79 lines
1.7 KiB
OCaml
79 lines
1.7 KiB
OCaml
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(* Pi digits computed with the sreaming algorithm given on pages 4, 6
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& 7 of "Unbounded Spigot Algorithms for the Digits of Pi", Jeremy
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Gibbons, August 2004. *)
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open Printf;;
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open Big_int;;
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let ( !$ ) = Big_int.big_int_of_int
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and ( +$ ) = Big_int.add_big_int
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and ( *$ ) = Big_int.mult_big_int
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and ( =$ ) = Big_int.eq_big_int
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;;
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let zero = Big_int.zero_big_int
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and one = Big_int.unit_big_int
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and three = !$ 3
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and four = !$ 4
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and ten = !$ 10
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and neg_ten = !$(-10)
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;;
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(* Linear Fractional (aka M=F6bius) Transformations *)
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module LFT = struct
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let floor_ev (q, r, s, t) x = div_big_int (q *$ x +$ r) (s *$ x +$ t);;
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let unit = (one, zero, zero, one);;
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let comp (q, r, s, t) (q', r', s', t') =
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(q *$ q' +$ r *$ s', q *$ r' +$ r *$ t',
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s *$ q' +$ t *$ s', s *$ r' +$ t *$ t')
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;;
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end
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;;
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let next z = LFT.floor_ev z three
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and safe z n = (n =$ LFT.floor_ev z four)
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and prod z n = LFT.comp (ten, neg_ten *$ n, zero, one) z
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and cons z k =
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let den = 2 * k + 1 in
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LFT.comp z (!$ k, !$(2 * den), zero, !$ den)
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;;
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let rec digit k z n row col =
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if n > 0 then
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let y = next z in
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if safe z y then
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if col = 10 then (
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let row = row + 10 in
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printf "\t:%i\n%s" row (string_of_big_int y);
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digit k (prod z y) (n - 1) row 1
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)
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else (
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print_string(string_of_big_int y);
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digit k (prod z y) (n - 1) row (col + 1)
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)
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else digit (k + 1) (cons z k) n row col
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else
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printf "%*s\t:%i\n" (10 - col) "" (row + col)
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;;
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let digits n = digit 1 LFT.unit n 0 0
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;;
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let usage () =
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prerr_endline "Usage: pi_big_int <number of digits to compute for pi>";
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exit 2
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;;
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let main () =
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let args = Sys.argv in
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if Array.length args <> 2 then usage () else
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digits (int_of_string Sys.argv.(1))
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;;
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main ()
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;;
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