Fix testsuite breakage due to floating-point theories for Coq and Gappa provers.

drivers/gappa.drv

@@ -187,7 +187,7 @@ theory floating_point.Rounding
   syntax function ToZero "zr"
   syntax function Up "up"
   syntax function Down "dn"
-  syntax function NearTiesToAway "na"
+  syntax function NearestTiesToAway "na"
 
 end
 

examples/programs/my_cosine/my_cosine_M_WP_parameter_my_cosine_1.v

@@ -6,58 +6,34 @@ Require Import Rbasic_fun.
 Require Import R_sqrt.
 Require Import Rtrigo.
 Require Import AltSeries. (* for def of pi *)
+Require int.Int.
+Require real.Real.
+Require real.Abs.
+Require real.FromInt.
+Require real.Square.
+Require floating_point.Rounding.
+Require floating_point.Single.
 Definition unit  := unit.
 
-Parameter mark : Type.
+Parameter qtmark : Type.
 
-Parameter at1: forall (a:Type), a -> mark  -> a.
+Parameter at1: forall (a:Type), a -> qtmark -> a.
 
 Implicit Arguments at1.
 
-Parameter old: forall (a:Type), a  -> a.
+Parameter old: forall (a:Type), a -> a.
 
 Implicit Arguments old.
 
-Axiom assoc_mul_div : forall (x:R) (y:R) (z:R), (~ (z = (0)%R)) ->
-  ((Rdiv (x * y)%R z)%R = (x * (Rdiv y z)%R)%R).
-
-Axiom assoc_div_mul : forall (x:R) (y:R) (z:R), ((~ (y = (0)%R)) /\
-  ~ (z = (0)%R)) -> ((Rdiv (Rdiv x y)%R z)%R = (Rdiv x (y * z)%R)%R).
-
-Axiom assoc_div_div : forall (x:R) (y:R) (z:R), ((~ (y = (0)%R)) /\
-  ~ (z = (0)%R)) -> ((Rdiv x (Rdiv y z)%R)%R = (Rdiv (x * z)%R y)%R).
-
-Axiom Abs_le : forall (x:R) (y:R), ((Rabs x) <= y)%R <-> (((-y)%R <= x)%R /\
-  (x <= y)%R).
-
-Axiom Sqrt_positive : forall (x:R), ((0)%R <= x)%R -> ((0)%R <= (sqrt x))%R.
-
-Axiom Sqrt_square : forall (x:R), ((0)%R <= x)%R -> ((Rsqr (sqrt x)) = x).
-
-Axiom Square_sqrt : forall (x:R), ((0)%R <= x)%R -> ((sqrt (x * x)%R) = x).
-
-Axiom Pythagorean_identity : forall (x:R),
-  (((Rsqr (Rtrigo_def.cos x)) + (Rsqr (Rtrigo_def.sin x)))%R = (1)%R).
-
-Axiom Cos_le_one : forall (x:R), ((Rabs (Rtrigo_def.cos x)) <= (1)%R)%R.
-
-Axiom Sin_le_one : forall (x:R), ((Rabs (Rtrigo_def.sin x)) <= (1)%R)%R.
-
-Axiom Cos_0 : ((Rtrigo_def.cos (0)%R) = (1)%R).
-
-Axiom Sin_0 : ((Rtrigo_def.sin (0)%R) = (0)%R).
+Definition implb(x:bool) (y:bool): bool := match (x,
+  y) with
+  | (true, false) => false
+  | (_, _) => true
+  end.
 
 Axiom Pi_interval : ((314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R <  PI)%R /\
   (PI <  (314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038197 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R)%R.
 
-Axiom Cos_pi : ((Rtrigo_def.cos PI) = (-(1)%R)%R).
-
-Axiom Sin_pi : ((Rtrigo_def.sin PI) = (0)%R).
-
-Axiom Cos_pi2 : ((Rtrigo_def.cos ((05 / 10)%R * PI)%R) = (0)%R).
-
-Axiom Sin_pi2 : ((Rtrigo_def.sin ((05 / 10)%R * PI)%R) = (1)%R).
-
 Axiom Cos_plus_pi : forall (x:R),
   ((Rtrigo_def.cos (x + PI)%R) = (-(Rtrigo_def.cos x))%R).
 
