Retour en arriere sur le precedent commit
git-svn-id: http://caml.inria.fr/svn/ocaml/trunk@4845 f963ae5c-01c2-4b8c-9fe0-0dff7051ff02master
Pierre Weis
parent
75ef6798a9
commit
00d14a727a
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@ -13,51 +13,45 @@
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(* $Id$ *)
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open Int_misc;;
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open Nat;;
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open Int_misc
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open Nat
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type big_int =
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{ sign : int;
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abs_value : nat }
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;;
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(* Sign of a big_int *)
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let sign_big_int bi = bi.sign;;
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let create_big_int sign nat =
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if sign == 1 || sign == -1 ||
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(sign == 0 &&
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if sign = 1 || sign = -1 ||
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(sign = 0 &&
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is_zero_nat nat 0 (num_digits_nat nat 0 (length_nat nat)))
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then { sign = sign;
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abs_value = nat }
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else invalid_arg "create_big_int"
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;;
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(* Sign of a big_int *)
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let sign_big_int bi = bi.sign
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let zero_big_int =
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{ sign = 0;
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abs_value = make_nat 1 }
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;;
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let unit_big_int =
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{ sign = 1;
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abs_value = nat_of_int 1 }
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;;
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(* Number of digits in a big_int *)
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let num_digits_big_int bi =
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num_digits_nat (bi.abs_value) 0 (length_nat bi.abs_value);;
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num_digits_nat (bi.abs_value) 0 (length_nat bi.abs_value)
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(* Opposite of a big_int *)
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let minus_big_int bi =
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{ sign = - bi.sign;
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abs_value = copy_nat (bi.abs_value) 0 (num_digits_big_int bi)}
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;;
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(* Absolute value of a big_int *)
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let abs_big_int bi =
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{ sign = if bi.sign == 0 then 0 else 1;
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{ sign = if bi.sign = 0 then 0 else 1;
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abs_value = copy_nat (bi.abs_value) 0 (num_digits_big_int bi)}
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;;
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(* Comparison operators on big_int *)
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@ -68,33 +62,30 @@ let abs_big_int bi =
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-1 if bi < bi2
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*)
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let compare_big_int bi1 bi2 =
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if bi1.sign == 0 && bi2.sign == 0 then 0 else
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if bi1.sign < bi2.sign then -1 else
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if bi1.sign > bi2.sign then 1 else
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if bi1.sign == 1 then
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if bi1.sign = 0 && bi2.sign = 0 then 0
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else if bi1.sign < bi2.sign then -1
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else if bi1.sign > bi2.sign then 1
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else if bi1.sign = 1 then
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compare_nat (bi1.abs_value) 0 (num_digits_big_int bi1)
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(bi2.abs_value) 0 (num_digits_big_int bi2)
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else
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compare_nat (bi2.abs_value) 0 (num_digits_big_int bi2)
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(bi1.abs_value) 0 (num_digits_big_int bi1)
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;;
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let eq_big_int bi1 bi2 = compare_big_int bi1 bi2 == 0
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let eq_big_int bi1 bi2 = compare_big_int bi1 bi2 = 0
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and le_big_int bi1 bi2 = compare_big_int bi1 bi2 <= 0
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and ge_big_int bi1 bi2 = compare_big_int bi1 bi2 >= 0
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and lt_big_int bi1 bi2 = compare_big_int bi1 bi2 < 0
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and gt_big_int bi1 bi2 = compare_big_int bi1 bi2 > 0
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;;
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let max_big_int bi1 bi2 = if lt_big_int bi1 bi2 then bi2 else bi1
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and min_big_int bi1 bi2 = if gt_big_int bi1 bi2 then bi2 else bi1
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;;
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(* Operations on big_int *)
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let pred_big_int bi =
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match bi.sign with
