#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)
projects / platform / kernel / linux-rpi.git / commitdiff