[sledge] Clamp result of binary Z ops to bitwidth

Summary:
Previously only the arguments of binary operations on integers were
clamped to the given bitwidth, but the results could overflow. This
was incorrect.

Also, use a clamped version of equality to simplify equality
expressions. This was previously overlooked.

Reviewed By: mbouaziz

Differential Revision: D12854502

fbshipit-source-id: 8786b4217

sledge/src/llair/exp.ml

@@ -30,28 +30,33 @@ module Z = struct
   let clamp ~signed bits z =
     if signed then Z.signed_extract z 0 bits else Z.extract z 0 bits
 
-  let clamp_binop ~signed bits op x y =
+  let clamp_cmp ~signed bits op x y =
     op (clamp ~signed bits x) (clamp ~signed bits y)
 
-  let leq ~bits x y = clamp_binop ~signed:true bits Z.leq x y
-  let geq ~bits x y = clamp_binop ~signed:true bits Z.geq x y
-  let lt ~bits x y = clamp_binop ~signed:true bits Z.lt x y
-  let gt ~bits x y = clamp_binop ~signed:true bits Z.gt x y
-  let uleq ~bits x y = clamp_binop ~signed:false bits Z.leq x y
-  let ugeq ~bits x y = clamp_binop ~signed:false bits Z.geq x y
-  let ult ~bits x y = clamp_binop ~signed:false bits Z.lt x y
-  let ugt ~bits x y = clamp_binop ~signed:false bits Z.gt x y
   let neg ~bits z = Z.neg (clamp bits ~signed:true z)
-  let add ~bits x y = clamp_binop ~signed:true bits Z.add x y
+
-  let sub ~bits x y = clamp_binop ~signed:true bits Z.sub x y
+  let clamp_bop ~signed bits op x y =
-  let mul ~bits x y = clamp_binop ~signed:true bits Z.mul x y
+    clamp ~signed bits (op (clamp ~signed bits x) (clamp ~signed bits y))
-  let div ~bits x y = clamp_binop ~signed:true bits Z.div x y
+
-  let rem ~bits x y = clamp_binop ~signed:true bits Z.rem x y
+  let eq ~bits x y = clamp_cmp ~signed:true bits Z.equal x y
-  let udiv ~bits x y = clamp_binop ~signed:false bits Z.div x y
+  let leq ~bits x y = clamp_cmp ~signed:true bits Z.leq x y
-  let urem ~bits x y = clamp_binop ~signed:false bits Z.rem x y
+  let geq ~bits x y = clamp_cmp ~signed:true bits Z.geq x y
-  let logand ~bits x y = clamp_binop ~signed:true bits Z.logand x y
+  let lt ~bits x y = clamp_cmp ~signed:true bits Z.lt x y
-  let logor ~bits x y = clamp_binop ~signed:true bits Z.logor x y
+  let gt ~bits x y = clamp_cmp ~signed:true bits Z.gt x y
-  let logxor ~bits x y = clamp_binop ~signed:true bits Z.logxor x y
+  let uleq ~bits x y = clamp_cmp ~signed:false bits Z.leq x y
+  let ugeq ~bits x y = clamp_cmp ~signed:false bits Z.geq x y
+  let ult ~bits x y = clamp_cmp ~signed:false bits Z.lt x y
+  let ugt ~bits x y = clamp_cmp ~signed:false bits Z.gt x y
+  let add ~bits x y = clamp_bop ~signed:true bits Z.add x y
+  let sub ~bits x y = clamp_bop ~signed:true bits Z.sub x y
+  let mul ~bits x y = clamp_bop ~signed:true bits Z.mul x y
+  let div ~bits x y = clamp_bop ~signed:true bits Z.div x y
+  let rem ~bits x y = clamp_bop ~signed:true bits Z.rem x y
+  let udiv ~bits x y = clamp_bop ~signed:false bits Z.div x y
+  let urem ~bits x y = clamp_bop ~signed:false bits Z.rem x y
+  let logand ~bits x y = clamp_bop ~signed:true bits Z.logand x y
+  let logor ~bits x y = clamp_bop ~signed:true bits Z.logor x y
+  let logxor ~bits x y = clamp_bop ~signed:true bits Z.logxor x y
   let shift_left ~bits z i = Z.shift_left (clamp bits ~signed:true z) i
   let shift_right ~bits z i = Z.shift_right (clamp bits ~signed:true z) i
 
@@ -552,7 +557,8 @@ let rec simp_not (typ : Typ.t) exp =
 and simp_eq x y =
   match (x, y) with
   (* i = j *)
-  | Integer {data= i}, Integer {data= j} -> bool (Z.equal i j)
+  | Integer {data= i; typ= Integer {bits}}, Integer {data= j} ->
+      bool (Z.eq ~bits i j)
   (* e+i = j ==> e = j-i *)
   | ( App {op= App {op= Add; arg= e}; arg= Integer {data= i}}
     , Integer {data= j; typ= Integer {bits} as typ} ) ->
@@ -577,7 +583,8 @@ and simp_eq x y =
 and simp_dq x y =
   match (x, y) with
   (* i != j *)
-  | Integer {data= i}, Integer {data= j} -> bool (not (Z.equal i j))
+  | Integer {data= i; typ= Integer {bits}}, Integer {data= j} ->
+      bool (not (Z.eq ~bits i j))
   (* e+i != j ==> e != j-i *)
   | ( App {op= App {op= Add; arg= e}; arg= Integer {data= i}}
     , Integer {data= j; typ= Integer {bits} as typ} ) ->

sledge/src/llair/exp_test.ml

@@ -0,0 +1,50 @@
+(*
+ * Copyright (c) 2018-present, Facebook, Inc.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ *)
+
+let%test_module _ =
+  ( module struct
+    let pf = Format.printf "%t%a@." (fun _ -> Trace.flush ()) Exp.pp
+    let char = Typ.integer ~bits:8
+    let ( ! ) i = Exp.integer (Z.of_int i) char
+    let ( + ) = Exp.add
+    let ( && ) = Exp.and_
+    let ( || ) = Exp.or_
+
+    let%test "booleans distinct" =
+      Exp.is_false
+        (Exp.eq
+           (Exp.integer Z.minus_one Typ.bool)
+           (Exp.integer Z.zero Typ.bool))
+
+    let%test "unsigned booleans distinct" =
+      Exp.is_false
+        (Exp.eq (Exp.integer Z.one Typ.bool) (Exp.integer Z.zero Typ.bool))
+
+    let%test "boolean overflow" =
+      Exp.is_true
+        (Exp.eq
+           (Exp.integer Z.minus_one Typ.bool)
+           (Exp.integer Z.one Typ.bool))
+
+    let%test "unsigned boolean overflow" =
+      Exp.is_true
+        (Exp.uge
+           (Exp.integer Z.minus_one Typ.bool)
+           (Exp.integer Z.one Typ.bool))
+
+    let%expect_test _ =
+      pf (!42 + !13) ;
+      [%expect {| 55 |}]
+
+    let%expect_test _ =
+      pf (!(-128) && !127) ;
+      [%expect {| 0 |}]
+
+    let%expect_test _ =
+      pf (!(-128) || !127) ;
+      [%expect {| -1 |}]
+  end )