ocaml/otherlibs/num/nat.mlp

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(***********************************************************************)
(* *)
(* Objective Caml *)
(* *)
(* Valerie Menissier-Morain, projet Cristal, INRIA Rocquencourt *)
(* *)
(* Copyright 1996 Institut National de Recherche en Informatique et *)
(* Automatique. Distributed only by permission. *)
(* *)
(***********************************************************************)
(* $Id$ *)
(*
#include "../../config/m.h"
*)
open Int_misc
type nat;;
external create_nat: int -> nat = "create_nat"
external set_to_zero_nat: nat -> int -> int -> unit = "set_to_zero_nat"
external blit_nat: nat -> int -> nat -> int -> int -> unit = "blit_nat"
external set_digit_nat: nat -> int -> int -> unit = "set_digit_nat"
external nth_digit_nat: nat -> int -> int = "nth_digit_nat"
external length_nat: nat -> int = "%array_length"
external num_digits_nat: nat -> int -> int -> int = "num_digits_nat"
external num_leading_zero_bits_in_digit: nat -> int -> int = "num_leading_zero_bits_in_digit"
external is_digit_int: nat -> int -> bool = "is_digit_int"
external is_digit_zero: nat -> int -> bool = "is_digit_zero"
external is_digit_normalized: nat -> int -> bool = "is_digit_normalized"
external is_digit_odd: nat -> int -> bool = "is_digit_odd"
external incr_nat: nat -> int -> int -> int -> int = "incr_nat"
external add_nat: nat -> int -> int -> nat -> int -> int -> int -> int = "add_nat" "add_nat_native"
external complement_nat: nat -> int -> int -> unit = "complement_nat"
external decr_nat: nat -> int -> int -> int -> int = "decr_nat"
external sub_nat: nat -> int -> int -> nat -> int -> int -> int -> int = "sub_nat" "sub_nat_native"
external mult_digit_nat: nat -> int -> int -> nat -> int -> int -> nat -> int -> int = "mult_digit_nat" "mult_digit_nat_native"
external mult_nat: nat -> int -> int -> nat -> int -> int -> nat -> int -> int -> int = "mult_nat" "mult_nat_native"
external shift_left_nat: nat -> int -> int -> nat -> int -> int -> unit = "shift_left_nat" "shift_left_nat_native"
external div_digit_nat: nat -> int -> nat -> int -> nat -> int -> int -> nat -> int -> unit = "div_digit_nat" "div_digit_nat_native"
external div_nat: nat -> int -> int -> nat -> int -> int -> unit = "div_nat" "div_nat_native"
external shift_right_nat: nat -> int -> int -> nat -> int -> int -> unit = "shift_right_nat" "shift_right_nat_native"
external compare_digits_nat: nat -> int -> nat -> int -> int = "compare_digits_nat"
external compare_nat: nat -> int -> int -> nat -> int -> int -> int = "compare_nat" "compare_nat_native"
external land_digit_nat: nat -> int -> nat -> int -> unit = "land_digit_nat"
external lor_digit_nat: nat -> int -> nat -> int -> unit = "lor_digit_nat"
external lxor_digit_nat: nat -> int -> nat -> int -> unit = "lxor_digit_nat"
#ifdef SIXTYFOUR
let length_of_digit = 64
#else
let length_of_digit = 32
#endif
let make_nat len =
if len < 0 then invalid_arg "make_nat" else
let res = create_nat len in set_to_zero_nat res 0 len; res
let copy_nat nat off_set length =
let res = create_nat (length) in
blit_nat res 0 nat off_set length;
res
let is_zero_nat n off len =
compare_nat (make_nat 1) 0 1 n off (num_digits_nat n off len) = 0
let is_nat_int nat off len =
num_digits_nat nat off len = 1 & is_digit_int nat off
