open System
open System.Numerics
open System.Globalization

let (|BigInt|_|) str = 
    Some(System.Numerics.BigInteger.Parse(str, NumberStyles.None))

let (|Even|_|) (i: BigInteger) = if i.IsEven then Some Even else None
let (|Odd|_|) (i: BigInteger) = if i.IsEven then None else Some Odd

let collatzify (i: BigInteger) = 
    let rec stepCountingCollatzify step (input: BigInteger) =
        printf "Step %A: %A\n" step input
        match input with
        | _ when input.IsOne -> step
        | Even -> stepCountingCollatzify (step + 1) (input / (bigint 2))
        | Odd -> 
            let newInput = ((bigint 3) * input + (bigint 1))
            printf "Step %A: %A\n" (step + 1) newInput                      // Performs 2 steps at once
            stepCountingCollatzify (step + 2) ( newInput / (bigint 2) )
        | _ -> printf "\nReached %A at step %A in error!" input step; -1
    let steps = stepCountingCollatzify 0 i 
    printf "\nCollatzified  %A to 1 in %i steps." i steps

[<EntryPoint>]
let main args =
    match args.Length with
    | 0  -> printf "Pass a starting value to test the collatz conjecture"
    | _ ->
        match args.[0] with
        | BigInt i -> collatzify i 
        | _ -> printf "Invalid input"
    0