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# Cyclic Poly

This crate is an implementation of the hashing algorithm given in Section 2.3 of the paper:
> Jonathan D. Cohen, Recursive Hashing Functions for n-Grams,
> ACM Trans. Inf. Syst. 15 (3), 1997.

Other opensource implementations from this paper usually concentrate on other algorithms that
appear in later sections.

This hashing algorithm has features that stand out in comparison to other hashing algorithms:
* The algorithm supports recurrent/rolling hash calculations.
  * The rolling hash calculation is around 5 times faster than Adler32.
* Hash values are decomposable.

## Recurrent/Rolling


A rolling hash (sometimes called a recurrent hash), can calculate a new hash value from a previous hash value and a
small change in the data. Rolling hashes are useful to hash a window of data that slides along a collection of data:

![Rolling Hash](docs/rolling.png)

This is much faster than recalculating a hash value for every block.

Rolling hashes are an efficient way for finding a block of data that has a given hash value.

## Decomposable

A decomposable hash, can calculate a hash value for a block of data given a hash value for a bigger block of data and
the hash value for the remaining data:

![Decomposable Hash](docs/decomposable.png)

In the example above, the hash $`h_3`$ can be calculated from the hashes $`h_1`$ and $`h_2`$.

# Alternative Algorithms

The Adler32 hash/checksum algorithm can be used as a rolling hash and was made popular by the `zlib` library and `rsync` tool.

# Performance

Performance comparisons were done on a laptop and are relative to the [adler32 crate](https://docs.rs/adler32/latest/adler32/). To run this comparison execute `cargo bench`.

## Single block

The Cyclic Polynomial hashing is slower than Adler32 when hashing a single block.

| Algorithm         | MB/sec |
| ----------------- | ------ |
| Cyclic Poly 32bit | 2127   |
| Cyclic Poly 64bit | 2126   |
| Adler32           | 2562   |

## Rolling

The calculation of rolling hashes is faster than Adler32.

| Algorithm         | MB/sec |
| ----------------- | ------ |
| Cyclic Poly 32bit | 1254   |
| Cyclic Poly 64bit | 1048   |
| Adler32           | 170    |

## Collisions

To calculate hash collisions on random data execute:

```
cargo run --example collisions
```
This will output the number of collisions.

| Algorithm               | Collisions |
| ----------------------- | ---------- |
| Random Number Generator | 118        |
| Cyclic Poly 32bit       | 140        |
| Adler32                 | 2872       |
