binary number with a decimal point

bindec1.hs

module Bindec1 where
import Debug.Trace
{-
# binary number with a "decimal" point
Compilers 2nd ed. 
  Exercise 5.2.4 (p.317)
  Exercise 5.2.5 (p.317)
  Exercise 5.5.6 (p.352)
Compilers 1st ed.
  Exercise 5.8 (p.337)
  
https://gist.github.com/yamasushi/a1aa7b14b1afa678512f3a1378303d49

S -> L . L | L
L -> L B | B
B -> 0 | 1

------

S -> { L.side=0 } 
     L {F.ival=L.val} F { S.val=F.val } 

F -> . { L.side=1 }
     L { F.val=F.ival + L.val }

F -> ε { F.val=F.ival }

L -> B {  R.side = L.side 
          R.ival = case L.side of
                    0 -> B.val
                    1 -> B.val/2 
          R.ik = 1}
     R { L.val=R.val , L.k=R.k}

R -> B  { R1.side = R.side
          R1.ik   = R.k + 1
          R1.ival = case R.side of 
                      0 -> R.ival*2 + B.val
                      1 -> R.ival   + B.val/(2^(R.k+1))
        }
     R1 { R.val = R1.val ,R.k = R1.k}

R -> ε { R.val = R.ival }

B -> 0 { B.val =0 } 

B -> 1 { B.val =1 } 

-}

bindec1 :: String -> Float
bindec1 xs = snd.s$xs

s :: String -> (String,Float)
s xs = let (xs0,_,val0)= (l xs 0) in
         let (xs1,val1)=(f xs0 val0) in
           ( xs1 , val1 )

f :: String -> Float -> (String,Float)
f ('.':xs) ival = let (xs0,_,val)=  (l xs 1) in
                    (xs0,ival+val)
f xs val = (xs,val) {-ipsilon-}

l :: String -> Int -> (String,Int,Float)
l xs side = let (xs0,bit) = (b xs) in
              let ival=case side of
                         0 -> bit
                         1 -> bit/2.0 in
                (r xs0 side 1 ival)

r :: String -> Int->Int->Float -> (String,Int,Float)
r [] _ ik ival = ([],ik,ival) {-ipsilon-}
r xs@(bit:_) side ik ival
  | bit=='0' || bit=='1' =
      let (xs0,bval)= (b xs) in
        let
          ik0  =ik+1
          ival0=case side of
                    0 -> ival*2 + bval
                    1 -> ival   + bval/(2^(ik+1)) in
          (r xs0 side ik0 ival0)
  | otherwise = (xs,ik,ival) {-ipsilon-}

b :: String -> (String,Float)
b ('0':xs) = (xs,0.0)
b ('1':xs) = (xs,1.0)