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|
(* file exemples/ocaml/pi.ml: compute some digits of pi
*-----------------------------------------------------------------------+
| Copyright 2005-2006, Michel Quercia (michel.quercia@prepas.org) |
| |
| This file is part of Numerix. Numerix is free software; you can |
| redistribute it and/or modify it under the terms of the GNU Lesser |
| General Public License as published by the Free Software Foundation; |
| either version 2.1 of the License, or (at your option) any later |
| version. |
| |
| The Numerix Library is distributed in the hope that it will be |
| useful, but WITHOUT ANY WARRANTY; without even the implied warranty |
| of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU MP Library; see the file COPYING. If not, |
| write to the Free Software Foundation, Inc., 59 Temple Place - |
| Suite 330, Boston, MA 02111-1307, USA. |
+-----------------------------------------------------------------------+
| |
| Calcul de Pi, formule de Ramanujan |
| |
+-----------------------------------------------------------------------*)
(* cf. "The Caml Numbers Reference Manual", Inria, RT-0141 *)
(* annexe A, pp. 115 et suivantes. *)
open Numerix
open Printf
module Main(E:Int_type) = struct
module I = Infixes(E)
(* les 1000 premiers chiffres de pi pour contrle *)
let true_pi = "\
31415926535897932384626433832795028841971693993751\
05820974944592307816406286208998628034825342117067\
98214808651328230664709384460955058223172535940812\
84811174502841027019385211055596446229489549303819\
64428810975665933446128475648233786783165271201909\
14564856692346034861045432664821339360726024914127\
37245870066063155881748815209209628292540917153643\
67892590360011330530548820466521384146951941511609\
43305727036575959195309218611738193261179310511854\
80744623799627495673518857527248912279381830119491\
29833673362440656643086021394946395224737190702179\
86094370277053921717629317675238467481846766940513\
20005681271452635608277857713427577896091736371787\
21468440901224953430146549585371050792279689258923\
54201995611212902196086403441815981362977477130996\
05187072113499999983729780499510597317328160963185\
95024459455346908302642522308253344685035261931188\
17101000313783875288658753320838142061717766914730\
35982534904287554687311595628638823537875937519577\
81857780532171226806613001927876611195909216420198"
(* Affichage par tranches de 5 chiffres, lignes de 10 tranches *)
let pretty_print s i skip =
let j = ref i in
while !j < String.length(s) do
print_char s.[!j];
j := !j + 1;
if (!j-i) mod 250 = 0 then print_string "\n\n"
else if (!j-i) mod 50 = 0 then print_string "\n"
else if (!j-i) mod 10 = 0 then print_string " "
else if (!j-i) mod 5 = 0 then print_string " ";
if skip && ((!j-i) mod 50 = 0) then begin
let k = (String.length(s) - !j)/50 - 1 in
if k > 0 then begin
printf "... (%d lines omitted)\n" k;
j := !j + 50*k
end;
end;
done;
if (String.length(s)-1-i) mod 50 <> 49 then print_string "\n"
(* +----------------------+
| somme dichotomique |
+----------------------+ *)
open E
open I
let somme prec =
(* constantes *)
let cinq = of_int 5
and a = of_int 13591409
and b = of_int 545140134
and c = ((of_int 320160) ^^ 3) /. 3
and c0 = of_int 53360
in
(* tat du calcul :
p = index srie
alpha = 2p+1
beta = 6p+1
gamma = 6p+5
delta = c*p^3
eps = a + b*p
*)
(* calcule et retranche les termes de rangs p et p+1 *)
let calc2 (p,alpha,beta,gamma,delta,eps) =
