Dear OCaml users,

to close this topic, here are some statistics for my use case with different hash functions. All hash methods I tried lead to identical statistics as random numbers. Simply using Hashtbl.hash on lists of hashes of substructures (Method 2 below) worked very well, is easy to write down and offers sufficient flexibility.

NItems   =  3277598
NBuckets = 16777216

        | Theoretical | Method1  |  Method2 |  Method3
--------+-------------+----------+----------+---------
Empty   |  13799905.0 | 13800062 | 13799864 | 13801452
Single  |   2695950.5 |  2695830 |  2696131 |  2693130
2 items |    263340.5 |   263101 |   263042 |   264318
3 items |     17148.7 |    17350 |    17368 |    17463
4 items |       837.5 |      849 |      779 |      822
5 items |        32.7 |       24 |       29 |       31
6 items |         1.1 |        0 |        3 |        3
--------+-------------+----------+----------+---------
Runtime |             |     119s |     122s |     110s

Note 1: the expected random deviation of the counts is sqrt(count).

Note 2: The speed differences between Method 1 and 2 are random – Method 2 should be faster.

Note 3: using Hashtbl.hash on the complete structure doesn't work for me for two reasons:
- parts of the structure should be ignored
- I have maps as substructures and require that logically equal maps result in the same hash

Theoretical:
collision numbers for a random process with same parameters (used exact Bernoulli statistics, not Poisson approximation)

Method1:
Hashtbl.hash used on structures recursively (create list of hash values for substructures and use Hashtbl.hash on list).
Maps (<10 elements) are converted to lists and the list is hashed with Hashtbl.hash.
Multiply each hash list entry with a distinct prime.
Use prime values for variants and prime multipliers for variant arguments.

Method2:
Hashtbl.hash used on structures recursively (create list of hash values for substructures and use Hashtbl.hash on list).
Maps (<10 elements) are converted to lists and the list is hashed with Hashtbl.hash.
Use prime values for variants and prime multipliers for variant arguments.

Method3:
( ( ( (v1 * p1 + v2) * p2) + v3 ) *p3 + v4) * p4
where vi are values and pi are distinct prime numbers. For lists I use 4 primes alternatingly and 4 different primes for empty cases

Btw.: I added a function “worst_bucketlist” to Hashtbl, which returns the keys of the largest bucket. This is useful for optimizing (or bug fixing) hash and equality functions – try to make a feature request for it.

Best regards,

Michael
Intel Deutschland GmbH
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