Author Bitonic at English Wikipedia (CC0 1.0)
Code Snippets
default.nix
# Version by Robert (rycee) to point to a specific LTS version
{ pkgs ? import <nixpkgs> {
overlays = [(
self: super: {
dotnet-sdk-lts = super.dotnet-sdk.overrideAttrs (
old: rec {
version = "3.1.102";
src = super.fetchurl {
url = "https://dotnetcli.azureedge.net/dotnet/Sdk/${version}/dotnet-sdk-${version}-linux-x64.tar.gz";
sha256 = "e03ceeb5beaf7c228bd8dcbf7712cf12f5ccbfcd6d426afff78bfbd4524ff558";
};
}
);
}
)];
}}:
with pkgs;
mkShell {
buildInputs = [
ncurses # for `clear`
emacs
dotnet-sdk-lts
];
}
[…@nixosT480:~/code/dotnet/bitonic/src]$ nix-shell --pure
[nix-shell:~/code/dotnet/bitonic/src]$
bitonic.fsproj
<Project Sdk="Microsoft.NET.Sdk">
<PropertyGroup>
<OutputType>Exe</OutputType>
<TargetFramework>netcoreapp3.1</TargetFramework>
</PropertyGroup>
<PropertyGroup>
<ServerGarbageCollection>true</ServerGarbageCollection>
</PropertyGroup>
<ItemGroup>
<Compile Include="bitonic.fs" />
<None Include="bitonic.sh">
<CopyToOutputDirectory>Always</CopyToOutputDirectory>
</None>
</ItemGroup>
</Project>
runtimeconfig.template.json
{
"configProperties": {
"System.Globalization.Invariant": true
}
}
bitonic.fs
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| (* This construct is for ML compatibility. The syntax '(typ,...,typ) ident'
is not used in F# code. Consider using 'ident<typ,...,typ>' instead. *)
#nowarn "62"
[<RequireQualifiedAccess>]
module Assert =
let inline ensure condition msg f =
if condition
then f ()
else failwith msg
[<RequireQualifiedAccess>]
module Performance =
open System.Diagnostics
let private w = Stopwatch ()
let start ( ) = w.Restart ()
let stop ( ) = w.Stop (); w.Elapsed.TotalSeconds
[<RequireQualifiedAccess>]
module QualityAssurance =
let inline issorted (a : 'a [] when 'a : comparison) : bool =
let rec aux = function
| 0 -> a.[0] <= a.[ 1]
| i -> a.[i] <= a.[i+1] && aux (i-1)
match a with
| [| |] -> true
| [|_|] -> true
| _____ -> aux (Array.length a - 2)
[<RequireQualifiedAccess>]
module BadImplementation =
let inline isPow2 x =
match x with
| 0 -> false
| _ -> x &&& (x - 1) = 0
let comparator x y =
match x with
| _ when x < y -> (x,y)
| _ -> (y,x)
let halfCleaner bs =
let n = bs |> Array.length
let m = n/2
match isPow2(n) with
| true -> ()
| false -> failwithf "Input array %A, must be n=2^k" bs
Array.mapi(fun i x ->
match i with
| _ when i < m -> fst (comparator x bs.[m+i])
| _ -> snd (comparator x bs.[i-m])) bs
let rec bitonicSorter bs =
let n = bs |> Array.length
let m = n/2
match isPow2(n) with
| true -> ()
| false -> failwithf "Input array %A, must be n=2^k" bs
let bs' = halfCleaner bs
let bs1 = bs'.[0 .. (m - 1)]
let bs2 = bs'.[m .. (n - 1)]
match n with
| _ when 2 < n ->
Array.append (bitonicSorter bs1) (bitonicSorter bs2)
| _ -> bs'
let merger ss1 ss2 =
let m1 = ss1 |> Array.length
let m2 = ss2 |> Array.length
let n = m1 + m2
let m = n/2
match (m1 = m2) with
| true -> ()
| false -> failwithf "Input arrays (%A,%A), must have the same length" ss1 ss2
match isPow2(n) with
| true -> ()
| false -> failwithf "Comibnation of (%A,%A) arrays, must be n=2^k" ss1 ss2
let ss2' = ss2 |> Array.rev
let ss1'' = Array.map2(fun x y -> fst (comparator x y)) ss1 ss2'
let ss2'' = Array.map2(fun x y -> snd (comparator x y)) ss1 ss2'
match n with
| _ when 2 < n -> Array.append (bitonicSorter ss1'') (bitonicSorter ss2'')
| _ -> Array.append ss1'' ss2''
let rec sorter array =
let n = array |> Array.length
