 * in a nicer way with the proper circular array structure
+	 * type but with the cost of extra computation in the
+	 * interrupt handler hot path. We choose efficiency.
+	 */
+	if (irqts->count >= IRQ_TIMINGS_SIZE) {
+		count = IRQ_TIMINGS_SIZE;
+		index = irqts->count & IRQ_TIMINGS_MASK;
+	} else {
+		count = irqts->count;
+		index = 0;
+	}
+
+	/*
+	 * Inject measured irq/timestamp to the statistical model.
+	 */
+	for (i = 0; i < count; i++) {
+
+		irqt = &irqts->values[(index + i) & IRQ_TIMINGS_MASK];
+
+		s = idr_find(&irq_stats, irqt->irq);
+
+		irqs = this_cpu_ptr(s);
+
+		irqs_update(irqs, irqt->ts);
+	}
+
+	/*
+	 * Reset the counter, we consumed all the data from our
+	 * circular buffer.
+	 */
+	irqts->count = 0;
+
+	/*
+	 * Look in the list of interrupts' statistics, the earliest
+	 * next event.
+	 */
+	idr_for_each_entry(&irq_stats, s, i) {
+
+		irqs = this_cpu_ptr(s);
+
+		if (!irqs->valid)
+			continue;
+
+		if (irqs->ne <= now) {
+			irq = i;
+			ne = now;
+
+			/*
+			 * This interrupt mustn't use in the future
+			 * until new events occur and update the
+			 * statistics.
+			 */
+			irqs->valid = 0;
+			break;
+		}
+
+		if (irqs->ne < ne) {
+			irq = i;
+			ne = irqs->ne;
+		}
+	}
+
+	return ne;
+}
+
+void irq_timings_free(int irq)
+{
+	struct irq_stat __percpu *s;
+
+	s = idr_find(&irq_stats, irq);
+	if (s) {
+		free_percpu(s);
+		idr_remove(&irq_stats, irq);
+	}
+}
+
+int irq_timings_alloc(int irq)
+{
+	int id;
+	struct irq_stat __percpu *s;
+
+	/*
+	 * Some platforms can have the same private interrupt per cpu,
+	 * so this function may be be called several times with the
+	 * same interrupt number. Just bail out in case the per cpu
+	 * stat structure is already allocated.
+	 */
+	s = idr_find(&irq_stats, irq);
+	if (s)
+		return 0;
+
+	s = alloc_percpu(*s);
+	if (!s)
+		return -ENOMEM;
+
+	idr_preload(GFP_KERNEL);
+	id = idr_alloc(&irq_stats, s, irq, irq + 1, GFP_NOWAIT);
+	idr_preload_end();
+
+	if (id < 0) {
+		free_percpu(s);
+		return id;
+	}
+
+	return 0;
+}
-- 
1.9.1