Renamed generic_*_pt into round_*_pt.

src/Appli/Fappli_sqrt_FLT_ne.v

@@ -41,7 +41,7 @@ Theorem Fsqrt_FLT_ne_correct :
 Proof.
 intros x.
 replace (F2R (Fsqrt_FLT_ne x)) with (round beta (FLT_exp emin prec) rndNE (sqrt (F2R x))).
-apply generic_NE_pt_FLT.
+apply round_NE_pt_FLT.
 omega.
 now right.
 unfold Fsqrt_FLT_ne.

src/Core/Fcore_FLT.v

@@ -296,12 +296,12 @@ generalize (Zmax_spec (emin + 1 - prec) emin).
 omega.
 Qed.
 
-Theorem generic_NE_pt_FLT :
+Theorem round_NE_pt_FLT :
   forall x,
   Rnd_NE_pt beta FLT_exp x (round beta FLT_exp rndNE x).
 Proof.
 intros x.
-apply generic_NE_pt.
+apply round_NE_pt.
 apply FLT_exp_correct.
 apply NE_ex_prop_FLT.
 Qed.

src/Core/Fcore_FLX.v

@@ -256,12 +256,12 @@ unfold FLX_exp.
 split ; omega.
 Qed.
 
-Theorem generic_NE_pt_FLX :
+Theorem round_NE_pt_FLX :
   forall x,
   Rnd_NE_pt beta FLX_exp x (round beta FLX_exp rndNE x).
 Proof.
 intros x.
-apply generic_NE_pt.
+apply round_NE_pt.
 apply FLX_exp_correct.
 apply NE_ex_prop_FLX.
 Qed.

src/Core/Fcore_generic_fmt.v

@@ -890,7 +890,7 @@ apply generic_format_0.
 now apply generic_format_round_pos.
 Qed.
 
-Theorem generic_DN_pt :
+Theorem round_DN_pt :
   forall x,
   Rnd_DN_pt generic_format x (round rndDN x).
 Proof.
@@ -918,10 +918,10 @@ exact generic_format_opp.
 (* round down *)
 intros x.
 exists (round rndDN x).
-apply generic_DN_pt.
+apply round_DN_pt.
 Qed.
 
-Theorem generic_UP_pt :
+Theorem round_UP_pt :
   forall x,
   Rnd_UP_pt generic_format x (round rndUP x).
 Proof.
@@ -930,10 +930,10 @@ rewrite <- (Ropp_involutive x).
 rewrite round_UP_opp.
 apply Rnd_DN_UP_pt_sym.
 apply generic_format_opp.
-apply generic_DN_pt.
+apply round_DN_pt.
 Qed.
 
-Theorem generic_ZR_pt :
+Theorem round_ZR_pt :
   forall x,
   Rnd_ZR_pt generic_format x (round rndZR x).
 Proof.
@@ -941,7 +941,7 @@ intros x.
 split ; intros Hx.
 (* *)
 replace (round rndZR x) with (round rndDN x).
-apply generic_DN_pt.
+apply round_DN_pt.
 apply (f_equal (fun v => F2R (Float beta v _))).
 apply sym_eq.
 apply Ztrunc_floor.
@@ -950,7 +950,7 @@ apply Rmult_le_compat_r with (2 := Hx).
 apply bpow_ge_0.
 (* *)
 replace (round rndZR x) with (round rndUP x).
-apply generic_UP_pt.
+apply round_UP_pt.
 apply (f_equal (fun v => F2R (Float beta v _))).
 apply sym_eq.
 apply Ztrunc_ceil.
@@ -1040,14 +1040,14 @@ destruct (ln_beta beta x) as (ex, He).
 simpl.
 assert (Hx: (0 < x)%R).
 apply Rlt_le_trans with (1 := Hd).
-apply (generic_DN_pt x).
+apply (round_DN_pt x).
 specialize (He (Rgt_not_eq _ _ Hx)).
 rewrite Rabs_pos_eq in He. 2: now apply Rlt_le.
 split.
 apply round_large_pos_ge_pow with (1 := Hd).
 apply He.
 apply Rle_lt_trans with (2 := proj2 He).
-apply (generic_DN_pt x).
+apply (round_DN_pt x).
 Qed.
 