let m = n/2
match isPow2(n) with
| true -> ()
| false -> failwithf "Input array %A, must be n=2^k" array
let as1 = array.[0 .. (m - 1)]
let as2 = array.[m .. (n - 1)]
match n with
| _ when 2 < n -> merger (sorter as1) (sorter as2)
| _ -> merger as1 as2
[<RequireQualifiedAccess>]
module Array =
[<RequireQualifiedAccess>]
module Bitonic =
open System.Threading.Tasks
let inline subi index offset f (a : 'a []) : unit =
let n = Array.length a
let i = index
let j = index + offset
let g = OptimizedClosures.FSharpFunc<_,_,_>.Adapt(f)
let inline h _ =
Parallel.For (i, j, fun k -> g.Invoke(k, a.[k])) |> ignore
let m =
sprintf
"Index %i: or index+offset: %i are out of bounds (n = %i)" i j n
Assert.ensure (0 <= i && j <= n) m h
let inline private sync xs = Array.Parallel.iter (fun f -> f ()) xs
[<RequireQualifiedAccess>]
module Classical =
let inline ispow2 x =
if 0 = x
then false
else x &&& (x-1) = 0
let inline private comp (a : 'a [] when 'a : comparison) i j : unit =
let x = a.[i]
let y = a.[j]
a.[i] <- min x y
a.[j] <- max x y
[<RequireQualifiedAccess>]
module Sequential =
let inline private halfcleaner a n i : unit =
let m = n >>> 1
for j in i .. 1 .. (i+m-1) do comp a j (m+j)
let inline private sorter a n i : unit =
let rec aux a n i =
let m = n >>> 1
halfcleaner a n i
if 2 < n
then
aux a m i
aux a m (i+m)
aux a n i
let inline private merger a n i : unit =
let m = n >>> 1
let k = n - 1 + 2 * i
for j in i .. 1 .. (i+m-1) do comp a (j) (k-j)
if 2 < n
then
sorter a m i
sorter a m (i+m)
let inline sort inplace a : 'a [] when 'a : comparison =
let rec aux a n i =
let m = n >>> 1
if 2 < n
then
aux a m i
aux a m (i+m)
merger a n i
let b = if inplace then a else Array.map id a
let n = Array.length b
aux b n 0
b
[<RequireQualifiedAccess>]
module Parallel =
let inline private halfcleaner threadshold a n i : unit =
let m = n >>> 1
if threadshold < m
then
subi i (m-1) (fun j _ -> comp a j (m+j)) a
else
for j in i .. 1 .. (i+m-1) do comp a j (m+j)
let inline private sorter threadshold a n i : unit =
let rec aux a n i =
let m = n >>> 1
halfcleaner threadshold a n i
if 2 < n
then
if threadshold < n
then
sync
[| fun () -> aux a m i
; fun () -> aux a m (i+m)
|]
else
aux a m i
aux a m (i+m)
aux a n i
let inline private merger threadshold a n i : unit =
let m = n >>> 1
let k = n - 1 + 2 * i
if threadshold < m
then
subi i m (fun j _ -> comp a j (k-j)) a
else
for j in i .. 1 .. (i+m-1) do comp a j (k-j)
if 2 < n
then
if threadshold < n
then
sync
[| fun () -> sorter threadshold a m i
; fun () -> sorter threadshold a m (i+m)
|]
else
sorter threadshold a m i
sorter threadshold a m (i+m)
let inline sort threadshold inplace a : 'a [] when 'a : comparison =
let rec aux a n i =
let m = n >>> 1
if 2 < n
then
if threadshold < n
then
sync
[| fun () -> aux a m i
; fun () -> aux a m (i+m)
|]
else
aux a m i
aux a m (i+m)
merger threadshold a n i
let b = if inplace then a else Array.Parallel.map id a
let n = Array.length b
aux b n 0
b
(* Bitonic sorting network for n not a power of 2:
https://www.inf.hs-flensburg.de/lang/algorithmen/sortieren/bitonic/oddn.htm
*)
[<RequireQualifiedAccess>]
module Arbitrary =
let inline log02b b n =
let rec aux acc = function
| 0 -> acc
| x -> aux (acc + 1) (x >>> b)
aux 0 (n >>> b)
let inline log2 n =
log02b 1 n
let inline private comp (a : 'a [] when 'a : comparison) i j d : unit =
let x = a.[i]
let y = a.[j]
if d = (x > y)
then
a.[i] <- y
a.[j] <- x
[<RequireQualifiedAccess>]
module Sequential =
