Make it compile with both Coq 8.4 and trunk.

.gitignore

@@ -13,3 +13,7 @@ html
 src/Flocq_version.v
 *.vo
 *.glob
+.*.aux
+N*.cm*
+N*.native
+N*.o

src/Appli/Fappli_IEEE.v

@@ -46,6 +46,8 @@ End AnyRadix.
 
 Section Binary.
 
+Implicit Arguments exist [[A] [P]].
+
 (** prec is the number of bits of the mantissa including the implicit one
     emax is the exponent of the infinities
     Typically p=24 and emax = 128 in single precision *)
@@ -89,7 +91,7 @@ Definition FF2B x :=
   | F754_finite s m e => B754_finite s m e
   | F754_infinity s => fun _ => B754_infinity s
   | F754_zero s => fun _ => B754_zero s
-  | F754_nan b pl => fun H => B754_nan b (exist _ pl H)
+  | F754_nan b pl => fun H => B754_nan b (exist pl H)
   end.
 
 Definition B2FF x :=
@@ -601,7 +603,7 @@ induction (nat_of_P n).
 simpl.
 rewrite Zplus_0_r.
 now destruct l as [|[| |]].
-simpl iter_nat.
+simpl nat_rect.
 rewrite inj_S.
 unfold Zsucc.
 rewrite  Zplus_assoc.

src/Appli/Fappli_IEEE_bits.v

@@ -25,6 +25,12 @@ Require Import Fappli_IEEE.
 
 Section Binary_Bits.
 
+Implicit Arguments exist [[A] [P]].
+Implicit Arguments B754_zero [[prec] [emax]].
+Implicit Arguments B754_infinity [[prec] [emax]].
+Implicit Arguments B754_nan [[prec] [emax]].
+Implicit Arguments B754_finite [[prec] [emax]].
+
 (** Number of bits for the fraction and exponent *)
 Variable mw ew : Z.
 Hypothesis Hmw : (0 < mw)%Z.
@@ -516,6 +522,8 @@ End Binary_Bits.
 (** Specialization for IEEE single precision operations *)
 Section B32_Bits.
 
+Implicit Arguments B754_nan [[prec] [emax]].
+
 Definition binary32 := binary_float 24 128.
 
 Let Hprec : (0 < 24)%Z.
@@ -527,7 +535,7 @@ apply refl_equal.
 Qed.
 
 Definition default_nan_pl32 : bool * nan_pl 24 :=
-  (false, exist _ (nat_iter 22 xO xH) (refl_equal true)).
+  (false, exist _ (iter_nat 22 _ xO xH) (refl_equal true)).
 
 Definition unop_nan_pl32 (f : binary32) : bool * nan_pl 24 :=
   match f with
@@ -557,6 +565,8 @@ End B32_Bits.
 (** Specialization for IEEE double precision operations *)
 Section B64_Bits.
 
+Implicit Arguments B754_nan [[prec] [emax]].
+
 Definition binary64 := binary_float 53 1024.
 
 Let Hprec : (0 < 53)%Z.
@@ -568,7 +578,7 @@ apply refl_equal.
 Qed.
 
 Definition default_nan_pl64 : bool * nan_pl 53 :=
-  (false, exist _ (nat_iter 51 xO xH) (refl_equal true)).
+  (false, exist _ (iter_nat 51 _ xO xH) (refl_equal true)).
 
 Definition unop_nan_pl64 (f : binary64) : bool * nan_pl 53 :=
   match f with

src/Calc/Fcalc_bracket.v

@@ -168,7 +168,7 @@ apply Rplus_lt_reg_r with (d * (v - 1))%R.
 ring_simplify.
 rewrite Rmult_comm.
 now apply Rmult_lt_compat_l.
-apply Rplus_lt_reg_r with (-u * v)%R.
+apply Rplus_lt_reg_l with (-u * v)%R.
 replace (- u * v + (d + v * (u - d)))%R with (d * (1 - v))%R by ring.
 replace (- u * v + u)%R with (u * (1 - v))%R by ring.
 apply Rmult_lt_compat_r.

src/Calc/Fcalc_ops.v

@@ -28,6 +28,8 @@ Variable beta : radix.
 
