/**
* lib/minmax.c: windowed min/max tracker
*
* Kathleen Nichols' algorithm for tracking the minimum (or maximum)
* value of a data stream over some fixed time interval. (E.g.,
* the minimum RTT over the past five minutes.) It uses constant
* space and constant time per update yet almost always delivers
* the same minimum as an implementation that has to keep all the
* data in the window.
*
* The algorithm keeps track of the best, 2nd best & 3rd best min
* values, maintaining an invariant that the measurement time of
* the n'th best >= n-1'th best. It also makes sure that the three
* values are widely separated in the time window since that bounds
* the worse case error when that data is monotonically increasing
* over the window.
*
* Upon getting a new min, we can forget everything earlier because
* it has no value - the new min is <= everything else in the window
* by definition and it's the most recent. So we restart fresh on
* every new min and overwrites 2nd & 3rd choices. The same property
* holds for 2nd & 3rd best.
*/
#include
#include
/* As time advances, update the 1st, 2nd, and 3rd choices. */
static u32 minmax_subwin_update(struct minmax *m, u32 win,
const struct minmax_sample *val)
{
u32 dt = val->t - m->s[0].t;
if (unlikely(dt > win)) {
/*
* Passed entire window without a new val so make 2nd
* choice the new val & 3rd choice the new 2nd choice.
* we may have to iterate this since our 2nd choice
* may also be outside the window (we checked on entry
* that the third choice was in the window).
*/
m->s[0] = m->s[1];
m->s[1] = m->s[2];
m->s[2] = *val;
if (unlikely(val->t - m->s[0].t > win)) {
m->s[0] = m->s[1];
m->s[1] = m->s[2];
m->s[2] = *val;
}
} else if (unlikely(m->s[1].t == m->s[0].t) && dt > win/4) {
/*
* We've passed a quarter of the window without a new val
* so take a 2nd choice from the 2nd quarter of the window.
*/
m->s[2] = m->s[1] = *val;
} else if (unlikely(m->s[2].t == m->s[1].t) && dt > win/2) {
/*
* We've passed half the window without finding a new val
* so take a 3rd choice from the last half of the window
*/
m->s[2] = *val;
}
return m->s[0].v;
}
/* Check if new measurement updates the 1st, 2nd or 3rd choice max. */
u32 minmax_running_max(struct minmax *m, u32 win, u32 t, u32 meas)
{
struct minmax_sample val = { .t = t, .v = meas };
if (unlikely(val.v >= m->s[0].v) || /* found new max? */
unlikely(val.t - m->s[2].t > win)) /* nothing left in window? */
return minmax_reset(m, t, meas); /* forget earlier samples */
if (unlikely(val.v >= m->s[1].v))
m->s[2] = m->s[1] = val;
else if (unlikely(val.v >= m->s[2].v))
m->s[2] = val;
return minmax_subwin_update(m, win, &val);
}
EXPORT_SYMBOL(minmax_running_max);
/* Check if new measurement updates the 1st, 2nd or 3rd choice min. */
u32 minmax_running_min(struct minmax *m, u32 win, u32 t, u32 meas)
{
struct minmax_sample val = { .t = t, .v = meas };
if (unlikely(val.v <= m->s[0].v) || /* found new min? */
unlikely(val.t - m->s[2].t > win)) /* nothing left in window? */
return minmax_reset(m, t, meas); /* forget earlier samples */
if (unlikely(val.v <= m->s[1].v))
m->s[2] = m->s[1] = val;
else if (unlikely(val.v <= m->s[2].v))
m->s[2] = val;
return minmax_subwin_update(m, win, &val);
}