let sys_int_of_nat nat off len =
if is_nat_int nat off len
then nth_digit_nat nat off
else failwith "int_of_nat"
let int_of_nat nat =
sys_int_of_nat nat 0 (length_nat nat)
let nat_of_int i =
if i < 0 then invalid_arg "nat_of_int" else
let res = make_nat 1 in
if i = 0 then res else begin set_digit_nat res 0 i; res end
let eq_nat nat1 off1 len1 nat2 off2 len2 =
compare_nat nat1 off1 (num_digits_nat nat1 off1 len1)
nat2 off2 (num_digits_nat nat2 off2 len2) = 0
and le_nat nat1 off1 len1 nat2 off2 len2 =
compare_nat nat1 off1 (num_digits_nat nat1 off1 len1)
nat2 off2 (num_digits_nat nat2 off2 len2) <= 0
and lt_nat nat1 off1 len1 nat2 off2 len2 =
compare_nat nat1 off1 (num_digits_nat nat1 off1 len1)
nat2 off2 (num_digits_nat nat2 off2 len2) < 0
and ge_nat nat1 off1 len1 nat2 off2 len2 =
compare_nat nat1 off1 (num_digits_nat nat1 off1 len1)
nat2 off2 (num_digits_nat nat2 off2 len2) >= 0
and gt_nat nat1 off1 len1 nat2 off2 len2 =
compare_nat nat1 off1 (num_digits_nat nat1 off1 len1)
nat2 off2 (num_digits_nat nat2 off2 len2) > 0
let square_nat nat1 off1 len1 nat2 off2 len2 =
let c = ref 0
and trash = make_nat 1 in
(* Double product *)
for i = 0 to len2 - 2 do
c := !c + mult_digit_nat
nat1
(succ (off1 + 2 * i))
(2 * (pred (len2 - i)))
nat2
(succ (off2 + i))
(pred (len2 - i))
nat2
(off2 + i)
done;
shift_left_nat nat1 0 len1 trash 0 1;
(* Square of digit *)
for i = 0 to len2 - 1 do
c := !c + mult_digit_nat
nat1
(off1 + 2 * i)
(len1 - 2 * i)
nat2
(off2 + i)
1
nat2
(off2 + i)
done;
!c
let gcd_int_nat i nat off len =
if i = 0 then 1 else
if is_nat_int nat off len then begin
set_digit_nat nat off (gcd_int (nth_digit_nat nat off) i); 0
end else begin
let len_copy = succ len in
let copy = create_nat len_copy
and quotient = create_nat 1
and remainder = create_nat 1 in
blit_nat copy 0 nat off len;
set_digit_nat copy len 0;
div_digit_nat quotient 0 remainder 0 copy 0 len_copy (nat_of_int i) 0;
set_digit_nat nat off (gcd_int (nth_digit_nat remainder 0) i);
0
end
let exchange r1 r2 =
let old1 = !r1 in r1 := !r2; r2 := old1
let gcd_nat nat1 off1 len1 nat2 off2 len2 =
if is_zero_nat nat1 off1 len1 then begin
blit_nat nat1 off1 nat2 off2 len2; len2
end else begin
let copy1 = ref (create_nat (succ len1))
and copy2 = ref (create_nat (succ len2)) in
blit_nat !copy1 0 nat1 off1 len1;
blit_nat !copy2 0 nat2 off2 len2;
set_digit_nat !copy1 len1 0;
set_digit_nat !copy2 len2 0;
if lt_nat !copy1 0 len1 !copy2 0 len2
then exchange copy1 copy2;
let real_len1 =
ref (num_digits_nat !copy1 0 (length_nat !copy1))
and real_len2 =
ref (num_digits_nat !copy2 0 (length_nat !copy2)) in
while not (is_zero_nat !copy2 0 !real_len2) do
set_digit_nat !copy1 !real_len1 0;
div_nat !copy1 0 (succ !real_len1) !copy2 0 !real_len2;
exchange copy1 copy2;
real_len1 := !real_len2;
real_len2 := num_digits_nat !copy2 0 !real_len2
done;
blit_nat nat1 off1 !copy1 0 !real_len1;
!real_len1
end
let sqrt_nat nat off len =
let size_copy = succ len in
let size_sqrt = len / 2 + len mod 2 in
let candidate = make_nat (size_sqrt)
and beginning = make_nat (size_sqrt) in
set_digit_nat candidate (size_sqrt - 1) 1;
shift_left_nat candidate (size_sqrt - 1) 1 beginning 0
(((if len mod 2 = 0 then 31 else 15) -
num_leading_zero_bits_in_digit nat (off + len - 1)) / 2);
let size_aux = size_copy - size_sqrt in
