Task: Zeckendorf arithmetic
C#: using System;
using System.Text;

namespace ZeckendorfArithmetic {
    class Zeckendorf : IComparable<Zeckendorf> {
        private static readonly string[] dig = { "00", "01", "10" };
        private static readonly string[] dig1 = { "", "1", "10" };

        private int dVal = 0;
        private int dLen = 0;

        public Zeckendorf() : this("0") {
            
        }

        public Zeckendorf(string x) {
            int q = 1;
            int i = x.Length - 1;
            dLen = i / 2;
            while (i >= 0) {
                dVal += (x[i] - '0') * q;
                q *= 2;
                i--;
            }
        }

        private void A(int n) {
            int i = n;
            while (true) {
                if (dLen < i) dLen = i;
                int j = (dVal >> (i * 2)) & 3;
                switch (j) {
                    case 0:
                    case 1:
                        return;
                    case 2:
                        if (((dVal >> ((i + 1) * 2)) & 1) != 1) return;
                        dVal += 1 << (i * 2 + 1);
                        return;
                    case 3:
                        int temp = 3 << (i * 2);
                        temp ^= -1;
                        dVal = dVal & temp;
                        B((i + 1) * 2);
                        break;
                }
                i++;
            }
        }

        private void B(int pos) {
            if (pos == 0) {
                Inc();
                return;
            }
            if (((dVal >> pos) & 1) == 0) {
                dVal += 1 << pos;
                A(pos / 2);
                if (pos > 1) A(pos / 2 - 1);
            }
            else {
                int temp = 1 << pos;
                temp ^= -1;
                dVal = dVal & temp;
                B(pos + 1);
                B(pos - (pos > 1 ? 2 : 1));
            }
        }

        private void C(int pos) {
            if (((dVal >> pos) & 1) == 1) {
                int temp = 1 << pos;
                temp ^= -1;
                dVal = dVal & temp;
                return;
            }
            C(pos + 1);
            if (pos > 0) {
                B(pos - 1);
            }
            else {
                Inc();
            }
        }

        public Zeckendorf Inc() {
            dVal++;
            A(0);
            return this;
        }

        public Zeckendorf Copy() {
            Zeckendorf z = new Zeckendorf {
                dVal = dVal,
                dLen = dLen
            };
            return z;
        }

        public void PlusAssign(Zeckendorf other) {
            for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
                if (((other.dVal >> gn) & 1) == 1) {
                    B(gn);
                }
            }
        }

        public void MinusAssign(Zeckendorf other) {
            for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
                if (((other.dVal >> gn) & 1) == 1) {
                    C(gn);
                }
            }
            while ((((dVal >> dLen * 2) & 3) == 0) || (dLen == 0)) {
                dLen--;
            }
        }

        public void TimesAssign(Zeckendorf other) {
            Zeckendorf na = other.Copy();
            Zeckendorf nb = other.Copy();
            Zeckendorf nt;
            Zeckendorf nr = new Zeckendorf();
            for (int i = 0; i < (dLen + 1) * 2; i++) {
                if (((dVal >> i) & 1) > 0) {
                    nr.PlusAssign(nb);
                }
                nt = nb.Copy();
                nb.PlusAssign(na);
                na = nt.Copy();
            }
            dVal = nr.dVal;
            dLen = nr.dLen;
        }

        public int CompareTo(Zeckendorf other) {
            return dVal.CompareTo(other.dVal);
        }

        public override string ToString() {
            if (dVal == 0) {
                return "0";
            }

            int idx = (dVal >> (dLen * 2)) & 3;
            StringBuilder sb = new StringBuilder(dig1[idx]);
            for (int i = dLen - 1; i >= 0; i--) {
                idx = (dVal >> (i * 2)) & 3;
                sb.Append(dig[idx]);
            }
            return sb.ToString();
        }
    }

    class Program {
        static void Main(string[] args) {
            Console.WriteLine("Addition:");
            Zeckendorf g = new Zeckendorf("10");
            g.PlusAssign(new Zeckendorf("10"));
            Console.WriteLine(g);
            g.PlusAssign(new Zeckendorf("10"));
            Console.WriteLine(g);
            g.PlusAssign(new Zeckendorf("1001"));
            Console.WriteLine(g);
            g.PlusAssign(new Zeckendorf("1000"));
            Console.WriteLine(g);
            g.PlusAssign(new Zeckendorf("10101"));
            Console.WriteLine(g);
            Console.WriteLine();

