Extend F# Arrays with lookup for bigint - f#

Question

I would like to extend F# Arrays such that I can use arrays without converting to the finite int. Instead I want to work with bigint directly.
I was able to add a second length method to the array type as follows:
type 'T ``[]`` with
member this.LengthI: bigint =
bigint this.Length
member this.Item(index: bigint): 'T =
this.[int index]
However the Item method cannot be called with the .[ ] syntax.
Any ideas how this could be achieved? I this possible at all?

Answer 1

I strongly suspect this isn't possible for native arrays. You can verify yourself that you can overload indexed access just fine for other collections.
If you compile the following code:
let myArray = [| "a" |]
let myList = [ "a" ]
let arrayElement = myArray.[11111]
let listElement = myList.[22222]
and inspect the resulting IL, you'll see that while accessing the list element compiles to a regular virtual call, there is a special CIL instruction for accessing a native array element, ldelem.
//000004: let arrayElement = myArray.[11111]
IL_002c: call string[] Fuduoqv1565::get_myArray()
IL_0031: ldc.i4 0x2b67
IL_0036: ldelem [mscorlib]System.String
IL_003b: stsfld string '<StartupCode$51dff40d-e00b-40e4-b9cc-15309089d437>'.$Fuduoqv1565::arrayElement#4
.line 5,5 : 1,33 ''
//000005: let listElement = myList.[22222]
IL_0040: call class [FSharp.Core]Microsoft.FSharp.Collections.FSharpList`1<string> Fuduoqv1565::get_myList()
IL_0045: ldc.i4 0x56ce
IL_004a: callvirt instance !0 class [FSharp.Core]Microsoft.FSharp.Collections.FSharpList`1<string>::get_Item(int32)
IL_004f: stsfld string '<StartupCode$51dff40d-e00b-40e4-b9cc-15309089d437>'.$Fuduoqv1565::listElement#5
IL_0054: ret
I would guess that the same compiler logic that special-case array access to that single instruction also bypass any overload resolution involving extension methods and the like.
One way to circumvent this is to wrap the array in a custom type, where overloaded indexers will work as you expect. Making the wrapper type a struct should reduce the performance loss in most cases:
type [<Struct>] BigArray<'T>(array : 'T[]) =
member this.LengthI: bigint =
bigint array.Length
member this.Item
with get(index : int) = array.[index]
and set (index : int) value = array.[index] <- value
member this.Item
with get(index : bigint) = array.[int index]
and set (index : bigint) value = array.[int index] <- value
let bigArray = BigArray myArray
let bigArrayElement = bigArray.[0]
let bigArrayElement2 = bigArray.[bigint 0]
Another one is to upcast the array to the base System.Array class, on which you can then define the same overloaded operator. This removes the need to create a wrapper type and duplicate all members of 'T[], as you can just upcast/downcast the same array object as necessary. However, since the base class is untyped, you will lose type safety and have to box/unbox the elements when using the indexed access, which is quite ugly:
type System.Array with
member this.Item
with get (index : int) = (this :?> 'T[]).[index]
and set (index : int) (value : 'T) = (this :?> 'T[]).[index] <- value
member this.Item
with get(index : bigint) : 'T = (this :?> 'T[]).[int index]
and set(index : bigint) (value : 'T) = (this :?> 'T[]).[int index] <- value
let untypedArray = myArray :> System.Array
let untypedArrayElement = box untypedArray.[0] :?> string
let untypedArrayElement2 = box untypedArray.[bigint 0] :?> string