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| 0 -> { sign = -1; abs_value = nat_of_int 1}
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0 -> { sign = -1; abs_value = nat_of_int 1}
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| 1 -> let size_bi = num_digits_big_int bi in
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let copy_bi = copy_nat (bi.abs_value) 0 size_bi in
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decr_nat copy_bi 0 size_bi 0;
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@ -108,11 +99,10 @@ let pred_big_int bi =
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incr_nat copy_bi 0 size_res 1;
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{ sign = -1;
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abs_value = copy_bi }
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;;
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let succ_big_int bi =
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match bi.sign with
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| 0 -> {sign = 1; abs_value = nat_of_int 1}
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0 -> {sign = 1; abs_value = nat_of_int 1}
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| -1 -> let size_bi = num_digits_big_int bi in
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let copy_bi = copy_nat (bi.abs_value) 0 size_bi in
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decr_nat copy_bi 0 size_bi 0;
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@ -126,24 +116,23 @@ let succ_big_int bi =
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incr_nat copy_bi 0 size_res 1;
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{ sign = 1;
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abs_value = copy_bi }
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;;
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let add_big_int bi1 bi2 =
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let size_bi1 = num_digits_big_int bi1
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and size_bi2 = num_digits_big_int bi2 in
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if bi1.sign == bi2.sign
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if bi1.sign = bi2.sign
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then (* Add absolute values if signs are the same *)
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{ sign = bi1.sign;
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abs_value =
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match compare_nat (bi1.abs_value) 0 size_bi1
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(bi2.abs_value) 0 size_bi2 with
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| -1 -> let res = create_nat (succ size_bi2) in
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-1 -> let res = create_nat (succ size_bi2) in
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(blit_nat res 0 (bi2.abs_value) 0 size_bi2;
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set_digit_nat res size_bi2 0;
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add_nat res 0 (succ size_bi2)
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(bi1.abs_value) 0 size_bi1 0;
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res)
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| _ -> let res = create_nat (succ size_bi1) in
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|_ -> let res = create_nat (succ size_bi1) in
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(blit_nat res 0 (bi1.abs_value) 0 size_bi1;
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set_digit_nat res size_bi1 0;
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add_nat res 0 (succ size_bi1)
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@ -153,43 +142,40 @@ let add_big_int bi1 bi2 =
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else (* Subtract absolute values if signs are different *)
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match compare_nat (bi1.abs_value) 0 size_bi1
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(bi2.abs_value) 0 size_bi2 with
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| 0 -> zero_big_int
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0 -> zero_big_int
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| 1 -> { sign = bi1.sign;
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abs_value =
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let res = copy_nat (bi1.abs_value) 0 size_bi1 in
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sub_nat res 0 size_bi1
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(sub_nat res 0 size_bi1
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(bi2.abs_value) 0 size_bi2 1;
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res }
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res) }
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| _ -> { sign = bi2.sign;
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abs_value =
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let res = copy_nat (bi2.abs_value) 0 size_bi2 in
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sub_nat res 0 size_bi2
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(sub_nat res 0 size_bi2
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(bi1.abs_value) 0 size_bi1 1;
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res }
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;;
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res) }
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(* Coercion with int type *)
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let big_int_of_int i =
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{ sign = sign_int i;
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abs_value =
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let res = (create_nat 1)
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in (if i == monster_int
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in (if i = monster_int
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then (set_digit_nat res 0 biggest_int;
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incr_nat res 0 1 1;
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())
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incr_nat res 0 1 1; ())
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else set_digit_nat res 0 (abs i));
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res }
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;;
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let add_int_big_int i bi = add_big_int (big_int_of_int i) bi;;
