genirq/timings: Add array suffix computation code

#include <linux/interrupt.h>

#include <linux/idr.h>

#include <linux/irq.h>

#include <linux/math64.h>

#include <linux/log2.h>

#include <trace/events/irq.h>

DEFINE_PER_CPU(struct irq_timings, irq_timings);

struct irqt_stat {

	u64     next_evt;

};

static DEFINE_IDR(irqt_stats);

void irq_timings_enable(void)

	static_branch_disable(&irq_timing_enabled);

}

/*

 * The main goal of this algorithm is to predict the next interrupt

 * occurrence on the current CPU.

 *

 * Currently, the interrupt timings are stored in a circular array

 * buffer every time there is an interrupt, as a tuple: the interrupt

 * number and the associated timestamp when the event occurred <irq,

 * timestamp>.

 *

 * For every interrupt occurring in a short period of time, we can

 * measure the elapsed time between the occurrences for the same

 * interrupt and we end up with a suite of intervals. The experience

 * showed the interrupts are often coming following a periodic

 * pattern.

 *

 * The objective of the algorithm is to find out this periodic pattern

 * in a fastest way and use its period to predict the next irq event.

 *

 * When the next interrupt event is requested, we are in the situation

 * where the interrupts are disabled and the circular buffer

 * containing the timings is filled with the events which happened

 * after the previous next-interrupt-event request.

 *

 * At this point, we read the circular buffer and we fill the irq

 * related statistics structure. After this step, the circular array

 * containing the timings is empty because all the values are

 * dispatched in their corresponding buffers.

 *

 * Now for each interrupt, we can predict the next event by using the

 * suffix array, log interval and exponential moving average

 *

 * 1. Suffix array

 *

 * Suffix array is an array of all the suffixes of a string. It is

 * widely used as a data structure for compression, text search, ...

 * For instance for the word 'banana', the suffixes will be: 'banana'

 * 'anana' 'nana' 'ana' 'na' 'a'

 *

 * Usually, the suffix array is sorted but for our purpose it is

 * not necessary and won't provide any improvement in the context of

 * the solved problem where we clearly define the boundaries of the

 * search by a max period and min period.

 *

 * The suffix array will build a suite of intervals of different

 * length and will look for the repetition of each suite. If the suite

 * is repeating then we have the period because it is the length of

 * the suite whatever its position in the buffer.

 *

 * 2. Log interval

 *

 * We saw the irq timings allow to compute the interval of the

 * occurrences for a specific interrupt. We can reasonibly assume the

 * longer is the interval, the higher is the error for the next event

 * and we can consider storing those interval values into an array

 * where each slot in the array correspond to an interval at the power

 * of 2 of the index. For example, index 12 will contain values

 * between 2^11 and 2^12.

 *

 * At the end we have an array of values where at each index defines a

 * [2^index - 1, 2 ^ index] interval values allowing to store a large

 * number of values inside a small array.

 *

 * For example, if we have the value 1123, then we store it at

 * ilog2(1123) = 10 index value.

 *

 * Storing those value at the specific index is done by computing an

 * exponential moving average for this specific slot. For instance,

 * for values 1800, 1123, 1453, ... fall under the same slot (10) and

 * the exponential moving average is computed every time a new value

 * is stored at this slot.

 *

 * 3. Exponential Moving Average

 *

 * The EMA is largely used to track a signal for stocks or as a low

 * pass filter. The magic of the formula, is it is very simple and the

 * reactivity of the average can be tuned with the factors called

 * alpha.

 *

 * The higher the alphas are, the faster the average respond to the

 * signal change. In our case, if a slot in the array is a big

 * interval, we can have numbers with a big difference between

 * them. The impact of those differences in the average computation

 * can be tuned by changing the alpha value.

 *

 *

 *  -- The algorithm --

 *

 * We saw the different processing above, now let's see how they are

 * used together.

 *

 * For each interrupt:

 *	For each interval:

 *		Compute the index = ilog2(interval)

 *		Compute a new_ema(buffer[index], interval)

 *		Store the index in a circular buffer

 *

 *	Compute the suffix array of the indexes

 *

 *	For each suffix:

 *		If the suffix is reverse-found 3 times

 *			Return suffix

 *

 *	Return Not found

 *

 * However we can not have endless suffix array to be build, it won't

 * make sense and it will add an extra overhead, so we can restrict

 * this to a maximum suffix length of 5 and a minimum suffix length of

 * 2. The experience showed 5 is the majority of the maximum pattern

 * period found for different devices.

 *

 * The result is a pattern finding less than 1us for an interrupt.

