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

[Sergey Fedorov <serge.fdrv@gmail.com>]

On 25/05/16 04:13, Emilio G. Cota wrote:
> diff --git a/util/qdist.c b/util/qdist.c
> new file mode 100644
> index 0000000..3343640
> --- /dev/null
> +++ b/util/qdist.c
> @@ -0,0 +1,386 @@
(snip)
> +
> +void qdist_add(struct qdist *dist, double x, long count)
> +{
> +    struct qdist_entry *entry = NULL;
> +
> +    if (dist->entries) {
> +        struct qdist_entry e;
> +
> +        e.x = x;
> +        entry = bsearch(&e, dist->entries, dist->n, sizeof(e), qdist_cmp);
> +    }
> +
> +    if (entry) {
> +        entry->count += count;
> +        return;
> +    }
> +
> +    dist->entries = g_realloc(dist->entries,
> +                              sizeof(*dist->entries) * (dist->n + 1));

Repeated doubling?

> +    dist->n++;
> +    entry = &dist->entries[dist->n - 1];

What if we combine the above two lines:

    entry = &dist->entries[dist->n++];

or just reverse them:

    entry = &dist->entries[dist->n];
    dist->n++;


> +    entry->x = x;
> +    entry->count = count;
> +    qsort(dist->entries, dist->n, sizeof(*entry), qdist_cmp);
> +}
> +
(snip)
> +static char *qdist_pr_internal(const struct qdist *dist)
> +{
> +    double min, max, step;
> +    GString *s = g_string_new("");
> +    size_t i;
> +
> +    /* if only one entry, its printout will be either full or empty */
> +    if (dist->n == 1) {
> +        if (dist->entries[0].count) {
> +            g_string_append_unichar(s, qdist_blocks[QDIST_NR_BLOCK_CODES - 1]);
> +        } else {
> +            g_string_append_c(s, ' ');
> +        }
> +        goto out;
> +    }
> +
> +    /* get min and max counts */
> +    min = dist->entries[0].count;
> +    max = min;
> +    for (i = 0; i < dist->n; i++) {
> +        struct qdist_entry *e = &dist->entries[i];
> +
> +        if (e->count < min) {
> +            min = e->count;
> +        }
> +        if (e->count > max) {
> +            max = e->count;
> +        }
> +    }
> +
> +    /* floor((count - min) * step) will give us the block index */
> +    step = (QDIST_NR_BLOCK_CODES - 1) / (max - min);
> +
> +    for (i = 0; i < dist->n; i++) {
> +        struct qdist_entry *e = &dist->entries[i];
> +        int index;
> +
> +        /* make an exception with 0; instead of using block[0], print a space */
> +        if (e->count) {
> +            index = (int)((e->count - min) * step);

So "e->count == min" gives us one eighth block instead of just space?

> +            g_string_append_unichar(s, qdist_blocks[index]);
> +        } else {
> +            g_string_append_c(s, ' ');
> +        }
> +    }
> + out:
> +    return g_string_free(s, FALSE);
> +}
> +
> +/*
> + * Bin the distribution in @from into @n bins of consecutive, non-overlapping
> + * intervals, copying the result to @to.
> + *
> + * This function is internal to qdist: only this file and test code should
> + * ever call it.
> + *
> + * Note: calling this function on an already-binned qdist is a bug.
> + *
> + * If @n == 0 or @from->n == 1, use @from->n.
> + */
> +void qdist_bin__internal(struct qdist *to, const struct qdist *from, size_t n)
> +{
> +    double xmin, xmax;
> +    double step;
> +    size_t i, j, j_min;
> +
> +    qdist_init(to);
> +
> +    if (!from->entries) {
> +        return;
> +    }
> +    if (!n || from->n == 1) {
> +        n = from->n;
> +    }
> +
> +    /* set equally-sized bins between @from's left and right */
> +    xmin = qdist_xmin(from);
> +    xmax = qdist_xmax(from);
> +    step = (xmax - xmin) / n;
> +
> +    if (n == from->n) {
> +        /* if @from's entries are equally spaced, no need to re-bin */
> +        for (i = 0; i < from->n; i++) {
> +            if (from->entries[i].x != xmin + i * step) {
> +                goto rebin;

static inline function instead of goto?

> +            }
> +        }
> +        /* they're equally spaced, so copy the dist and bail out */
> +        to->entries = g_malloc(sizeof(*to->entries) * from->n);

g_new()?

> +        to->n = from->n;
> +        memcpy(to->entries, from->entries, sizeof(*to->entries) * to->n);
> +        return;
> +    }
> +
> + rebin:
> +    j_min = 0;
> +    for (i = 0; i < n; i++) {
> +        double x;
> +        double left, right;
> +
> +        left = xmin + i * step;
> +        right = xmin + (i + 1) * step;
> +
> +        /* Add x, even if it might not get any counts later */
> +        x = left;

This way we round down to the left margin of each bin like this:

    xmin [*---*---*---*---*] xmax   -- from
          |  /|  /|  /|  /
          | / | / | / | /
          |/  |/  |/  |/
          |   |   |   |
          V   V   V   V
         [*   *   *   *]            -- to


instead of e.g. rounding to the middle of each bin with:

    x = left + step / 2;

which would give the picture like this:


    xmin [*---*---*---*---*] xmax   -- from
          |   |   |   |   |
           \ / \ / \ / \ /
            |   |   |   |
            V   V   V   V
           [*   *   *   *]          -- to

or even:

    left = xmin + (i - 0.5) * step;
    right = left + step;
    x = left + step / 2;

with corresponding changes in the following loop. That would give us
this picture (with the same 'n'):

    xmin [*----*----*----*] xmax    -- from
        \   /\   /\   /\   /
         \ /  \ /  \ /  \ /
          |    |    |    |
          V    V    V    V
         [*    *    *    *]         -- to

I'm not sure which is the more correct option from the mathematical
point of view; but multiple-binning with the last variant of the
algorithm we would still give the same result.

> +        qdist_add(to, x, 0);
> +
> +        /*
> +         * To avoid double-counting we capture [left, right) ranges, except for
> +         * the righmost bin, which captures a [left, right] range.
> +         */
> +        for (j = j_min; j < from->n; j++) {

Looks like we don't need to keep both 'j' and 'j_min'. We could just use
'j', initialize it before the outer loop, and do the inner loop with
"while".

> +            struct qdist_entry *o = &from->entries[j];
> +
> +            /* entries are ordered so do not check beyond right */
> +            if (o->x > right) {
> +                break;
> +            }
> +            if (o->x >= left && (o->x < right ||
> +                                   (i == n - 1 && o->x == right))) {
> +                qdist_add(to, x, o->count);
> +                /* don't check this entry again */
> +                j_min = j + 1;
> +            }
> +        }
> +    }
> +}
> +
(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.

> +    }
> +    return ret;
> +}