            Console.WriteLine("Subtraction:");
            g = new Zeckendorf("1000");
            g.MinusAssign(new Zeckendorf("101"));
            Console.WriteLine(g);
            g = new Zeckendorf("10101010");
            g.MinusAssign(new Zeckendorf("1010101"));
            Console.WriteLine(g);
            Console.WriteLine();

            Console.WriteLine("Multiplication:");
            g = new Zeckendorf("1001");
            g.TimesAssign(new Zeckendorf("101"));
            Console.WriteLine(g);
            g = new Zeckendorf("101010");
            g.PlusAssign(new Zeckendorf("101"));
            Console.WriteLine(g);
        }
    }
}

Python: import copy

class Zeckendorf:
    def __init__(self, x='0'):
        q = 1
        i = len(x) - 1
        self.dLen = int(i / 2)
        self.dVal = 0
        while i >= 0:
            self.dVal = self.dVal + (ord(x[i]) - ord('0')) * q
            q = q * 2
            i = i -1

    def a(self, n):
        i = n
        while True:
            if self.dLen < i:
                self.dLen = i
            j = (self.dVal >> (i * 2)) & 3
            if j == 0 or j == 1:
                return
            if j == 2:
                if (self.dVal >> ((i + 1) * 2) & 1) != 1:
                    return
                self.dVal = self.dVal + (1 << (i * 2 + 1))
                return
            if j == 3:
                temp = 3 << (i * 2)
                temp = temp ^ -1
                self.dVal = self.dVal & temp
                self.b((i + 1) * 2)
            i = i + 1

    def b(self, pos):
        if pos == 0:
            self.inc()
            return
        if (self.dVal >> pos) & 1 == 0:
            self.dVal = self.dVal + (1 << pos)
            self.a(int(pos / 2))
            if pos > 1:
                self.a(int(pos / 2) - 1)
        else:
            temp = 1 << pos
            temp = temp ^ -1
            self.dVal = self.dVal & temp
            self.b(pos + 1)
            self.b(pos - (2 if pos > 1 else 1))

    def c(self, pos):
        if (self.dVal >> pos) & 1 == 1:
            temp = 1 << pos
            temp = temp ^ -1
            self.dVal = self.dVal & temp
            return
        self.c(pos + 1)
        if pos > 0:
            self.b(pos - 1)
        else:
            self.inc()

    def inc(self):
        self.dVal = self.dVal + 1
        self.a(0)

    def __add__(self, rhs):
        copy = self
        rhs_dVal = rhs.dVal
        limit = (rhs.dLen + 1) * 2
        for gn in range(0, limit):
            if ((rhs_dVal >> gn) & 1) == 1:
                copy.b(gn)
        return copy

    def __sub__(self, rhs):
        copy = self
        rhs_dVal = rhs.dVal
        limit = (rhs.dLen + 1) * 2
        for gn in range(0, limit):
            if (rhs_dVal >> gn) & 1 == 1:
                copy.c(gn)
        while (((copy.dVal >> ((copy.dLen * 2) & 31)) & 3) == 0) or (copy.dLen == 0):
            copy.dLen = copy.dLen - 1
        return copy

    def __mul__(self, rhs):
        na = copy.deepcopy(rhs)
        nb = copy.deepcopy(rhs)
        nr = Zeckendorf()
        dVal = self.dVal
        for i in range(0, (self.dLen + 1) * 2):
            if ((dVal >> i) & 1) > 0:
                nr = nr + nb
            nt = copy.deepcopy(nb)
            nb = nb + na
            na = copy.deepcopy(nt)
        return nr

    def __str__(self):
        dig = ["00", "01", "10"]
        dig1 = ["", "1", "10"]

        if self.dVal == 0:
            return '0'
        idx = (self.dVal >> ((self.dLen * 2) & 31)) & 3
        sb = dig1[idx]
        i = self.dLen - 1
        while i >= 0:
            idx = (self.dVal >> (i * 2)) & 3
            sb = sb + dig[idx]
            i = i - 1
        return sb


print "Addition:"
g = Zeckendorf("10")
g = g + Zeckendorf("10")
print g
g = g + Zeckendorf("10")
print g
g = g + Zeckendorf("1001")
print g
g = g + Zeckendorf("1000")
print g
g = g + Zeckendorf("10101")
print g
print

print "Subtraction:"
g = Zeckendorf("1000")
g = g - Zeckendorf("101")
print g
g = Zeckendorf("10101010")
g = g - Zeckendorf("1010101")
print g
print

print "Multiplication:"
g = Zeckendorf("1001")
g = g * Zeckendorf("101")
print g
g = Zeckendorf("101010")
g = g + Zeckendorf("101")
print g