Re: [Qemu-devel] [PATCH v6 08/15] qdist: add module to represent frequency distributions of data

["Emilio G. Cota" <cota@braap.org>]

On Fri, Jun 03, 2016 at 20:46:07 +0300, Sergey Fedorov wrote:
> On 03/06/16 20:29, Sergey Fedorov wrote:
> > On 03/06/16 20:22, Emilio G. Cota wrote:
> >> On Sat, May 28, 2016 at 21:15:06 +0300, Sergey Fedorov wrote:
> >>> On 25/05/16 04:13, Emilio G. Cota wrote:
> >>> (snip)
> >>>> +double qdist_avg(const struct qdist *dist)
> >>>> +{
> >>>> +    unsigned long count;
> >>>> +    size_t i;
> >>>> +    double ret = 0;
> >>>> +
> >>>> +    count = qdist_sample_count(dist);
> >>>> +    if (!count) {
> >>>> +        return NAN;
> >>>> +    }
> >>>> +    for (i = 0; i < dist->n; i++) {
> >>>> +        struct qdist_entry *e = &dist->entries[i];
> >>>> +
> >>>> +        ret += e->x * e->count / count;
> >>> Please use Welford’s method or something like that, see
> >>> http://stackoverflow.com/a/1346890.
> >> Yes, the way the mean is computed right now, we might suffer
> >> from underflow if count is huge. But I'd rather take that, than the
> >> perf penalty of an iterative method (such as the one used
> >> in Welford's). Note that we might have huge amounts of
> >> items, e.g. one item per head bucket in qht's occupancy qdist
> >> (and 0.5M head buckets is easy to achieve).
> >>
> >> If we were to use an iterative method, we'd need to do something
> >> like:
> >>
> >> double qdist_avg(const struct qdist *dist)
> >> {
> >>     size_t i, j;
> >>     double ret = 0;
> >>
> >>     if (!qdist_sample_count(dist)) {
> >>         return NAN;
> >>     }
> >>     /* compute moving average to prevent under/overflow */
> >>     for (i = 0; i < dist->n; i++) {
> >>         struct qdist_entry *e = &dist->entries[i];
> >>
> >>         for (j = 0; j < e->count; j++) {
> >>
> >>             ret += (e->x - ret) / (i + j + 1);
> >>         }
> >>     }
> >>     return ret;
> >> }
> >>
> >> Note that skipping the inner loop would be incorrect.
> > Ah, it's a shame. I'm wondering if there is some other algorithm that
> > could work for us?
> 
> Maybe something like
> https://en.wikipedia.org/wiki/Kahan_summation_algorithm could help?

That algorithm is overkill for what we're doing. Pairwise summation
should suffice:

diff --git a/util/qdist.c b/util/qdist.c
index 3343640..909bd2b 100644
--- a/util/qdist.c
+++ b/util/qdist.c
@@ -367,20 +367,34 @@ unsigned long qdist_sample_count(const struct qdist *dist)
     return count;
 }
 
+static double qdist_pairwise_avg(const struct qdist *dist, size_t index,
+                                 size_t n, unsigned long count)
+{
+    if (n <= 2) {
+        size_t i;
+        double ret = 0;
+
+        for (i = 0; i < n; i++) {
+            struct qdist_entry *e = &dist->entries[index + i];
+
+            ret += e->x * e->count / count;
+        }
+        return ret;
+    } else {
+        size_t n2 = n / 2;
+
+        return qdist_pairwise_avg(dist, index, n2, count) +
+               qdist_pairwise_avg(dist, index + n2, n - n2, count);
+    }
+}
+
 double qdist_avg(const struct qdist *dist)
 {
     unsigned long count;
-    size_t i;
-    double ret = 0;
 
     count = qdist_sample_count(dist);
     if (!count) {
         return NAN;
     }
-    for (i = 0; i < dist->n; i++) {
-        struct qdist_entry *e = &dist->entries[i];
-
-        ret += e->x * e->count / count;
-    }
-    return ret;
+    return qdist_pairwise_avg(dist, 0, dist->n, count);
 }

		Emilio