sched: Make __update_entity_runnable_avg() fast
__update_entity_runnable_avg forms the core of maintaining an entity's runnable
load average. In this function we charge the accumulated run-time since last
update and handle appropriate decay. In some cases, e.g. a waking task, this
time interval may be much larger than our period unit.
Fortunately we can exploit some properties of our series to perform decay for a
blocked update in constant time and account the contribution for a running
update in essentially-constant* time.
[*]: For any running entity they should be performing updates at the tick which
gives us a soft limit of 1 jiffy between updates, and we can compute up to a
32 jiffy update in a single pass.
C program to generate the magic constants in the arrays:
#include <math.h>
#include <stdio.h>
#define N 32
#define WMULT_SHIFT 32
const long WMULT_CONST = ((1UL << N) - 1);
double y;
long runnable_avg_yN_inv[N];
void calc_mult_inv() {
int i;
double yn = 0;
printf("inverses\n");
for (i = 0; i < N; i++) {
yn = (double)WMULT_CONST * pow(y, i);
runnable_avg_yN_inv[i] = yn;
printf("%2d: 0x%8lx\n", i, runnable_avg_yN_inv[i]);
}
printf("\n");
}
long mult_inv(long c, int n) {
return (c * runnable_avg_yN_inv[n]) >> WMULT_SHIFT;
}
void calc_yn_sum(int n)
{
int i;
double sum = 0, sum_fl = 0, diff = 0;
/*
* We take the floored sum to ensure the sum of partial sums is never
* larger than the actual sum.
*/
printf("sum y^n\n");
printf(" %8s %8s %8s\n", "exact", "floor", "error");
for (i = 1; i <= n; i++) {
sum = (y * sum + y * 1024);
sum_fl = floor(y * sum_fl+ y * 1024);
printf("%2d: %8.0f %8.0f %8.0f\n", i, sum, sum_fl,
sum_fl - sum);
}
printf("\n");
}
void calc_conv(long n) {
long old_n;
int i = -1;
printf("convergence (LOAD_AVG_MAX, LOAD_AVG_MAX_N)\n");
do {
old_n = n;
n = mult_inv(n, 1) + 1024;
i++;
} while (n != old_n);
printf("%d> %ld\n", i - 1, n);
printf("\n");
}
void main() {
y = pow(0.5, 1/(double)N);
calc_mult_inv();
calc_conv(1024);
calc_yn_sum(N);
}
[ Compile with -lm ]
Signed-off-by: Paul Turner <pjt@google.com>
Reviewed-by: Ben Segall <bsegall@google.com>
Signed-off-by: Peter Zijlstra <a.p.zijlstra@chello.nl>
Link: http://lkml.kernel.org/r/20120823141507.277808946@google.com
Signed-off-by: Ingo Molnar <mingo@kernel.org>
This commit is contained in:
Paul Turner
Ingo Molnar
parent
f269ae0469
commit
5b51f2f80b
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@ -883,18 +883,93 @@ static inline void update_cfs_shares(struct cfs_rq *cfs_rq)
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#endif /* CONFIG_FAIR_GROUP_SCHED */
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#ifdef CONFIG_SMP
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/*
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* We choose a half-life close to 1 scheduling period.
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* Note: The tables below are dependent on this value.
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*/
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#define LOAD_AVG_PERIOD 32
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#define LOAD_AVG_MAX 47742 /* maximum possible load avg */
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#define LOAD_AVG_MAX_N 345 /* number of full periods to produce LOAD_MAX_AVG */
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/* Precomputed fixed inverse multiplies for multiplication by y^n */
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static const u32 runnable_avg_yN_inv[] = {
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0xffffffff, 0xfa83b2da, 0xf5257d14, 0xefe4b99a, 0xeac0c6e6, 0xe5b906e6,
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0xe0ccdeeb, 0xdbfbb796, 0xd744fcc9, 0xd2a81d91, 0xce248c14, 0xc9b9bd85,
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0xc5672a10, 0xc12c4cc9, 0xbd08a39e, 0xb8fbaf46, 0xb504f333, 0xb123f581,
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0xad583ee9, 0xa9a15ab4, 0xa5fed6a9, 0xa2704302, 0x9ef5325f, 0x9b8d39b9,
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0x9837f050, 0x94f4efa8, 0x91c3d373, 0x8ea4398a, 0x8b95c1e3, 0x88980e80,
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0x85aac367, 0x82cd8698,
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};
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/*
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* Precomputed \Sum y^k { 1<=k<=n }. These are floor(true_value) to prevent
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* over-estimates when re-combining.
