% modeling of a suanpan (Chinese abacus)
% D. Roegel 9 September - 12 October 2008
%
% These macros provide basic functions for producing suanpan (Chinese abacus)
% figures as well as soroban ones (Japanese abacus)

numeric u;
u=1cm;

% key-val mechanism (from LGC2, p. 59-60)
vardef executekeyval(text k)=
 save _equals;
 let _equals= =;
 tertiarydef _ll_ _assign _rr_ =
   hide(_ll_ _equals _rr_ ) 1
 enddef;
 save =;
 let = _equals _assign ;
 for _xx_ _equals k:endfor;
enddef;

numeric n; % number of digits
numeric nbl,vbu,nbu; % number of beads (lower/upper)
                    % vbu=value of a bead in the upper deck
numeric hsep,vsep,beadw,thframe,beadsp,wdvline,hlwindow,huwindow;
numeric wdframe,huwindow;

numeric beadtype;
boolean rod_numbers;
rod_numbers=true; % default

boolean overflow;

numeric abacus_units;
abacus_units=0; % a value of 1 marks every third rod by a dot
               % other values may be used in the future

n=13; % default
vbu=5; % value of a bead in the upper deck
nbl=5; % total beads below (lower deck)
nbu=2; % total beads above (upper deck)
hsep=.8u; % distance between lines of beads
ihsep=.5hsep; % initial hsep
vsep=.5u; % smallest distance between bead centers
beadw=.4hsep; % bead width
thframe=.3u; % frame thickness
beadsp=u; % bead spacing
wdvline=.1u; % thickness of bamboo lines
beadtype=1; % 1=round (suanpan), 2=biconal (soroban)

vardef setup_abacus(text kv)=
 save N,NBL,NBU,bead,units; % key names
 numeric N,NBL,NBU,units;
 string bead;
 executekeyval(kv);
 n:=N;
 nbl:=NBL;
 nbu:=NBU;
 abacus_units:=units;
 wdframe:=(n-1)*hsep+2ihsep+2thframe;
 htframe:=3thframe+(nbl+nbu-2)*vsep+vsep+vsep+2beadsp;
 hlwindow:=(nbl-1)*vsep+vsep+beadsp;  % height of lower window
 huwindow:=htframe-3thframe-hlwindow; % height of upper window
 if bead="suanpan":
   beadtype:=1;
 elseif bead="soroban":
   beadtype:=2;
 fi;
enddef;

vardef draw_abacus_frame=
 save P;pair P[];
 % -------------- outer frame --------------
 P0=origin;
 P1-P0=P2-P3=wdframe*right;
 P2-P1=htframe*up;
 draw P0--P1--P2--P3--cycle;
 %--------- lower inner frame --------------
 P4-P0=(thframe,thframe);
 P5-P1=(-thframe,thframe);
 P9=P0+(1.5thframe+hlwindow)*up;
 P10-P9=P1-P0;
 P7=P9+(thframe,-.5thframe);
 P6-P7=P5-P4;
 draw P4--P5--P6--P7--cycle;
 %--------- upper inner frame --------------
 P14-P9=(thframe,.5thframe);
 P15-P10=(-thframe,.5thframe);
 P16-P2=(-thframe,-thframe);
 P17-P3=(thframe,-thframe);
 draw P14--P15--P16--P17--cycle;
enddef;

vardef draw_abacus_rods=
 save h,ha,hb,savep;
 savep=savepen;
 ha=hlwindow;
 hb=huwindow;
 h=ha+hb+thframe;
 for i=1 upto n:
   draw (thframe+ihsep+(i-1)*hsep-.5wdvline,thframe)
        --(thframe+ihsep+(i-1)*hsep-.5wdvline,thframe+ha);
   draw (thframe+ihsep+(i-1)*hsep+.5wdvline,thframe)
        --(thframe+ihsep+(i-1)*hsep+.5wdvline,thframe+ha);
   draw (thframe+ihsep+(i-1)*hsep-.5wdvline,thframe+h-hb)
        --(thframe+ihsep+(i-1)*hsep-.5wdvline,thframe+h);
   draw (thframe+ihsep+(i-1)*hsep+.5wdvline,thframe+h-hb)
        --(thframe+ihsep+(i-1)*hsep+.5wdvline,thframe+h);
   if rod_numbers:
     label.bot(decimal i,(thframe+ihsep+(n-i)*hsep,0));
     label.top(decimal i,(thframe+ihsep+(n-i)*hsep,2thframe+h));
   fi
 endfor;
 pickup pencircle scaled 3pt;
 if abacus_units=1:
   for i=3 step 3 until n:
     draw (thframe+ihsep+(n-i)*hsep,thframe+ha+.5thframe);
   endfor;
 fi;
 pickup savep;
enddef;

