bloom2

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A fast 2-level, sparse bloom filter implementation

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## bloom2

A fast 2-level, sparse bloom filter implementation consuming 2% of memory when
empty compared to a standard bloom filter.

* Sparse allocation grows memory usuage proportionally w.r.t filter load
* Low overhead, fast `O(1)` lookups with amortised `O(1)` inserts
* 32bit and 64bit safe
* Maintains same false positive probabilities as standard bloom filters
* No 'unsafe' code

The `CompressedBitmap` maintains the same false-positive properties and similar
performance properties as a normal bloom filter while lazily initialising the
backing memory as it is needed, resulting in smaller memory footprints for all
except completely loaded filters.

As the false positive probability for a bloom filter increases as the number of
entries increases, they are typically sized to maintain a small load factor,
resulting in inefficient use of the underlying bitmap:

```text
        ┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
        │ 0 │ 0 │ 0 │ 0 │ 1 │ 0 │ 0 │ 1 │ 0 │ 0 │ 0 │ 0 │
        └───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘
```

This 2-level bloom filter splits the bitmap up into blocks of `usize` bits, and
uses a second bitmap to mark populated blocks, lazily allocating them as
required:

```text

┌───┬───┬───┬───┐
	      Block map: │ 0 │ 1 │ 0 │ 0 │
	                 └───┴─┬─┴───┴───┘
	                       └──────┐
	    ┌ ─ ┬ ─ ┬ ─ ┬ ─ ┐ ┌───┬───▼───┬───┐ ┌ ─ ┬ ─ ┬ ─ ┬ ─ ┐
	      0   0   0   0   │ 1 │ 0 │ 0 │ 1 │   0   0   0   0
	    └ ─ ┴ ─ ┴ ─ ┴ ─ ┘ └───┴───┴───┴───┘ └ ─ ┴ ─ ┴ ─ ┴ ─ ┘
```

Lookups for indexes that land in unpopulated blocks check the single block map
bit and return immediately.

Lookups for indexes in populated blocks first check the block map bit, before
computing the offset to the bitmap block in the bitmap array by counting the
number of 1 bits preceding it in the block map. This is highly efficient as it
uses the `POPCNT` instruction on modern CPUs when available.

## Use case

Perfect for long lived, sparsely populated bloom filters held in RAM or on disk.

If the filter is larger than available RAM / stored on disk, mmap can be used to
load in 2-level bloom filters for a significant performance improvement. The OS
lazily loads bitmap blocks from disk as they're accessed, while the frequently
accessed block map remains in memory to provide a fast negative response for
unpopulated blocks.

### Bulk Loading

To pre-load a bloom filter with a large amount of data, prefer using the
`VecBitmap` backing store for fast write throughput which is implemented as a
"normal" single-level bloom filter (true `O(1)` inserts).

Once loading is complete, it can be compressed to the `CompressedBitmap` storage
type to minimise RAM usage while retaining fast reads.

## Serialisation

Enable optional serialisation with the `serde` feature - disabled by default.

Note that the use of the default `RandomHasher` yields a different bitmap that
is not reusable in a different process; for serialised filters a different
hasher should be used. By default, derived [`Hash`] implementation is not
considered portable but a hand-wrote implementation can be.

If you are using the `BytesBitmap` as your bitmap storage, it is recommended to use
the `bincode` library due to performance reasons. In initial testing, using 
`serde_json` was very slow to encode the bitmap.

[`Hash`]: https://doc.rust-lang.org/stable/std/hash/trait.Hash.html#portability

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