/*
* linux/kernel/irq/timings.c
*
* Copyright (C) 2016, Linaro Ltd - Daniel Lezcano <daniel.lezcano@linaro.org>
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2 as
* 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"
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);
}
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;
}
