Signed Binary Average

The implementation of the signed binary average algorithm is also extremely simple once we have the algorithm description. In section 4.3.1, we describe the algorithm as follows:

$\begin{array} {lrcl} \lefteqn{\mathrm{average}(x,y) \ = \ \mathrm{average'}(x,y... ... 2)\ -1 & \qquad \textrm{if }\ (-6 \leq d<-2)\end{array} \right.\ \end{array}$



The sign function is defined as follows:



$\begin{array} {l}\mathrm{sign}(x) \ = \ \left\{\begin{array} {rl} -1&\qquad \te... ...xtrm{if }\ (x=0)\ 1&\qquad \textrm{if }\ (x\gt)\end{array} \right. \end{array}$

This is implemented in Haskell as follows.

-- sbAv : Signed binary stream average operation
sbAv :: SBinStream -> SBinStream -> SBinStream
sbAv x y = sbAv' x y 0 

-- sbAv' : Auxiliary function for sbAv
sbAv' :: SBinStream -> SBinStream -> Int -> SBinStream
sbAv' (a0:x) (b0:y) c = if (d' `mod` 2 == 0) then
                           ((signum d'):(sbAv' x y 0))
                        else sbAv'' x y d'
        where d' = (a0 + b0 + 2*c)


-- sbAv'' : Auxiliary function for sbAv
sbAv'' :: SBinStream -> SBinStream -> Int -> SBinStream
sbAv'' (a1:x') (b1:y') d' = (e : sbAv' (a1:x') (b1:y') c')
        where {d = (2*d' + a1 + b1);
               e = if (d >  2) then  1 else 
                   if (d < -2) then -1 else 0;
               c' = d' - (2*e)}