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       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. */
      29                 :          0 : static u32 minmax_subwin_update(struct minmax *m, u32 win,
      30                 :            :                                 const struct minmax_sample *val)
      31                 :            : {
      32                 :          0 :         u32 dt = val->t - m->s[0].t;
      33                 :            : 
      34         [ #  # ]:          0 :         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                 :          0 :                 m->s[0] = m->s[1];
      43                 :          0 :                 m->s[1] = m->s[2];
      44                 :          0 :                 m->s[2] = *val;
      45         [ #  # ]:          0 :                 if (unlikely(val->t - m->s[0].t > win)) {
      46                 :          0 :                         m->s[0] = m->s[1];
      47                 :          0 :                         m->s[1] = m->s[2];
      48                 :          0 :                         m->s[2] = *val;
      49                 :            :                 }
      50   [ #  #  #  # ]:          0 :         } 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                 :          0 :                 m->s[2] = m->s[1] = *val;
      56   [ #  #  #  # ]:          0 :         } 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                 :          0 :                 m->s[2] = *val;
      62                 :            :         }
      63                 :          0 :         return m->s[0].v;
      64                 :            : }
      65                 :            : 
      66                 :            : /* Check if new measurement updates the 1st, 2nd or 3rd choice max. */
      67                 :          0 : u32 minmax_running_max(struct minmax *m, u32 win, u32 t, u32 meas)
      68                 :            : {
      69                 :          0 :         struct minmax_sample val = { .t = t, .v = meas };
      70                 :            : 
      71         [ #  # ]:          0 :         if (unlikely(val.v >= m->s[0].v) ||         /* found new max? */
      72         [ #  # ]:          0 :             unlikely(val.t - m->s[2].t > win))      /* nothing left in window? */
      73                 :          0 :                 return minmax_reset(m, t, meas);  /* forget earlier samples */
      74                 :            : 
      75         [ #  # ]:          0 :         if (unlikely(val.v >= m->s[1].v))
      76                 :          0 :                 m->s[2] = m->s[1] = val;
      77         [ #  # ]:          0 :         else if (unlikely(val.v >= m->s[2].v))
      78                 :          0 :                 m->s[2] = val;
      79                 :            : 
      80                 :          0 :         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. */
      85                 :          0 : u32 minmax_running_min(struct minmax *m, u32 win, u32 t, u32 meas)
      86                 :            : {
      87                 :          0 :         struct minmax_sample val = { .t = t, .v = meas };
      88                 :            : 
      89         [ #  # ]:          0 :         if (unlikely(val.v <= m->s[0].v) ||         /* found new min? */
      90         [ #  # ]:          0 :             unlikely(val.t - m->s[2].t > win))      /* nothing left in window? */
      91                 :          0 :                 return minmax_reset(m, t, meas);  /* forget earlier samples */
      92                 :            : 
      93         [ #  # ]:          0 :         if (unlikely(val.v <= m->s[1].v))
      94                 :          0 :                 m->s[2] = m->s[1] = val;
      95         [ #  # ]:          0 :         else if (unlikely(val.v <= m->s[2].v))
      96                 :          0 :                 m->s[2] = val;
      97                 :            : 
      98                 :          0 :         return minmax_subwin_update(m, win, &val);
      99                 :            : }