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-Require Export Gappa_tactic.
-Require Export Reals.
-
-Open Scope Z_scope.
-Open Scope R_scope.
-
-Lemma test_base10 :
- forall x y:R,
- 0 <= x <= 4 ->
- 0 <= x * (24 * powerRZ 10 (-1)) <= 10.
-Proof.
- gappa.
-Qed.
-
-(*
-@rnd = float< ieee_32, zr >;
-a = rnd(a_); b = rnd(b_);
-{ a in [3.2,3.3] /\ b in [1.4,1.9] ->
- rnd(a - b) - (a - b) in [0,0] }
-*)
-
-Definition rnd := gappa_rounding (rounding_float roundZR 43 (120)).
-
-Lemma test_float3 :
- forall a_ b_ a b : R,
- a = rnd a_ ->
- b = rnd b_ ->
- 52 / 16 <= a <= 53 / 16 ->
- 22 / 16 <= b <= 30 / 16 ->
- 0 <= rnd (a - b) - (a - b) <= 0.
-Proof.
- unfold rnd.
- gappa.
-Qed.
-
-Lemma test_float2 :
- forall x y:R,
- 0 <= x <= 1 ->
- 0 <= y <= 1 ->
- 0 <= gappa_rounding (rounding_float roundNE 53 (1074)) (x+y) <= 2.
-Proof.
- gappa.
-Qed.
-
-Lemma test_float1 :
- forall x y:R,
- 0 <= gappa_rounding (rounding_fixed roundDN (0)) x -
- gappa_rounding (rounding_fixed roundDN (0)) y <= 0 ->
- Rabs (x - y) <= 1.
-Proof.
- gappa.
-Qed.
-
-Lemma test1 :
- forall x y:R,
- 0 <= x <= 1 ->
- 0 <= -y <= 1 ->
- 0 <= x * (-y) <= 1.
-Proof.
- gappa.
-Qed.
-
-Lemma test2 :
- forall x y:R,
- 3/4 <= x <= 3 ->
- 0 <= sqrt x <= 1775 * (powerRZ 2 (-10)).
-Proof.
- gappa.
-Qed.
-
-Lemma test3 :
- forall x y z:R,
- 0 <= x - y <= 3 ->
- -2 <= y - z <= 4 ->
- -2 <= x - z <= 7.
-Proof.
- gappa.
-Qed.
-
-Lemma test4 :
- forall x1 x2 y1 y2 : R,
- 1 <= Rabs y1 <= 1000 ->
- 1 <= Rabs y2 <= 1000 ->
- - powerRZ 2 (-53) <= (x1 - y1) / y1 <= powerRZ 2 (-53) ->
- - powerRZ 2 (-53) <= (x2 - y2) / y2 <= powerRZ 2 (-53) ->
- - powerRZ 2 (-51) <= (x1 * x2 - y1 * y2) / (y1 * y2) <= powerRZ 2 (-51).
-Proof.
- gappa.
-Qed.
-
-