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let add_int_big_int i bi = add_big_int (big_int_of_int i) bi
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let sub_big_int bi1 bi2 = add_big_int bi1 (minus_big_int bi2);;
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let sub_big_int bi1 bi2 = add_big_int bi1 (minus_big_int bi2)
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(* Returns i * bi *)
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let mult_int_big_int i bi =
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let size_bi = num_digits_big_int bi in
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let size_res = succ size_bi in
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if i == monster_int
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if i = monster_int
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then let res = create_nat size_res in
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blit_nat res 0 (bi.abs_value) 0 size_bi;
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mult_digit_nat res 0 size_res (bi.abs_value) 0 size_bi
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@ -201,7 +187,6 @@ let mult_int_big_int i bi =
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(nat_of_int (abs i)) 0;
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{ sign = (sign_int i) * (sign_big_int bi);
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abs_value = res }
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;;
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let mult_big_int bi1 bi2 =
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let size_bi1 = num_digits_big_int bi1
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@ -212,27 +197,24 @@ let mult_big_int bi1 bi2 =
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abs_value =
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if size_bi2 > size_bi1
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then (mult_nat res 0 size_res (bi2.abs_value) 0 size_bi2
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(bi1.abs_value) 0 size_bi1;
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res)
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(bi1.abs_value) 0 size_bi1;res)
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else (mult_nat res 0 size_res (bi1.abs_value) 0 size_bi1
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(bi2.abs_value) 0 size_bi2;
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res) }
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;;
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(bi2.abs_value) 0 size_bi2;res) }
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(* (quotient, rest) of the euclidian division of 2 big_int *)
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let quomod_big_int bi1 bi2 =
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if bi2.sign == 0 then raise Division_by_zero
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if bi2.sign = 0 then raise Division_by_zero
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else
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let size_bi1 = num_digits_big_int bi1
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and size_bi2 = num_digits_big_int bi2 in
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match compare_nat (bi1.abs_value) 0 size_bi1
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(bi2.abs_value) 0 size_bi2 with
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| -1 -> (* 1/2 -> 0, reste 1, -1/2 -> -1, reste 1 *)
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if bi1.sign == -1
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-1 -> (* 1/2 -> 0, reste 1, -1/2 -> -1, reste 1 *)
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if bi1.sign = -1
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then (big_int_of_int(-1), add_big_int bi2 bi1)
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else (zero_big_int, bi1)
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else (big_int_of_int 0, bi1)
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| 0 -> (big_int_of_int (bi1.sign * bi2.sign), zero_big_int)
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| _ -> let bi1_negatif = bi1.sign == -1 in
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| _ -> let bi1_negatif = bi1.sign = -1 in
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let size_q =
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if bi1_negatif
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then succ (max (succ (size_bi1 - size_bi2)) 1)
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@ -276,10 +258,8 @@ let quomod_big_int bi1 bi2 =
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(let new_r = copy_nat (bi2.abs_value) 0 size_bi2 in
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(* new_r contains (r, size_bi2) the remainder *)
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{ sign = - bi2.sign;
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abs_value =
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(set_digit_nat q (pred size_q) 0;
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incr_nat q 0 size_q 1;
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q) },
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abs_value = (set_digit_nat q (pred size_q) 0;
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incr_nat q 0 size_q 1; q) },
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{ sign = 1;
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abs_value =
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(sub_nat new_r 0 size_bi2 r 0 size_bi2 1;
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@ -292,11 +272,9 @@ let quomod_big_int bi1 bi2 =
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abs_value = q },
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{ sign = if not_null_mod then 1 else 0;
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abs_value = copy_nat r 0 size_bi2 })
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;;
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let div_big_int bi1 bi2 = fst (quomod_big_int bi1 bi2)
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and mod_big_int bi1 bi2 = snd (quomod_big_int bi1 bi2)
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;;
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let gcd_big_int bi1 bi2 =
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let size_bi1 = num_digits_big_int bi1
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@ -310,7 +288,7 @@ let gcd_big_int bi1 bi2 =
