[#stats]
== Statistics

:idprefix: stats_

Open-addressing and concurrent containers can be configured to keep running statistics
of some internal operations affected by the quality of the supplied hash function.

=== Synopsis

[listing,subs="+macros,+quotes"]
-----
struct xref:#stats_stats_summary_type[__stats-summary-type__]
{
  double average;
  double variance;
  double deviation;
};

struct xref:#stats_insertion_stats_type[__insertion-stats-type__]
{
  std::size_t        count;
  xref:#stats_stats_summary_type[__stats-summary-type__] probe_length;
};

struct xref:stats_lookup_stats_type[__lookup-stats-type__]
{
  std::size_t        count;
  xref:#stats_stats_summary_type[__stats-summary-type__] probe_length;
  xref:#stats_stats_summary_type[__stats-summary-type__] num_comparisons;
};

struct xref:stats_stats_type[__stats-type__]
{
  xref:#stats_insertion_stats_type[__insertion-stats-type__] insertion;
  xref:stats_lookup_stats_type[__lookup-stats-type__]    successful_lookup,
                       unsuccessful_lookup;
};
-----

==== __stats-summary-type__

Provides the average value, variance and standard deviation of a sequence of numerical values.

==== __insertion-stats-type__

Provides the number of insertion operations performed by a container and
statistics on the associated __probe length__ (number of
xref:#structures_open_addressing_containers[bucket groups] accessed per operation).

==== __lookup-stats-type__

For successful (element found) or unsuccessful (not found) lookup,
provides the number of operations performed by a container and
statistics on the associated __probe length__ (number of
xref:#structures_open_addressing_containers[bucket groups] accessed)
and number of element comparisons per operation.

==== __stats-type__

Provides statistics on insertion, successful and unsuccessful lookups performed by a container.
If the supplied hash function has good quality, then:

* Average probe lenghts should be close to 1.0.
* For successful lookups, the average number of element comparisons should be close to 1.0.
* For unsuccessful lookups, the average number of element comparisons should be close to 0.0.

These statistics can be used to determine if a given hash function
can be marked as xref:hash_traits_hash_is_avalanching[__avalanching__].

---
