Add new assembly-mimicking operations rshi, cc_m, and cc_l

1 files changed, 32 insertions, 0 deletions

diff --git a/src/Util/ZUtil/CC.v b/src/Util/ZUtil/CC.v
new file mode 100644
index 000000000..fb2fb1b93
--- /dev/null
+++ b/src/Util/ZUtil/CC.v
@@ -0,0 +1,32 @@
+Require Import Coq.ZArith.ZArith Coq.micromega.Lia.
+Require Import Crypto.Util.Tactics.BreakMatch.
+Require Import Crypto.Util.ZUtil.Definitions.
+Require Import Crypto.Util.ZUtil.Hints.PullPush.
+Require Import Crypto.Util.ZUtil.Tactics.DivModToQuotRem.
+Require Import Crypto.Util.ZUtil.Tactics.ZeroBounds.
+Local Open Scope Z_scope.
+
+Module Z.
+  Hint Rewrite Z.log2_pow2 Z.pow_1_r using solve [auto using Z.log2_nonneg with zarith] : push_Zpow.
+
+  Lemma cc_m_eq : forall s x, 2 < s -> Z.cc_m s x = x / (s / 2).
+  Proof.
+    intros; cbv [Z.cc_m].
+    assert (1 <= Z.log2 s) by (rewrite <-Z.log2_2; auto using Z.log2_le_mono with lia).
+    break_match; [ | reflexivity ].
+    match goal with H : _ = s |- _ => rewrite <-H end.
+    autorewrite with Zshift_to_pow push_Zpow.
+    reflexivity.
+  Qed.
+
+  Lemma cc_m_small : forall s x, 2 < s -> s mod 2 = 0 -> 0 <= x < s -> 0 <= Z.cc_m s x < 2.
+  Proof.
+    intros. rewrite cc_m_eq by auto.
+    repeat match goal with
+           | _ => split
+           | _ => apply Z.div_lt_upper_bound
+           | _ => solve [Z.zero_bounds]
+           end.
+    Z.div_mod_to_quot_rem; lia.
+  Qed.
+End Z.
\ No newline at end of file