# pdhi(x) - Pan Digital Halving Index
# Returns how many times x must be divided by 2 before
# the result contains all digits from 0 to 9 (if ibase = 10).
# e.g. 3339 -> 1669.5 -> 834.75 -> 417.375 ->
#      208.6875 -> 104.34375 -> 52.171875 ->
#      26.0859375 -> 13.04296875, i.e. 8 times

# Uses ibase as the base for divisions (usually 10)

define pdhi(x) {
  auto d[],xi,xf,c,r,pdhi,lim,i;
  if(x<0)x*=-1
  c=1;pdhi=-1;lim=int(10/ibase+3)*scale
  while(c){
    pdhi+=1
    xi=int(x);xf=x-xi
    while(xi){
      r=int(xi/ibase)
      d[xi-ibase*r]=1
      xi=r
    }
    for(i=lim ; i && xf ; i--){
    #while(xf){
      xf*=ibase
      r=int(xf)
      d[r]=1
      xf-=r
    }
    c=ibase
    for(r=0;r<ibase;r++){c-=d[r];d[r]=0}
    x/=2
  }
  return pdhi;
}

# pdmi(x, m) - Pan Digital Multiplying Index
# Returns how many times x must be multiplied by m before
# the result contains all digits from 0 to 9 (if ibase = 10).
# e.g. pdmi(3339,0.5) -> 1669.5 -> 834.75 -> 417.375 ->
#      208.6875 -> 104.34375 -> 52.171875 ->
#      26.0859375 -> 13.04296875, i.e. 8 times

# Uses ibase as the base for divisions (usually 10)

define pdmi(x,m) {
  auto d[],xi,xf,c,r,pdmi,lim,i;
  if(x<0)x*=-1
  c=1;pdmi=-1;lim=int(10/ibase+3)*scale
  while(c){
    pdmi+=1
    xi=int(x);xf=x-xi
    while(xi){
      r=int(xi/ibase)
      d[xi-ibase*r]=1
      xi=r
    }
    for(i=lim ; i && xf ; i--){
    #while(xf){
      xf*=ibase
      r=int(xf)
      d[r]=1
      xf-=r
    }
    c=ibase
    for(r=0;r<ibase;r++){c-=d[r];d[r]=0}
    x*=m
  }
  return pdmi;
}