4 bits floating point number manipulation

floatBitOperations.fs

//F# Compiler for F# 4.0 (Open Source Edition), Mono 4.2.1

open System

let u : byte = (byte) 0b11110000

let highMask : byte = (byte) 0b11110000
let lowMask  : byte = (byte) 0b00001111

let uHigh : byte = u &&& highMask
let uLow : byte  = u &&& lowMask

printfn "u %s" (((float) u).ToString())
printfn "u %s" (((float) u / 255.0).ToString())
printfn "u %s" (Convert.ToString(u, 2).PadLeft(8, '0'))
printfn ""

let lowerByteToFloat b = 
    let zeroedHighBits = b &&& lowMask
    (float) zeroedHighBits / 15.0

let higherByteToFloat b = 
    let zeroedHighits = b &&& highMask
    let offseted = zeroedHighits >>> 4
    lowerByteToFloat offseted

let byteToTwo4BitsFloats b =
    let high = higherByteToFloat b
    let low = lowerByteToFloat b
    (high, low)

let (uHighFloat, uLowFloat) = byteToTwo4BitsFloats u

let fixedHigh = uHighFloat / 1.0625 // 1.0625 is 1 + 1 - (1/2 + 1/4 + 1/8 + 1/16) or 17/16
let fixedLow = uLowFloat / 16.0 / 1.0625
let sum = fixedHigh + fixedLow

let uHighFloatByte = (byte) (uHighFloat * 255.0)
let uLowFloatByte = (byte) (uLowFloat * 255.0)

let fixedHighByte = (byte) (fixedHigh * 255.0)
let fixedLowByte = (byte) (fixedLow * 255.0)

printfn "%s %s" (uHighFloat.ToString()) (uLowFloat.ToString())
printfn "%s + %s = %s" (fixedHigh.ToString()) (fixedLow.ToString()) (sum.ToString())

printfn "%s %s" ((Convert.ToString(uHighFloatByte, 2).PadLeft(8, '0'))) ((Convert.ToString(uLowFloatByte, 2).PadLeft(8, '0')))
printfn "%s %s" ((Convert.ToString(fixedHighByte, 2).PadLeft(8, '0'))) ((Convert.ToString(fixedLowByte, 2).PadLeft(8, '0')))


if sum = ((float) u / 255.0) then
    printfn "good"
else