linux-kernel - Re: [PATCH] blk-wbt: use fast inverse square root to optimize window size calculation

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Message-ID: <a945646d-279a-ba10-2ee6-94eb09431bd9@huaweicloud.com>
Date: Mon, 28 Jul 2025 09:19:11 +0800
From: Yu Kuai <yukuai1@...weicloud.com>
To: Meng Shao Liu <sau525@...il.com>, axboe@...nel.dk
Cc: linux-block@...r.kernel.org, linux-kernel@...r.kernel.org,
 "yukuai (C)" <yukuai3@...wei.com>
Subject: Re: [PATCH] blk-wbt: use fast inverse square root to optimize window
 size calculation

Hi,

在 2025/07/27 19:21, Meng Shao Liu 写道:
> Optimize the computation of cur_win_nsec = win_nsec / sqrt(scale_step + 1)
> in blk-wbt by introducing a fast inverse square root algorithm.
> This approach replaces the original use of int_sqrt and division with a
> more efficient and accurate approximation method.
> 
> Signed-off-by: Meng Shao Liu <sau525@...il.com>
> ---
> Since this fast inverse square root algorithm now appears in three locations
> (blk-wbt, sch_cake, codel), it might be worth considering refactoring
> the implementation into a shared helper to reduce duplication and ensure consistency.
> However, this patch focuses solely on introducing the optimization in blk-wbt.
> 
>   block/blk-wbt.c | 60 +++++++++++++++++++++++++++++++++++++++++--------
>   1 file changed, 51 insertions(+), 9 deletions(-)
> 

Do you have numbers how this optimization is helper for wbt? Any
difference for IO perforamce or other overhead?

I don't feel this is much helper in the slow path. Please consider
introducing a shared helper first, then convert wbt to use that new
helper.

Thanks,
Kuai

> diff --git a/block/blk-wbt.c b/block/blk-wbt.c
> index a50d4cd55..1fd5af3ba 100644
> --- a/block/blk-wbt.c
> +++ b/block/blk-wbt.c
> @@ -80,6 +80,8 @@ struct rq_wb {
>   	u64 win_nsec;				/* default window size */
>   	u64 cur_win_nsec;			/* current window size */
>   
> +	u32 rec_inv_sqrt;   /* reciprocal value of sqrt(scaling step + 1) */
>   	struct blk_stat_callback *cb;
>   
>   	u64 sync_issue;
> @@ -130,6 +132,11 @@ enum {
>   	 */
>   	RWB_WINDOW_NSEC		= 100 * 1000 * 1000ULL,
>   
> +	/*
> +	 * Initial reciprocal value of sqrt(scaling step + 1)
> +	 */
> +	RWB_REC_INV_SQRT    = 0,
> +
>   	/*
>   	 * Disregard stats, if we don't meet this minimum
>   	 */
> @@ -395,20 +402,55 @@ static void scale_down(struct rq_wb *rwb, bool hard_throttle)
>   	rwb_trace_step(rwb, tracepoint_string("scale down"));
>   }
>   
> +#define REC_INV_SQRT_CACHE (16)
> +static const u32 inv_sqrt_cache[REC_INV_SQRT_CACHE] = {
> +		~0,         ~0, 3037000500, 2479700525,
> +	2147483647, 1920767767, 1753413056, 1623345051,
> +	1518500250, 1431655765, 1358187914, 1294981364,
> +	1239850263, 1191209601, 1147878294, 1108955788
> +};
> +
> +/* http://en.wikipedia.org/wiki/Methods_of_computing_square_roots
> + * new_invsqrt = (invsqrt / 2) * (3 - count * invsqrt^2)
> + *
> + * Here, invsqrt is a fixed point number (< 1.0), 32bit mantissa, aka Q0.32
> + */
> +
> +static void rwb_newton_step(struct rq_wb *rwb)
> +{
> +	struct rq_depth *rqd = &rwb->rq_depth;
> +	u32 invsqrt, invsqrt2;
> +	u64 val;
> +
> +	invsqrt = rwb->rec_inv_sqrt;
> +	invsqrt2 = ((u64)invsqrt * invsqrt) >> 32;
> +	val = (3LL << 32) - ((u64)(rqd->scale_step + 1) * invsqrt2);
> +
> +	val >>= 2; /* avoid overflow in following multiply */
> +	val = (val * invsqrt) >> (32 - 2 + 1);
> +
> +	rwb->rec_inv_sqrt = val;
> +}
> +
> +static void rwb_invsqrt(struct rq_wb *rwb)
> +{
> +	struct rq_depth *rqd = &rwb->rq_depth;
> +
> +	if (rqd->scale_step + 1 < REC_INV_SQRT_CACHE)
> +		rwb->rec_inv_sqrt = inv_sqrt_cache[rqd->scale_step + 1];
> +	else
> +		rwb_newton_step(rwb);
> +}
> +
>   static void rwb_arm_timer(struct rq_wb *rwb)
>   {
>   	struct rq_depth *rqd = &rwb->rq_depth;
>   
>   	if (rqd->scale_step > 0) {
> -		/*
> -		 * We should speed this up, using some variant of a fast
> -		 * integer inverse square root calculation. Since we only do
> -		 * this for every window expiration, it's not a huge deal,
> -		 * though.
> -		 */
> -		rwb->cur_win_nsec = div_u64(rwb->win_nsec << 4,
> -					int_sqrt((rqd->scale_step + 1) << 8));
> -	} else {
> +		rwb_invsqrt(rwb);
> +		rwb->cur_win_nsec = reciprocal_scale(rwb->win_nsec,
> +					     rwb->rec_inv_sqrt);
> +	} else {
>   		/*
>   		 * For step < 0, we don't want to increase/decrease the
>   		 * window size.
> @@ -911,6 +953,7 @@ int wbt_init(struct gendisk *disk)
>   
>   	rwb->last_comp = rwb->last_issue = jiffies;
>   	rwb->win_nsec = RWB_WINDOW_NSEC;
> +	rwb->rec_inv_sqrt = RWB_REC_INV_SQRT;
>   	rwb->enable_state = WBT_STATE_ON_DEFAULT;
>   	rwb->rq_depth.default_depth = RWB_DEF_DEPTH;
>   	rwb->min_lat_nsec = wbt_default_latency_nsec(q);
>