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sched/fair: Optimize ___update_sched_avg() 

The main PELT function ___update_load_avg(), which implements the
accumulation and progression of the geometric average series, is
implemented along the following lines for the scenario where the time
delta spans all 3 possible sections (see figure below):

  1. add the remainder of the last incomplete period
  2. decay old sum
  3. accumulate new sum in full periods since last_update_time
  4. accumulate the current incomplete period
  5. update averages

Or:

            d1          d2           d3
            ^           ^            ^
            |           |            |
          |<->|<----------------->|<--->|
  ... |---x---|------| ... |------|-----x (now)

  load_sum' = (load_sum + weight * scale * d1) * y^(p+1) +	(1,2)

                                        p
	      weight * scale * 1024 * \Sum y^n +		(3)
                                       n=1

	      weight * scale * d3 * y^0				(4)

  load_avg' = load_sum' / LOAD_AVG_MAX				(5)

Where:

 d1 - is the delta part completing the remainder of the last
      incomplete period,
 d2 - is the delta part spannind complete periods, and
 d3 - is the delta part starting the current incomplete period.

We can simplify the code in two steps; the first step is to separate
the first term into new and old parts like:

  (load_sum + weight * scale * d1) * y^(p+1) = load_sum * y^(p+1) +
					       weight * scale * d1 * y^(p+1)

Once we've done that, its easy to see that all new terms carry the
common factors:

  weight * scale

If we factor those out, we arrive at the form:

  load_sum' = load_sum * y^(p+1) +

	      weight * scale * (d1 * y^(p+1) +

					 p
			        1024 * \Sum y^n +
					n=1

				d3 * y^0)

Which results in a simpler, smaller and faster implementation.

