Commit 5f43eaf0 authored by Guillaume Melquiond's avatar Guillaume Melquiond
Browse files

Replaced Fplus by a custom radix-2 sequence in Bplus.

parent 8d7e413b
......@@ -869,6 +869,22 @@ now rewrite Hd.
apply Zle_refl.
Theorem snd_shl :
forall mx ex ex',
(ex' <= ex)%Z ->
snd (shl mx ex ex') = ex'.
intros mx ex ex' He.
unfold shl.
case_eq (ex' - ex)%Z ; simpl.
intros H.
now rewrite Zminus_eq with (1 := H).
intros p.
clear -He ; zify ; omega.
apply refl_equal.
Definition shl_fexp mx ex :=
shl mx ex (fexp (Z_of_nat (S (digits2_Pnat mx)) + ex)).
......@@ -938,14 +954,13 @@ Definition Bplus m x y :=
| B754_zero _, _ => y
| _, B754_zero _ => x
| B754_finite sx mx ex Hx, B754_finite sy my ey Hy =>
let fx := Float radix2 (cond_Zopp sx (Zpos mx)) ex in
let fy := Float radix2 (cond_Zopp sy (Zpos my)) ey in
match Fplus radix2 fx fy with
| Float Z0 _ =>
let ez := Zmin ex ey in
match Zplus (cond_Zopp sx (Zpos (fst (shl mx ex ez)))) (cond_Zopp sy (Zpos (fst (shl my ey ez)))) with
| Z0 =>
match m with mode_DN => B754_zero true | _ => B754_zero false end
| Float (Zpos mz) ez =>
| Zpos mz =>
FF2B (binary_round_sign_shl m false mz ez) (proj1 (binary_round_sign_shl_correct _ _ _ _))
| Float (Zneg mz) ez =>
| Zneg mz =>
FF2B (binary_round_sign_shl m true mz ez) (proj1 (binary_round_sign_shl_correct _ _ _ _))
......@@ -979,14 +994,31 @@ apply generic_format_B2R.
(* *)
clear Fx Fy.
rewrite <- plus_F2R.
case_eq (Fplus radix2 (Float radix2 (cond_Zopp sx (Zpos mx)) ex)
(Float radix2 (cond_Zopp sy (Zpos my)) ey)).
intros mz ez Hz.
set (ez := Zmin ex ey).
set (mz := (cond_Zopp sx (Zpos (fst (shl mx ex ez))) + cond_Zopp sy (Zpos (fst (shl my ey ez))))%Z).
assert (Hp: (F2R (Float radix2 (cond_Zopp sx (Zpos mx)) ex) +
F2R (Float radix2 (cond_Zopp sy (Zpos my)) ey))%R = F2R (Float radix2 mz ez)).
rewrite 2!F2R_cond_Zopp.
generalize (shl_correct mx ex ez).
generalize (shl_correct my ey ez).
generalize (snd_shl mx ex ez (Zle_min_l ex ey)).
generalize (snd_shl my ey ez (Zle_min_r ex ey)).
destruct (shl mx ex ez) as (mx', ex').
destruct (shl my ey ez) as (my', ey').
intros H1 H2.
rewrite H1, H2.
clear H1 H2.
intros (H1, _) (H2, _).
rewrite H1, H2.
clear H1 H2.
rewrite <- 2!F2R_cond_Zopp.
unfold F2R. simpl.
now rewrite <- Rmult_plus_distr_r, <- Z2R_plus.
rewrite Hp.
assert (Sz: (bpow radix2 emax <= Rabs (round radix2 fexp (round_mode m) (F2R (Float radix2 mz ez))))%R -> sx = Rlt_bool (F2R (Float radix2 mz ez)) 0 /\ sx = sy).
(* . *)
rewrite <- Hz.
rewrite plus_F2R.
rewrite <- Hp.
intros Bz.
destruct (Bool.bool_dec sx sy) as [Hs|Hs].
(* .. *)
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