# hw-rankselect-base
[](https://circleci.com/gh/haskell-works/hw-rankselect-base)
Rank and select operations.
This library will use support for some BMI2 CPU instructions on some x86 based
CPUs if compiled with the appropriate flags on `ghc-8.4.1` or later.
## Rank and select
This library provides the following functions on various types:
* `rank1`
* `rank0`
* `select1`
* `select0`
Type class instances are provided for the following primitive types:
* `Bool`
* `Word8`
* `Word16`
* `Word32`
* `Word64`
Moreover additional type class instances are provided for `[]`, `Vector`
from both `Data.Vector`, and `Data.Vector.Storable` of these primitive
types.
The collection-based type classes instances are not intended to be used
in high-performance code because they have poor performance for most
purposes and are provided purely as reference implementations.
Bit-vectors larger than 64-bits need indexing to achieve higher performance.
A indexed bit-vector implementation can found in the
[hw-rankselect](https://hackage.haskell.org/package/hw-rankselect) package.
## Notes
This library follows standard 1-based counting conventions typically found in
Computer Science literature where `select1 10 2 = 4` as illustrated here:
```text
8 7 6 5 [4]3 2 1
0 0 0 0 1 0 1 0
```
The standard convention for the `bmi2` implementation, comes at a small cost.
An internal function `select1Word64Bmi2Base0` demonstrates 0-based counting
that is slightly faster when implemented with the `bmi2` instruction set where
`select1 10 1 = 3` as illustrated here:
```text
7 6 5 4 [3]2 1 0
0 0 0 0 1 0 1 0
```
## Compilation
It is sufficient to build, test and benchmark the library as follows
for emulated behaviour:
```text
stack build
stack test
stack bench
```
To target the BMI2 instruction set, add the `bmi2` flag:
```text
stack build --flag bits-extra:bmi2 --flag hw-rankselect-base:bmi2
stack test --flag bits-extra:bmi2 --flag hw-rankselect-base:bmi2
stack bench --flag bits-extra:bmi2 --flag hw-rankselect-base:bmi2
```
## Benchmark results
The following benchmark shows the kinds of performance gain that can
be expected from enabling the BMI2 instruction set for CPU targets
that support them:
```text
benchmarking 64-bit/Once: Select1 Broadword
time 14.75 ns (14.63 ns .. 14.90 ns)
0.996 R² (0.987 R² .. 0.999 R²)
mean 15.35 ns (14.92 ns .. 16.70 ns)
std dev 2.355 ns (607.2 ps .. 4.849 ns)
variance introduced by outliers: 96% (severely inflated)
benchmarking 64-bit/Once: Select1 Bmi2
time 6.026 ns (5.933 ns .. 6.134 ns)
0.999 R² (0.998 R² .. 0.999 R²)
mean 6.024 ns (5.966 ns .. 6.096 ns)
std dev 224.4 ps (176.9 ps .. 318.6 ps)
variance introduced by outliers: 62% (severely inflated)
benchmarking 32-bit/Once: Select1 Broadword
time 26.09 ns (25.84 ns .. 26.40 ns)
0.999 R² (0.998 R² .. 0.999 R²)
mean 26.67 ns (26.37 ns .. 27.01 ns)
std dev 1.017 ns (848.4 ps .. 1.291 ns)
variance introduced by outliers: 61% (severely inflated)
benchmarking 32-bit/Once: Select1 Bmi2
time 8.613 ns (8.543 ns .. 8.687 ns)
0.999 R² (0.999 R² .. 1.000 R²)
mean 8.592 ns (8.515 ns .. 8.671 ns)
std dev 248.3 ps (216.2 ps .. 294.8 ps)
variance introduced by outliers: 48% (moderately inflated)
```