Signed-off-by: Yuyang Du <yuyang.du@intel.com>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Cc: Linus Torvalds <torvalds@linux-foundation.org>
Cc: Peter Zijlstra <peterz@infradead.org>
Cc: Thomas Gleixner <tglx@linutronix.de>
Cc: bsegall@google.com
Cc: dietmar.eggemann@arm.com
Cc: matt@codeblueprint.co.uk
Cc: morten.rasmussen@arm.com
Cc: pjt@google.com
Cc: umgwanakikbuti@gmail.com
Cc: vincent.guittot@linaro.org
Link: http://lkml.kernel.org/r/1486935863-25251-3-git-send-email-yuyang.du@intel.com
Signed-off-by: Ingo Molnar <mingo@kernel.org>
This commit is contained in:
Yuyang Du 2017-02-13 05:44:23 +08:00 committed by Ingo Molnar
parent 0ccb977f4c
commit a481db34b9
1 changed files with 118 additions and 94 deletions
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212
kernel/sched/fair.c
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@ -2767,7 +2767,7 @@ static const u32 __accumulated_sum_N32[] = {
* Approximate:
* val * y^n, where y^32 ~= 0.5 (~1 scheduling period)
*/
static __always_inline u64 decay_load(u64 val, u64 n)
static u64 decay_load(u64 val, u64 n)
{
unsigned int local_n;
@ -2795,31 +2795,112 @@ static __always_inline u64 decay_load(u64 val, u64 n)
return val;
}
/*
* For updates fully spanning n periods, the contribution to runnable
* average will be: \Sum 1024*y^n
*
* We can compute this reasonably efficiently by combining:
* y^PERIOD = 1/2 with precomputed \Sum 1024*y^n {for n <PERIOD}
*/
static u32 __compute_runnable_contrib(u64 n)
static u32 __accumulate_sum(u64 periods, u32 period_contrib, u32 remainder)
{
u32 contrib = 0;
u32 c1, c2, c3 = remainder; /* y^0 == 1 */
if (likely(n <= LOAD_AVG_PERIOD))
return runnable_avg_yN_sum[n];
else if (unlikely(n >= LOAD_AVG_MAX_N))
if (!periods)
return remainder - period_contrib;
if (unlikely(periods >= LOAD_AVG_MAX_N))
return LOAD_AVG_MAX;
/* Since n < LOAD_AVG_MAX_N, n/LOAD_AVG_PERIOD < 11 */
contrib = __accumulated_sum_N32[n/LOAD_AVG_PERIOD];
n %= LOAD_AVG_PERIOD;
contrib = decay_load(contrib, n);
return contrib + runnable_avg_yN_sum[n];
/*
* c1 = d1 y^(p+1)
*/
c1 = decay_load((u64)(1024 - period_contrib), periods);
periods -= 1;
/*
* For updates fully spanning n periods, the contribution to runnable
* average will be:
*
* c2 = 1024 \Sum y^n
*
* We can compute this reasonably efficiently by combining:
*
* y^PERIOD = 1/2 with precomputed 1024 \Sum y^n {for: n < PERIOD}
*/
if (likely(periods <= LOAD_AVG_PERIOD)) {
c2 = runnable_avg_yN_sum[periods];
} else {
c2 = __accumulated_sum_N32[periods/LOAD_AVG_PERIOD];
periods %= LOAD_AVG_PERIOD;
c2 = decay_load(c2, periods);
c2 += runnable_avg_yN_sum[periods];
}
return c1 + c2 + c3;
}
#define cap_scale(v, s) ((v)*(s) >> SCHED_CAPACITY_SHIFT)
/*
* Accumulate the three separate parts of the sum; d1 the remainder
* of the last (incomplete) period, d2 the span of full periods and d3
* the remainder of the (incomplete) current period.
*
* d1 d2 d3
* ^ ^ ^
* | | |
* |<->|<----------------->|<--->|
* ... |---x---|------| ... |------|-----x (now)
*
* p
* u' = (u + d1) y^(p+1) + 1024 \Sum y^n + d3 y^0
* n=1
*
* = u y^(p+1) + (Step 1)
*
* p
* d1 y^(p+1) + 1024 \Sum y^n + d3 y^0 (Step 2)
* n=1
*/
static __always_inline u32
accumulate_sum(u64 delta, int cpu, struct sched_avg *sa,
unsigned long weight, int running, struct cfs_rq *cfs_rq)
{
unsigned long scale_freq, scale_cpu;
u64 periods;
u32 contrib;
scale_freq = arch_scale_freq_capacity(NULL, cpu);
scale_cpu = arch_scale_cpu_capacity(NULL, cpu);
delta += sa->period_contrib;
periods = delta / 1024; /* A period is 1024us (~1ms) */
/*
* Step 1: decay old *_sum if we crossed period boundaries.
*/
if (periods) {
sa->load_sum = decay_load(sa->load_sum, periods);
if (cfs_rq) {
cfs_rq->runnable_load_sum =
decay_load(cfs_rq->runnable_load_sum, periods);
}
sa->util_sum = decay_load((u64)(sa->util_sum), periods);
}
/*
* Step 2
*/
delta %= 1024;
contrib = __accumulate_sum(periods, sa->period_contrib, delta);
sa->period_contrib = delta;
contrib = cap_scale(contrib, scale_freq);
if (weight) {
sa->load_sum += weight * contrib;
if (cfs_rq)
cfs_rq->runnable_load_sum += weight * contrib;
}
if (running)
sa->util_sum += contrib * scale_cpu;
return periods;
}
/*
* We can represent the historical contribution to runnable average as the
* coefficients of a geometric series. To do this we sub-divide our runnable
@ -2852,10 +2933,7 @@ static __always_inline int
___update_load_avg(u64 now, int cpu, struct sched_avg *sa,
unsigned long weight, int running, struct cfs_rq *cfs_rq)
{
u64 delta, scaled_delta, periods;
u32 contrib;
unsigned int delta_w, scaled_delta_w, decayed = 0;
unsigned long scale_freq, scale_cpu;
u64 delta;
delta = now - sa->last_update_time;
/*
@ -2876,81 +2954,27 @@ ___update_load_avg(u64 now, int cpu, struct sched_avg *sa,
return 0;
sa->last_update_time = now;
scale_freq = arch_scale_freq_capacity(NULL, cpu);
scale_cpu = arch_scale_cpu_capacity(NULL, cpu);
/*
* Now we know we crossed measurement unit boundaries. The *_avg
* accrues by two steps:
*
* Step 1: accumulate *_sum since last_update_time. If we haven't
* crossed period boundaries, finish.
*/
if (!accumulate_sum(delta, cpu, sa, weight, running, cfs_rq))
return 0;
/* delta_w is the amount already accumulated against our next period */
delta_w = sa->period_contrib;
if (delta + delta_w >= 1024) {
decayed = 1;
/* how much left for next period will start over, we don't know yet */
sa->period_contrib = 0;
/*
* Now that we know we're crossing a period boundary, figure
* out how much from delta we need to complete the current
* period and accrue it.
*/
delta_w = 1024 - delta_w;
scaled_delta_w = cap_scale(delta_w, scale_freq);
if (weight) {
sa->load_sum += weight * scaled_delta_w;
if (cfs_rq) {
cfs_rq->runnable_load_sum +=
weight * scaled_delta_w;
}
}
if (running)
sa->util_sum += scaled_delta_w * scale_cpu;
delta -= delta_w;
/* Figure out how many additional periods this update spans */
periods = delta / 1024;
delta %= 1024;
sa->load_sum = decay_load(sa->load_sum, periods + 1);
if (cfs_rq) {
cfs_rq->runnable_load_sum =
decay_load(cfs_rq->runnable_load_sum, periods + 1);
}
sa->util_sum = decay_load((u64)(sa->util_sum), periods + 1);
/* Efficiently calculate \sum (1..n_period) 1024*y^i */
contrib = __compute_runnable_contrib(periods);
contrib = cap_scale(contrib, scale_freq);
if (weight) {
sa->load_sum += weight * contrib;
if (cfs_rq)
cfs_rq->runnable_load_sum += weight * contrib;
}
if (running)
sa->util_sum += contrib * scale_cpu;
/*
* Step 2: update *_avg.
*/
sa->load_avg = div_u64(sa->load_sum, LOAD_AVG_MAX);
if (cfs_rq) {
cfs_rq->runnable_load_avg =
div_u64(cfs_rq->runnable_load_sum, LOAD_AVG_MAX);
}
sa->util_avg = sa->util_sum / LOAD_AVG_MAX;
/* Remainder of delta accrued against u_0` */
scaled_delta = cap_scale(delta, scale_freq);
if (weight) {
sa->load_sum += weight * scaled_delta;
if (cfs_rq)
cfs_rq->runnable_load_sum += weight * scaled_delta;
}
if (running)
sa->util_sum += scaled_delta * scale_cpu;
sa->period_contrib += delta;
if (decayed) {
sa->load_avg = div_u64(sa->load_sum, LOAD_AVG_MAX);
if (cfs_rq) {
cfs_rq->runnable_load_avg =
div_u64(cfs_rq->runnable_load_sum, LOAD_AVG_MAX);
}
sa->util_avg = sa->util_sum / LOAD_AVG_MAX;
}
return decayed;
return 1;
}
static int