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author | David Monniaux <David.Monniaux@univ-grenoble-alpes.fr> | 2022-02-09 16:10:59 +0100 |
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committer | David Monniaux <David.Monniaux@univ-grenoble-alpes.fr> | 2022-02-09 16:10:59 +0100 |
commit | 57c868e304df143918fa3a99d6272437a14299cc (patch) | |
tree | a0101f670b65c738c0c1c0b0b4b6564ff5d57b40 /kvx | |
parent | 7b4583e6c008469a4300b2fe2d405c8de3753238 (diff) | |
download | compcert-kvx-57c868e304df143918fa3a99d6272437a14299cc.tar.gz compcert-kvx-57c868e304df143918fa3a99d6272437a14299cc.zip |
full2_div_longu_correct
Diffstat (limited to 'kvx')
-rw-r--r-- | kvx/FPDivision64.v | 93 |
1 files changed, 93 insertions, 0 deletions
diff --git a/kvx/FPDivision64.v b/kvx/FPDivision64.v index 53961294..38eb6c1b 100644 --- a/kvx/FPDivision64.v +++ b/kvx/FPDivision64.v @@ -2227,3 +2227,96 @@ Proof. f_equal. f_equal. ring. Qed. + +Definition full2_div_longu a b m := + let is_big := Val.cmpl_bool Clt b (Vlong Int64.zero) in + let is_one := Val.cmplu_bool (Mem.valid_pointer m) Cle b (Vlong Int64.one) in + let is_special := Val.or (Val.of_optbool is_big) (Val.of_optbool is_one) in + let if_big := Val.select (Val.cmplu_bool (Mem.valid_pointer m) Clt a b) + (Vlong Int64.zero) (Vlong Int64.one) Tlong in + let if_special := Val.select is_big if_big a Tlong in + Val.select (Val.cmp_bool Cne is_special (Vint Int.zero)) + if_special + (twostep_div_longu a b) Tlong. + +Lemma full2_div_longu_correct : + forall a b m + (b_NOT0 : (0 < Int64.unsigned b)%Z), + full2_div_longu (Vlong a) (Vlong b) m = Vlong (Int64.repr (Int64.unsigned a / Int64.unsigned b))%Z. +Proof. + + Local Opaque twostep_div_longu. + intros. + unfold full2_div_longu. + cbn. + unfold Int64.lt, Int64.ltu. + pose proof (Int64.unsigned_range a). + pose proof (Int64.unsigned_range b). + set (a' := Int64.unsigned a) in *. + set (b' := Int64.unsigned b) in *. + rewrite Int64.signed_zero. + rewrite Int64.unsigned_one. + destruct zlt. + { replace (Val.cmp_bool Cne + (Val.or Vtrue + (if negb (if zlt 1 b' then true else false) then Vtrue else Vfalse)) + (Vint Int.zero)) with (Some true) ; cycle 1. + { destruct zlt; reflexivity. + } + cbn. + destruct zlt; cbn. + { rewrite Zdiv_small by lia. + reflexivity. + } + rewrite one_bigb_div. + reflexivity. + { + change Int64.modulus with 18446744073709551616%Z in *. + split. 2: lia. + unfold b'. + rewrite Int64.unsigned_signed. + unfold Int64.lt. + rewrite Int64.signed_zero. + rewrite zlt_true by lia. + pose proof (Int64.signed_range b). + change Int64.min_signed with (-9223372036854775808)%Z in *. + change Int64.max_signed with (9223372036854775807)%Z in *. + change Int64.modulus with 18446744073709551616%Z in *. + lia. + } + change Int64.modulus with 18446744073709551616%Z in *. + lia. + } + destruct zlt; cbn. + { change (negb (Int.eq (Int.or Int.zero Int.zero) Int.zero)) with false. + cbn. + rewrite twostep_div_longu_mostb_correct. + { + cbn. + unfold Int64.eq. + fold b'. + rewrite Int64.unsigned_zero. + rewrite zeq_false by lia. + reflexivity. + } + + change Int64.modulus with 18446744073709551616%Z in *. + split. lia. + rewrite Int64.unsigned_signed. + unfold Int64.lt. + rewrite Int64.signed_zero. + rewrite zlt_false by lia. + pose proof (Int64.signed_range b). + change Int64.min_signed with (-9223372036854775808)%Z in *. + change Int64.max_signed with (9223372036854775807)%Z in *. + change Int64.modulus with 18446744073709551616%Z in *. + lia. + } + change (negb (Int.eq (Int.or Int.zero Int.one) Int.zero)) with true. + cbn. + replace b' with 1%Z by lia. + rewrite Z.div_1_r. + unfold a'. + rewrite Int64.repr_unsigned. + reflexivity. +Qed. |