let ma = (alpha ** beta) ** gamma in
let mb = delta in
let ms = eps in
let p = p +. 1 in
let alpha = alpha +. 2 in
let beta = beta +. 6 in
let gamma = gamma +. 6 in
let delta = sqr(p) ** p ** c in
let eps = eps ++ b in
let ms = delta ** ms -- ma ** eps in
let ma = (alpha ** beta ** gamma)** ma in
let mb = mb ** delta in
let p = p +. 1 in
let alpha = alpha +. 2 in
let beta = beta +. 6 in
let gamma = gamma +. 6 in
let delta = sqr(p) ** p ** c in
let eps = eps ++ b in
(ma,mb,ms), (p,alpha,beta,gamma,delta,eps) in
(* calcule et additionne 2*k termes *)
let rec calc k etat =
if k = 1 then calc2 etat
else let (a0, b0, s0), etat = calc (k/2) etat in
let (a1, b1, s1), etat = calc (k - k/2) etat in
(a0**a1, b0**b1, a0**s1 ++ b1**s0), etat
in
(* lance les calculs *)
let k = (prec + 197)/94 in
let etat = (zero, one, one, cinq, c0, a) in
let (a,b,s),_ = calc k etat in (b,s)
(* +--------------------------------------+
| calcule pi avec digits+2 dcimales |
+--------------------------------------+ *)
let pi digits pgcd prt skip debug test cmd =
if debug then chrono("module = " ^ name());
(* p5 <- 5^(digits+2) *)
let p5 = 5 ^. (digits+2) in
if debug then chrono "puiss-5";
(* rac <- floor( sqrt(640320) * 10^(digits+2) ) *)
let rac = sqrt((sqr(p5) *. 640320) << (2*digits + 4)) in
if debug then chrono "sqrt";
(* num/den <- somme de la srie env. 10^(-digits-2) prs *)
let prec = nbits(p5) + digits in
let (num,den) = somme prec in
if debug then chrono(sprintf "srie lb=%d" (nbits num));
(* simplifie la fraction si demand (ceci ne vaut pas le coup, le
temps de calcul du pgcd est trs suprieur au temps de calcul
de la division sans simplification) *)
let num,den = if pgcd then begin
let _,_,_,num,den = cfrac num den in
if debug then chrono(sprintf "pgcd lb=%d" (nbits num));
num,den
end else num,den in
(* pi <- sqrt(640320)*num/den * 10^digits+2) *)
let pi = (rac**num)//den in
if debug then chrono "quotient";
(* affiche le rsultat *)
if prt then begin
let s = string_of pi in
if debug then chrono "conversion";
print_char s.[0];
print_string ".\n";
pretty_print s 1 skip;
end
(* contrle *)
else if test then begin
let s = string_of pi in
let l1 = String.length s
and l2 = String.length true_pi in
let l = min l1 l2 in
let s1 = String.sub s 0 l
and s2 = String.sub true_pi 0 l in
if s1 = s2 then printf "%s\t%s\ttest ok\n" cmd (name())
else begin
printf "error in the %s %s test, value computed:\n" cmd (name());
for i=0 to l-1 do
printf "%c" s.[i];
if (i mod 50 = 49) then printf "\n"
done;
if l mod 50 > 0 then printf "\n"
end
end
(* +-------------------------+
| Interface utilisateur |
+-------------------------+ *)
let main arglist =
let digits = ref 100
and pgcd = ref false
and print = ref true
and skip = ref false
and debug = ref false
and test = ref false
and help = ref false in
let rec parse = function
| "-h"::s -> help := true
| "-d"::s -> debug := true; parse s
| "-noprint"::s -> print := false; parse s
| "-skip"::s -> skip := true; parse s
| "-gcd"::s -> pgcd := true; parse s;
| "-test"::s -> digits := 1000;
print := false;
skip := false;
debug := false;
pgcd := false;
test := true
| d::s -> digits := int_of_string d; parse s
| [] -> ()
in parse (List.tl arglist);
if !help
then printf "usage: %s <digits> [-d] [-noprint] [-skip] [-gcd]\n" (List.hd arglist)
else pi (!digits-2) !pgcd !print !skip !debug !test (List.hd arglist);
flush stdout
end
let _ = let module S = Start(Main) in S.start()
|
