genirq/timings: Remove variance computation code

#include <linux/interrupt.h>

#include <linux/idr.h>

#include <linux/irq.h>

#include <linux/math64.h>

#include <trace/events/irq.h>

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);

	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

 *

 */

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

	 */

	lockdep_assert_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;

	return 0;

}

void irq_timings_free(int irq)