@@ -81,87 +57,23 @@ Axiom Cos_sum : forall (x:R) (y:R),
 Axiom Sin_sum : forall (x:R) (y:R),
   ((Rtrigo_def.sin (x + y)%R) = (((Rtrigo_def.sin x) * (Rtrigo_def.cos y))%R + ((Rtrigo_def.cos x) * (Rtrigo_def.sin y))%R)%R).
 
-Parameter atan: R  -> R.
+Parameter atan: R -> R.
 
 
 Axiom Tan_atan : forall (x:R), ((Rtrigo.tan (atan x)) = x).
 
-Inductive mode  :=
-  | NearestTiesToEven : mode 
-  | ToZero : mode 
-  | Up : mode 
-  | Down : mode 
-  | NearTiesToAway : mode .
-
-Parameter single : Type.
-
-Axiom Zero : ((IZR 0%Z) = (0)%R).
-
-Axiom One : ((IZR 1%Z) = (1)%R).
-
-Axiom Add : forall (x:Z) (y:Z), ((IZR (x + y)%Z) = ((IZR x) + (IZR y))%R).
-
-Axiom Sub : forall (x:Z) (y:Z), ((IZR (x - y)%Z) = ((IZR x) - (IZR y))%R).
-
-Axiom Mul : forall (x:Z) (y:Z), ((IZR (x * y)%Z) = ((IZR x) * (IZR y))%R).
-
-Axiom Neg : forall (x:Z), ((IZR (-x)%Z) = (-(IZR x))%R).
-
-Parameter round: mode -> R  -> R.
-
-
-Parameter round_logic: mode -> R  -> single.
-
-
-Parameter value: single  -> R.
-
-
-Parameter exact: single  -> R.
-
-
-Parameter model: single  -> R.
-
-
-Definition round_error(x:single): R := (Rabs ((value x) - (exact x))%R).
-
-Definition total_error(x:single): R := (Rabs ((value x) - (model x))%R).
-
-Definition no_overflow(m:mode) (x:R): Prop := ((Rabs (round m
-  x)) <= (33554430 * 10141204801825835211973625643008)%R)%R.
-
-Axiom Bounded_real_no_overflow : forall (m:mode) (x:R),
-  ((Rabs x) <= (33554430 * 10141204801825835211973625643008)%R)%R ->
-  (no_overflow m x).
-
-Axiom Round_monotonic : forall (m:mode) (x:R) (y:R), (x <= y)%R -> ((round m
-  x) <= (round m y))%R.
-
-Axiom Exact_rounding_for_integers : forall (m:mode) (i:Z),
-  (((-16777216%Z)%Z <= i)%Z /\ (i <= 16777216%Z)%Z) -> ((round m
-  (IZR i)) = (IZR i)).
-
-Axiom Round_down_le : forall (x:R), ((round (Down ) x) <= x)%R.
-
-Axiom Round_up_ge : forall (x:R), (x <= (round (Up ) x))%R.
-
-Axiom Round_down_neg : forall (x:R), ((round (Down ) (-x)%R) = (-(round (Up )
-  x))%R).
-
-Axiom Round_up_neg : forall (x:R), ((round (Up ) (-x)%R) = (-(round (Down )
-  x))%R).
-
 (* YOU MAY EDIT THE CONTEXT BELOW *)
 
 Require Import Interval_tactic.
 
 (* DO NOT EDIT BELOW *)
 
-Theorem WP_parameter_my_cosine : forall (x:single),
-  ((Rabs (value x)) <= (1 / 32)%R)%R ->
-  ((Rabs (((1)%R - (((value x) * (value x))%R * (05 / 10)%R)%R)%R - (Rtrigo_def.cos (value x)))%R) <= (1 / 16777216)%R)%R.
+Theorem WP_parameter_my_cosine : forall (x:floating_point.Single.single),
+  ((Rabs (floating_point.Single.value x)) <= (1 / 32)%R)%R ->
+  ((Rabs ((1%R - (((floating_point.Single.value x) * (floating_point.Single.value x))%R * (05 / 10)%R)%R)%R - (Rtrigo_def.cos (floating_point.Single.value x)))%R) <= (1 / 16777216)%R)%R.
 (* YOU MAY EDIT THE PROOF BELOW *)
 intros x H.
-interval with (i_bisect_diff (value x)).
+interval with (i_bisect_diff (Single.value x)).
 Qed.
 (* DO NOT EDIT BELOW *)