function showdiv(w){
    var d=(document[w] ? document[w]  : eval(w).style );
	d.visibility='visible'
}
var  BASE=10,MAXINT=2*(Math.pow(2,30)-1)+1 , pstart="[",pend="]";

var maxDIGlen=MAXINT.toString().length;

var clearansTXT='In the box below, the recurring part of a decimal is shown between '+pstart+' and '+pend
     +' brackets: eg\r3/44 = 0.06'+pstart+'81'+pend
     +' means 3/44 = 0.06818181...\r';

function IgnoreError(){self.onerror=ProcessErrors; return true};
function ProcessErrors(){return false};
function STOP(){  self.onerror=IgnoreError;  xxhaltxx() };
function ERR(xx){ alert(xx);  STOP()};
function ERRoverflow(m){ERR('Sorry, I cannot compute the answer because\r'
  +'the calculations involve numbers that have become too large!')};
function isOK(msg){ 
  if(arguments.length>1)msg=arguments.join('');
  if(!confirm(msg))STOP() 
};

function maxdps(w){return getn("ndps",w)[0]};

function setmaxdps(w){var fld=document["frac"+w].ndps;
  var MAXNDP=getn("ndps",w)[0];
  if(isNaN(MAXNDP) || MAXNDP<1)
    {fld.value=10;
     ERR("Your 'Number of dps' value is not a valid number so I've reset it to "+MAXNDP) }
  else if(MAXNDP>1000)
         if( ! confirm("Do you really want more than 1,000 decimal places computed?"))
            fld.value=1000;
};

function put(w,X){  var s=""; 
  for(var i=1;i<arguments.length;i++)  s=s+arguments[i];
  s=s+"\r";  
  putmsg(s);
};

function mul(a,b){if(a==0)return 0
  else if((a*b)/a!=b){ERRoverflow(a+" MUL "+b)}else{return a*b}
};
function add(a,b){if((a+b)-a!=b){ERRoverflow(a+" ADD "+b)}else{return a+b}
};
function isINT(N,nm){if(typeof N != "string")N=N.toString();
  if(N.length>maxDIGlen )
        ERR("Sorry - your "+nm+" number "+N+" is too large.\rIt must have no more than "+maxDIGlen+" digits.");
  if(N>MAXINT)ERR("Sorry - your "+nm+" number "+N+" is too big.\rThe maximum number I can use is "+MAXINT+".");
};

function getn(fld,w){  
  var boxname=(fld=="numer"?"top (numerator)"
              :fld=="denom"?"bottom (denominator)"
              :fld=="ndps"?"number of decimal places"
              :"");
  var str=stripspace(eval("document.frac"+w+"."+fld+".value"));
  if(str.match(/[^0-9,]/)!=null)
    ERR("The "+boxname+" box must only contain digits:\n"+str);
  var nbsRAW=str.replace(/\s|,/g,"").match(/\d+/g); 
  var nbs=nbsRAW;  
  if(!nbs || typeof nbs!="object" || nbs.length==0)ERR("I didn't find a number in the "+boxname+" input box.\n \nPlease enter a number and try again.");
  isINT(nbs[0],boxname); if(nbs[1]){isINT(nbs[1],"")}else{nbs[1]=nbs[0]};
  for(var i=0;i<nbs.length;i++)nbs[i]=parseInt(nbs[i],10);
  if(nbs.length==2)
      {if(nbs[1]<nbs[0])
         ERR("The end of the range ("+nbs[1]+") is less that its start ("+nbs[0]+")")}
  else if(nbs.length==1)nbs[1]=nbs[0]
  else ERR('You have given me '+nbs.length+' numbers in the "+boxname+" box. Please give just 1.');
  if(fld=="denom" && nbs[0]<2)ERR("The denominator must be 2 or more");  
  return nbs  
};

function getF(w){  return ratsimp(getn("numer",w)[0] ,getn("denom",w)[0] ) } ;
function ratsimp(n,d){ 
  if(typeof n=="string")n=parseInt(n,10);    if(typeof d=="string")d=parseInt(d,10);
   var g=gcd(n,d); 
   if(g>1){var ans= {num:Math.round(n/g), den:Math.round(d/g)}}
   else var ans= {num:n, den:d} ;
   return ans
};
function top(){return getF().num};
function bot(){return getF().den};