 Notation bpow e := (bpow beta e).
 
+Implicit Arguments Float [[beta]].
+
 Definition Falign (f1 f2 : float beta) :=
   let '(Float m1 e1) := f1 in
   let '(Float m2 e2) := f2 in
@@ -38,7 +40,7 @@ Definition Falign (f1 f2 : float beta) :=
 Theorem Falign_spec :
   forall f1 f2 : float beta,
   let '(m1, m2, e) := Falign f1 f2 in
-  F2R f1 = F2R (Float beta m1 e) /\ F2R f2 = F2R (Float beta m2 e).
+  F2R f1 = @F2R beta (Float m1 e) /\ F2R f2 = @F2R beta (Float m2 e).
 Proof.
 unfold Falign.
 intros (m1, e1) (m2, e2).
@@ -61,9 +63,9 @@ case (Zmin_spec e1 e2); intros (H1,H2); easy.
 case (Zmin_spec e1 e2); intros (H1,H2); easy.
 Qed.
 
-Definition Fopp (f1: float beta) :=
+Definition Fopp (f1 : float beta) : float beta :=
   let '(Float m1 e1) := f1 in
-  Float beta (-m1)%Z e1.
+  Float (-m1)%Z e1.
 
 Theorem F2R_opp :
   forall f1 : float beta,
@@ -72,9 +74,9 @@ intros (m1,e1).
 apply F2R_Zopp.
 Qed.
 
-Definition Fabs (f1: float beta) :=
+Definition Fabs (f1 : float beta) : float beta :=
   let '(Float m1 e1) := f1 in
-  Float beta (Zabs m1)%Z e1.
+  Float (Zabs m1)%Z e1.
 
 Theorem F2R_abs :
   forall f1 : float beta,
@@ -83,9 +85,9 @@ intros (m1,e1).
 apply F2R_Zabs.
 Qed.
 
-Definition Fplus (f1 f2 : float beta) :=
+Definition Fplus (f1 f2 : float beta) : float beta :=
   let '(m1, m2 ,e) := Falign f1 f2 in
-  Float beta (m1 + m2) e.
+  Float (m1 + m2) e.
 
 Theorem F2R_plus :
   forall f1 f2 : float beta,
@@ -104,7 +106,7 @@ Qed.
 
 Theorem Fplus_same_exp :
   forall m1 m2 e,
-  Fplus (Float beta m1 e) (Float beta m2 e) = Float beta (m1 + m2) e.
+  Fplus (Float m1 e) (Float m2 e) = Float (m1 + m2) e.
 Proof.
 intros m1 m2 e.
 unfold Fplus.
@@ -136,17 +138,17 @@ Qed.
 
 Theorem Fminus_same_exp :
   forall m1 m2 e,
-  Fminus (Float beta m1 e) (Float beta m2 e) = Float beta (m1 - m2) e.
+  Fminus (Float m1 e) (Float m2 e) = Float (m1 - m2) e.
 Proof.
 intros m1 m2 e.
 unfold Fminus.
 apply Fplus_same_exp.
 Qed.
 
-Definition Fmult (f1 f2 : float beta) :=
+Definition Fmult (f1 f2 : float beta) : float beta :=
   let '(Float m1 e1) := f1 in
   let '(Float m2 e2) := f2 in
-  Float beta (m1 * m2) (e1 + e2).
+  Float (m1 * m2) (e1 + e2).
 
 Theorem F2R_mult :
   forall f1 f2 : float beta,

src/Core/Fcore_Raux.v

@@ -73,6 +73,24 @@ apply Rplus_eq_reg_l with r.
 now rewrite 2!(Rplus_comm r).
 Qed.
 