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abs_value =
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match compare_nat (bi1.abs_value) 0 size_bi1
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(bi2.abs_value) 0 size_bi2 with
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| 0 -> bi1.abs_value
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0 -> bi1.abs_value
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| 1 ->
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let res = copy_nat (bi1.abs_value) 0 size_bi1 in
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let len =
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@ -322,7 +300,6 @@ let gcd_big_int bi1 bi2 =
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gcd_nat res 0 size_bi2 (bi1.abs_value) 0 size_bi1 in
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copy_nat res 0 len
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}
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;;
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(* Coercion operators *)
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@ -342,33 +319,29 @@ let int_of_big_int bi =
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if bi.sign = -1 then - n else n
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with Failure _ ->
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if eq_big_int bi monster_big_int then monster_int
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else failwith "int_of_big_int"
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;;
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else failwith "int_of_big_int";;
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(* Coercion with nat type *)
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let nat_of_big_int bi =
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if bi.sign == -1
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if bi.sign = -1
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then failwith "nat_of_big_int"
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else copy_nat (bi.abs_value) 0 (num_digits_big_int bi)
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;;
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let sys_big_int_of_nat nat off len =
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let length = num_digits_nat nat off len in
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{ sign = if is_zero_nat nat off length then 0 else 1;
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abs_value = copy_nat nat off length }
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;;
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let big_int_of_nat nat =
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sys_big_int_of_nat nat 0 (length_nat nat)
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;;
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(* Coercion with string type *)
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let string_of_big_int bi =
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if bi.sign == -1
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if bi.sign = -1
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then "-" ^ string_of_nat bi.abs_value
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else string_of_nat bi.abs_value
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;;
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let sys_big_int_of_string_aux s ofs len sgn =
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if len < 1 then failwith "sys_big_int_of_string";
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@ -379,14 +352,13 @@ let sys_big_int_of_string_aux s ofs len sgn =
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let sys_big_int_of_string s ofs len =
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match s.[ofs] with
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| '-' -> sys_big_int_of_string_aux s (ofs + 1) (len - 1) (-1)
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| '+' -> sys_big_int_of_string_aux s (ofs + 1) (len - 1) 1
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| '-' -> sys_big_int_of_string_aux s (ofs+1) (len-1) (-1)
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| '+' -> sys_big_int_of_string_aux s (ofs+1) (len-1) 1
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| _ -> sys_big_int_of_string_aux s ofs len 1
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;;
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let big_int_of_string s =
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sys_big_int_of_string s 0 (String.length s)
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;;
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let power_base_nat base nat off len =
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if is_zero_nat nat off len then nat_of_int 1 else
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@ -396,7 +368,7 @@ let power_base_nat base nat off len =
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let (x, y) = quomod_big_int (sys_big_int_of_nat nat off len)
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(big_int_of_int (succ pmax)) in
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(int_of_big_int x, int_of_big_int y) in
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if n == 0 then copy_nat power_base (pred rem) 1 else
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if n = 0 then copy_nat power_base (pred rem) 1 else
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begin
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let res = make_nat n
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and res2 = make_nat (succ n)
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@ -413,8 +385,7 @@ let power_base_nat base nat off len =
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then (set_to_zero_nat res 0 len;
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mult_digit_nat res 0 succ_len2
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res2 0 len2
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power_base pmax;
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())
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power_base pmax; ())
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else blit_nat res 0 res2 0 len2
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end;
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set_to_zero_nat res2 0 len2;
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@ -422,26 +393,26 @@ let power_base_nat base nat off len =