let inline private merger a =
let rec aux a n i d =
let m = (1 <<< (log2 n)) >>> 1
let k = n - 1
for j in i .. 1 .. (i+k-m) do comp a j (j+m) d
if 2 < n
then
aux a m i d
aux a (n-m) (i+m) d
aux a
let inline sort inplace a : 'a [] when 'a : comparison =
let rec aux a n i d =
let m = n >>> 1
if 2 < n
then
aux a m i (not d)
aux a (n-m) (i+m) d
merger a n i d
let b = if inplace then a else Array.map id a
let n = Array.length b
aux b n 0 true
b
[<RequireQualifiedAccess>]
module Parallel =
let inline private merger threadshold =
let rec aux a n i d =
let m = (1 <<< (log2 n)) >>> 1
let k = n - 1
if threadshold > 0 && threadshold < m
then
subi i (k-m) (fun j _ -> comp a j (j+m) d) a
else
for j in i .. 1 .. (i+k-m) do comp a j (j+m) d
if 2 < n
then
if threadshold < n
then
sync
[| fun () -> aux a m i d
; fun () -> aux a (n-m) (i+m) d
|]
else
aux a m i d
aux a (n-m) (i+m) d
aux
let inline sort threadshold inplace a : 'a [] when 'a : comparison =
let rec aux a n i d =
let m = n >>> 1
if 2 < n
then
if threadshold < n
then
sync
[| fun () -> aux a m i (not d)
; fun () -> aux a (n-m) (i+m) d
|]
else
aux a m i (not d)
aux a (n-m) (i+m) d
merger threadshold a n i d
let b = if inplace then a else Array.Parallel.map id a
let n = Array.length b
aux b n 0 true
b
[<EntryPoint>]
let main argv =
printfn "# Bitonicsort in F# (revised)"
printfn ""
let k = if 0 = Array.length argv then 20 else int argv.[0]
let n = 1 <<< k // n = 2^k
printfn "## CPU (cores, threads per core and threadshold size of array)"
let cs = System.Environment.ProcessorCount
(* Ex: lscpu | grep "Thread(s) per core:" -> Thread(s) per core: 2 *)
let ts = 2
let th = n / (cs * ts)
printfn "* Cores: %i, threads/core: %i and threadshold/size: %i." cs ts th
printfn ""
printfn "## Init array (length = 2^%i): [| 0; 1; 0; 1; … |]." k
Performance.start ()
let a = Array.init n (fun i -> i % 2)
let r = Performance.stop ()
printfn "* Length: %i." (Array.length a)
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted a
printfn ""
printfn "## Init (parallel) array (length = 2^%i): [| 0; 1; 0; 1; … |]." k
Performance.start ()
let b = Array.Parallel.init n (fun i -> i % 2)
let r = Performance.stop ()
printfn "* Length: %i." (Array.length b)
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted b
printfn ""
printfn "## Array.map id array."
Performance.start ()
let c = Array.map id a
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted c
printfn ""
printfn "## Array.Parallel.map id array."
Performance.start ()
let d = Array.Parallel.map id a
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted d
printfn ""
if Array.Bitonic.Classical.ispow2 n (* Devs responsibility to test *)
then
printfn "## Classical Bitonic sort array with bad (buggy) version."
Performance.start()
let e = BadImplementation.sorter a
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted e
printfn ""
printfn "## Classical Bitonic sort array with sequential version."
Performance.start()
let f = Array.Bitonic.Classical.Sequential.sort false a
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted f
printfn ""
printfn "## Classical Bitonic sort array with sequential in-place version."
let g = Array.init n (fun i -> i % 2)
printfn "* Sorted: %b." <| QualityAssurance.issorted g
Performance.start()
let h = Array.Bitonic.Classical.Sequential.sort true g
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted h
printfn ""
printfn "## Classical Bitonic sort array with parallel version."
