Re: [PATCH 03/15] sched/fair: Add lag based placement

[Abel Wu]

On 5/31/23 7:58 PM, Peter Zijlstra Wrote:
>   		/*
> -		 * Halve their sleep time's effect, to allow
> -		 * for a gentler effect of sleepers:
> +		 * If we want to place a task and preserve lag, we have to
> +		 * consider the effect of the new entity on the weighted
> +		 * average and compensate for this, otherwise lag can quickly
> +		 * evaporate.
> +		 *
> +		 * Lag is defined as:
> +		 *
> +		 *   lag_i = S - s_i = w_i * (V - v_i)
> +		 *
> +		 * To avoid the 'w_i' term all over the place, we only track
> +		 * the virtual lag:
> +		 *
> +		 *   vl_i = V - v_i <=> v_i = V - vl_i
> +		 *
> +		 * And we take V to be the weighted average of all v:
> +		 *
> +		 *   V = (\Sum w_j*v_j) / W
> +		 *
> +		 * Where W is: \Sum w_j
> +		 *
> +		 * Then, the weighted average after adding an entity with lag
> +		 * vl_i is given by:
> +		 *
> +		 *   V' = (\Sum w_j*v_j + w_i*v_i) / (W + w_i)
> +		 *      = (W*V + w_i*(V - vl_i)) / (W + w_i)
> +		 *      = (W*V + w_i*V - w_i*vl_i) / (W + w_i)
> +		 *      = (V*(W + w_i) - w_i*l) / (W + w_i)
> +		 *      = V - w_i*vl_i / (W + w_i)
> +		 *
> +		 * And the actual lag after adding an entity with vl_i is:
> +		 *
> +		 *   vl'_i = V' - v_i
> +		 *         = V - w_i*vl_i / (W + w_i) - (V - vl_i)
> +		 *         = vl_i - w_i*vl_i / (W + w_i)
> +		 *
> +		 * Which is strictly less than vl_i. So in order to preserve lag

Maybe a stupid question, but why vl'_i < vl_i? Since vl_i can be negative.

> +		 * we should inflate the lag before placement such that the
> +		 * effective lag after placement comes out right.
> +		 *
> +		 * As such, invert the above relation for vl'_i to get the vl_i
> +		 * we need to use such that the lag after placement is the lag
> +		 * we computed before dequeue.
> +		 *
> +		 *   vl'_i = vl_i - w_i*vl_i / (W + w_i)
> +		 *         = ((W + w_i)*vl_i - w_i*vl_i) / (W + w_i)
> +		 *
> +		 *   (W + w_i)*vl'_i = (W + w_i)*vl_i - w_i*vl_i
> +		 *                   = W*vl_i
> +		 *
> +		 *   vl_i = (W + w_i)*vl'_i / W
>   		 */
> -		if (sched_feat(GENTLE_FAIR_SLEEPERS))
> -			thresh >>= 1;
> +		load = cfs_rq->avg_load;
> +		if (curr && curr->on_rq)
> +			load += curr->load.weight;
>   
> -		vruntime -= thresh;
> +		lag *= load + se->load.weight;
> +		if (WARN_ON_ONCE(!load))
> +			load = 1;
> +		lag = div_s64(lag, load);
> +
> +		vruntime -= lag;
>   	}