On Sun, Jul 27, 2025 at 7:22 PM Meng Shao Liu <sau525@xxxxxxxxx> 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@xxxxxxxxx>
> ---
> 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
>
>
