Taylor series of i[x]

[Xorter]

Okey, here is a website: http://jwbales.us/ where you can calculate the sign by a programme. I checked the source of it, and I take the important part of it out. You can read it at the bottom.
I have made an own java html code, and it works. So we have a recursive formula for the signs. The next question is how to make just one formula and how to interpolate (to reals) and extrapolate (to complexes).
We are really close to have its Taylor series!

Code:

function bitValue(number,bit){

var result = (number & (1<<bit)) >>> bit;
return result;
}

function twist(p,q){
var state="A0";
var pbit=0;
var qbit=0;
var result=1;
var p0=p;
var q0=q;
var pplus=1+p0;
var qplus=1+q0;
var stateA0 = [];
var stateA  = [];
var stateB  = [];
var stateNB = [];
var stateC  = [];
var stateNC = [];
var loopIndex=Math.ceil(Math.LOG2E*Math.log((Math.max(pplus,qplus))));
var pXORq =eval(p0) ^ eval(q0);
stateA0[0] = "A0"
stateA0[1] = "A"
stateA0[2] = "B"
stateA0[3] = "NB"

stateA[0]  = "A";
stateA[1]  = "A";
stateA[2]  = "C";
stateA[3]  = "NC";

stateB[0]  = "B";
stateB[1]  = "NC";
stateB[2]  = "B";
stateB[3]  = "C";

stateNB[0] = "NB";
stateNB[1] = "C";
stateNB[2] = "NC";
stateNB[3] = "NB";

stateC[0]  = "C";
stateC[1]  = "NC";
stateC[2]  = "NC";
stateC[3]  = "NC";

stateNC[0] = "NC";
stateNC[1] = "C";
stateNC[2] = "C";
stateNC[3] = "C";

if (p < 0 || q < 0){
p=p0;
  q=q0;
  str = "Values of p and q cannot be negative!";
  alert(str);
}

for (var i = 0; i < loopIndex; i++){
   var j = loopIndex - i - 1;
   var k = 2*bitValue(p,j)+bitValue(q,j);
   if (state == 'C'){
       state = stateC[k];
       continue;
   }
   if (state == 'NC'){
       state = stateNC[k];
       continue;
   }
   if (state == 'B'){
       state = stateB[k];
       continue;
   }
   if (state == 'NB'){
       state = stateNB[k];
       continue;
   }
   if (state == 'A'){
       state = stateA[k];
       continue;
   }
   if (state == 'A0'){
       state = stateA0[k];
       continue;
   }
}
   if (state=="NB" || state=="NC") {
       result="-1";
   }
   return result;    
}