 Theorem scaled_mantissa_DN :
@@ -1071,10 +1071,10 @@ intros x f Hxf.
 destruct (Rnd_N_pt_DN_or_UP _ _ _ Hxf).
 left.
 apply Rnd_DN_pt_unicity with (1 := H).
-apply generic_DN_pt.
+apply round_DN_pt.
 right.
 apply Rnd_UP_pt_unicity with (1 := H).
-apply generic_UP_pt.
+apply round_UP_pt.
 Qed.
 
 Section not_FTZ.
@@ -1419,8 +1419,8 @@ apply Zceil_ub.
 (* . *)
 apply Rnd_DN_UP_pt_N with d u.
 now apply generic_format_round.
-now apply generic_DN_pt.
-now apply generic_UP_pt.
+now apply round_DN_pt.
+now apply round_UP_pt.
 apply Rle_trans with (1 := H).
 apply Rmin_l.
 apply Rle_trans with (1 := H).
@@ -1459,7 +1459,7 @@ Section rndNA.
 
 Definition rndNA := rndN (Zle_bool 0).
 
-Theorem generic_NA_pt :
+Theorem round_NA_pt :
   forall x,
   Rnd_NA_pt generic_format x (round rndNA x).
 Proof.
@@ -1480,7 +1480,7 @@ rewrite Rabs_pos_eq.
 unfold f, rndNA.
 rewrite round_N_middle with (1 := Hm).
 rewrite Zle_bool_true.
-apply (generic_UP_pt x).
+apply (round_UP_pt x).
 apply Zfloor_lub.
 apply Rmult_le_pos with (1 := Hx).
 apply bpow_ge_0.
@@ -1493,7 +1493,7 @@ apply Ropp_le_contravar.
 unfold f, rndNA.
 rewrite round_N_middle with (1 := Hm).
 rewrite Zle_bool_false.
-apply (generic_DN_pt x).
+apply (round_DN_pt x).
 apply lt_Z2R.
 apply Rle_lt_trans with (scaled_mantissa x).
 apply Zfloor_lb.
@@ -1510,8 +1510,8 @@ apply Rxf.
 intros g Rxg.
 rewrite Rnd_N_pt_unicity with (3 := Hm) (4 := Rxf) (5 := Rxg).
 apply Rle_refl.
-apply generic_DN_pt.
-apply generic_UP_pt.
+apply round_DN_pt.
+apply round_UP_pt.
 Qed.
 
 End rndNA.

src/Core/Fcore_rnd_ne.v

@@ -147,15 +147,15 @@ assert (Hd4: (bpow (ex - 1) <= Rabs (F2R xd) < bpow ex)%R).
 rewrite Rabs_pos_eq.
 rewrite Hxd.
 split.
-apply (generic_DN_pt beta fexp prop_exp x).
+apply (round_DN_pt beta fexp prop_exp x).
 apply generic_format_bpow.
 ring_simplify (ex - 1 + 1)%Z.
 omega.
 apply Hex.
 apply Rle_lt_trans with (2 := proj2 Hex).
-apply (generic_DN_pt beta fexp prop_exp x).
+apply (round_DN_pt beta fexp prop_exp x).
 rewrite Hxd.
-apply (generic_DN_pt beta fexp prop_exp x).
+apply (round_DN_pt beta fexp prop_exp x).
 apply generic_format_0.
 now apply Rlt_le.
 assert (Hxe2 : (fexp (ex + 1) <= ex)%Z) by now eapply prop_exp.
@@ -242,12 +242,12 @@ rewrite Rabs_pos_eq.
 split.
 apply Rle_trans with (1 := proj1 Hex).
 rewrite Hxu.
-apply (generic_UP_pt beta fexp prop_exp x).
+apply (round_UP_pt beta fexp prop_exp x).
 exact Hu2.
 apply Rlt_le.
 apply Rlt_le_trans with (1 := H0x).
 rewrite Hxu.
-apply (generic_UP_pt beta fexp prop_exp x).
+apply (round_UP_pt beta fexp prop_exp x).
 Qed.
 
