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 /** * 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); }