Find Missing Number implementations

open System.Collections.Generic

let findImperative (xs:int[]) =
    System.Array.Sort(xs)
    let mutable i = 1
    while i <= xs.Length && xs.[i-1] = i do i <- i + 1
    i

open System.Collections

let findBits (xs:IList<int>) =
    let ys = BitArray(xs.Count)
    for x in xs do ys.[x-1] <- true
    let mutable i = 1
    while i <= xs.Count && ys.[i-1] do i <- i + 1
    i

let find (xs:IList<int>) =
    let rec f (a,b) =
        let m = a + (b - a) / 2
        if a = b then m + 1
        elif xs.[m] = m then m
        elif xs.[m] = m + 1 then f (m+1,b)
        else f (a,m)
    f (0,xs.Count)