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| author | Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2022-04-26 11:14:06 +0200 |
|---|---|---|
| committer | Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2022-04-26 11:14:06 +0200 |
| commit | e8c312eecf96ae1703f7ba0b65f107233d340238 (patch) | |
| tree | f05cdd8084fcbc2098bbad14dc5b3fe38bf34ba4 /flocq/Calc | |
| parent | a4da014c354bff05c24210e694a3b4593d3f38ee (diff) | |
| download | compcert-e8c312eecf96ae1703f7ba0b65f107233d340238.tar.gz compcert-e8c312eecf96ae1703f7ba0b65f107233d340238.zip | |
Upgrade to Flocq 4.1.
Diffstat (limited to 'flocq/Calc')
| -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 |