 *

 * Example based on real values:

 *

 * Example 1 : MMC write/read interrupt interval:

 *

 *	223947, 1240, 1384, 1386, 1386,

 *	217416, 1236, 1384, 1386, 1387,

 *	214719, 1241, 1386, 1387, 1384,

 *	213696, 1234, 1384, 1386, 1388,

 *	219904, 1240, 1385, 1389, 1385,

 *	212240, 1240, 1386, 1386, 1386,

 *	214415, 1236, 1384, 1386, 1387,

 *	214276, 1234, 1384, 1388, ?

 *

 * For each element, apply ilog2(value)

 *

 *	15, 8, 8, 8, 8,

 *	15, 8, 8, 8, 8,

 *	15, 8, 8, 8, 8,

 *	15, 8, 8, 8, 8,

 *	15, 8, 8, 8, 8,

 *	15, 8, 8, 8, 8,

 *	15, 8, 8, 8, 8,

 *	15, 8, 8, 8, ?

 *

 * Max period of 5, we take the last (max_period * 3) 15 elements as

 * we can be confident if the pattern repeats itself three times it is

 * a repeating pattern.

 *

 *	             8,

 *	15, 8, 8, 8, 8,

 *	15, 8, 8, 8, 8,

 *	15, 8, 8, 8, ?

 *

 * Suffixes are:

 *

 *  1) 8, 15, 8, 8, 8  <- max period

 *  2) 8, 15, 8, 8

 *  3) 8, 15, 8

 *  4) 8, 15           <- min period

 *

 * From there we search the repeating pattern for each suffix.

 *

 * buffer: 8, 15, 8, 8, 8, 8, 15, 8, 8, 8, 8, 15, 8, 8, 8

 *         |   |  |  |  |  |   |  |  |  |  |   |  |  |  |

 *         8, 15, 8, 8, 8  |   |  |  |  |  |   |  |  |  |

 *                         8, 15, 8, 8, 8  |   |  |  |  |

 *                                         8, 15, 8, 8, 8

 *

 * When moving the suffix, we found exactly 3 matches.

 *

 * The first suffix with period 5 is repeating.

 *

 * The next event is (3 * max_period) % suffix_period

 *

 * In this example, the result 0, so the next event is suffix[0] => 8

 *

 * However, 8 is the index in the array of exponential moving average

 * which was calculated on the fly when storing the values, so the

 * interval is ema[8] = 1366

 *

 *

 * Example 2:

 *

 *	4, 3, 5, 100,

 *	3, 3, 5, 117,

 *	4, 4, 5, 112,

 *	4, 3, 4, 110,

 *	3, 5, 3, 117,

 *	4, 4, 5, 112,

 *	4, 3, 4, 110,

 *	3, 4, 5, 112,

 *	4, 3, 4, 110

 *

 * ilog2

 *

 *	0, 0, 0, 4,

 *	0, 0, 0, 4,

 *	0, 0, 0, 4,

 *	0, 0, 0, 4,

 *	0, 0, 0, 4,

 *	0, 0, 0, 4,

 *	0, 0, 0, 4,

 *	0, 0, 0, 4,

 *	0, 0, 0, 4

 *

 * Max period 5:

 *	   0, 0, 4,

 *	0, 0, 0, 4,

 *	0, 0, 0, 4,

 *	0, 0, 0, 4

 *

 * Suffixes:

 *

 *  1) 0, 0, 4, 0, 0

 *  2) 0, 0, 4, 0

 *  3) 0, 0, 4

 *  4) 0, 0

 *

 * buffer: 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4

 *         |  |  |  |  |  |  X

 *         0, 0, 4, 0, 0, |  X

 *                        0, 0

 *

 * buffer: 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4

 *         |  |  |  |  |  |  |  |  |  |  |  |  |  |  |

 *         0, 0, 4, 0, |  |  |  |  |  |  |  |  |  |  |

 *                     0, 0, 4, 0, |  |  |  |  |  |  |

 *                                 0, 0, 4, 0, |  |  |

 *                                             0  0  4

 *

 * Pattern is found 3 times, the remaining is 1 which results from

 * (max_period * 3) % suffix_period. This value is the index in the

 * suffix arrays. The suffix array for a period 4 has the value 4

 * at index 1.

 */

#define EMA_ALPHA_VAL		64

#define EMA_ALPHA_SHIFT		7

#define PREDICTION_PERIOD_MIN	2

#define PREDICTION_PERIOD_MAX	5

#define PREDICTION_FACTOR	4

#define PREDICTION_MAX		10 /* 2 ^ PREDICTION_MAX useconds */

#define PREDICTION_BUFFER_SIZE	16 /* slots for EMAs, hardly more than 16 */

struct irqt_stat {

	u64	last_ts;

	u64	ema_time[PREDICTION_BUFFER_SIZE];

	int	timings[IRQ_TIMINGS_SIZE];

	int	circ_timings[IRQ_TIMINGS_SIZE];

	int	count;

};

/*

 * Exponential moving average computation

 */

static u64 irq_timings_ema_new(u64 value, u64 ema_old)

{

	s64 diff;

	if (unlikely(!ema_old))

		return value;

	diff = (value - ema_old) * EMA_ALPHA_VAL;

	/*

	 * We can use a s64 type variable to be added with the u64

	 * ema_old variable as this one will never have its topmost

	 * bit set, it will be always smaller than 2^63 nanosec

	 * interrupt interval (292 years).

