34 lines
994 B
OCaml
34 lines
994 B
OCaml
(** Basic arithmetics for ordered euclidian ring. *)
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open Scalable
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let sign l =
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match sign_b l with
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1 -> [0;1]
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| _ -> [1;1]
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(** Greater common (positive) divisor of two non-zero integers.
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@param bA non-zero bitarray.
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@param bB non-zero bitarray.
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*)
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let rec gcd_b bA bB =
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let r = mod_b (mult_b (sign bA) bA) (mult_b (sign bB) bB)
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in if (>>!) r [] then
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gcd_b (mult_b (sign bB) bB) r
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else bB;;
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(** Extended euclidean division of two integers NOT OCAML DEFAULT.
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Given non-zero entries a b computes triple (u, v, d) such that
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a*u + b*v = d and d is gcd of a and b.
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@param bA non-zero bitarray.
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@param bB non-zero bitarray.
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*)
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let bezout_b bA bB =
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let rec bezout_b_rec u v r u1 v1 r1=
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if r1 = [] then
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(u, v, add_b (mult_b bA u) (mult_b bB v))
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else
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let q = quot_b r r1 in
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bezout_b_rec u1 v1 r1 (diff_b u (mult_b q u1)) (diff_b v (mult_b q v1)) (diff_b r (mult_b q r1))
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in bezout_b_rec [0;1] [] bA [] [0;1] bB;;
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