Uniterated bitwise ops

[Xorter]

It is not so hard to expand bitwise operators to reals, we just need to start the sum from -infinity: .
But for instance, it is harder to do it with complexes.
Here is a graph of y = x xor pi*x
https://www.dropbox.com/s/51zz9lnzce53vi...).bmp?dl=0

We can iterate them, for exapmple: x iand y = x and x and ... and x, y times.
Here is my pari/gp code:

r kneser.gp
tenyez=2^200;
xor(x,y)={return(bitxor(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
or(x,y)={return(bitor(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
and(x,y)={return(bitand(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
nand(x,y)={return(bitnegimply(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
not(x)={return(bitneg(round(x*tenyez))/tenyez);}
ixor(x,y)={return(if(y>2,ixor(x,y-1),xor(x,x)))}
ior(x,y)={return(if(y>1,ixor(x,y-1),or(x,x)))}
iand(x,y)={return(if(y>1,ixor(x,y-1),and(x,x)))}
inand(x,y)={return(if(y>1,ixor(x,y-1),nand(x)))}

My question is that: What is the uniterated op of these ones? So I have been looking for operators whose iterated ops are the and, or, nand, xor ... etc.
Any idea?