using Printf

"""
  calc precision backwards from answer
"""
function calcprecision(value::BigFloat)
  max(exponent(value) + 16, 64)  # 16 digit = margin, 64 digit = minimum precision
end

# initial value of a[0]
a0 = 0

const DIR = "./csv"
fpath_old = ""

# mkdir
mkpath(DIR)

# loop of a0
while true

  global a0, fpath_old

  a0 += 1

  # output file name
  million = div(a0, 1000000) * 1000000
  fpath = @sprintf("%s/%d-%d.csv", DIR, million, million + 1000000 - 1)
  if fpath != fpath_old
    open(fpath, "w") do f
      # header
      println(f, "a[0],steps to reach 1,argmax,max-term")
    end
    fpath_old = fpath
  end

  # initial values
  a_k = BigFloat(a0)
  amax = a_k
  kmax = 0
  k = 0
  
  # initial precision
  precision = calcprecision( a_k )
  setprecision(precision)
  
  # loop of k
  while a_k > 1
  
    k += 1
  
    while true
  
      # odd
      if mod(a_k,2) == 0
        a_kpp = floor( sqrt(a_k) )
        
      # even
      else
        a_kpp = floor( a_k * sqrt(a_k) )
        #a_kpp = floor( a_k^(1.5))
  
      end
  
      # increase precision and retry
      if calcprecision( a_kpp ) > precision
        renewprecision = true
        retry = true
  
      # decrease precision
      elseif calcprecision( a_kpp ) < precision / 10
        renewprecision = true
        retry = false
  
      # keep
      else
        renewprecision = false
        retry = false
  
      end
  
      # setprecision
      if renewprecision
        precision = calcprecision( a_kpp )
        setprecision(precision)
      end
  
      # break
      if ! retry
        a_k = a_kpp
        break
      end
  
    end
  
    # update max-term
    if a_k > amax
      amax = a_k
      kmax = k
    end
  
  end

  # output
  open(fpath, "a") do f

    # less than 100 digit -> write as integer
    if exponent(amax) * log10(2) <= 100
      @printf(f, "%d,%d,%d,%d\n", a0, k, kmax, amax)

    # write as float
    else
      @printf(f, "%d,%d,%d,%.5e\n", a0, k, kmax, amax)

    end

  end

end