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done;
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if rem > 0
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then (mult_digit_nat res2 0 (succ n)
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res 0 n
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power_base (pred rem);
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res 0 n power_base (pred rem);
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res2)
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else res
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end
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;;
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let power_int_positive_int i n =
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match sign_int n with
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| 0 -> unit_big_int
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0 -> unit_big_int
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| -1 -> invalid_arg "power_int_positive_int"
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| _ -> let nat = power_base_int (abs i) n in
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{ sign = if i >= 0 then sign_int i else
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if n land 1 == 0 then 1 else -1;
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{ sign = if i >= 0
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then sign_int i
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else if n land 1 = 0
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then 1
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else -1;
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abs_value = nat}
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;;
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let power_big_int_positive_int bi n =
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match sign_int n with
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| 0 -> unit_big_int
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0 -> unit_big_int
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| -1 -> invalid_arg "power_big_int_positive_int"
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| _ -> let bi_len = num_digits_big_int bi in
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let res_len = bi_len * n in
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@ -464,25 +435,29 @@ let power_big_int_positive_int bi n =
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set_to_zero_nat res2 0 len2);
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p := !p lsr 1
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done;
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{sign = if bi.sign >= 0 then bi.sign else
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if n land 1 == 0 then 1 else -1;
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{sign = if bi.sign >= 0
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then bi.sign
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else if n land 1 = 0
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then 1
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else -1;
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abs_value = res}
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;;
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let power_int_positive_big_int i bi =
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match sign_big_int bi with
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| 0 -> unit_big_int
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0 -> unit_big_int
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| -1 -> invalid_arg "power_int_positive_big_int"
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| _ -> let nat = power_base_nat
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(abs i) (bi.abs_value) 0 (num_digits_big_int bi) in
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{ sign = if i >= 0 then sign_int i else
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if is_digit_odd (bi.abs_value) 0 then -1 else 1;
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{ sign = if i >= 0
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then sign_int i
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else if is_digit_odd (bi.abs_value) 0
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||||
then -1
|
||||
else 1;
|
||||
abs_value = nat }
|
||||
;;
|
||||
|
||||
let power_big_int_positive_big_int bi1 bi2 =
|
||||
match sign_big_int bi2 with
|
||||
| 0 -> unit_big_int
|
||||
0 -> unit_big_int
|
||||
| -1 -> invalid_arg "power_big_int_positive_big_int"
|
||||
| _ -> let nat = bi2.abs_value
|
||||
and off = 0
|
||||
|
|
@ -511,15 +486,17 @@ let power_big_int_positive_big_int bi1 bi2 =
|
|||
set_to_zero_nat res2 0 len2);
|
||||
p := !p lsr 1
|
||||
done;
|
||||
{sign = if bi1.sign >= 0 then bi1.sign else
|
||||
if is_digit_odd (bi2.abs_value) 0 then -1 else 1;
|
||||
{sign = if bi1.sign >= 0
|
||||
then bi1.sign
|
||||
else if is_digit_odd (bi2.abs_value) 0
|
||||
then -1
|
||||
else 1;
|
||||
abs_value = res}
|
||||
;;
|
||||
|
||||
(* base_power_big_int compute bi*base^n *)
|
||||
let base_power_big_int base n bi =
|
||||
match sign_int n with
|
||||
| 0 -> bi
|
||||
0 -> bi
|
||||
| -1 -> let nat = power_base_int base (-n) in
|
||||
let len_nat = num_digits_nat nat 0 (length_nat nat)
|
||||
and len_bi = num_digits_big_int bi in
|
||||
|
|
@ -552,12 +529,12 @@ let base_power_big_int base n bi =
|
|||
(bi.abs_value) 0 len_bi)
|
||||
; if is_zero_nat res 0 new_len
|
||||
then zero_big_int
|
||||
else create_big_int (bi.sign) res;;
|
||||
else create_big_int (bi.sign) res
|
||||
|
||||
(* Coercion with float type *)
|
||||
|
||||
let float_of_big_int bi =
|
||||
float_of_string (string_of_big_int bi);;
|
||||
float_of_string (string_of_big_int bi)
|
||||
|
||||
(* XL: suppression de big_int_of_float et nat_of_float. *)
|
||||
|
||||
|
|
@ -570,7 +547,6 @@ let sqrt_big_int bi =
|
|||
| -1 -> invalid_arg "sqrt_big_int"
|
||||
| _ -> {sign = 1;
|
||||
abs_value = sqrt_nat (bi.abs_value) 0 (num_digits_big_int bi)}
|
||||
;;
|
||||
|
||||
let square_big_int bi =
|
||||
if bi.sign == 0 then zero_big_int else
|
||||
|
|
@ -579,7 +555,6 @@ let square_big_int bi =
|
|||
let res = make_nat len_res in
|
||||
square_nat res 0 len_res (bi.abs_value) 0 len_bi;
|
||||
{sign = 1; abs_value = res}
|
||||
;;
|
||||
|
||||
(* round off of the futur last digit (of the integer represented by the string
|
||||
argument of the function) that is now the previous one.