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*/
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static const u32 runnable_avg_yN_sum[] = {
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0, 1002, 1982, 2941, 3880, 4798, 5697, 6576, 7437, 8279, 9103,
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9909,10698,11470,12226,12966,13690,14398,15091,15769,16433,17082,
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17718,18340,18949,19545,20128,20698,21256,21802,22336,22859,23371,
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};
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/*
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* Approximate:
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* val * y^n, where y^32 ~= 0.5 (~1 scheduling period)
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*/
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static __always_inline u64 decay_load(u64 val, u64 n)
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{
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for (; n && val; n--) {
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val *= 4008;
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val >>= 12;
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unsigned int local_n;
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if (!n)
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return val;
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else if (unlikely(n > LOAD_AVG_PERIOD * 63))
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return 0;
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/* after bounds checking we can collapse to 32-bit */
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local_n = n;
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/*
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* As y^PERIOD = 1/2, we can combine
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* y^n = 1/2^(n/PERIOD) * k^(n%PERIOD)
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* With a look-up table which covers k^n (n<PERIOD)
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*
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* To achieve constant time decay_load.
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*/
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if (unlikely(local_n >= LOAD_AVG_PERIOD)) {
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val >>= local_n / LOAD_AVG_PERIOD;
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local_n %= LOAD_AVG_PERIOD;
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}
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return val;
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val *= runnable_avg_yN_inv[local_n];
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/* We don't use SRR here since we always want to round down. */
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return val >> 32;
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}
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/*
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* For updates fully spanning n periods, the contribution to runnable
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* average will be: \Sum 1024*y^n
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*
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* We can compute this reasonably efficiently by combining:
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* y^PERIOD = 1/2 with precomputed \Sum 1024*y^n {for n <PERIOD}
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*/
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static u32 __compute_runnable_contrib(u64 n)
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{
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u32 contrib = 0;
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if (likely(n <= LOAD_AVG_PERIOD))
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return runnable_avg_yN_sum[n];
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else if (unlikely(n >= LOAD_AVG_MAX_N))
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return LOAD_AVG_MAX;
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/* Compute \Sum k^n combining precomputed values for k^i, \Sum k^j */
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do {
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contrib /= 2; /* y^LOAD_AVG_PERIOD = 1/2 */
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contrib += runnable_avg_yN_sum[LOAD_AVG_PERIOD];
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n -= LOAD_AVG_PERIOD;
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} while (n > LOAD_AVG_PERIOD);
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contrib = decay_load(contrib, n);
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return contrib + runnable_avg_yN_sum[n];
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}
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/*
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@ -929,7 +1004,8 @@ static __always_inline int __update_entity_runnable_avg(u64 now,
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struct sched_avg *sa,
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int runnable)
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{
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u64 delta;
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u64 delta, periods;
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u32 runnable_contrib;
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int delta_w, decayed = 0;
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delta = now - sa->last_runnable_update;
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@ -963,25 +1039,26 @@ static __always_inline int __update_entity_runnable_avg(u64 now,
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* period and accrue it.
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*/
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delta_w = 1024 - delta_w;
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BUG_ON(delta_w > delta);
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do {
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if (runnable)
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sa->runnable_avg_sum += delta_w;
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sa->runnable_avg_period += delta_w;
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if (runnable)
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sa->runnable_avg_sum += delta_w;
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sa->runnable_avg_period += delta_w;
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/*
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* Remainder of delta initiates a new period, roll over
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* the previous.
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*/
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sa->runnable_avg_sum =
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decay_load(sa->runnable_avg_sum, 1);
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sa->runnable_avg_period =
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decay_load(sa->runnable_avg_period, 1);
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delta -= delta_w;
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delta -= delta_w;
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/* New period is empty */
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delta_w = 1024;
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} while (delta >= 1024);
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/* Figure out how many additional periods this update spans */
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periods = delta / 1024;
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delta %= 1024;
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sa->runnable_avg_sum = decay_load(sa->runnable_avg_sum,
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periods + 1);
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sa->runnable_avg_period = decay_load(sa->runnable_avg_period,
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periods + 1);
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/* Efficiently calculate \sum (1..n_period) 1024*y^i */
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runnable_contrib = __compute_runnable_contrib(periods);
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if (runnable)
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sa->runnable_avg_sum += runnable_contrib;
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sa->runnable_avg_period += runnable_contrib;
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}
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/* Remainder of delta accrued against u_0` */
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