win_minmax.c

  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}
100EXPORT_SYMBOL(minmax_running_min);