diff options
Diffstat (limited to 'lib/coq/Sail2_operators_mwords.v')
| -rw-r--r-- | lib/coq/Sail2_operators_mwords.v | 16 |
1 files changed, 16 insertions, 0 deletions
diff --git a/lib/coq/Sail2_operators_mwords.v b/lib/coq/Sail2_operators_mwords.v index e37e9d26..7e4abe29 100644 --- a/lib/coq/Sail2_operators_mwords.v +++ b/lib/coq/Sail2_operators_mwords.v @@ -172,16 +172,32 @@ Definition zero_extend {a} (v : mword a) (n : Z) `{ArithFact (n >= a)} : mword n Definition sign_extend {a} (v : mword a) (n : Z) `{ArithFact (n >= a)} : mword n := exts_vec n v. +Definition zeros (n : Z) `{ArithFact (n >= 0)} : mword n. +refine (cast_to_mword (Word.wzero (Z.to_nat n)) _). +unwrap_ArithFacts. +apply Z2Nat.id. +auto with zarith. +Defined. + Lemma truncate_eq {m n} : m >= 0 -> m <= n -> (Z.to_nat n = Z.to_nat m + (Z.to_nat n - Z.to_nat m))%nat. intros. assert ((Z.to_nat m <= Z.to_nat n)%nat). { apply Z2Nat.inj_le; omega. } omega. Qed. +Lemma truncateLSB_eq {m n} : m >= 0 -> m <= n -> (Z.to_nat n = (Z.to_nat n - Z.to_nat m) + Z.to_nat m)%nat. +intros. +assert ((Z.to_nat m <= Z.to_nat n)%nat). +{ apply Z2Nat.inj_le; omega. } +omega. +Qed. Definition vector_truncate {n} (v : mword n) (m : Z) `{ArithFact (m >= 0)} `{ArithFact (m <= n)} : mword m := cast_to_mword (Word.split1 _ _ (cast_word (get_word v) (ltac:(unwrap_ArithFacts; apply truncate_eq; auto) : Z.to_nat n = Z.to_nat m + (Z.to_nat n - Z.to_nat m))%nat)) (ltac:(unwrap_ArithFacts; apply Z2Nat.id; omega) : Z.of_nat (Z.to_nat m) = m). +Definition vector_truncateLSB {n} (v : mword n) (m : Z) `{ArithFact (m >= 0)} `{ArithFact (m <= n)} : mword m := + cast_to_mword (Word.split2 _ _ (cast_word (get_word v) (ltac:(unwrap_ArithFacts; apply truncateLSB_eq; auto) : Z.to_nat n = (Z.to_nat n - Z.to_nat m) + Z.to_nat m)%nat)) (ltac:(unwrap_ArithFacts; apply Z2Nat.id; omega) : Z.of_nat (Z.to_nat m) = m). + Lemma concat_eq {a b} : a >= 0 -> b >= 0 -> Z.of_nat (Z.to_nat b + Z.to_nat a)%nat = a + b. intros. rewrite Nat2Z.inj_add. |