Performance.start()
let i = Array.Bitonic.Classical.Parallel.sort th false a
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted i
printfn ""
printfn "## Classical Bitonic sort array with parallel in-place version."
let j = Array.init n (fun i -> i % 2)
printfn "* Sorted: %b." <| QualityAssurance.issorted j
Performance.start()
let l = Array.Bitonic.Classical.Parallel.sort th true j
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted l
printfn ""
else
printfn "Input array %i, must be n=2^k" n
System.Environment.Exit(1)
printfn "## Arbitrary Bitonic sort array with sequential version."
Performance.start()
let f = Array.Bitonic.Arbitrary.Sequential.sort false a
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted f
printfn ""
printfn "## Arbitrary Bitonic sort array with sequential in-place version."
let g = Array.init (n+1) (fun i -> i % 2)
printfn "* Length: %i." (Array.length g)
printfn "* Sorted: %b." <| QualityAssurance.issorted g
Performance.start()
let h = Array.Bitonic.Arbitrary.Sequential.sort true g
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted h
printfn "> Remark: Array length is odd (2^%i + 1)" k
printfn ""
printfn "## Arbitrary Bitonic sort array with parallel version."
Performance.start()
let i = Array.Bitonic.Arbitrary.Parallel.sort th false a
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted i
printfn ""
printfn "## Arbitrary Bitonic sort array with parallel in-place version."
let j = Array.init (n+1) (fun i -> i % 2)
printfn "* Length: %i." (Array.length j)
printfn "* Sorted: %b." <| QualityAssurance.issorted j
Performance.start()
let l = Array.Bitonic.Arbitrary.Parallel.sort th true j
let r = Performance.stop ()
printfn "* Result: %f seconds." r
printfn "* Sorted: %b." <| QualityAssurance.issorted l
printfn "> Remark: Array length is odd (2^%i + 1)" k
printfn ""
System.Environment.Exit(0)
0
|
build.sh
#!/bin/sh
# Clean screen
clear
# Clean previous build (if any)
dotnet clean --configuration Release
# Build in Release mode
dotnet build --configuration Release
# References
# ==========
#
# - `dotnet clean`
# https://docs.microsoft.com/en-us/dotnet/core/tools/dotnet-clean
# - `dotnet publish` > Options > `--configuration`
# https://docs.microsoft.com/en-us/dotnet/core/tools/dotnet-publish#options
stand.sh
#!/bin/sh
net=netcoreapp3.1
run=linux-x64
pub="$(pwd)/pub/"
# Clean screen
clear
# Clean previous build (if any)
dotnet clean --configuration Release
# Remove previous publish folder (if any)
if [ -d $pub ]; then rm -rf $pub; fi
# Publish in Release mode (self-contained)
dotnet publish \
--configuration Release \
--force \
--self-contained \
--framework $net \
--runtime $run \
--output $pub
# References
# ==========
#
# - `dotnet clean`
# https://docs.microsoft.com/en-us/dotnet/core/tools/dotnet-clean
# - `dotnet publish` > Options > `--configuration`
# https://docs.microsoft.com/en-us/dotnet/core/tools/dotnet-publish#options
# - `dotnet publish` > Options > `--force` `--self-contained` / `--framework` / `--runtime`
# https://docs.microsoft.com/en-us/dotnet/core/tools/dotnet-publish#options
# - .NET Core RID Catalog > Linux RIDs
# https://docs.microsoft.com/en-us/dotnet/core/rid-catalog#linux-rids
# - Target frameworks > Supported target framework versions
# https://docs.microsoft.com/en-us/dotnet/standard/frameworks
bitonic.sh
#!/bin/sh
log=$(pwd)/log
iso8601=$(date +"%Y%m%dT%H%M%S")
# Clean screen
clear
# Ensure log folder exists
mkdir -p "$log"
# Execute and split output to stdout and stderr
dotnet bitonic.dll $1 2> "$log/$iso8601.log"
# References
# ==========
#
# - `dotnet run` > Options > `--configuration`
# https://docs.microsoft.com/en-us/dotnet/core/tools/dotnet-run
#
# - Redirecting Error Messages from Command Prompt: STDERR/STDOUT
# https://support.microsoft.com/en-us/help/110930/redirecting-error-messages-from-command-prompt-stderr-stdout
Code Output:
[nix-shell:~/code/dotnet/bitonic/src/pub]$ ./bitonic.sh
# Bitonicsort in F# (revised)
## CPU (cores, threads per core and threadshold size of array)
* Cores: 8, threads/core: 2 and threadshold/size: 65536.
