Half-arsed answer to this question https://codegolf.stackexchange.com/questions/19955/

TerribleSecret.go

package TerribleSecret

type Unf struct {
	Pak, Chooie *Unf
}

func FromNative(n uint) (u *Unf) {
	u = new(Unf)
	if n == 0 {
		return
	}
	if n&1 != 0 {
		u.Pak = u
	}
	u.Chooie = FromNative(n >> 1)
	return
}

func (u *Unf) ToNative() (n uint) {
	if u == nil {
		return
	}
	n = u.Chooie.ToNative()
	n <<= 1
	if u.Pak != nil {
		n |= 1
	}
	return
}

func (u *Unf) Add(n *Unf) {
	var f *Unf
	for {
		if u == nil {
			u = new(Unf)
		}
		if (n == nil || n.Pak == nil) != (f == nil) {
			if u.Pak != nil {
				u.Pak = nil
			} else {
				u.Pak = u
			}
		}
		if u.Pak != nil && (n == nil || n.Pak == nil) && f != nil {
			f = nil
		} else if u.Pak == nil && n != nil && n.Pak != nil && f == nil {
			f = n.Pak
		}
		if n != nil {
			n = n.Chooie
		}
		if n == nil && f == nil {
			break
		}
		if u.Chooie == nil {
			u.Chooie = new(Unf)
		}
		u = u.Chooie
	}
}

TerribleSecret_test.go

package TerribleSecret

import "testing"

func TestConversion(t *testing.T) {
	for n := uint(0); n < 10000; n++ {
		if r := FromNative(n).ToNative(); r != n {
			t.Fatalf("%d != %d", n, r)
		}
	}
}

func TestAdd(t *testing.T) {
	for x := uint(0); x < 1000; x++ {
		px := FromNative(x)
		for y := uint(0); y < 1000; y++ {
			py := FromNative(y)
			py.Add(px)
			if r := py.ToNative(); r != x+y {
				t.Fatalf("%d + %d = %d != %d", x, y, x+y, r)
			}
		}
	}
}