24 lines
499 B
Plaintext
24 lines
499 B
Plaintext
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(* Division entière par l'algorithme d'Euclide *)
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module Division
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use int.Int
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use ref.Refint
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let division (a b: int) (* renvoie une paire d'entiers (quotient,reste) *)
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requires { 0 <= a && 0 < b }
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ensures { let (q,r) = result in q * b + r = a && 0 <= r < b }
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=
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let q = ref 0 in
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let r = ref a in
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while !r >= b do
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invariant { a = !q * b + !r && 0 <= !q && 0 <= !r }
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variant { !r - b }
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q := (!q) + 1;
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r := (!r) - b
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done;
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(!q,!r)
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end
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