Re: [Caml-list] Divide and print with precision

[Marek Kubica <marek@xivilization.net>]

Hello Török,

Sorry, I somehow missed your reply.

On Wed, 15 Oct 2014 23:25:49 +0300
Török Edwin <edwin+ml-ocaml@etorok.net> wrote:

> This uses Gmp.default_prec (120 bits by default) for the conversion.
> 
> So if you want to use Gmp.F I think you have to specify the ~prec
> otherwise you might loose digits in the znum or zden conversion
> already:
> 
>   let znum = Gmp.F.from_string_prec_base ~prec ~base:10 (Z.to_string
> num) in let zden = Gmp.F.from_string_prec_base ~prec ~base:10
> (Z.to_string den) in let f = Gmp.F.div_prec ~prec znum zden in
>   Gmp.F.to_string_base_digits ~base:10 ~digits:0 f
> 
> Another possibility is to use from_q_prec. I would've used
> Gmp.Q.from_q_prec except for some odd reason it takes a Z.t instead
> of a Q.t, so here is the code that uses Gmp.FR.from_q_prec:
> 
> let string_of_q_prec num den =
>   let znum = Gmp.Z.from_string (Z.to_string num) in
>   let zden = Gmp.Z.from_string (Z.to_string den) in
>   let f = Gmp.FR.from_q_prec ~prec ~mode (Gmp.Q.from_zs znum zden) in
>   Gmp.FR.to_string_base_digits ~mode ~base:10 ~digits:0 f

Thank you, that worked and outputs a lot of digits which is "good
enough" for me. Great!

For the record, here's the complete program:

let prec = 1_000_000
let max_n = 205_211
let mode = Gmp.GMP_RNDN

let euler_fraction n =
  let open Z in
  let numerator = ref one in
  let denominator = ref one in
  for i = 1 to n do
    numerator := succ (!numerator * (of_int i));
    denominator := (of_int i) * !denominator;
  done;
  (!numerator, !denominator)

let f () =
  let (num, den) = euler_fraction max_n in
  let znum = Gmp.Z.from_string @@ Z.to_string num in
  let zden = Gmp.Z.from_string @@ Z.to_string den in
  let euler = Gmp.FR.from_q_prec ~mode ~prec @@ Gmp.Q.from_zs znum zden
in
  print_endline @@ Gmp.FR.to_string_base_digits ~mode ~base:10
~digits:0 euler

let () = f ()

> I don't really like going through string to convert from Z.t to
> Gmp.Z.t, there ought to be a more efficient way.

Neither do I, but I suppose I'd need a C stub to take the Z.t value
(which if I understand Zarith correctly can be a GMP value, but for
small values isn't) and convert it into a Gmp.Z.t. But for such a
simple program and a constant amount of conversions, its not really
worth it.

regards,
Marek