+Theorem Rplus_lt_reg_l :
+  forall r r1 r2 : R,
+  (r + r1 < r + r2)%R -> (r1 < r2)%R.
+Proof.
+intros.
+solve [ apply Rplus_lt_reg_l with (1 := H) |
+        apply Rplus_lt_reg_r with (1 := H) ].
+Qed.
+
+Theorem Rplus_lt_reg_r :
+  forall r r1 r2 : R,
+  (r1 + r < r2 + r)%R -> (r1 < r2)%R.
+Proof.
+intros.
+apply Rplus_lt_reg_l with r.
+now rewrite 2!(Rplus_comm r).
+Qed.
+
 Theorem Rplus_le_reg_r :
   forall r r1 r2 : R,
   (r1 + r <= r2 + r)%R -> (r1 <= r2)%R.

src/Core/Fcore_Zaux.v

@@ -18,7 +18,7 @@ COPYING file for more details.
 *)
 
 Require Import ZArith.
-Require Import ZOdiv.
+Require Import Zquot.
 
 Section Zmissing.
 
@@ -385,26 +385,26 @@ Qed.
 
 Theorem ZOmod_eq :
   forall a b,
-  ZOmod a b = (a - ZOdiv a b * b)%Z.
+  Z.rem a b = (a - Z.quot a b * b)%Z.
 Proof.
 intros a b.
-rewrite (ZO_div_mod_eq a b) at 2.
+rewrite (Z.quot_rem' a b) at 2.
 ring.
 Qed.
 
 Theorem ZOmod_mod_mult :
   forall n a b,
-  ZOmod (ZOmod n (a * b)) b = ZOmod n b.
+  Z.rem (Z.rem n (a * b)) b = Z.rem n b.
 Proof.
 intros n a b.
-assert (ZOmod n (a * b) = n + - (ZOdiv n (a * b) * a) * b)%Z.
+assert (Z.rem n (a * b) = n + - (Z.quot n (a * b) * a) * b)%Z.
 rewrite <- Zopp_mult_distr_l.
 rewrite <- Zmult_assoc.
 apply ZOmod_eq.
 rewrite H.
-apply ZO_mod_plus.
+apply Z_rem_plus.
 rewrite <- H.
-apply ZOmod_sgn2.
+apply Zrem_sgn2.
 Qed.
 
 Theorem Zdiv_mod_mult :
@@ -434,73 +434,73 @@ Qed.
 
 Theorem ZOdiv_mod_mult :
   forall n a b,
-  (ZOdiv (ZOmod n (a * b)) a) = ZOmod (ZOdiv n a) b.
+  (Z.quot (Z.rem n (a * b)) a) = Z.rem (Z.quot n a) b.
 Proof.
 intros n a b.
 destruct (Z_eq_dec a 0) as [Za|Za].
 rewrite Za.
-now rewrite 2!ZOdiv_0_r, ZOmod_0_l.
-assert (ZOmod n (a * b) = n + - (ZOdiv (ZOdiv n a) b * b) * a)%Z.
+now rewrite 2!Zquot_0_r, Zrem_0_l.
+assert (Z.rem n (a * b) = n + - (Z.quot (Z.quot n a) b * b) * a)%Z.
 rewrite (ZOmod_eq n (a * b)) at 1.
-rewrite ZOdiv_ZOdiv.
+rewrite Zquot_Zquot.
 ring.
 rewrite H.
-rewrite ZO_div_plus with (2 := Za).
+rewrite Z_quot_plus with (2 := Za).
 apply sym_eq.
 apply ZOmod_eq.
 rewrite <- H.
-apply ZOmod_sgn2.
+apply Zrem_sgn2.
 Qed.
 
 Theorem ZOdiv_small_abs :
   forall a b,
-  (Zabs a < b)%Z -> ZOdiv a b = Z0.
+  (Zabs a < b)%Z -> Z.quot a b = Z0.
 Proof.
 intros a b Ha.
 destruct (Zle_or_lt 0 a) as [H|H].
-apply ZOdiv_small.
+apply Zquot_small.
 split.
 exact H.
 now rewrite Zabs_eq in Ha.
 apply Zopp_inj.
-rewrite <- ZOdiv_opp_l, Zopp_0.
-apply ZOdiv_small.
+rewrite <- Zquot_opp_l, Zopp_0.
+apply Zquot_small.
 generalize (Zabs_non_eq a).
 omega.
 Qed.
 