numeric valU[],valL[],vl; % stores the abacus values and the number of digits
numeric valUMu[],valUMs[],valLMs[],valLMu[]; % moved values will be in gray

def reset_abacus=
 for i=1 upto n:
   valU[i]:=0;
   valL[i]:=0;
 endfor;
 reset_abacus_gray_above;
 reset_abacus_gray_below;
enddef;

def reset_abacus_gray_above=
 for i=1 upto n:
   valUMs[i]:=0;valUMu[i]:=0;
 endfor;
enddef;

def reset_abacus_gray_below=
 for i=1 upto n:
   valLMu[i]:=0;valLMs[i]:=0;
 endfor;
enddef;

def suanpan_bead(expr X,Y)=
 fullcircle xscaled 2beadw yscaled vsep shifted (X,Y)
enddef;

def draw_suanpan_bead(expr X,Y) text options=
 fill suanpan_bead(X,Y) options;
enddef;

def draw_suanpan_gray_bead(expr X,Y) text options=
 fill suanpan_bead(X,Y) options;
 draw suanpan_bead(X,Y);
enddef;

def draw_suanpan_bead_contour(expr X,Y) text options=
 draw_suanpan_gray_bead(X,Y) withcolor white;
enddef;

def define_soroban_bead_points(expr X,Y)=
 save p,pa;pair p[];path pa;
 p0=(X,Y);p1=p0+(beadw,.5wdvline);p2=p0+(.5wdvline,.5vsep);
 p3=p0+(-.5wdvline,.5vsep);p4=p0+(-beadw,.5wdvline);
 p5=p0+(-beadw,-.5wdvline);p6=p0+(-.5wdvline,-.5vsep);
 p7=p0+(.5wdvline,-.5vsep);p8=p0+(beadw,-.5wdvline);
 pa=p1--p2--p3--p4--p5--p6--p7--p8--cycle;
enddef;

% this macro draws a biconal bead, like on a soroban
vardef draw_soroban_bead(expr X,Y) text options=
 define_soroban_bead_points(X,Y);
 unfill pa;
 draw pa;draw p1--p4;draw p5--p8;
enddef;

% this macro draws a biconal bead, like on a soroban
vardef draw_soroban_gray_bead(expr X,Y) text options=
 define_soroban_bead_points(X,Y);
 fill pa withcolor .7white;
 draw pa;draw p1--p4;draw p5--p8;
enddef;

vardef draw_soroban_bead_contour(expr X,Y)=
 define_soroban_bead_points(X,Y);
 unfill pa;
 draw pa;
enddef;

def draw_bead_contour(expr X,Y) text options=
 if beadtype=1:
   draw_suanpan_bead_contour(X,Y);
 else:
   draw_soroban_bead_contour(X,Y);
 fi;
enddef;

def draw_bead(expr X,Y) text options=
 if beadtype=1:
   draw_suanpan_bead(X,Y) options;
 elseif beadtype=2:
   draw_soroban_bead(X,Y) options;
 fi;
enddef;

def draw_gray_bead(expr X,Y)=
 if beadtype=1:
   draw_suanpan_gray_bead(X,Y) withcolor .7white;
 elseif beadtype=2:
   draw_soroban_gray_bead(X,Y) withcolor .7white;
 fi;
enddef;

vardef draw_abacus_beads=
 save na,nb,X,Y;
 % we go through every bead line:
 for i=1 upto n:
   X:=thframe+ihsep+(n-i)*hsep;
   % first, we handle the lower beads:
   na:=nbl-valL[i];
   nb:=valL[i];
   % ------------------------------------------------------------
   % these are the lower beads which have not been raised (unset)
   for j=1 upto na:
     Y:=thframe+.5vsep+(j-1)*vsep;
     draw_bead(X,Y);
   endfor;
   % some of the previous ones are in gray:
   for j=na downto na-(valLMu[i]-1):
     Y:=thframe+.5vsep+(j-1)*vsep;
     draw_gray_bead(X,Y);