let copy = create_nat size_copy in
let aux = make_nat size_aux in
set_digit_nat copy len 0;
blit_nat copy 0 nat off len;
div_nat copy 0 size_copy candidate 0 size_sqrt;
blit_nat aux 0 copy size_sqrt size_aux;
add_nat aux 0 size_aux candidate 0 (num_digits_nat candidate 0 size_sqrt) 0;
shift_right_nat aux 0 size_aux beginning 0 1;
while not
(eq_nat aux 0 (num_digits_nat aux 0 size_aux)
candidate 0 (num_digits_nat candidate 0 size_sqrt))
do
blit_nat candidate 0 aux 0 size_aux;
set_digit_nat copy len 0;
blit_nat copy 0 nat off len;
div_nat copy 0 size_copy candidate 0 size_sqrt;
blit_nat aux 0 copy size_sqrt size_aux;
add_nat aux 0 size_aux candidate 0 (num_digits_nat candidate 0 size_sqrt) 0;
shift_right_nat aux 0 size_aux beginning 0 1
done;
candidate
let power_base_max = make_nat 2
#ifdef SIXTYFOUR
let _ =
set_digit_nat power_base_max 0 1000000000000000000;
mult_digit_nat power_base_max 0 2
power_base_max 0 1 (nat_of_int 9) 0
let pmax = 19
#else
let _ = set_digit_nat power_base_max 0 1000000000
let pmax = 9
#endif
(* Nat temporaries *)
let a_2 = make_nat 2
and a_1 = make_nat 1
and b_2 = make_nat 2
#ifdef SIXTYFOUR
let max_superscript_10_power_in_int = 18
let max_power_10_power_in_int = nat_of_int 1000000000000000000
#else
let max_superscript_10_power_in_int = 9
let max_power_10_power_in_int = nat_of_int 1000000000
#endif
let raw_string_of_digit nat off =
if is_nat_int nat off 1
then begin string_of_int (nth_digit_nat nat off) end
else begin
blit_nat b_2 0 nat off 1;
div_digit_nat a_2 0 a_1 0 b_2 0 2 max_power_10_power_in_int 0;
let leading_digits = nth_digit_nat a_2 0
and s1 = string_of_int (nth_digit_nat a_1 0) in
let len = String.length s1 in
if leading_digits < 10 then begin
let result = String.make (max_superscript_10_power_in_int+1) '0' in
String.set result 0
(Char.chr (48 + leading_digits));
String.blit s1 0
result (String.length result - len) len;
result
end else begin
let result = String.make (max_superscript_10_power_in_int+2) '0' in
String.blit (string_of_int leading_digits) 0 result 0 2;
String.blit s1 0
result (String.length result - len) len;
result
end
end
(* XL: suppression de string_of_digit et de sys_string_of_digit.
La copie est de toute facon faite dans string_of_nat, qui est le
seul point d entree public dans ce code. *)
(******
let sys_string_of_digit nat off =
let s = raw_string_of_digit nat off in
let result = String.create (String.length s) in
String.blit s 0 result 0 (String.length s);
s
let string_of_digit nat =
sys_string_of_digit nat 0
*******)
let digits = "0123456789ABCDEF"
(*
make_power_base affecte power_base des puissances successives de base a
partir de la puissance 1-ieme.
A la fin de la boucle i-1 est la plus grande puissance de la base qui tient
sur un seul digit et j est la plus grande puissance de la base qui tient
sur un int.
*)
let make_power_base base power_base =
let i = ref 0
and j = ref 0 in
set_digit_nat power_base 0 base;
while incr i; is_digit_zero power_base !i do
mult_digit_nat power_base !i 2
power_base (pred !i) 1
power_base 0
done;
while !j <= !i & is_digit_int power_base !j do incr j done;
(!i - 2, !j)
(*
int_to_string place la representation de l entier int en base base
dans la chaine s en le rangeant de la fin indiquee par pos vers le
debut, sur times places et affecte a pos sa nouvelle valeur.