function newPFs(w){
  document["frac"+w].denomPFs.value=ordlistToZbag(primefactors(getF(w).den)); 
};
function nonrecPer(w,N,D){ 
  if(N/D>=1){ERR(N+"/"+D+" is not a proper fraction (it must be < 1)")}
  else {var F=ratsimp(N,D);N=F.num;D=F.den;    
        var p2=0;  while(D%2==0){p2++;D=Math.round(D/2)};
        var p5=0;  while(D%5==0){p5++;D=Math.round(D/5)};        var nonrecLen=Math.max(p2,p5);    
        return [nonrecLen,(D==1 ? 0 : order10(D)) ]
       }
};
function firstdp(N,D){ 
  var p1=Math.floor(10*N/D);
  return [p1,10*N-p1*D]
};
function putdecs(w,N,D,maxnb){  
  if(arguments.length<4)maxnb=maxdps(w);
  var np=nonrecPer(w,N,D);
  var nonreclen=np[0], per=np[1],i=0;
  if(np.length==0){putrawdecs(w,N,D,maxnb);return};
  var dps="0.",R=N,dr;
  for(var i=1;i<=Math.min(nonreclen,maxnb);i++)
      {dr=firstdp(R,D); dps=dps+dr[0].toString(); R=dr[1] };
  if(i>maxnb){dps=dps+"...";return dps};
  if(per>0)dps=dps+pstart;
  for(var i=nonreclen+1;i<=Math.min(nonreclen+per,maxnb);i++)
      {dr=firstdp(R,D);dps=dps+dr[0].toString();R=dr[1] };
  if(i<=nonreclen+per)dps=dps+"...";
  if(per>0)dps=dps+pend;
  return dps
};
function putrawdecs(w,N,D,maxnb){
  if(arguments.length<4)maxnb=maxdps(w);
  var dps="0.",R=N,dr;
  for(var i=1;R>0 && i<=maxnb;i++)
      {dr=firstdp(R,D); dps=dps+dr[0].toString(); R=dr[1] };
  if(R>0)dps+="...";
  return dps
};

function doPowMod(w){
  var b=getn("numer")[0],pp=getn("denom");
  for(p=pp[0];p<=pp[1];p++)put(w,b,"^",p," mod 10 = ",powmod(b,p,10))
};
function order10(N){ 
  if(N==1)return 1;    
  var fs=factors(EulerPhi(N)),i=0;  
  while(powmod(10,fs[i],N)!=1)
    {  i++;if(i>fs.length)ERR("ERROR found [overrun in order10].\rPlease email your input numbers to R.Knott@ronknott.com. Thank you.")};
  return fs[i]
};

function doTerminates(w){ 
 var ds=getn("denom",w);
 var nn=getn("numer",w)[0]; 
  
 for(var d=ds[0];d<=ds[1];d++)
    {var F=ratsimp(nn,d); 
     
     var np=nonrecPer(w,F.num,F.den);
     put(w,nn,'/',d,(nn==F.num?"":"="+F.num+'/'+F.den),
           (np[0]>0
           ?(np[1]==0
             ?" terminates after "+np[0]+" digit"+(np[0]>1?"s":"") 
             : " has "+np[0]+" initial digit" +(np[0]>1?"s":"") 
              +" followed by a period of "+np[1]+" digit"+(np[1]>1?"s":"")
             )
           :" is purely recurring with a period of "+np[1] +" digit"+(np[1]>1?"s":"")
           ),".")
     };
};

function doDecs(w,raw){
  var ds=getn("denom",w),nn=getn("numer",w)[0];
  for(var d=ds[0];d<=ds[1];d++)
     {var F=ratsimp(nn,d);       
      put(w,F.num,'/',F.den," = ",(raw?putrawdecs:putdecs)(w,F.num,F.den)) }
};
function stripspace(s){ 
  if(typeof s != "string")s=s.toString();
  return s.replace(/\s/g,"")
};
function nbdigs(n){ 
    if(typeof n!="string")ERR("nbdigs applied to non-string: "+n);
    return (n+" ").indexOf(" ")
};

function decToFrac(w){  
  var fxd=document["frac"+w].decf.value,  rpt=document["frac"+w].decrpt.value,F;
  fxd = stripspace(fxd);  rpt = stripspace(rpt);
  if(fxd.match(/[^0-9]/)!=null)
      {if(document["frac"+w].decf.value.indexOf(".")!=-1)
          ERR("Only give the part of the number AFTER the decimal point (the fractional part).");
        else ERR("The fixed part must be only digits")
      };
  if(rpt.match(/[^0-9]/)!=null)ERR("The repeating part must be only igits");
  if(fxd=="" && rpt=="") ERR("To use this button, first type in a decimal number to be converted to a fraction .");
  isINT(fxd,"FIXED"); isINT(rpt,"RECURRING");
  if(rpt=="") {F=ratsimp(fxd,Math.pow(10, nbdigs(fxd)))}
  else { var rexp=nbdigs(rpt),             fexp=nbdigs(fxd);  
         if(fxd=="")fxd='0';         
         F=ratsimp(add(mul(fxd,(Math.pow(10,rexp)-1)),parseInt(rpt,10)),
                   mul(Math.pow(10,fexp),(Math.pow(10,rexp)-1)))
     };  
  document["frac"+w].Dnumer.value=F.num;  document["frac"+w].Ddenom.value=F.den;
  put(w,"0."+document["frac"+w].decf.value+(document["frac"+w].decrpt.value==""?"":pstart+document["frac"+w].decrpt.value+pend)+"="
      +F.num+"/"+F.den);
};

function clearDecToFrac(w,x){ 
  document["frac"+w].Dnumer.value="";document["frac"+w].Ddenom.value="";
  if(arguments.length>1){document["frac"+w].decf.value=""; document["frac"+w].decrpt.value=""}
};

function selectfrac(w){
  if(document["frac"+w].egs.selectedIndex>0)
    {var nd=document["frac"+w].egs[document["frac"+w].egs.selectedIndex].value; 
     var nd="document.frac"+w+".numer.value="+nd.replace(",",";document.frac"+w+".denom.value="); 
     eval(nd)
    }
};


