Implementing the Fast inverse square root (InvSqrt) in F#

castvalue.fs

#load "FsharpChart.fsx"
open MSDN.FSharp.Charting

let castValue (value : 'TSource) :'TResult =
    let an = new System.Reflection.AssemblyName("CastUtil")
    let ab = System.AppDomain.CurrentDomain.DefineDynamicAssembly(an, System.Reflection.Emit.AssemblyBuilderAccess.RunAndSave)
    let mb = ab.DefineDynamicModule(an.Name)
    let tb = mb.DefineType("CastUtil", System.Reflection.TypeAttributes.Public ||| System.Reflection.TypeAttributes.Class)
    let fb = tb.DefineMethod("Read", System.Reflection.MethodAttributes.Public ||| System.Reflection.MethodAttributes.Static, typeof<'TResult>, ([|typeof<'TSource>|]))
    let ig = fb.GetILGenerator()
    ig.Emit(System.Reflection.Emit.OpCodes.Ldarg_0)
    let local = ig.DeclareLocal(typeof<'TSource>)
    ig.Emit(System.Reflection.Emit.OpCodes.Stloc, local)
    ig.Emit(System.Reflection.Emit.OpCodes.Ldloca_S, local)
    ig.Emit(System.Reflection.Emit.OpCodes.Ldobj, typeof<'TResult>)
    ig.Emit(System.Reflection.Emit.OpCodes.Ret)
    let cl = tb.CreateType()
    let readMethod = cl.GetMethod("Read", System.Reflection.BindingFlags.Static ||| System.Reflection.BindingFlags.Public)
    readMethod.Invoke(null, [|value|]) :?> 'TResult
    
let readPtr1 (value : nativeptr<'TSource>) :'TResult = (# "ldobj !0" type ('TResult) value : 'TResult #) 
let invsqrt_1 xx =
    let halfx = 0.5F * xx
    let mutable x = xx
    let mutable i = (0x5f3759df) - ((readPtr1 &&x) >>> 1)
    x <- readPtr1 &&i
    x * (1.5F - halfx*x*x)

let invsqrt_2 xx =
    let halfx = 0.5F * xx
    let x:int = castValue xx
    let mutable i = (0x5f3759df) - (x >>> 1)
    let x:float32 = castValue i
    x * (1.5F - halfx*x*x)

let z = 0.1
let y:int = castValue z

let normal = 1./System.Math.Sqrt(0.01)
let fast = invsqrt_2 0.01F
printfn "%f %f" normal fast


let getValue x = 
    let fast = (invsqrt (x))
    let slow = (1./(System.Math.Sqrt((float)x)))
    fast - (float32)slow

[for x in 0.01 .. 0.001 ..10. -> getValue ((float32)x)] |> FSharpChart.Line

// See http://jheriko-rtw.blogspot.com/2009/04/understanding-and-improving-fast.html 
// for original algorithm

Keep in mind that this is just a WIP version of proof-of-concept of how to implement/use "pointers" in F#. :-)