   endfor;
   %-------------------------------------------------------------
   % these are the lower beads which have been raised (set)
   for j=1 upto nb:
     Y:=thframe+hlwindow-(.5vsep+(j-1)*vsep);
     draw_bead(X,Y);
   endfor;
   % some of the previous ones are in gray:
   for j=nb downto nb-(valLMs[i]-1):
     Y:=thframe+hlwindow-(.5vsep+(j-1)*vsep);
     draw_gray_bead(X,Y);
   endfor;
   %-------------------------------------------------------------
   % then we handle the upper beads:
   na:=nbu-valU[i];
   nb:=valU[i];
   %--------------------------------------------------------------
   % these are the upper beads which have not been lowered (unset)
   for j=1 upto na:
     Y:=htframe-(thframe+.5vsep+(j-1)*vsep);
     draw_bead(X,Y);
   endfor;
   for j=na downto na-(valUMu[i]-1):
     Y:=htframe-(thframe+.5vsep+(j-1)*vsep);
     draw_gray_bead(X,Y);
   endfor;
   %--------------------------------------------------------------
   % these are the upper beads which have been lowered (set)
   for j=1 upto nb:
     Y:=2thframe+hlwindow+(.5vsep+(j-1)*vsep);
     draw_bead(X,Y);
   endfor;
   for j=nb downto nb-(valUMs[i]-1):
     Y:=2thframe+hlwindow+(.5vsep+(j-1)*vsep);
     draw_gray_bead(X,Y);
   endfor;
   %--------------------------------------------------------------
 endfor;
enddef;

def draw_abacus=
 draw_abacus_frame;
 draw_abacus_rods;
 draw_abacus_beads;
enddef;

% v must be a string
vardef set_abacus_val(expr v)=
 save vx;
 numeric vx[];
 reset_abacus;
 vl:=min(length(v),n)-1; % handle overflows in the input
 for i=0 upto length(v)-1:
   vx[i]=ASCII(substring(i,i+1) of v)-ASCII("0");
 endfor;
 for i=1 upto length(v):
   valL[i]:=vx[length(v)-i];
   if valL[i]>vbu-1: % we must use vbu and not nbl, although
                     % they are usually the same
     valU[i]:=1;
     valL[i]:=valL[i]-vbu; % same remark
   fi;
 endfor;
enddef;

vardef reset_abacus_gray=
 save s;
 string s;
 s="";
 for i=1 upto n:s:=s & "0";endfor;
 set_abacus_gray(deck="lower",below=s,above=s);
 set_abacus_gray(deck="upper",below=s,above=s);
enddef;

vardef set_abacus_gray_below=
 save vx;
 numeric vx[];
 reset_abacus_gray_below;
 % reading the first string, for the lower part (which beads are gray)
 for i=0 upto length(below)-1:
   vx[i]:=ASCII(substring(i,i+1) of below)-ASCII("0");
 endfor;
 for i=1 upto length(below):
   valLMu[i]:=vx[length(below)-i];
 endfor;
 % reading the second string, for the upper part (which beads are gray)
 for i=0 upto length(above)-1:
   vx[i]:=ASCII(substring(i,i+1) of above)-ASCII("0");
 endfor;
 for i=1 upto length(above):
   valLMs[i]:=vx[length(above)-i];
 endfor;
 % we check that there is no conflict in the graying of beads:
 %   a bead can only be grayed if it exists
 for i=1 upto n:
   % lower beads ...............................
   na:=nbl-valL[i];
   nb:=valL[i];
   % we force threshholds if necessary:
   if valLMs[i]>valL[i]:valLMs[i]:=valL[i];fi
   if valLMu[i]>na:valLMu[i]:=na;fi
 endfor;
enddef;

vardef set_abacus_gray_above=
 save vx;
 numeric vx[];
 reset_abacus_gray_above;
 % reading the first string, for the lower part (which beads are gray)
 for i=0 upto length(below)-1:
   vx[i]:=ASCII(substring(i,i+1) of below)-ASCII("0");
 endfor;
 for i=1 upto length(below):
   valUMs[i]:=vx[length(below)-i];
 endfor;
 % reading the second string, for the upper part (which beads are gray)
 for i=0 upto length(above)-1:
   vx[i]:=ASCII(substring(i,i+1) of above)-ASCII("0");
 endfor;
 for i=1 upto length(above):
   valUMu[i]:=vx[length(above)-i];
 endfor;
 % we check that there is no conflict in the graying of beads:
 %   a bead can only be grayed if it exists
 for i=1 upto n:
   % upper beads ...............................
   na:=nbu-valU[i];
   nb:=valU[i];
   % we force threshholds if necessary:
   if valUMs[i]>valU[i]:valUMs[i]:=valU[i];fi
   if valUMu[i]>na:valUMu[i]:=na;fi
 endfor;
enddef;

vardef set_abacus_gray(text kv)=
 save deck,below,above; % key names
 string deck,below,above;
 executekeyval(kv);
 if deck="lower":
   set_abacus_gray_below;
 elseif deck="upper":
   set_abacus_gray_above;
 fi;
enddef;

