(* For d=2 *)
tranr[d_,k_,t_]:=
(Module[{bd,cd,ii,j,jj,tt,KM,km,be,kb},
bd=1;
tt:=t;xx={1};
Do[bd=2^ii-bd+1;AppendTo[xx,1],{ii,d-1}];
cd=bd*2^(-d);

(* teraz liczmy numery przeksztalcen od 0 do 2^d-1 *)
km={};
(*Print["tt=",tt]; *)
Do[(* Print["j=",j]; *)
   kb=Floor[(tt-cd/2^d)*2^d]+1;
   tt=2^d*(tt-cd/2^d-(kb-1)*2^(-d));
 (* Print["tt=",tt]; 
   Print["kb=",kb];  *)
   If[kb==2^d,kb=0,];
   (* jesli mamy nieparzyste kb, to zmieniamy kierunek przechodzenia *)
(* poczawszy od 000 , 001 do 111 a nast 100 i 000 *)
   If[ Floor[kb/2]<kb/2,tt=1-tt,];
   AppendTo[km,kb] 
            ,{j,k}];
(*Print["km=",km];*)
(* w km sa kolejne numery funkcji 
teraz bedziemy je rozkodowywac i przeksztalcac 1111 *)
Do[ KM=km[[k-j+1]];
    ww={};
  Do[ If[KM< 2^(d-jj),be=0,be=1];
      AppendTo[ww,be];
      KM=KM-be*2^(d-jj);
      If[be==1,KM=2^(d-jj)-KM-1,]; 
            ,{jj,d}];
   (*   Print["wartosci beta=",ww]; *)
(* tu mamy zdefiniowane w ww wartosci wsp beta w przekszt. *)
(* w kolejno\'sci od d do 1 *)
Do[xx[[d-jj+1]]=1/2-(1/2-ww[[jj]])*xx[[d-jj+1]] ,{jj,d}];           
(* skonczylismy przekszt. wkm *)
            ,{j,k}];
xx])


(* For d=2 *)
In[8]:= Kodr[d_,k_,x_List]:=(
Module[{xx,bd,cd,ii,jj,KM,km,kb,be,tt},
bd=1;
xx=x;
(*Print["xx=",xx];*)
beta={};
KM={};
Do[bd=2^ii-bd+1,{ii,d-1}];
cd=bd*2^(-d);
tt=1-cd;
(*Print["tt=",tt];*)
(* dla kazdego x wyznaczamy be 0lub 1 w zaleznosci,czy x,0.5 czy nie *)
Do[ (* k razy *) beta={};
Do[xi=xx[[ii]];
   If[xi<1/2,be=0,be=1];
   AppendTo[beta,be];
   xx[[ii]]=(xi-1/2)/(-1/2+be),
             {ii,d}];
(*Print["xxp=",xx];*)
(* teraz wyznaczamy numer odwzorowania kb *)
ww=0;kb=0;
Do[be=beta[[d-ii+1]];
     If[be+ww==1,kb=kb+2^(d-ii),];
     ww=Abs[be-ww], {ii,d}];
If[kb==2^d,kb=0,];
AppendTo[KM,kb],{jj,k}];
(*Print["KM=",KM];*)
Do[kb=KM[[k-jj+1]];

(* teraz sprawdzamy czy parzyste kb czy nie *)
  If[ Floor[kb/2]<kb/2,tt=1-tt,]; 
tt=(cd+(kb-1)+tt)/2^d;
(*Print["tt=",tt];*)
If[tt<0,tt=1+tt,],
                   {jj,k}];
tt])


%%%%%%%%%%%%%%%%%
In[9]:= Kodr[	2,20,{0.5,0.5}]
Out[9]= 3/8
%%%%%%%%%%%%%%%
Kod[d_,k_,x_List]:=(
Module[{xx,bd,cd,ii,jj,KM,km,kb,be,tt},
bd=1;
xx=x;
(*Print["xx=",xx];*)
beta={};
KM={};
Do[bd=2^ii-bd+1,{ii,d-1}];
cd=bd*2^(-d);
tt=1-cd;
(*Print["tt=",tt];*)
(* dla kazdego x wyznaczamy be 0lub 1 w zaleznosci,czy x,0.5 czy nie *)
Do[ (* k razy *) beta={};
Do[xi=xx[[ii]];
   If[xi<1/2,be=0,be=1];
   AppendTo[beta,be];
   xx[[ii]]=(xi-1/2)/(-1/2+be),
             {ii,d}];
(*Print["xxp=",xx];*)
(* teraz wyznaczamy numer odwzorowania kb *)
ww=0;kb=0;
Do[be=beta[[d-ii+1]];
     If[be+ww==1,kb=kb+2^(d-ii),];
     ww=Abs[be-ww], {ii,d}];
If[kb==2^d,kb=0,];
AppendTo[KM,kb],{jj,k}];
(*Print["KM=",KM];*)
Do[kb=KM[[k-jj+1]];
tt=(cd+(kb-1)+tt)/2^d; 
(*Print["tt=",tt];*)
If[tt<0,tt=1+tt,],
                   {jj,k}];
tt])
%%%%%%%%%%%%%%%%%%%
(* to bedzie trans. z odwroconymi nieparzystymi odcinkami *)
(* podaje punkt w Id dla ustalonego t w I1 *)
tran[d_,k_,t_]:=
(Module[{bd,cd,ii,j,jj,tt,KM,km,be,kb},
bd=1;
tt:=t;xx={1};
Do[bd=2^ii-bd+1;AppendTo[xx,1],{ii,d-1}];
cd=bd*2^(-d);

