(* Pi digits computed with the sreaming algorithm given on pages 4, 6
   & 7 of "Unbounded Spigot Algorithms for the Digits of Pi", Jeremy
   Gibbons, August 2004.  *)

open Printf
open Num

let zero = num_of_int 0
and one  = num_of_int 1
and three = num_of_int 3
and four = num_of_int 4
and ten  = num_of_int 10
and neg_ten = num_of_int(-10)

(* Linear Fractional Transformation *)
module LFT =
struct
  let floor_ev (q,r,s,t) x = quo_num (q */ x +/ r) (s */ x +/ t)

  let unit = (one, zero, zero, one)

  let comp (q,r,s,t) (q',r',s',t') =
    (q */ q' +/ r */ s',  q */ r' +/ r */ t',
     s */ q' +/ t */ s',  s */ r' +/ t */ t')
end

let next z = LFT.floor_ev z three
and safe z n = (n =/ LFT.floor_ev z four)
and prod z n = LFT.comp (ten, neg_ten */ n, zero, one) z
and cons z k =
  let den = 2*k+1 in
  LFT.comp z (num_of_int k, num_of_int(2*den), zero, num_of_int den)

let rec digit k z n row col =
  if n > 0 then
    let y = next z in
    if safe z y then
      if col = 10 then (
	let row = row + 10 in
	printf "\t:%i\n%s" row (string_of_num y);
	digit k (prod z y) (n-1) row 1
      )
      else (
	print_string(string_of_num y);
	digit k (prod z y) (n-1) row (col+1)
      )
    else digit (k+1) (cons z k) n row col
  else
    printf "%*s\t:%i\n" (10 - col) "" (row + col)

let digits n = digit 1 LFT.unit n 0 0

let () =
  digits(int_of_string Sys.argv.(1))