#!/usr/local/bin/bc -l

## Calculate the hyper-exponential Ackermann function

# There's not much point to this function as it's pretty much
# incalculable for most values... and burns CPU while it tries

define ack(x,y) {
  if (x==0)return(y+1)
  if (x==1)return(y+2)
  if (x==2)return(y+y+3)
  if (x==3)return(2^(y+3)-3)

  if (y==0)return(ack(x-1,1))
  return(ack(x-1,ack(x,y-1)))
}

k_l2 = l(2);
define ackz(x,y) {
  if (x<=0)return(y+1)
  if (x<=1)return(y+2)
  if (x<=2)return(y+y+3)
  if (x<=3)return(e(l2*(y+3))-3)

  if (y<=0)return(ack(x-1,1))
  return(ack(x-1,ack(x,y-1)))
}