Commit 84335f01 authored by Guillaume Melquiond's avatar Guillaume Melquiond

Simplified proofs on rounding DN and UP for generic format.

parent ccbe9e16
This diff is collapsed.
......@@ -73,9 +73,9 @@ rewrite <- Ropp_involutive.
now apply generic_format_opp.
now apply canonic_opp.
now apply canonic_opp.
rewrite generic_DN_opp, <- opp_F2R.
rewrite rounding_DN_opp, <- opp_F2R.
now apply f_equal.
rewrite generic_UP_opp, <- opp_F2R.
rewrite rounding_UP_opp, <- opp_F2R.
now apply f_equal.
Qed.
......@@ -98,7 +98,7 @@ assert (Hd3 : Fnum xd = Z0).
apply F2R_eq_0_reg with beta (Fexp xd).
change (F2R xd = R0).
rewrite Hxd.
apply generic_DN_small_pos with (1 := Hex) (2 := Hxe).
apply rounding_DN_small_pos with (1 := Hex) (2 := Hxe).
assert (Hu3 : xu = Float beta (1 * Zpower (radix_val beta) (fexp ex - fexp (fexp ex + 1))) (fexp (fexp ex + 1))).
apply canonic_unicity with (1 := Hu).
apply (f_equal fexp).
......@@ -110,7 +110,7 @@ rewrite F2R_bpow.
apply sym_eq.
rewrite Hxu.
apply sym_eq.
apply generic_UP_small_pos with (1 := Hex) (2 := Hxe).
apply rounding_UP_small_pos with (1 := Hex) (2 := Hxe).
now eapply prop_exp.
rewrite Hd3, Hu3.
rewrite Zmult_1_l.
......@@ -146,7 +146,7 @@ destruct (total_order_T (bpow ex) (F2R xu)) as [[Hu2|Hu2]|Hu2].
(* - xu > bpow ex *)
elim (Rlt_not_le _ _ Hu2).
rewrite Hxu.
now apply generic_UP_large_pos_le_pow.
now apply (rounding_bounded_large_pos beta fexp ZrndUP x ex).
(* - xu = bpow ex *)
assert (Hu3: xu = Float beta (1 * Zpower (radix_val beta) (ex - fexp (ex + 1))) (fexp (ex + 1))).
apply canonic_unicity with (1 := Hu).
......
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