 Theorem DN_UP_parity_generic :
@@ -294,10 +294,10 @@ unfold Fcore_generic_fmt.canonic.
 now rewrite <- Hu1.
 rewrite <- Hd1.
 apply Rnd_DN_pt_unicity with (1 := Hd).
-now apply generic_DN_pt.
+now apply round_DN_pt.
 rewrite <- Hu1.
 apply Rnd_UP_pt_unicity with (1 := Hu).
-now apply generic_UP_pt.
+now apply round_UP_pt.
 Qed.
 
 Theorem Rnd_NE_pt_monotone :
@@ -319,10 +319,10 @@ apply sym_eq.
 now apply Rnd_DN_pt_idempotent with (1 := Hd).
 rewrite <- Hd1.
 apply Rnd_DN_pt_unicity with (1 := Hd).
-now apply generic_DN_pt.
+now apply round_DN_pt.
 rewrite <- Hu1.
 apply Rnd_UP_pt_unicity with (1 := Hu).
-now apply generic_UP_pt.
+now apply round_UP_pt.
 Qed.
 
 Theorem Rnd_NE_pt_round :
@@ -334,7 +334,7 @@ Qed.
 
 Definition rndNE := rndN (fun x => negb (Zeven x)).
 
-Theorem generic_NE_pt_pos :
+Theorem round_NE_pt_pos :
   forall x,
   (0 < x)%R ->
   Rnd_NE_pt x (round beta fexp rndNE x).
@@ -455,8 +455,8 @@ apply Hg.
 set (d := round beta fexp rndDN x).
 set (u := round beta fexp rndUP x).
 apply Rnd_N_pt_unicity with (d := d) (u := u) (4 := Hg).
-now apply generic_DN_pt.
-now apply generic_UP_pt.
+now apply round_DN_pt.
+now apply round_UP_pt.
 2: now apply generic_N_pt.
 rewrite <- (scaled_mantissa_bpow beta fexp x).
 unfold d, u, round, F2R. simpl. fold mx.
@@ -474,7 +474,7 @@ rewrite <- (scaled_mantissa_bpow beta fexp x).
 fold mx.
 rewrite <- Hxg.
 change (Z2R (Zfloor mx) * bpow (canonic_exponent beta fexp x))%R with d.
-now eapply generic_DN_pt.
+now eapply round_DN_pt.
 apply Rgt_not_eq.
 apply bpow_gt_0.
 Qed.
@@ -499,7 +499,7 @@ rewrite Zeven_plus.
 now rewrite eqb_sym.
 Qed.
 
-Theorem generic_NE_pt :
+Theorem round_NE_pt :
   forall x,
   Rnd_NE_pt x (round beta fexp rndNE x).
 Proof.
@@ -517,12 +517,12 @@ now apply canonic_opp.
 simpl.
 now rewrite Zeven_opp.
 rewrite <- round_NE_opp.
-apply generic_NE_pt_pos.
+apply round_NE_pt_pos.
 now apply Ropp_0_gt_lt_contravar.
 rewrite Hx, round_0.
 apply Rnd_NG_pt_refl.
 apply generic_format_0.
-now apply generic_NE_pt_pos.
+now apply round_NE_pt_pos.
 Qed.
 
 End Fcore_rnd_NE.

src/Core/Fcore_ulp.v

@@ -331,28 +331,28 @@ apply Rplus_lt_reg_r with (round beta fexp rndDN x).
 rewrite <- ulp_DN_UP with (1 := Hx).
 ring_simplify.
 assert (Hu: (x <= round beta fexp rndUP x)%R).
-apply (generic_UP_pt beta fexp prop_exp x).
+apply (round_UP_pt beta fexp prop_exp x).
 destruct Hu as [Hu|Hu].
 exact Hu.
 elim Hx.
 rewrite Hu.
 now apply generic_format_round.
 apply Rle_minus.
-apply (generic_DN_pt beta fexp prop_exp x).
+apply (round_DN_pt beta fexp prop_exp x).
 (* . *)
 rewrite Rabs_pos_eq.
 rewrite ulp_DN_UP with (1 := Hx).
 apply Rplus_lt_reg_r with (x - ulp x)%R.
 ring_simplify.
 assert (Hd: (round beta fexp rndDN x <= x)%R).
-apply (generic_DN_pt beta fexp prop_exp x).
+apply (round_DN_pt beta fexp prop_exp x).
 destruct Hd as [Hd|Hd].
 exact Hd.
 elim Hx.
 rewrite <- Hd.
 now apply generic_format_round.
 apply Rle_0_minus.
-apply (generic_UP_pt beta fexp prop_exp x).
+apply (round_UP_pt beta fexp prop_exp x).
 Qed.
 
