diff options
Diffstat (limited to 'flocq/Calc/Round.v')
| -rw-r--r-- | flocq/Calc/Round.v | 16 |
1 files changed, 16 insertions, 0 deletions
diff --git a/flocq/Calc/Round.v b/flocq/Calc/Round.v index 40da2f08..b4693ed7 100644 --- a/flocq/Calc/Round.v +++ b/flocq/Calc/Round.v @@ -114,6 +114,12 @@ Qed. Definition cond_incr (b : bool) m := if b then (m + 1)%Z else m. +Lemma le_cond_incr_le : + forall b m, (m <= cond_incr b m <= m + 1)%Z. +Proof. +unfold cond_incr; intros b; case b; lia. +Qed. + Theorem inbetween_float_round_sign : forall rnd choice, ( forall x m l, inbetween_int m (Rabs x) l -> @@ -590,6 +596,16 @@ now case Rlt_bool. lia. Qed. +Theorem inbetween_float_NA_sign : + forall x m l, + let e := cexp beta fexp x in + inbetween_float beta m e (Rabs x) l -> + round beta fexp ZnearestA x = F2R (Float beta (cond_Zopp (Rlt_bool x 0) (cond_incr (round_N true l) m)) e). +Proof. +apply inbetween_float_round_sign with (choice := fun s m l => cond_incr (round_N true l) m). +exact inbetween_int_NA_sign. +Qed. + Definition truncate_aux t k := let '(m, e, l) := t in let p := Zpower beta k in |