Re: [PATCH 1/4] sched/fair: Optimize sum computation with a lookup table

[Juri Lelli <juri.lelli@arm.com>]

Hi,

On 11/04/16 06:36, Yuyang Du wrote:
> __compute_runnable_contrib() uses a loop to compute sum, whereas a
> table loopup can do it faster in a constant time.
> 
> The following python script can be used to generate the constants:
> 
> print " #:     yN_inv   yN_sum"
> print "-----------------------"
> y = (0.5)**(1/32.0)
> x = 2**32
> xx = 1024
> for i in range(0, 32):
> 	if i == 0:
> 		x = x-1
> 		xx = xx*y
> 	else:
> 		x = x*y
> 		xx = int(xx*y + 1024*y)
> 	print "%2d: %#x %8d" % (i, int(x), int(xx))
> 
> print " #:  sum_N32"
> print "------------"
> xxx = xx
> for i in range(0, 11):
> 	if i == 0:
> 		xxx = xx
> 	else:
> 		xxx = xxx/2 + xx
> 	print "%2d: %8d" % (i, xxx)
> 

Thanks for the script, really useful. Do you think there is value in
making it general? Like if we want to play with/need changing LOAD_AVG_
PERIOD in the future to something different than 32.

Also, does the following assume LOAD_AVG_PERIOD == 32? And if yes, do
you think there is any value in removing that assumption?

Best,

- Juri

> Signed-off-by: Yuyang Du <yuyang.du@intel.com>
> Reviewed-by: Morten Rasmussen <morten.rasmussen@arm.com>
> ---
>  kernel/sched/fair.c | 20 ++++++++++++--------
>  1 file changed, 12 insertions(+), 8 deletions(-)
> 
> diff --git a/kernel/sched/fair.c b/kernel/sched/fair.c
> index b8cc1c3..6e0eec0 100644
> --- a/kernel/sched/fair.c
> +++ b/kernel/sched/fair.c
> @@ -2603,6 +2603,15 @@ static const u32 runnable_avg_yN_sum[] = {
>  };
>  
>  /*
> + * Precomputed \Sum y^k { 1<=k<=n, where n%32=0). Values are rolled down to
> + * lower integers.
> + */
> +static const u32 __accumulated_sum_N32[] = {
> +	    0, 23371, 35056, 40899, 43820, 45281,
> +	46011, 46376, 46559, 46650, 46696, 46719,
> +};
> +
> +/*
>   * Approximate:
>   *   val * y^n,    where y^32 ~= 0.5 (~1 scheduling period)
>   */
> @@ -2650,14 +2659,9 @@ static u32 __compute_runnable_contrib(u64 n)
>  	else if (unlikely(n >= LOAD_AVG_MAX_N))
>  		return LOAD_AVG_MAX;
>  
> -	/* Compute \Sum k^n combining precomputed values for k^i, \Sum k^j */
> -	do {
> -		contrib /= 2; /* y^LOAD_AVG_PERIOD = 1/2 */
> -		contrib += runnable_avg_yN_sum[LOAD_AVG_PERIOD];
> -
> -		n -= LOAD_AVG_PERIOD;
> -	} while (n > LOAD_AVG_PERIOD);
> -
> +	/* Since n < LOAD_AVG_MAX_N, n/LOAD_AVG_PERIOD < 11 */
> +	contrib = __accumulated_sum_N32[n>>5]; /* =n/LOAD_AVG_PERIOD */
> +	n %= LOAD_AVG_PERIOD;
>  	contrib = decay_load(contrib, n);
>  	return contrib + runnable_avg_yN_sum[n];
>  }
> -- 
> 2.1.4
>