```Issue #12142 has been updated by Vladimir Makarov.

Yura Sokolov wrote:
> > Quadratic probing is most probably not faster on modern super-scalar OOO CPUs
> than the secondary hash function I use. Quadratic probing will traverse all
> entries for sure if # of entries is a prime number.
>
> Looks like you didn't do your homework :-(
>

No, I did not. Sorry.  My memory failed me.

>
> > For m = 2^n, a good choice for the constants are c1 = c2 = 1/2, as the values of h(k,i) for i in [0,m-1] are all distinct. This leads to a probe sequence of h(k), h(k)+1, h(k)+3, h(k)+6, ... where the values increase by 1, 2, 3, ...
>
> So usually it is implemented as:
>
> ````
>    pos = hash & mask;
>    d = 1;
>    while (not_found && not_empty) {
>       pos = (pos + d) & mask;
>       d++;
>    }
> ````

I believe your code above is incorrect for tables of sizes of power of 2.  The function should look like `h(k,i) = (h(k) + c1 * i + c2 * i^2) mod m`, where "c1 = c2 = 1/2 is a good choice".  You can not simplify it. The same Wikipedia article contains

```
With the exception of the triangular number case for a power-of-two-sized hash table, there is no guarantee of finding an empty cell once the table gets more than half full, or even before the table gets half full if the table size is not *prime*.
```

I don't see the quadratic function for sizes of power of 2 is simpler than what I use.

> It probes all elements of table of size 2^n and has good cache locality for first few probes. So if you store 32bit hash sum there, it will be very fast to check.

The only idea I like in your proposal is a better code locality argument. Also as I wrote before your proposal means just throwing away the biggest part of hash value even if it is a 32-bit hash.  I don't think ignoring the big part of the hash is a good idea as it probably worsens collision avoiding.   Better code locality also means more collision probability.  However only benchmarking can tell this for sure.  But I have reasonable doubts that it will be better.

Also about storing only part of the hash.  Can it affect rubygems?  It may be a part of API.  But I don't know anything about it.

In any case trying your proposal is a very low-priority task for me (high priority task is a small table representation).  May be somebody else will try it.  It is not a wise approach to try it all and then stop.  I prefer improvements step by step.

----------------------------------------
Feature #12142: Hash tables with open addressing
https://bugs.ruby-lang.org/issues/12142#change-57308

* Status: Open
* Priority: Normal
* Assignee:
----------------------------------------
~~~
Hello, the following patch contains a new implementation of hash
tables (major files st.c and include/ruby/st.h).

Modern processors have several levels of cache.  Usually,the CPU
reads one or a few lines of the cache from memory (or another level of
cache).  So CPU is much faster at reading data stored close to each
other.  The current implementation of Ruby hash tables does not fit
well to modern processor cache organization, which requires better
data locality for faster program speed.

The new hash table implementation achieves a better data locality
mainly by

o switching to open addressing hash tables for access by keys.
Removing hash collision lists lets us avoid *pointer chasing*, a
common problem that produces bad data locality.  I see a tendency
to move from chaining hash tables to open addressing hash tables
due to their better fit to modern CPU memory organizations.
(https://hg.python.org/cpython/file/ff1938d12240/Objects/dictobject.c).
PHP did this a bit earlier
https://nikic.github.io/2014/12/22/PHPs-new-hashtable-implementation.html.
GCC has widely-used such hash tables
(https://gcc.gnu.org/svn/gcc/trunk/libiberty/hashtab.c) internally
for more than 15 years.

o removing doubly linked lists and putting the elements into an array
for accessing to elements by their inclusion order.  That also
removes pointer chaising on the doubly linked lists used for
traversing elements by their inclusion order.

A more detailed description of the proposed implementation can be
found in the top comment of the file st.c.

The new implementation was benchmarked on 21 MRI hash table benchmarks
for two most widely used targets x86-64 (Intel 4.2GHz i7-4790K) and ARM
(Exynos 5410 - 1.6GHz Cortex-A15):

make benchmark-each ITEM=bm_hash OPTS='-r 3 -v' COMPARE_RUBY='<trunk ruby>'

Here the results for x86-64:

hash_aref_dsym       1.094
hash_aref_dsym_long          1.383
hash_aref_fix        1.048
hash_aref_flo        1.860
hash_aref_miss       1.107
hash_aref_str        1.107
hash_aref_sym        1.191
hash_aref_sym_long           1.113
hash_flatten         1.258
hash_ident_flo       1.627
hash_ident_num       1.045
hash_ident_obj       1.143
hash_ident_str       1.127
hash_ident_sym       1.152
hash_keys            2.714
hash_shift           2.209
hash_shift_u16       1.442
hash_shift_u24       1.413
hash_shift_u32       1.396
hash_to_proc         2.831
hash_values          2.701

The average performance improvement is more 50%.  ARM results are
same average improvement.

The patch can be seen as

or in a less convenient way as pull request changes

https://github.com/ruby/ruby/pull/1264/files

This is my first patch for MRI and may be my proposal and
implementation have pitfalls.  But I am keen to learn and work on
inclusion of this code into MRI.

~~~

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