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Commit a0f1ebb4 by Guillaume Melquiond

### Factored exponent equalities between FLT and FIX.

parent b6a382bd
 ... ... @@ -170,6 +170,34 @@ apply iff_sym. now apply FLX_format_generic. Qed. Theorem FLT_exp_FIX : forall x, x <> R0 -> (Rabs x < bpow (emin + prec))%R -> FLT_exp (projT1 (ln_beta beta x)) = FIX_exp emin (projT1 (ln_beta beta x)). Proof. intros x Hx0 Hx. unfold FIX_exp, FLT_exp. rewrite Zmax_right. apply refl_equal. destruct (ln_beta beta x) as (ex, Hex). simpl. cut (ex - 1 < emin + prec)%Z. omega. apply <- (bpow_lt beta). apply Rle_lt_trans with (2 := Hx). now apply Hex. Qed. Theorem FLT_canonic_FIX : forall x : R, x <> R0 -> (Rabs x < bpow (emin + prec))%R -> forall f : float beta, ( canonic beta FLT_exp x f <-> canonic beta (FIX_exp emin) x f ). Proof. intros x Hx0 Hx f. unfold canonic. now rewrite FLT_exp_FIX. Qed. Theorem FLT_format_FIX : forall x, (Rabs x <= bpow (emin + prec))%R -> ... ...
 ... ... @@ -549,23 +549,6 @@ Variable Hp : Zlt 0 prec. Notation FLTf := (FLT_exp emin prec). Theorem FIX_FLT_exp_subnormal : forall x, x <> R0 -> (Rabs x < bpow (emin + prec))%R -> FIX_exp emin (projT1 (ln_beta beta x)) = FLTf (projT1 (ln_beta beta x)). Proof. intros x Hx0 Hx. unfold FIX_exp, FLT_exp. rewrite Zmax_right. apply refl_equal. destruct (ln_beta beta x) as (ex, Hex). simpl. cut (ex - 1 < emin + prec)%Z. omega. apply <- bpow_lt. eapply Rle_lt_trans with (2 := Hx). now apply Hex. Qed. Theorem DN_UP_parity_FLT_pos : DN_UP_parity_pos_prop FLTf. Proof. ... ... @@ -653,11 +636,9 @@ apply (DN_UP_parity_FIX emin x xd xu cd cu) ; trivial. intros H. apply Hfx. apply generic_format_fun_eq with (2 := H). apply FIX_FLT_exp_subnormal. intros H1. apply Hfx. rewrite H1. apply generic_format_0. apply sym_eq. apply FLT_exp_FIX. now apply Rgt_not_eq. rewrite Rabs_pos_eq. apply Rle_lt_trans with (1 := Hx). apply -> bpow_lt. ... ... @@ -665,8 +646,7 @@ apply Zlt_pred. now apply Rlt_le. (* .. *) apply canonic_fun_eq with (2 := Hd). apply sym_eq. apply FIX_FLT_exp_subnormal. apply FLT_exp_FIX. intros Hxd0. apply Zeven_not_Zodd with (1 := Heu). rewrite canonic_unicity with (f2 := Float beta 1 emin) (1 := Hu). ... ... @@ -714,8 +694,7 @@ apply generic_format_0. now apply Rlt_le. (* .. *) apply canonic_fun_eq with (2 := Hu). apply sym_eq. apply FIX_FLT_exp_subnormal. apply FLT_exp_FIX. apply Rgt_not_eq. apply Rlt_le_trans with (1 := Hx0). apply Hxu. ... ...
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