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Diffstat (limited to 'contrib/dp/test_gappa.v')
-rw-r--r-- | contrib/dp/test_gappa.v | 91 |
1 files changed, 0 insertions, 91 deletions
diff --git a/contrib/dp/test_gappa.v b/contrib/dp/test_gappa.v deleted file mode 100644 index eb65a59d..00000000 --- a/contrib/dp/test_gappa.v +++ /dev/null @@ -1,91 +0,0 @@ -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. - - |