*)
let int_to_string int s pos_ref base times =
let i = ref int
and j = ref times in
while ((!i != 0) or (!j != 0)) & (!pos_ref != -1) do
String.set s !pos_ref (String.get digits (!i mod base));
decr pos_ref;
decr j;
i := !i / base
done
(* XL: suppression de adjust_string *)
let power_base_int base i =
if i = 0 then
nat_of_int 1
else if i < 0 then
invalid_arg "power_base_int"
else begin
let power_base = make_nat (succ length_of_digit) in
let (pmax, pint) = make_power_base base power_base in
let n = i / (succ pmax)
and rem = i mod (succ pmax) in
if n > 0 then begin
let newn =
if i = biggest_int then n else (succ n) in
let res = make_nat newn
and res2 = make_nat newn
and l = num_bits_int n - 2 in
let p = ref (1 lsl l) in
blit_nat res 0 power_base pmax 1;
for i = l downto 0 do
let len = num_digits_nat res 0 newn in
let len2 = min n (2 * len) in
let succ_len2 = succ len2 in
square_nat res2 0 len2 res 0 len;
if n land !p > 0 then begin
set_to_zero_nat res 0 len;
mult_digit_nat res 0 succ_len2
res2 0 len2
power_base pmax;
()
end else
blit_nat res 0 res2 0 len2;
set_to_zero_nat res2 0 len2;
p := !p lsr 1
done;
if rem > 0 then begin
mult_digit_nat res2 0 newn
res 0 n power_base (pred rem);
res2
end else res
end else
copy_nat power_base (pred rem) 1
end
(* the ith element (i >= 2) of num_digits_max_vector is :
| |
| biggest_string_length * log (i) |
| ------------------------------- | + 1
| length_of_digit * log (2) |
-- --
*)
(* XL: ai specialise le code d origine a length_of_digit = 32. *)
(* Puis suppression (inutile?) *)
(******
let num_digits_max_vector =
[|0; 0; 1024; 1623; 2048; 2378; 2647; 2875; 3072; 3246; 3402;
3543; 3671; 3789; 3899; 4001; 4096|]
let num_digits_max_vector =
match length_of_digit with
16 -> [|0; 0; 2048; 3246; 4096; 4755; 5294; 5749; 6144; 6492; 6803;
7085; 7342; 7578; 7797; 8001; 8192|]
(* If really exotic machines !!!!
| 17 -> [|0; 0; 1928; 3055; 3855; 4476; 4983; 5411; 5783; 6110; 6403;
6668; 6910; 7133; 7339; 7530; 7710|]
| 18 -> [|0; 0; 1821; 2886; 3641; 4227; 4706; 5111; 5461; 5771; 6047;
6298; 6526; 6736; 6931; 7112; 7282|]
| 19 -> [|0; 0; 1725; 2734; 3449; 4005; 4458; 4842; 5174; 5467; 5729;
5966; 6183; 6382; 6566; 6738; 6898|]
| 20 -> [|0; 0; 1639; 2597; 3277; 3804; 4235; 4600; 4915; 5194; 5443;
5668; 5874; 6063; 6238; 6401; 6553|]
| 21 -> [|0; 0; 1561; 2473; 3121; 3623; 4034; 4381; 4681; 4946; 5183;
5398; 5594; 5774; 5941; 6096; 6241|]
| 22 -> [|0; 0; 1490; 2361; 2979; 3459; 3850; 4182; 4468; 4722; 4948;
5153; 5340; 5512; 5671; 5819; 5958|]
| 23 -> [|0; 0; 1425; 2258; 2850; 3308; 3683; 4000; 4274; 4516; 4733;
4929; 5108; 5272; 5424; 5566; 5699|]
| 24 -> [|0; 0; 1366; 2164; 2731; 3170; 3530; 3833; 4096; 4328; 4536;
4723; 4895; 5052; 5198; 5334; 5461|]
| 25 -> [|0; 0; 1311; 2078; 2622; 3044; 3388; 3680; 3932; 4155; 4354;
4534; 4699; 4850; 4990; 5121; 5243|]
| 26 -> [|0; 0; 1261; 1998; 2521; 2927; 3258; 3538; 3781; 3995; 4187;
4360; 4518; 4664; 4798; 4924; 5041|]
| 27 -> [|0; 0; 1214; 1924; 2428; 2818; 3137; 3407; 3641; 3847; 4032;
4199; 4351; 4491; 4621; 4742; 4855|]
| 28 -> [|0; 0; 1171; 1855; 2341; 2718; 3025; 3286; 3511; 3710; 3888;
4049; 4196; 4331; 4456; 4572; 4681|]
| 29 -> [|0; 0; 1130; 1791; 2260; 2624; 2921; 3172; 3390; 3582; 3754;
3909; 4051; 4181; 4302; 4415; 4520|]
| 30 -> [|0; 0; 1093; 1732; 2185; 2536; 2824; 3067; 3277; 3463; 3629;