 Theorem ZOmod_small_abs :
   forall a b,
-  (Zabs a < b)%Z -> ZOmod a b = a.
+  (Zabs a < b)%Z -> Z.rem a b = a.
 Proof.
 intros a b Ha.
 destruct (Zle_or_lt 0 a) as [H|H].
-apply ZOmod_small.
+apply Zrem_small.
 split.
 exact H.
 now rewrite Zabs_eq in Ha.
 apply Zopp_inj.
-rewrite <- ZOmod_opp_l.
-apply ZOmod_small.
+rewrite <- Zrem_opp_l.
+apply Zrem_small.
 generalize (Zabs_non_eq a).
 omega.
 Qed.
 
 Theorem ZOdiv_plus :
   forall a b c, (0 <= a * b)%Z ->
-  (ZOdiv (a + b) c = ZOdiv a c + ZOdiv b c + ZOdiv (ZOmod a c + ZOmod b c) c)%Z.
+  (Z.quot (a + b) c = Z.quot a c + Z.quot b c + Z.quot (Z.rem a c + Z.rem b c) c)%Z.
 Proof.
 intros a b c Hab.
 destruct (Z_eq_dec c 0) as [Zc|Zc].
-now rewrite Zc, 4!ZOdiv_0_r.
+now rewrite Zc, 4!Zquot_0_r.
 apply Zmult_reg_r with (1 := Zc).
 rewrite 2!Zmult_plus_distr_l.
-assert (forall d, ZOdiv d c * c = d - ZOmod d c)%Z.
+assert (forall d, Z.quot d c * c = d - Z.rem d c)%Z.
 intros d.
 rewrite ZOmod_eq.
 ring.
 rewrite 4!H.
-rewrite <- ZOplus_mod with (1 := Hab).
+rewrite <- Zplus_rem with (1 := Hab).
 ring.
 Qed.
 
@@ -543,14 +543,14 @@ Qed.
 
 Theorem Zsame_sign_odiv :
   forall u v, (0 <= v)%Z ->
-  (0 <= u * ZOdiv u v)%Z.
+  (0 <= u * Z.quot u v)%Z.
 Proof.
 intros u v Hv.
 apply Zsame_sign_imp ; intros Hu.
-apply ZO_div_pos with (2 := Hv).
+apply Z_quot_pos with (2 := Hv).
 now apply Zlt_le_weak.
-rewrite <- ZOdiv_opp_l.
-apply ZO_div_pos with (2 := Hv).
+rewrite <- Zquot_opp_l.
+apply Z_quot_pos with (2 := Hv).
 now apply Zlt_le_weak.
 Qed.
 

src/Core/Fcore_generic_fmt.v

@@ -1793,7 +1793,7 @@ rewrite Z2R_plus. simpl.
 destruct (Rcompare_spec (x - Z2R (Zfloor x)) (/ 2)) as [H1|H1|H1] ; apply sym_eq.
 (* . *)
 apply Rcompare_Lt.
-apply Rplus_lt_reg_r with (x - Z2R (Zfloor x))%R.
+apply Rplus_lt_reg_l with (x - Z2R (Zfloor x))%R.
 replace (x - Z2R (Zfloor x) + (x - Z2R (Zfloor x)))%R with ((x - Z2R (Zfloor x)) * 2)%R by ring.
 replace (x - Z2R (Zfloor x) + (Z2R (Zfloor x) + 1 - x))%R with (/2 * 2)%R by field.
 apply Rmult_lt_compat_r with (2 := H1).
@@ -1805,7 +1805,7 @@ rewrite H1.
 field.
 (* . *)
 apply Rcompare_Gt.
-apply Rplus_lt_reg_r with (x - Z2R (Zfloor x))%R.
+apply Rplus_lt_reg_l with (x - Z2R (Zfloor x))%R.
 replace (x - Z2R (Zfloor x) + (x - Z2R (Zfloor x)))%R with ((x - Z2R (Zfloor x)) * 2)%R by ring.
 replace (x - Z2R (Zfloor x) + (Z2R (Zfloor x) + 1 - x))%R with (/2 * 2)%R by field.
 apply Rmult_lt_compat_r with (2 := H1).
@@ -1823,7 +1823,7 @@ rewrite Z2R_plus. simpl.
 destruct (Rcompare_spec (Z2R (Zfloor x) + 1 - x) (/ 2)) as [H1|H1|H1] ; apply sym_eq.
 (* . *)
 apply Rcompare_Lt.
-apply Rplus_lt_reg_r with (Z2R (Zfloor x) + 1 - x)%R.
+apply Rplus_lt_reg_l with (Z2R (Zfloor x) + 1 - x)%R.
 replace (Z2R (Zfloor x) + 1 - x + (Z2R (Zfloor x) + 1 - x))%R with ((Z2R (Zfloor x) + 1 - x) * 2)%R by ring.
 replace (Z2R (Zfloor x) + 1 - x + (x - Z2R (Zfloor x)))%R with (/2 * 2)%R by field.
 apply Rmult_lt_compat_r with (2 := H1).
@@ -1835,7 +1835,7 @@ rewrite H1.
 field.
 (* . *)
 apply Rcompare_Gt.
-apply Rplus_lt_reg_r with (Z2R (Zfloor x) + 1 - x)%R.
+apply Rplus_lt_reg_l with (Z2R (Zfloor x) + 1 - x)%R.
 replace (Z2R (Zfloor x) + 1 - x + (Z2R (Zfloor x) + 1 - x))%R with ((Z2R (Zfloor x) + 1 - x) * 2)%R by ring.
 replace (Z2R (Zfloor x) + 1 - x + (x - Z2R (Zfloor x)))%R with (/2 * 2)%R by field.
 apply Rmult_lt_compat_r with (2 := H1).
@@ -1861,11 +1861,11 @@ rewrite Zceil_floor_neq.
 rewrite Z2R_plus.
 simpl.
 apply Ropp_lt_cancel.
-apply Rplus_lt_reg_r with R1.
+apply Rplus_lt_reg_l with R1.
 replace (1 + -/2)%R with (/2)%R by field.
 now replace (1 + - (Z2R (Zfloor x) + 1 - x))%R with (x - Z2R (Zfloor x))%R by ring.
 apply Rlt_not_eq.
-apply Rplus_lt_reg_r with (- Z2R (Zfloor x))%R.
+apply Rplus_lt_reg_l with (- Z2R (Zfloor x))%R.
 apply Rlt_trans with (/2)%R.
 rewrite Rplus_opp_l.
 apply Rinv_0_lt_compat.
@@ -1897,7 +1897,7 @@ rewrite Hx.
 rewrite Rabs_minus_sym.
 now replace (1 - /2)%R with (/2)%R by field.
 apply Rlt_not_eq.
-apply Rplus_lt_reg_r with (- Z2R (Zfloor x))%R.
+apply Rplus_lt_reg_l with (- Z2R (Zfloor x))%R.
 rewrite Rplus_opp_l, Rplus_comm.
 fold (x - Z2R (Zfloor x))%R.
 rewrite Hx.

src/Core/Fcore_ulp.v

@@ -325,7 +325,7 @@ destruct (round_DN_or_UP beta fexp rnd x) as [H|H] ; rewrite H ; clear H.
 (* . *)
 rewrite Rabs_left1.
 rewrite Ropp_minus_distr.
-apply Rplus_lt_reg_r with (round beta fexp Zfloor x).
+apply Rplus_lt_reg_l with (round beta fexp Zfloor x).
 rewrite <- ulp_DN_UP with (1 := Hx).
 ring_simplify.
 assert (Hu: (x <= round beta fexp Zceil x)%R).