genirq/timings: Add infrastructure for estimating the next interrupt arrival time

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.

Add a mechanism to compute the statistics on all interrupts, except the
timers which are deterministic from a prediction point of view, as their
expiry time is known.

The goal is to extract the periodicity for each interrupt, with the last
timestamp and sum them, so the next event can be predicted to a certain
extent.

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

Signed-off-by: Daniel Lezcano <daniel.lezcano@linaro.org>
Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Cc: Nicolas Pitre <nicolas.pitre@linaro.org>
Cc: Jens Axboe <axboe@kernel.dk>
Cc: Hannes Reinecke <hare@suse.com>
Cc: Vincent Guittot <vincent.guittot@linaro.org>
Cc: "Rafael J . Wysocki" <rafael@kernel.org>
Cc: Peter Zijlstra <peterz@infradead.org>
Cc: Bjorn Helgaas <bhelgaas@google.com>
Link: http://lkml.kernel.org/r/1498227072-5980-2-git-send-email-daniel.lezcano@linaro.org

include/linux/interrupt.h

@@ -706,6 +706,7 @@ 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;

kernel/irq/internals.h

@@ -275,13 +275,21 @@ 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 irq_remove_timings(struct irq_desc *desc)
 {
 	desc->istate &= ~IRQS_TIMINGS;
+
+	irq_timings_free(irq_desc_get_irq(desc));
 }
 
 static inline void irq_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.
@@ -289,6 +297,17 @@ static inline void irq_setup_timings(struct irq_desc *desc, struct irqaction *ac
 	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;
 }
 

kernel/irq/timings.c

@@ -8,10 +8,16 @@
  * published by the Free Software Foundation.
  *
  */
+#include <linux/kernel.h>
 #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 +25,18 @@ DEFINE_STATIC_KEY_FALSE(irq_timing_enabled);
 
 DEFINE_PER_CPU(struct irq_timings, irq_timings);
 
+struct irqt_stat {
+	u64	next_evt;
+	u64	last_ts;
+	u64	variance;
+	u32	avg;
+	u32	nr_samples;
+	int	anomalies;
+	int	valid;
+};
+
+static DEFINE_IDR(irqt_stats);
+
 void irq_timings_enable(void)
 {
 	static_branch_enable(&irq_timing_enabled);
@@ -28,3 +46,324 @@ void irq_timings_disable(void)
 {
 	static_branch_disable(&irq_timing_enabled);
 }
+
+/**
+ * irqs_update - update the irq timing statistics with a new timestamp
+ *
+ * @irqs: an irqt_stat struct pointer
+ * @ts: the new timestamp
+ *
+ * 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 irqt_stat *irqs, u64 ts)
+{
+	u64 old_ts = irqs->last_ts;
+	u64 variance = 0;
+	u64 interval;
+	s64 diff;
+
+	/*
+	 * The timestamps are absolute time values, we need to compute
+	 * the timing interval between two interrupts.
+	 */
+	irqs->last_ts = 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 division.
+	 */
+	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->last_ts = 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->nr_samples++;
+
+	/*
+	 * Online variance divided by the number of elements if there
+	 * is more than one sample.  Normally the formula is division
+	 * by nr_samples - 1 but we assume the number of element will be
+	 * more than 32 and dividing by 32 instead of 31 is enough
+	 * precise.
+	 */
+	if (likely(irqs->nr_samples > 1))
+		variance = irqs->variance >> IRQ_TIMINGS_SHIFT;
+
+	/*
+	 * 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->nr_samples >= 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->last_ts = 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 + (diff >> IRQ_TIMINGS_SHIFT);
+
+	/*
+	 * 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->next_evt = ts + irqs->avg;
+}
+
+/**
+ * irq_timings_next_event - Return when the next event is supposed to arrive
+ *
+ * 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 irqt_stat *irqs;
+	struct irqt_stat __percpu *s;
+	u64 ts, next_evt = U64_MAX;
+	int i, irq = 0;
+
+	/*
+	 * This function must be called with the local irq disabled in
+	 * order to prevent the timings circular buffer to be updated
+	 * while we are reading it.
+	 */
+	WARN_ON_ONCE(!irqs_disabled());
+
+	/*
+	 * 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.
+	 *
+	 * Inject measured irq/timestamp to the statistical model
+	 * while decrementing the counter because we consume the data
+	 * from our circular buffer.
+	 */
+	for (i = irqts->count & IRQ_TIMINGS_MASK,
+		     irqts->count = min(IRQ_TIMINGS_SIZE, irqts->count);
+	     irqts->count > 0; irqts->count--, i = (i + 1) & IRQ_TIMINGS_MASK) {
+
+		irq = irq_timing_decode(irqts->values[i], &ts);
+
+		s = idr_find(&irqt_stats, irq);
+		if (s) {
+			irqs = this_cpu_ptr(s);
+			irqs_update(irqs, ts);
+		}
+	}
+
+	/*
+	 * Look in the list of interrupts' statistics, the earliest
+	 * next event.
+	 */
+	idr_for_each_entry(&irqt_stats, s, i) {
+
+		irqs = this_cpu_ptr(s);
+
+		if (!irqs->valid)
+			continue;
+
+		if (irqs->next_evt <= now) {
+			irq = i;
+			next_evt = now;
+
+			/*
+			 * This interrupt mustn't use in the future
+			 * until new events occur and update the
+			 * statistics.
+			 */
+			irqs->valid = 0;
+			break;
+		}
+
+		if (irqs->next_evt < next_evt) {
+			irq = i;
+			next_evt = irqs->next_evt;
+		}
+	}
+
+	return next_evt;
+}
+
+void irq_timings_free(int irq)
+{
+	struct irqt_stat __percpu *s;
+
+	s = idr_find(&irqt_stats, irq);
+	if (s) {
+		free_percpu(s);
+		idr_remove(&irqt_stats, irq);
+	}
+}
+
+int irq_timings_alloc(int irq)
+{
+	struct irqt_stat __percpu *s;
+	int id;
+
+	/*
+	 * 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(&irqt_stats, irq);
+	if (s)
+		return 0;
+
+	s = alloc_percpu(*s);
+	if (!s)
+		return -ENOMEM;
+
+	idr_preload(GFP_KERNEL);
+	id = idr_alloc(&irqt_stats, s, irq, irq + 1, GFP_NOWAIT);
+	idr_preload_end();
+
+	if (id < 0) {
+		free_percpu(s);
+		return id;
+	}
+
+	return 0;
+}