 Theorem ulp_half_error :
@@ -378,7 +378,7 @@ destruct (Rle_or_lt (x - d) (d + ulp x - x)) as [H|H].
 (* . rnd(x) = rndd(x) *)
 apply Rle_trans with (Rabs (d - x)).
 apply Hr2.
-apply (generic_DN_pt beta fexp prop_exp x).
+apply (round_DN_pt beta fexp prop_exp x).
 rewrite Rabs_left1.
 rewrite Ropp_minus_distr.
 apply Rmult_le_reg_r with 2%R.
@@ -388,7 +388,7 @@ ring_simplify.
 apply Rle_trans with (1 := H).
 right. field.
 apply Rle_minus.
-apply (generic_DN_pt beta fexp prop_exp x).
+apply (round_DN_pt beta fexp prop_exp x).
 (* . rnd(x) = rndu(x) *)
 assert (Hu: (d + ulp x)%R = round beta fexp rndUP x).
 unfold d.
@@ -396,7 +396,7 @@ now rewrite <- ulp_DN_UP.
 apply Rle_trans with (Rabs (d + ulp x - x)).
 apply Hr2.
 rewrite Hu.
-apply (generic_UP_pt beta fexp prop_exp x).
+apply (round_UP_pt beta fexp prop_exp x).
 rewrite Rabs_pos_eq.
 apply Rmult_le_reg_r with 2%R.
 now apply (Z2R_lt 0 2).
@@ -407,7 +407,7 @@ apply Rlt_le_trans with (1 := H).
 right. field.
 apply Rle_0_minus.
 rewrite Hu.
-apply (generic_UP_pt beta fexp prop_exp x).
+apply (round_UP_pt beta fexp prop_exp x).
 Qed.
 
 Theorem ulp_monotone :
@@ -474,7 +474,7 @@ apply Rle_not_lt.
 apply round_monotone_l; trivial.
 apply generic_format_0.
 apply Ropp_le_contravar; rewrite Hx.
-apply (generic_DN_pt beta fexp prop_exp x).
+apply (round_DN_pt beta fexp prop_exp x).
 (* *)
 rewrite Hx; case (Rle_or_lt 0 (round beta fexp rndUP x)).
 intros H; destruct H.
@@ -485,7 +485,7 @@ intros H1; contradict H.
 apply Rle_not_lt.
 apply round_monotone_r; trivial.
 apply generic_format_0.
-apply (generic_UP_pt beta fexp prop_exp x).
+apply (round_UP_pt beta fexp prop_exp x).
 rewrite Hx in Hfx; contradict Hfx; auto with real.
 intros H.
 rewrite <- (ulp_opp (round beta fexp rndUP x)).
@@ -526,7 +526,7 @@ apply Rle_not_lt.
 apply round_monotone_l; trivial.
 apply generic_format_0.
 apply Ropp_le_contravar; rewrite Hx.
-apply (generic_DN_pt beta fexp prop_exp x).
+apply (round_DN_pt beta fexp prop_exp x).
 (* *)
 case (Rle_or_lt 0 (round beta fexp rndUP x)).
 intros H; destruct H.
@@ -539,7 +539,7 @@ intros H1; contradict H.
 apply Rle_not_lt.
 apply round_monotone_r; trivial.
 apply generic_format_0.
-rewrite Hx; apply (generic_UP_pt beta fexp prop_exp x).
+rewrite Hx; apply (round_UP_pt beta fexp prop_exp x).
 rewrite Hx in Hfx; contradict Hfx; auto with real.
 intros H.
 rewrite Hx at 2; rewrite <- (ulp_opp (round beta fexp rndUP x)).