|
||||
|
|
@ -588,20 +563,20 @@ let square_big_int bi =
|
|||
else s <- the round number and the result_int is false *)
|
||||
let round_futur_last_digit s off_set length =
|
||||
let l = pred (length + off_set) in
|
||||
if int_of_char s.[l] >= int_of_char '5'
|
||||
if Char.code(String.get s l) >= Char.code '5'
|
||||
then
|
||||
let rec round_rec l =
|
||||
let current_char = s.[l] in
|
||||
if current_char == '9'
|
||||
let current_char = String.get s l in
|
||||
if current_char = '9'
|
||||
then
|
||||
(s.[l] <- '0';
|
||||
if l == off_set then true else round_rec (pred l))
|
||||
(String.set s l '0';
|
||||
if l = off_set then true else round_rec (pred l))
|
||||
else
|
||||
(s.[l] <- char_of_int (succ (int_of_char current_char));
|
||||
(String.set s l (Char.chr (succ (Char.code current_char)));
|
||||
false)
|
||||
in round_rec (pred l)
|
||||
else false
|
||||
;;
|
||||
|
||||
|
||||
(* Approximation with floating decimal point a` la approx_ratio_exp *)
|
||||
let approx_big_int prec bi =
|
||||
|
|
@ -610,18 +585,19 @@ let approx_big_int prec bi =
|
|||
max 0
|
||||
(int_of_big_int (
|
||||
add_int_big_int
|
||||
(- prec)
|
||||
(-prec)
|
||||
(div_big_int (mult_big_int (big_int_of_int (pred len_bi))
|
||||
(big_int_of_string "963295986"))
|
||||
(big_int_of_string "100000000")))) in
|
||||
let s =
|
||||
string_of_big_int (div_big_int bi (power_int_positive_int 10 n)) in
|
||||
let (sign, off, len) =
|
||||
if s.[0] == '-' then ("-", 1, succ prec) else ("", 0, prec) in
|
||||
if round_futur_last_digit s off (succ prec)
|
||||
then sign ^ "1." ^ String.make prec '0' ^ "e" ^
|
||||
string_of_int (n + 1 - off + String.length s)
|
||||
else sign ^ String.sub s off 1 ^ "." ^
|
||||
String.sub s (succ off) (pred prec) ^ "e" ^
|
||||
string_of_int (n - succ off + String.length s)
|
||||
;;
|
||||
if String.get s 0 = '-'
|
||||
then ("-", 1, succ prec)
|
||||
else ("", 0, prec) in
|
||||
if (round_futur_last_digit s off (succ prec))
|
||||
then (sign^"1."^(String.make prec '0')^"e"^
|
||||
(string_of_int (n + 1 - off + String.length s)))
|
||||
else (sign^(String.sub s off 1)^"."^
|
||||
(String.sub s (succ off) (pred prec))
|
||||
^"e"^(string_of_int (n - succ off + String.length s)))
|
||||
|
|
|
|||
|
|
@ -15,22 +15,22 @@
|
|||
|
||||
(* Some extra operations on integers *)
|
||||
|
||||
let rec gcd_int i1 i2 =
|
||||
if i2 = 0 then abs i1 else gcd_int i2 (i1 mod i2)
|
||||
;;
|
||||
|
||||
let rec num_bits_int_aux n =
|
||||
if n = 0 then 0 else succ(num_bits_int_aux (n lsr 1));;
|
||||
|
||||
let num_bits_int n = num_bits_int_aux (abs n);;
|
||||
|
||||
let sign_int i = if i = 0 then 0 else if i > 0 then 1 else -1;;
|
||||
|
||||
let length_of_int = Sys.word_size - 2;;
|
||||
|
||||
let monster_int = 1 lsl length_of_int;;
|
||||
let biggest_int = monster_int - 1;;
|
||||
let least_int = - biggest_int;;
|
||||
|
||||
let rec num_bits_int_aux n =
|
||||
if n == 0 then 0 else succ (num_bits_int_aux (n lsr 1));;
|
||||
|
||||
let num_bits_int n = num_bits_int_aux (abs n);;
|
||||
|
||||
let sign_int i = if i == 0 then 0 else if i > 0 then 1 else -1;;
|
||||
|
||||
let compare_int n1 n2 =
|
||||
if n1 == n2 then 0 else if n1 > n2 then 1 else -1;;
|
||||
|
||||
let rec gcd_int i1 i2 =
|
||||
if i2 == 0 then abs i1 else gcd_int i2 (i1 mod i2);;
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue