fixed point arithmetic in fsharp

fixed.fsx

open System

let scale (n3: int16) (n2: int16) (n1: int16) : int16 = (int n1) * (int n2) / (int n3) |> int16

let percent = scale 100s

let percent20 = percent 20s

let r = percent20 50s//10s

let test = 2000s * 34s / 100s//overflow 24s

let testFixed = percent 34s 2000s//680s

let roundedPercent percent value = (scale 10s value percent + 5s) / 10s

let testRounded = roundedPercent 32s 227s//73s

let test2 = 2.0f /3.0f * 171.0f//expected 113.9999 but 114 

let test2Fixed = scale 3s 2s 171s//114

let test3 = 7.105/12.250 * 150.0//87.0

let test3Fixed = scale 12250s 7105s 150s //87s 

let pi = scale 113s 355s  
let e = scale 10546s 28667s

let testPi = pi 1000s//3141s
let testE = e 1000s//3141s

let square (r:double) = System.Math.PI * (r ** 2.)

let squareFixed x=  pi ( x * x)

let testSquare = square 10.//314.1592654
let testSquareFixed = squareFixed 10s//314s

let _1 = 16384s

let inline (.*) (x:int16) (y:int16) = scale _1 y x 
let inline (./) (x:int16) (y:int16) = scale y _1 x 

let toDouble (x: int16) = x .* 10000s |> double |> fun x -> x / 10000.
let toFixed (x: double) : int16 = x * 10000. |> int16 |> fun x -> x ./ 10000s

let oneDivOneIsOne = 1s ./ 1s  = _1//true

let oneDivTwoIsHalf = 1s ./ 2s = (_1 / 2s)//true

let testFractions =  7./34.+23./99.//0.4382055853

let testFractionsFixed =  7s ./ 34s + 23s ./ 99s |> toDouble//0.4381


let sqrtFixed (n:int16) = 
    let rec si (root: int16)= 
        let newRoot = (n ./ root + root) / 2s
        if root = newRoot  then root else si newRoot 
    si (1s./10s) 

let sqrt = toFixed >> sqrtFixed >> toDouble 

let testSqrt = Math.Sqrt(0.01)//0.1
let testSqrtFixed = sqrt 0.01//0.0997