% put the label `lab' on the j-th bead on row i (i=1 at the right)
vardef mark_abacus(text kv)(expr lab)=
 save i,j; % key names
 numeric i,j;
 executekeyval(kv);

 save X,Y,na,nb,ju;
 X:=thframe+ihsep+(n-i)*hsep;
 if j<=nbl: % the bead to mark is below:
   % first, we handle the lower beads:
   na:=nbl-valL[i];
   nb:=valL[i];
   % ------------------------------------------------------------
   if j<=na:
     % these are the lower beads which have not been raised (unset)
     Y:=thframe+.5vsep+(j-1)*vsep;
   else:
     %-------------------------------------------------------------
     % these are the lower beads which have been raised (set)
     Y:=thframe+hlwindow-(.5vsep+(nb-(j-na))*vsep);
   fi
 else: % the bead to mark is above:
   ju=j-nbl;
   %-------------------------------------------------------------
   % then we handle the upper beads:
   na:=nbu-valU[i];
   nb:=valU[i];
   if ju>nb:
     %--------------------------------------------------------------
     % these are the upper beads which have not been lowered (unset)
     Y:=htframe-(thframe+.5vsep+(na-(ju-nb))*vsep);
   else:
     %--------------------------------------------------------------
     % these are the upper beads which have been lowered (set)
     Y:=2thframe+hlwindow+(.5vsep+(ju-1)*vsep);
   fi;
 fi;
 draw_bead_contour(X,Y);
 draw thelabel(lab,(X,Y)); % withcolor white;
enddef;

def show_val=
 for i=1 upto vl+1:
   message "valU[" & decimal i & "]=" & decimal (valU[i]);
   message "valL[" & decimal i & "]=" & decimal (valL[i]);
 endfor;
enddef;

% v=value, iv=image view
def add_val(text kv)=
 save v,iv,fig; % key names
 string v;numeric iv;boolean fig;
 executekeyval(kv);
 save vx,VL,VU,carry;
 numeric vx[],vL[],vU[],vx.len;
 overflow:=false;
 % we store the new value to add in one array
 vx.len=min(length(v),n)-1; % we consider at most n digits
 %message "vx.len=" & decimal vx.len;
 for i=0 upto vx.len:
   vx[i]=ASCII(substring(i,i+1) of v)-ASCII("0");
 endfor;
 for i=1 upto length(v):
   vL[i]:=vx[length(v)-i];
 endfor;

 % if necessary, we modify the size of the first number:
 if vx.len>vl:vl:=vx.len;fi
 % the result will be either this wide, or will have one more digit
 % to the left

 if fig:
   % the initial configuration:
   beginfig(iv);
     draw_abacus;
   endfig;
 fi

 % we add the digits from left to right:
 for i=vx.len+1 downto 1:
   valL[i]:=valL[i]+vL[i];
   % if there would be too many beads below, we adjust the upper ones:
   forever:
     if valL[i]>vbu-1:
       valL[i]:=valL[i]-vbu;
       valU[i]:=valU[i]+1;
     fi
     exitif valL[i]<vbu;
   endfor;
   % then, we propagate a carry if necessary:
   carry:=0;
   if valU[i]>1: % valU[i]=2 or 3 are possible values
     carry:=1;
     % propagate carry
     valU[i]:=valU[i]-2;
     for j=i+1 upto vl+1:
       valL[j]:=valL[j]+carry;
       if valL[j]>4:valL[j]:=0;valU[j]:=valU[j]+1;fi
       if valU[j]>1:carry:=1;valU[j]:=valU[j]-2;else:carry:=0;fi
       exitif carry=0; % no need to go all the way through,
                       % if the carry becomes 0
     endfor;
     if carry=1:
       % we increment vl and we add the carry:
       vl:=vl+1;
       valL[vl+1]:=1;
       if vl+1>n:overflow:=true;fi
     fi
   fi
   %message "adding " & decimal vL[i] & " at position " & decimal i
   %  & " and generating view " & decimal (iv+(vx.len+1-i)+1);
   if fig:
     beginfig(iv+(vx.len+1-i)+1);
       draw_abacus;
     endfig;
   fi
 endfor;

enddef;

endinput

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