source code
// The Computer Language Benchmarks Game
// https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
//
// ported from C# version with local variable changes by Anthony Lloyd
// Refactored for Span<> and Intrinsics, with optimizations from C# code by François-David Collin
#nowarn "9"
open System
open System.Runtime.Intrinsics
open System.Runtime.Intrinsics.X86
// Vector code
let ArraytoVec (v : float array) =
Vector256.Create(v.[0],v.[1],v.[2],0.)
[<Struct>]
type Body =
val mutable P: Vector256<float> // position
val mutable V: Vector256<float> // speed
val Mass: Vector256<float>
new(p: float[],v: float[],mass:float) = { P = ArraytoVec p
V = ArraytoVec v
Mass = Vector256.Create(mass) }
let inline (.*) (v1 : Vector256<float>) (v2 : Vector256<float>) = Avx.Multiply(v1,v2)
let inline (.+) (v1 : Vector256<float>) (v2 : Vector256<float>) = Avx.Add(v1,v2)
let inline (.-) (v1 : Vector256<float>) (v2 : Vector256<float>) = Avx.Subtract(v1,v2)
let inline (./) (v1 : Vector256<float>) (v2 : Vector256<float>) = Avx.Divide(v1,v2)
let inline (?*) (v1 : Vector256<float>) (f : float) = v1 .* Vector256.Create(f)
let inline Sum (v : Vector256<float>) = v.GetElement(1) + v.GetElement(0) + v.GetElement(2)
let inline Sqr (v : Vector256<float>) = Sum (v .* v)
// Global Variables
let N = 5
let DT = 0.01
let DaysPeryear = 365.24
let Solarmass = 39.4784176043574
let DaysPeryearV = Vector256.Create(DaysPeryear)
let SolarmassV = Vector256.Create(Solarmass)
let DTV = Vector256.Create(DT)
// Main functions
let initSystem (bodies: Span<Body>) =
for i in 1..N-1 do
bodies.[0].V <- bodies.[0].V .- bodies.[i].V .* bodies.[i].Mass
bodies.[0].V <- bodies.[0].V ./ SolarmassV
for i in 0..N-1 do
bodies.[i].V <- bodies.[i].V .* DaysPeryearV
let inline energy (bodies : Span<Body>)=
let mutable e = 0.0
for b in bodies do
e <- e + 0.5 * b.Mass.ToScalar() * (Sqr b.V)
for i in 0..N-2 do
for j in (i+1)..N-1 do
let dstv = bodies.[i].P .- bodies.[j].P
e <- e - bodies.[i].Mass.ToScalar() * bodies.[j].Mass.ToScalar() / (sqrt (Sqr dstv))
e
let inline advance (bodies : Span<Body>) repetitions =
for _ in 1..repetitions do
for i in 0..N-2 do
let mutable iv = bodies.[i].V
let bim = bodies.[i].Mass
for j in (i+1)..N-1 do
let Δx = bodies.[i].P .- bodies.[j].P
let dsq = Sum (Δx .* Δx)
let mag = Δx ?* (DT / ((sqrt dsq)*dsq))
iv <- iv .- (bodies.[j].Mass.*mag)
bodies.[j].V <- bodies.[j].V .+ (bim.*mag)
bodies.[i].V <- iv
for i in 0..4 do
bodies.[i].P <- bodies.[i].P .+ (bodies.[i].V .* DTV)
// Initial conditions
let bodiesOrig = [|
Body( // Sun
[|0.0;0.0;0.0|],
[|0.0;0.0;0.0|],
Solarmass
)
Body( // Jupiter
[|
4.84143144246472090e+00
-1.16032004402742839e+00
-1.03622044471123109e-01
|],
[|
1.66007664274403694e-03
7.69901118419740425e-03
-6.90460016972063023e-05
|],
Solarmass * 9.54791938424326609e-04
)
Body( // Saturn
[|
8.34336671824457987e+00
4.12479856412430479e+00
-4.03523417114321381e-01
|],
[|
-2.76742510726862411e-03
4.99852801234917238e-03
2.30417297573763929e-05
|],
Solarmass * 2.85885980666130812e-04
)
Body( // Uranus
[|
1.28943695621391310e+01
-1.51111514016986312e+01
-2.23307578892655734e-01
|],
[|
2.96460137564761618e-03
2.37847173959480950e-03
-2.96589568540237556e-05
|],
Solarmass * 4.36624404335156298e-05
)
Body( // Neptune
[|
1.53796971148509165e+01
-2.59193146099879641e+01
1.79258772950371181e-01
|],
[|
2.68067772490389322e-03
1.62824170038242295e-03
-9.51592254519715870e-05
|],
Solarmass * 5.15138902046611451e-05
)
|]
[<EntryPoint>]
let main args =
let repetitions = try int args.[0] with _ -> 1000
let bodies = Span<Body>(bodiesOrig)
initSystem bodies
energy bodies |> printfn "%.9f"
advance bodies repetitions
energy bodies |> printfn "%.9f"
0
notes, command-line, and program output
NOTES:
64-bit Ubuntu quad core
.NET SDK 8.0.200
Host Version: 8.0.2
Commit: 1381d5ebd2
<ServerGarbageCollection>true
F# 8.0
Wed, 06 Mar 2024 20:44:52 GMT
MAKE:
cp nbody.fsharpcore-5.fsharpcore Program.fs
cp Include/fsharpcore/tmp.fsproj .
mkdir obj
cp Include/fsharpcore/project.assets.json ./obj
/usr/bin/dotnet build -c Release --no-restore --no-self-contained -r linux-x64
MSBuild version 17.9.4+90725d08d for .NET
tmp -> /home/dunham/all-benchmarksgame/benchmarksgame_i53330/nbody/tmp/bin/Release/net8.0/linux-x64/tmp.dll
Build succeeded.
0 Warning(s)
0 Error(s)
Time Elapsed 00:00:08.11
10.37s to complete and log all make actions
COMMAND LINE:
./bin/Release/net8.0/linux-x64/tmp 50000000
PROGRAM OUTPUT:
-0.169075164
-0.169059907