Message-ID: <CAOB9oOZtKOSLw8YDyLB8Vepcpv3z9oJw+CQX16XKA_JJ4o7uew@mail.gmail.com>
Date: Mon, 28 Jul 2025 02:06:52 +0800
From: Yizhou Tang <tangyeechou@...il.com>
To: Meng Shao Liu <sau525@...il.com>
Cc: axboe@...nel.dk, linux-block@...r.kernel.org, linux-kernel@...r.kernel.org
Subject: Re: [PATCH] blk-wbt: use fast inverse square root to optimize window
 size calculation

On Sun, Jul 27, 2025 at 7:22 PM Meng Shao Liu <sau525@...il.com> wrote:
>
> 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(-)
>
> 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,

Hi Meng,

As the initial value of scale_step is 0, then sqrt(0 + 1) = 1, which is not 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);

I think placing the two lines of code involving mathematical formulas
directly in a core wbt code path is not a good idea. I suggest you
encapsulate them in a separate function and document its purpose.

Thanks,
Yi

> +       } 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);
> --
> 2.50.1
>
>

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