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Commit 00e1c682 by BOLDO Sylvie

### Des admits en plus :)

parent 12a3f692
 ... ... @@ -619,6 +619,8 @@ Definition mkZrounding2 rnd (mono : forall x y, (x <= y)%R -> (rnd x <= rnd y)%Z Definition ZrndDN := mkZrounding2 Zfloor Zfloor_le Zfloor_Z2R. Definition ZrndUP := mkZrounding2 Zceil Zceil_le Zceil_Z2R. (* Definition ZrndTZ := .. SB *) Theorem rounding_DN_or_UP : forall rnd x, ... ... @@ -679,6 +681,29 @@ now rewrite <- Hx. apply bpow_ge_0. Qed. Theorem rounding_monotone_l : forall rnd x y, generic_format x -> (x <= y)%R -> (x <= rounding rnd y)%R. Proof. Admitted. (* SB *) Theorem rounding_monotone_r : forall rnd x y, generic_format y -> (x <= y)%R -> (rounding rnd x <= y)%R. Proof. Admitted. (* SB *) Theorem rounding_monotone_abs_l : forall rnd x y, generic_format x -> (x <= Rabs y)%R -> (x <= Rabs (rounding rnd y))%R. Proof. Admitted. (* SB *) Theorem rounding_monotone_abs_r : forall rnd x y, generic_format y -> (Rabs x <= y)%R -> (Rabs (rounding rnd x) <= y)%R. Proof. Admitted. (* SB *) Theorem rounding_abs_abs : forall P : R -> R -> Prop, ( forall rnd x, P x (rounding rnd x) ) -> ... ...
 Require Import Fcore. Require Import Fcalc_ops. Section Fprop_divsqrt_error. Variable beta : radix. Notation bpow e := (bpow beta e). Variable fexp : Z -> Z. Hypothesis prop_exp : valid_exp fexp. Notation format := (generic_format beta fexp). Variable choice : R -> bool. Theorem div_error_N : forall x y, format x -> format y -> format (x - rounding beta fexp (ZrndN choice) (x/y) * y)%R. Proof. (* probablement seulement en FLX *) Admitted. (* SB *) (* Theorem div_error_Z : forall x y, format x -> format y -> format (x - rounding beta fexp (ZrndTZ) (x/y) * y)%R. Proof. (* probablement seulement en FLX *) Admitted. (* SB *) *) Theorem sqrt_error_N : forall x, (0 <= x)%R -> format x -> format (x - Rsqr (rounding beta fexp (ZrndN choice) (sqrt x)))%R. Proof. (* probablement seulement en FLX *) Admitted. (* SB *) End Fprop_divsqrt_error.
 ... ... @@ -511,6 +511,17 @@ omega. exact Hp. Qed. Theorem error_N_FLT : forall x, exists eps, exists eta, (Rabs eps <= /2 * bpow (-prec + 1))%R /\ (Rabs eta <= /2 * bpow (emin))%R /\ (eps*eta=0)%R /\ rounding beta (FLT_exp emin prec) (ZrndN choice) x = (x * (1 + eps) + eta)%R. Proof. Admitted. (* SB *) End Fprop_relative_FLT. Section Fprop_relative_FLX. ... ...
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