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

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Message-ID: <20250727112142.604373-1-sau525@gmail.com>
Date: Sun, 27 Jul 2025 07:21:42 -0400
From: Meng Shao Liu <sau525@...il.com>
To: axboe@...nel.dk
Cc: linux-block@...r.kernel.org,
	linux-kernel@...r.kernel.org,
	Meng Shao Liu <sau525@...il.com>
Subject: [PATCH] blk-wbt: use fast inverse square root to optimize window size calculation

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,
+
 	/*
 	 * 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);
-- 
2.50.1