(* teraz liczmy numery przeksztalcen od 0 do 2^d-1 *)
km={};
(*Print["tt=",tt]; *)
	przeksztalcac 1111 *)
Do[ KM=km[[k-j+1]];
    ww={};
  Do[ If[KM< 2^(d-jj),be=0,be=1];
      AppendTo[ww,be];
      KM=KM-be*2^(d-jj);
      If[be==1,KM=2^(d-jj)-KM-1,]; 
            ,{jj,d}];
   (*   Print["wartosci beta=",ww]; *)
(* tu mamy zdefiniowane w ww wartosci wsp beta w przekszt. *)
(* w kolejno\'sci od d do 1 *)
Do[xx[[d-jj+1]]=1/2-(1/2-ww[[jj]])*xx[[d-jj+1]] ,{jj,d}];           
(* skonczylismy przekszt. wkm *)
            ,{j,k}];
xx])

In[50]:= %%%%%%%%%%%%%%
tranr[2,20,7/352]

Out[51]= {60293/262144,7209/65536}
In[52]:= 
Kodr[2,20, {60293/262144,7209/65536}]



(5466322015/274877906944)

In[55]:= 
N[5466322015/274877906944]

0.01988636364330887`
In[56]:= 
N[7/352]
Out[56]= 0.0198864

0.019886363636363636`

In[59]:= 
N[tranr[2,20,7/352]]
Out[59]= {0.23,0.110001}
In[61]:= N[Kodr[2,20, {60293/262144,7209/65536}]]

Out[61]= 0.0198864
0.01988636364330887`
%%%%%%%%%%%%%%%
In[62]:= 
N[Kodr[2,20,{0.22999954223632812`,0.1100006103515625`}]]
Out[62]= 0.0198864
Kod[4,20,{1/2,1/2,0.5,0.5}]

Out[13]= 75/128
In[14]:= Kodr[4,20,{1/2,1/2,0.5,0.5}]
Out[14]= 75/128
In[17]:= {Kod[4,20,{1,1,1.,1.}],Kod[4,20,{0,0,0.,0.}]}
Out[17]= {5/8,0}
In[16]:= Kodr[4,20,{1,1,1.,1.}]
Out[16]= 5/8
In[18]:= {Kodr[4,20,{1,1,1.,1.}],Kodr[4,20,{0,0,0.,0.}]}
Out[18]= {5/8,0}
In[19]:= {Kod[2,20,{0,1.}],Kod[2,20,{1.,1.}],Kod[2,20,{1,0.}],Kod[2,20,{0,0.}]}
Out[19]= {3/4,1/2,1/4,0}
In[20]:= {Kodr[2,20,{0,1.}],Kodr[2,20,{1.,1.}],Kodr[2,20,{1,0.}],Kodr[2,20,{0,0.}]}
Out[20]= {3/4,1/2,1/4,0}
In[25]:= {Kod[3,20,{0,0.,1.}],Kod[3,20,{1,0.,1.}],Kod[3,20,{1,1.,1.}],Kod[3,20,{0,1.,1.}],Kod[3,20,{0,1.,0.}],Kod[3,20,{1.,1.,0.}],Kod[3,20,{1,0.,0.}],Kod[3,20,{0,0.,0.}]}
Out[25]= {7/8,3/4,5/8,1/2,3/8,1/4,1/8,0}
In[27]:= N[{Kodr[3,20,{0,0.,1.}],Kodr[3,20,{1,0.,1.}],Kodr[3,20,{1,1.,1.}],Kodr[3,20,{0,1.,1.}],Kodr[3,20,{0,1.,0.}],Kodr[3,20,{1.,1.,0.}],Kodr[3,20,{1,0.,0.}],Kodr[3,20,{0,0.,0.}]}]
Out[27]= {0.847222,0.746528,0.597222,0.496528,0.347222,0.246528,0.0972222,0.996528}
In[48]:= {Kod[4,20,{0,0,0.,1.}],Kod[4,20,{1,0,0.,1.}],Kod[4,20,{1,1.,0.,1}],Kod[4,20,{0,1,0.,1.}],Kod[4,20,{0.,1,1.,1.}],Kod[4,20,{1,1,1.,1.}],Kod[4,20,{1,0,1.,1.}],Kod[4,20,{0.,0.,1.,1.}],Kod[4,20,{0.,0.,1.,0.}],Kod[4,20,{1,0.,1.,0.}],Kod[4,20,{1,1,1.,0.}],Kod[4,20,{0.,1.,1.,0.}],Kod[4,20,{0.,1,0.,0.}],Kod[4,20,{1,1,0.,0.}],Kod[4,20,{1,0,0.,0.}],Kod[4,20,{0,0,0.,0.}]}
Out[48]= {15/16,7/8,13/16,3/4,11/16,5/8,9/16,1/2,7/16,3/8,5/16,1/4,3/16,1/8,1/16,0}
In[49]:= {Kodr[4,20,{0,0,0.,1.}],Kodr[4,20,{1,0,0.,1.}],Kodr[4,20,{1,1.,0.,1}],Kodr[4,20,{0,1,0.,1.}],Kodr[4,20,{0.,1,1.,1.}],Kodr[4,20,{1,1,1.,1.}],Kodr[4,20,{1,0,1.,1.}],Kodr[4,20,{0.,0.,1.,1.}],Kodr[4,20,{0.,0.,1.,0.}],Kodr[4,20,{1,0.,1.,0.}],Kodr[4,20,{1,1,1.,0.}],Kodr[4,20,{0.,1.,1.,0.}],Kodr[4,20,{0.,1,0.,0.}],Kodr[4,20,{1,1,0.,0.}],Kodr[4,20,{1,0,0.,0.}],Kodr[4,20,{0,0,0.,0.}]}
Out[49]= {59/64,7/8,51/64,3/4,43/64,5/8,35/64,1/2,27/64,3/8,19/64,1/4,11/64,1/8,3/64,0}