3779; 3916; 4042; 4159; 4267; 4369|]
| 31 -> [|0; 0; 1057; 1676; 2114; 2455; 2733; 2968; 3171; 3351; 3512;
3657; 3790; 3912; 4025; 4130; 4228|]
*)
| 32 -> [|0; 0; 1024; 1623; 2048; 2378; 2647; 2875; 3072; 3246; 3402;
3543; 3671; 3789; 3899; 4001; 4096|]
| n -> failwith "num_digits_max_vector"
******)
(* XL: suppression de string_list_of_nat *)
let unadjusted_string_of_nat nat off len_nat =
let len = num_digits_nat nat off len_nat in
if len = 1 then
raw_string_of_digit nat off
else
let len_copy = ref (succ len) in
let copy1 = create_nat !len_copy
and copy2 = make_nat !len_copy
and rest_digit = make_nat 2 in
if len > biggest_int / (succ pmax)
then failwith "number too long"
else let len_s = (succ pmax) * len in
let s = String.make len_s '0'
and pos_ref = ref len_s in
len_copy := pred !len_copy;
blit_nat copy1 0 nat off len;
set_digit_nat copy1 len 0;
while not (is_zero_nat copy1 0 !len_copy) do
div_digit_nat copy2 0
rest_digit 0
copy1 0 (succ !len_copy)
power_base_max 0;
let str = raw_string_of_digit rest_digit 0 in
String.blit str 0
s (!pos_ref - String.length str)
(String.length str);
(* XL: il y avait pmax a la place de String.length str
mais ca ne marche pas avec le blit de Caml Light,
qui ne verifie pas les debordements *)
pos_ref := !pos_ref - pmax;
len_copy := num_digits_nat copy2 0 !len_copy;
blit_nat copy1 0 copy2 0 !len_copy;
set_digit_nat copy1 !len_copy 0
done;
s
let string_of_nat nat =
let s = unadjusted_string_of_nat nat 0 (length_nat nat)
and index = ref 0 in
begin try
for i = 0 to String.length s - 2 do
if String.get s i <> '0' then (index:= i; raise Exit)
done
with Exit -> ()
end;
String.sub s !index (String.length s - !index)
(* XL: suppression de sys_string_of_nat *)
(* XL: suppression de debug_string_nat *)
let base_digit_of_char c base =
let n = Char.code c in
if n >= 48 & n <= 47 + min base 10 then n - 48
else if n >= 65 & n <= 65 + base - 11 then n - 55
else failwith "invalid digit"
(*
La sous-chaine (s, off, len) represente un nat en base base que
on determine ici
*)
let sys_nat_of_string base s off len =
let power_base = make_nat (succ length_of_digit) in
let (pmax, pint) = make_power_base base power_base in
let new_len = ref (1 + len / (pmax + 1))
and current_len = ref 1 in
let possible_len = ref (min 2 !new_len) in
let nat1 = make_nat !new_len
and nat2 = make_nat !new_len
and digits_read = ref 0
and bound = off + len - 1
and int = ref 0 in
for i = off to bound do
(*
on lit pint (au maximum) chiffres, on en fait un int
et on l integre au nombre
*)
let c = String.get s i in
begin match c with
' ' | '\t' | '\n' | '\r' | '\\' -> ()
| _ -> int := !int * base + base_digit_of_char c base;
incr digits_read
end;
if (!digits_read = pint or i = bound) & not (!digits_read = 0) then
begin
set_digit_nat nat1 0 !int;
for j = 1 to !current_len do
set_digit_nat nat1 j 0
done;
mult_digit_nat nat1 0 !possible_len
nat2 0 !current_len
power_base (pred !digits_read);
blit_nat nat2 0 nat1 0 !possible_len;
current_len := num_digits_nat nat1 0 !possible_len;
possible_len := min !new_len (succ !current_len);
int := 0;
digits_read := 0
end
done;
(*
On recadre le nat
*)
let nat = create_nat !current_len in
blit_nat nat 0 nat1 0 !current_len;
nat
let nat_of_string s = sys_nat_of_string 10 s 0 (String.length s)
let float_of_nat nat = float_of_string(string_of_nat nat)