// -------------------------  Farey Fractions and Stern-Brocot Tree -----------
function intdiv(a,b){  // floor(a/b)
   return Math.round((a-a%b)/b)};
function fnextRAT(r){halt('not implemented!')}

var fseq=new Array();

function fseqFAREY(maxd){var p; //GLOBAL fseq
  fseq[1]=new RAT(1,maxd);
  for(var i=2;fseq[i-1].top<fseq[i-1].bot;i++)
  { p=intdiv( fseq[i-2].bot+maxd , fseq[i-1].bot );
    fseq[i]=new RAT(p*fseq[i-1].top-fseq[i-2].top,
                    p*fseq[i-1].bot-fseq[i-2].bot)
   //alert(i+"="+fseq[i])
}  };

function fseqsbtfillin(f1,f2,rowlev,lev){
  var f=new RAT(f1.top+f2.top,f1.bot+f2.bot);
  if(rowlev==lev){fseq[fseq.length]=f;fseq[fseq.length]=f2;return};
  fseqsbtfillin(f1,f,rowlev+1,lev);fseqsbtfillin(f,f2,rowlev+1,lev)
};

function fseqsbtree(level){
  if(level==0){fseq[1]=new RAT(1,1);return};
  fseqsbtfillin(new RAT(0,1),new RAT(1,0),1,level);
}

function ff(maxd,ct,which,disp){var p,q;
  //alert("ff "+maxd+" "+which);
  if(arguments.length<2)ct=false;
  if(arguments.disp<4)disp="n/d";
  if(maxd<1 || !isInt(maxd))
   {if(which=="farey")
         halt('The order (maximum denominator) must be at least 1')
    else halt("The level must be a whole number")};
 
 fseq[0]=new RAT(0,1);fseq.length=1;
  switch(which){
  case "farey":fseqFAREY(maxd);break;
  case "sbt":  fseqsbtree(maxd);break;
  };
  var s=(disp=="top"?"Numerators of ":disp=="bot"?"Denominators of ":"")
         +(which=="farey"?"Farey series of order "
          :which=="sbt"?"Stern-Brocot tree at level ":"")+maxd+": ";
  if(!ct)
  { s=s+"<br>";
    if(disp=="n/d")s=s+"0/1, "+fseq.slice(1).join(', ')
    else {s=s+(disp=="top"?0:1)+", ";
        for(var i=1;i<fseq.length-1;i++)s=s+fseq[i][disp]+", ";
        s=s+"1"
        };
        s=s+"<br>"
  };
  s=s+fseq.length+" fractions";
  putmsg(s);
};   

function LRpath(t,b){
 // alert("LR path for "+Rat);
  var path="",Lt=0,Lb=1,Mt=1,Mb=1,Rt=1,Rb=0,plen=0;
  while(t!=Mt||b!=Mb)
  { // if(t*Mb<b*Mt)
      if(t/b<Mt/Mb)
                  {Rt=Mt;Rb=Mb;path=path+"L"} //RATis(Rat,"<",Med)
      else        {Lt=Mt;Lb=Mb;path=path+"R"};
    plen++;
    Mt=Lt+Rt;Mb=Lb+Rb;
   // putmsg(path+": "+Mt+"/"+Mb);
    if(! isInt(Mt) || !isInt(Mb) )
       {putmsg("!! overflow !!");
        halt("The numbers in the fractions have become too large for accurate computation")};
    if(plen>500)halt("The path has become too long (>"+500+" in length)");
  };
  return path
};

function RATfrompath(LRstr){LRstr=LRstr.toUpperCase();
  //alert("Fract for path "+LRstr);
  var LRind=0,Lt=0,Lb=1,Mt=1,Mb=1,Rt=1,Rb=0;
  while(LRind<LRstr.length)
  { if(LRstr.charAt(LRind)=="L")
         {Rt=Mt;Rb=Mb;;}
    else {Lt=Mt;Lb=Mb};
    LRind++;
    if( !isInt(Lt+Rt) || !isInt(Lb+Rb) )
       halt("The fractions has become too big for this Calculator");
    
    Mt=Lt+Rt;Mb=Lb+Rb;
  };
  return [Mt,Mb]
};