1 // SPDX-License-Identifier: GPL-2.0
2 /*
3  * lib/minmax.c: windowed min/max tracker
4  *
5  * Kathleen Nichols' algorithm for tracking the minimum (or maximum)
6  * value of a data stream over some fixed time interval.  (E.g.,
7  * the minimum RTT over the past five minutes.) It uses constant
8  * space and constant time per update yet almost always delivers
9  * the same minimum as an implementation that has to keep all the
10  * data in the window.
11  *
12  * The algorithm keeps track of the best, 2nd best & 3rd best min
13  * values, maintaining an invariant that the measurement time of
14  * the n'th best >= n-1'th best. It also makes sure that the three
15  * values are widely separated in the time window since that bounds
16  * the worse case error when that data is monotonically increasing
17  * over the window.
18  *
19  * Upon getting a new min, we can forget everything earlier because
20  * it has no value - the new min is <= everything else in the window
21  * by definition and it's the most recent. So we restart fresh on
22  * every new min and overwrites 2nd & 3rd choices. The same property
23  * holds for 2nd & 3rd best.
24  */
25 #include <linux/module.h>
26 #include <linux/win_minmax.h>
27 
28 /* As time advances, update the 1st, 2nd, and 3rd choices. */
minmax_subwin_update(struct minmax * m,u32 win,const struct minmax_sample * val)29 static u32 minmax_subwin_update(struct minmax *m, u32 win,
30 				const struct minmax_sample *val)
31 {
32 	u32 dt = val->t - m->s[0].t;
33 
34 	if (unlikely(dt > win)) {
35 		/*
36 		 * Passed entire window without a new val so make 2nd
37 		 * choice the new val & 3rd choice the new 2nd choice.
38 		 * we may have to iterate this since our 2nd choice
39 		 * may also be outside the window (we checked on entry
40 		 * that the third choice was in the window).
41 		 */
42 		m->s[0] = m->s[1];
43 		m->s[1] = m->s[2];
44 		m->s[2] = *val;
45 		if (unlikely(val->t - m->s[0].t > win)) {
46 			m->s[0] = m->s[1];
47 			m->s[1] = m->s[2];
48 			m->s[2] = *val;
49 		}
50 	} else if (unlikely(m->s[1].t == m->s[0].t) && dt > win/4) {
51 		/*
52 		 * We've passed a quarter of the window without a new val
53 		 * so take a 2nd choice from the 2nd quarter of the window.
54 		 */
55 		m->s[2] = m->s[1] = *val;
56 	} else if (unlikely(m->s[2].t == m->s[1].t) && dt > win/2) {
57 		/*
58 		 * We've passed half the window without finding a new val
59 		 * so take a 3rd choice from the last half of the window
60 		 */
61 		m->s[2] = *val;
62 	}
63 	return m->s[0].v;
64 }
65 
66 /* Check if new measurement updates the 1st, 2nd or 3rd choice max. */
minmax_running_max(struct minmax * m,u32 win,u32 t,u32 meas)67 u32 minmax_running_max(struct minmax *m, u32 win, u32 t, u32 meas)
68 {
69 	struct minmax_sample val = { .t = t, .v = meas };
70 
71 	if (unlikely(val.v >= m->s[0].v) ||	  /* found new max? */
72 	    unlikely(val.t - m->s[2].t > win))	  /* nothing left in window? */
73 		return minmax_reset(m, t, meas);  /* forget earlier samples */
74 
75 	if (unlikely(val.v >= m->s[1].v))
76 		m->s[2] = m->s[1] = val;
77 	else if (unlikely(val.v >= m->s[2].v))
78 		m->s[2] = val;
79 
80 	return minmax_subwin_update(m, win, &val);
81 }
82 EXPORT_SYMBOL(minmax_running_max);
83 
84 /* Check if new measurement updates the 1st, 2nd or 3rd choice min. */
minmax_running_min(struct minmax * m,u32 win,u32 t,u32 meas)85 u32 minmax_running_min(struct minmax *m, u32 win, u32 t, u32 meas)
86 {
87 	struct minmax_sample val = { .t = t, .v = meas };
88 
89 	if (unlikely(val.v <= m->s[0].v) ||	  /* found new min? */
90 	    unlikely(val.t - m->s[2].t > win))	  /* nothing left in window? */
91 		return minmax_reset(m, t, meas);  /* forget earlier samples */
92 
93 	if (unlikely(val.v <= m->s[1].v))
94 		m->s[2] = m->s[1] = val;
95 	else if (unlikely(val.v <= m->s[2].v))
96 		m->s[2] = val;
97 
98 	return minmax_subwin_update(m, win, &val);
99 }
100