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. */
29static 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. */
67u32 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}
82EXPORT_SYMBOL(minmax_running_max);
83
84/* Check if new measurement updates the 1st, 2nd or 3rd choice min. */
85u32 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