From 6d3702edad1a69a08565a288f1153b4853ba3b25 Mon Sep 17 00:00:00 2001
From: Jason Gross <jagro@google.com>
Date: Tue, 26 Jun 2018 13:23:40 -0400
Subject: Slightly better definitions of some ZUtil functions

This way we can just directly reify most of the primitives we care
about.
---
 src/Util/ZUtil/AddGetCarry.v |  3 +--
 src/Util/ZUtil/CPS.v         | 14 ++++++--------
 src/Util/ZUtil/Definitions.v | 18 ++++++++----------
 3 files changed, 15 insertions(+), 20 deletions(-)

diff --git a/src/Util/ZUtil/AddGetCarry.v b/src/Util/ZUtil/AddGetCarry.v
index e8f8d883d..5b8cbf13e 100644
--- a/src/Util/ZUtil/AddGetCarry.v
+++ b/src/Util/ZUtil/AddGetCarry.v
@@ -1,5 +1,4 @@
 Require Import Coq.ZArith.ZArith Coq.micromega.Lia.
-Require Import Crypto.Util.ZUtil.
 Require Import Crypto.Util.ZUtil.Definitions.
 Require Import Crypto.Util.ZUtil.Hints.ZArith.
 Require Import Crypto.Util.Prod.
@@ -64,7 +63,7 @@ Module Z.
         Z.add_get_carry_full Z.add_with_get_carry_full
         Z.add_get_carry Z.add_with_get_carry Z.add_with_carry
         Z.sub_get_borrow_full Z.sub_with_get_borrow_full
-        Z.sub_get_borrow Z.sub_with_get_borrow Z.sub_with_borrow.
+        Z.sub_get_borrow Z.sub_with_get_borrow Z.sub_with_borrow Let_In.
 
   Lemma add_get_carry_full_mod s x y :
     fst (Z.add_get_carry_full s x y)  = (x + y) mod s.
diff --git a/src/Util/ZUtil/CPS.v b/src/Util/ZUtil/CPS.v
index 3c0007c88..e2b21933b 100644
--- a/src/Util/ZUtil/CPS.v
+++ b/src/Util/ZUtil/CPS.v
@@ -121,14 +121,12 @@ Module Z.
 
   Definition mul_split_at_bitwidth_cps {T} (bitwidth : Z) (x y : Z) (f : Z * Z -> T) : T
     := dlet xy := x * y in
-        f (match bitwidth with
-           | Z.pos _ | Z0 => Z.land xy (Z.ones bitwidth)
-           | Z.neg _ => xy mod 2^bitwidth
-           end,
-           match bitwidth with
-           | Z.pos _ | Z0 => Z.shiftr xy bitwidth
-           | Z.neg _ => xy / 2^bitwidth
-           end).
+        f (if Z.geb bitwidth 0
+           then Z.land xy (Z.ones bitwidth)
+           else xy mod 2^bitwidth,
+           if Z.geb bitwidth 0
+           then Z.shiftr xy bitwidth
+           else xy / 2^bitwidth).
   Definition mul_split_at_bitwidth_cps_correct {T} (bitwidth : Z) (x y : Z) (f : Z * Z -> T)
     : @mul_split_at_bitwidth_cps T bitwidth x y f = f (Z.mul_split_at_bitwidth bitwidth x y)
     := eq_refl.
diff --git a/src/Util/ZUtil/Definitions.v b/src/Util/ZUtil/Definitions.v
index 67ccbc772..373c71763 100644
--- a/src/Util/ZUtil/Definitions.v
+++ b/src/Util/ZUtil/Definitions.v
@@ -31,7 +31,7 @@ Module Z.
   Definition add_with_carry (c : Z) (x y : Z) : Z
     := c + x + y.
   Definition add_with_get_carry (bitwidth : Z) (c : Z) (x y : Z) : Z * Z
-    := get_carry bitwidth (add_with_carry c x y).
+    := dlet v := add_with_carry c x y in get_carry bitwidth v.
   Definition add_get_carry (bitwidth : Z) (x y : Z) : Z * Z
     := add_with_get_carry bitwidth 0 x y.
 
@@ -41,7 +41,7 @@ Module Z.
   Definition sub_with_borrow (c : Z) (x y : Z) : Z
     := add_with_carry (-c) x (-y).
   Definition sub_with_get_borrow (bitwidth : Z) (c : Z) (x y : Z) : Z * Z
-    := get_borrow bitwidth (sub_with_borrow c x y).
+    := dlet v := sub_with_borrow c x y in get_borrow bitwidth v.
   Definition sub_get_borrow (bitwidth : Z) (x y : Z) : Z * Z
     := sub_with_get_borrow bitwidth 0 x y.
 
@@ -66,14 +66,12 @@ Module Z.
 
   Definition mul_split_at_bitwidth (bitwidth : Z) (x y : Z) : Z * Z
     := dlet xy := x * y in
-        (match bitwidth with
-         | Z.pos _ | Z0 => xy &' Z.ones bitwidth
-         | Z.neg _ => xy mod 2^bitwidth
-         end,
-         match bitwidth with
-         | Z.pos _ | Z0 => xy >> bitwidth
-         | Z.neg _ => xy / 2^bitwidth
-         end).
+       (if Z.geb bitwidth 0
+        then xy &' Z.ones bitwidth
+        else xy mod 2^bitwidth,
+        if Z.geb bitwidth 0
+        then xy >> bitwidth
+        else xy / 2^bitwidth).
   Definition mul_split (s x y : Z) : Z * Z
     := if s =? 2^Z.log2 s
        then mul_split_at_bitwidth (Z.log2 s) x y
-- 
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