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

["Török Edwin" <edwin+ml-ocaml@etorok.net>]

On 10/15/2014 12:22 PM, Marek Kubica wrote:
> Hello,
> 
> I've got this short program here:
> 
> let prec = 1_000_000

Do you mean this to be bits or digits?
AFAICT the ~prec in Gmp refers to bits.

> let max_n = 205_211
> let to_string = Gmp.F.to_string_base_digits ~base:10 ~digits:0
> 
> 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.F.from_string (Z.to_string num) in
>   let zden = Gmp.F.from_string (Z.to_string den) in

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

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.

There is also Num.approx_num_fix, but if you already use Zarith/Gmp you probably don't want that.

Best regards,
--Edwin