	 */

	return ema_old + (diff >> EMA_ALPHA_SHIFT);

}

static int irq_timings_next_event_index(int *buffer, size_t len, int period_max)

{

	int i;

	/*

	 * The buffer contains the suite of intervals, in a ilog2

	 * basis, we are looking for a repetition. We point the

	 * beginning of the search three times the length of the

	 * period beginning at the end of the buffer. We do that for

	 * each suffix.

	 */

	for (i = period_max; i >= PREDICTION_PERIOD_MIN ; i--) {

		int *begin = &buffer[len - (i * 3)];

		int *ptr = begin;

		/*

		 * We look if the suite with period 'i' repeat

		 * itself. If it is truncated at the end, as it

		 * repeats we can use the period to find out the next

		 * element.

		 */

		while (!memcmp(ptr, begin, i * sizeof(*ptr))) {

			ptr += i;

			if (ptr >= &buffer[len])

				return begin[((i * 3) % i)];

		}

	}

	return -1;

}

static u64 __irq_timings_next_event(struct irqt_stat *irqs, int irq, u64 now)

{

	int index, i, period_max, count, start, min = INT_MAX;

	if ((now - irqs->last_ts) >= NSEC_PER_SEC) {

		irqs->count = irqs->last_ts = 0;

		return U64_MAX;

	}

	/*

	 * As we want to find three times the repetition, we need a

	 * number of intervals greater or equal to three times the

	 * maximum period, otherwise we truncate the max period.

	 */

	period_max = irqs->count > (3 * PREDICTION_PERIOD_MAX) ?

		PREDICTION_PERIOD_MAX : irqs->count / 3;

	/*

	 * If we don't have enough irq timings for this prediction,

	 * just bail out.

	 */

	if (period_max <= PREDICTION_PERIOD_MIN)

		return U64_MAX;

	/*

	 * 'count' will depends if the circular buffer wrapped or not

	 */

	count = irqs->count < IRQ_TIMINGS_SIZE ?

		irqs->count : IRQ_TIMINGS_SIZE;

	start = irqs->count < IRQ_TIMINGS_SIZE ?

		0 : (irqs->count & IRQ_TIMINGS_MASK);

	/*

	 * Copy the content of the circular buffer into another buffer

	 * in order to linearize the buffer instead of dealing with

	 * wrapping indexes and shifted array which will be prone to

	 * error and extremelly difficult to debug.

	 */

	for (i = 0; i < count; i++) {

		int index = (start + i) & IRQ_TIMINGS_MASK;

		irqs->timings[i] = irqs->circ_timings[index];

		min = min_t(int, irqs->timings[i], min);

	}

	index = irq_timings_next_event_index(irqs->timings, count, period_max);

	if (index < 0)

		return irqs->last_ts + irqs->ema_time[min];

	return irqs->last_ts + irqs->ema_time[index];

}

static inline void irq_timings_store(int irq, struct irqt_stat *irqs, u64 ts)

{

	u64 old_ts = irqs->last_ts;

	u64 interval;

	int index;

	/*

	 * 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) {

		irqs->count = 0;

		return;

	}

	/*

	 * Get the index in the ema table for this interrupt. The

	 * PREDICTION_FACTOR increase the interval size for the array

	 * of exponential average.

	 */

	index = likely(interval) ?

		ilog2((interval >> 10) / PREDICTION_FACTOR) : 0;

	/*

	 * Store the index as an element of the pattern in another

	 * circular array.

	 */

	irqs->circ_timings[irqs->count & IRQ_TIMINGS_MASK] = index;

	irqs->ema_time[index] = irq_timings_ema_new(interval,

						    irqs->ema_time[index]);

	irqs->count++;

}

/**

 * 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();

	return 0;

	if (!irqts->count)

		return next_evt;

	/*

	 * 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 pattern prediction

	 * model while decrementing the counter because we consume the

	 * data from our circular buffer.

	 */

	i = (irqts->count & IRQ_TIMINGS_MASK) - 1;

	irqts->count = min(IRQ_TIMINGS_SIZE, irqts->count);

	for (; 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)

			irq_timings_store(irq, this_cpu_ptr(s), 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);

		ts = __irq_timings_next_event(irqs, i, now);

		if (ts <= now)

			return now;

		if (ts < next_evt)

			next_evt = ts;

	}

	return next_evt;

}

void irq_timings_free(int irq)