A data structure for optimistic concurrency control on ranges of bitwise-lexicographically-ordered keys.

Intended to replace FoundationDB's skip list.

Hardware for all benchmarks is a mac m1 2020.

# FoundationDB's benchmark

## Skip list

```
New conflict set: 1.962 sec
                  0.637 Mtransactions/sec
                  2.548 Mkeys/sec
Detect only:      1.842 sec
                  0.679 Mtransactions/sec
                  2.714 Mkeys/sec
Skiplist only:    1.261 sec
                  0.991 Mtransactions/sec
                  3.964 Mkeys/sec
Performance counters:
               Build: 0.0597
                 Add: 0.0587
              Detect: 1.84
              D.Sort: 0.411
           D.Combine: 0.0136
         D.CheckRead: 0.67
   D.CheckIntraBatch: 0.00671
        D.MergeWrite: 0.592
      D.RemoveBefore: 0.146
```

## Radix tree (this implementation)

```
New conflict set: 1.285 sec
                  0.973 Mtransactions/sec
                  3.892 Mkeys/sec
Detect only:      1.196 sec
                  1.045 Mtransactions/sec
                  4.180 Mkeys/sec
Skiplist only:    0.539 sec
                  2.320 Mtransactions/sec
                  9.281 Mkeys/sec
Performance counters:
               Build: 0.0377
                 Add: 0.0493
              Detect: 1.2
              D.Sort: 0.41
           D.Combine: 0.0135
         D.CheckRead: 0.219
   D.CheckIntraBatch: 0.00654
        D.MergeWrite: 0.319
      D.RemoveBefore: 0.224
```

# Our benchmark

## Skip list

|               ns/op |                op/s |    err% |     total | benchmark
|--------------------:|--------------------:|--------:|----------:|:----------
|              246.99 |        4,048,700.59 |    0.2% |      0.01 | `point reads`
|              260.16 |        3,843,784.65 |    0.1% |      0.01 | `prefix reads`
|              493.35 |        2,026,953.19 |    0.1% |      0.01 | `range reads`
|              462.05 |        2,164,289.23 |    0.6% |      0.01 | `point writes`
|              448.19 |        2,231,205.25 |    0.9% |      0.01 | `prefix writes`
|              255.83 |        3,908,845.72 |    1.5% |      0.02 | `range writes`
|              582.63 |        1,716,349.02 |    1.3% |      0.01 | `monotonic increasing point writes`

## Radix tree (this implementation)

|               ns/op |                op/s |    err% |     total | benchmark
|--------------------:|--------------------:|--------:|----------:|:----------
|               19.42 |       51,483,206.67 |    0.3% |      0.01 | `point reads`
|               58.43 |       17,115,612.57 |    0.1% |      0.01 | `prefix reads`
|              216.09 |        4,627,766.60 |    0.2% |      0.01 | `range reads`
|               28.35 |       35,267,567.72 |    0.2% |      0.01 | `point writes`
|               43.43 |       23,026,226.17 |    0.2% |      0.01 | `prefix writes`
|               50.00 |       20,000,000.00 |    0.0% |      0.01 | `range writes`
|               92.38 |       10,824,863.69 |    4.1% |      0.01 | `monotonic increasing point writes`

# "Real data" test

Point queries only, best of three runs. Gc ratio is the ratio of time spent doing garbage collection to time spent adding writes or doing garbage collection. Lower is better.

## skip list

```
Check: 11.3385 seconds, 329.718 MB/s, Add: 5.35612 seconds, 131.072 MB/s, Gc ratio: 45.7173%
```

## radix tree

```
Check: 2.48583 seconds, 1503.93 MB/s, Add: 2.12768 seconds, 329.954 MB/s, Gc ratio: 41.7943%
```

## hash table

(The hash table implementation doesn't work on range queries, and its purpose is to provide an idea of how fast point queries can be)

```
Check: 1.83386 seconds, 2038.6 MB/s, Add: 0.601411 seconds, 1167.32 MB/s, Gc ratio: 48.9776%
```