## Init array (length = 2^20): [| 0; 1; 0; 1; … |].
* Length: 1048576.
* Result: 0.002216 seconds.
* Sorted: false.
## Init (parallel) array (length = 2^20): [| 0; 1; 0; 1; … |].
* Length: 1048576.
* Result: 0.009313 seconds.
* Sorted: false.
## Array.map id array.
* Result: 0.002644 seconds.
* Sorted: false.
## Array.Parallel.map id array.
* Result: 0.003007 seconds.
* Sorted: false.
## Classical Bitonic sort array with bad (buggy) version.
* Result: 11.758988 seconds.
* Sorted: true.
## Classical Bitonic sort array with sequential version.
* Result: 8.277300 seconds.
* Sorted: true.
## Classical Bitonic sort array with sequential in-place version.
* Sorted: false.
* Result: 8.661613 seconds.
* Sorted: true.
## Classical Bitonic sort array with parallel version.
* Result: 3.149078 seconds.
* Sorted: true.
## Classical Bitonic sort array with parallel in-place version.
* Sorted: false.
* Result: 3.567784 seconds.
* Sorted: true.
## Arbitrary Bitonic sort array with sequential version.
* Result: 5.196947 seconds.
* Sorted: true.
## Arbitrary Bitonic sort array with sequential in-place version.
* Length: 1048577.
* Sorted: false.
* Result: 4.935209 seconds.
* Sorted: true.
> Remark: Array length is odd (2^20 + 1)
## Arbitrary Bitonic sort array with parallel version.
* Result: 1.614365 seconds.
* Sorted: true.
## Arbitrary Bitonic sort array with parallel in-place version.
* Length: 1048577.
* Sorted: false.
* Result: 1.704201 seconds.
* Sorted: true.
> Remark: Array length is odd (2^20 + 1)
[nix-shell:~/code/dotnet/bitonic/src/pub]$ ./bitonic.sh 21
# Bitonicsort in F# (revised)
## CPU (cores, threads per core and threadshold size of array)
* Cores: 8, threads/core: 2 and threadshold/size: 131072.
## Init array (length = 2^21): [| 0; 1; 0; 1; … |].
* Length: 2097152.
* Result: 0.004351 seconds.
* Sorted: false.
## Init (parallel) array (length = 2^21): [| 0; 1; 0; 1; … |].
* Length: 2097152.
* Result: 0.010732 seconds.
* Sorted: false.
## Array.map id array.
* Result: 0.005175 seconds.
* Sorted: false.
## Array.Parallel.map id array.
* Result: 0.005399 seconds.
* Sorted: false.
## Classical Bitonic sort array with bad (buggy) version.
* Result: 29.816791 seconds.
* Sorted: true.
## Classical Bitonic sort array with sequential version.
* Result: 21.015821 seconds.
* Sorted: true.
## Classical Bitonic sort array with sequential in-place version.
* Sorted: false.
* Result: 20.716299 seconds.
* Sorted: true.
## Classical Bitonic sort array with parallel version.
* Result: 6.554269 seconds.
* Sorted: true.
## Classical Bitonic sort array with parallel in-place version.
* Sorted: false.
* Result: 6.552851 seconds.
* Sorted: true.
## Arbitrary Bitonic sort array with sequential version.
* Result: 11.454322 seconds.
* Sorted: true.
## Arbitrary Bitonic sort array with sequential in-place version.
* Length: 2097153.
* Sorted: false.
* Result: 11.482118 seconds.
* Sorted: true.
> Remark: Array length is odd (2^21 + 1)
## Arbitrary Bitonic sort array with parallel version.
* Result: 3.711691 seconds.
* Sorted: true.
## Arbitrary Bitonic sort array with parallel in-place version.
* Length: 2097153.
* Sorted: false.
* Result: 3.940170 seconds.
* Sorted: true.
> Remark: Array length is odd (2^21 + 1)
References:
- Wikipedia:
- Blog: Mr. Mathiesen:
- Hochschule Flensburg, University of Applied Sciences:
- Microsoft:
- GitHub: