Uniterated bitwise ops - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Uniterated bitwise ops (/showthread.php?tid=1148) Uniterated bitwise ops - Xorter - 01/29/2017 It is not so hard to expand bitwise operators to reals, we just need to start the sum from -infinity: $\sum_{-infinty} (x_i Op y_i)2^i$. 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/51zz9lnzce53vi3/xor(x%2Cxpi).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?