From 0ca8a19bf72ca2a53e5cbb027832a4d3609d8bcf Mon Sep 17 00:00:00 2001
From: soyouzpanda <soyouzpanda@soyouzpanda.fr>
Date: Sun, 2 Jun 2024 00:49:58 +0200
Subject: [PATCH] Smarter bwd_binary in interval domain

---
 domains/interval.ml | 48 ++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 41 insertions(+), 7 deletions(-)

diff --git a/domains/interval.ml b/domains/interval.ml
index d7ad380..50debd1 100644
--- a/domains/interval.ml
+++ b/domains/interval.ml
@@ -8,6 +8,8 @@ module Interval : NAKED_VALUE_DOMAIN = struct
   let rand a b = { lower = Z.min a b; upper = Z.max a b }
   let infty = Z.of_int64_unsigned Int64.max_int
   let min_infty = Z.neg infty
+  let pos = rand Z.one infty
+  let neg = rand min_infty Z.minus_one
 
   let rand3 a b c =
     let mi = List.fold_left Z.min a [ a; b; c ] in
@@ -20,19 +22,20 @@ module Interval : NAKED_VALUE_DOMAIN = struct
     rand mi ma
 
   let minus z = rand (Z.neg z.upper) (Z.neg z.lower)
-  
   let join z1 z2 = rand4 z1.lower z2.lower z1.upper z2.upper
+
   let meet z1 z2 =
     if Z.lt z1.upper z2.lower || Z.lt z2.upper z1.lower then raise Absurd
     else rand (Z.max z1.lower z2.lower) (Z.min z1.upper z2.upper)
+
   let widen z1 z2 =
     rand
       (if Z.lt z1.lower z2.lower then z1.lower else min_infty)
       (if Z.gt z1.upper z2.upper then z1.upper else infty)
+
   let narrow = meet
   let subset z1 z2 = Z.geq z1.lower z2.lower && Z.leq z1.upper z2.upper
 
-
   let binary z1 z2 = function
     | AST_PLUS -> rand (Z.add z1.lower z2.lower) (Z.add z1.upper z2.upper)
     | AST_MINUS -> rand (Z.sub z1.lower z2.upper) (Z.sub z1.upper z2.lower)
@@ -46,7 +49,8 @@ module Interval : NAKED_VALUE_DOMAIN = struct
           rand4 (Z.div z1.lower z2.lower) (Z.div z1.upper z2.lower)
             (Z.div z1.lower z2.upper) (Z.div z1.upper z2.upper)
     | AST_MODULO ->
-        if Z.sign z2.lower <> Z.sign z2.upper || Z.sign z2.lower = 0 then raise Absurd
+        if Z.sign z2.lower <> Z.sign z2.upper || Z.sign z2.lower = 0 then
+          raise Absurd
         else
           rand4 (Z.rem z1.lower z2.lower) (Z.rem z1.upper z2.lower)
             (Z.rem z1.lower z2.upper) (Z.rem z1.upper z2.upper)
@@ -97,8 +101,29 @@ module Interval : NAKED_VALUE_DOMAIN = struct
           let r1 = rand z1.lower (Z.min z1.upper z2.upper) in
           let r2 = rand (Z.max z1.lower z2.lower) z2.upper in
           (r1, r2)
-    | AST_GREATER -> let r1, r2 = compare z2 z1 AST_LESS in r2, r1
-    | AST_GREATER_EQUAL -> let r1, r2 = compare z2 z1 AST_LESS_EQUAL in r2, r1
+    | AST_GREATER ->
+        let r1, r2 = compare z2 z1 AST_LESS in
+        (r2, r1)
+    | AST_GREATER_EQUAL ->
+        let r1, r2 = compare z2 z1 AST_LESS_EQUAL in
+        (r2, r1)
+
+  let has_zero z = Z.leq z.lower Z.zero && Z.geq z.upper Z.zero
+  let has_one z = Z.leq z.lower Z.one && Z.geq z.upper Z.one
+  let has_minus_one z = Z.leq z.lower Z.minus_one && Z.geq z.upper Z.minus_one
+
+  let three_part z1 z2 op =
+    if has_one z2 then
+      if has_minus_one z2 then
+        let a = meet pos z2 in
+        let b = meet neg z2 in
+        join (binary z1 a op) (binary z1 b op)
+      else
+        let a = meet pos z2 in
+        binary z1 a op
+    else
+      let a = meet neg z2 in
+      binary z1 a op
 
   let bwd_binary z1 z2 op r =
     match op with
@@ -107,12 +132,21 @@ module Interval : NAKED_VALUE_DOMAIN = struct
     | AST_MINUS ->
         (meet z1 (binary r z2 AST_PLUS), meet z2 (binary z1 r AST_MINUS))
     | AST_MULTIPLY ->
-        (meet z1 (binary r z2 AST_DIVIDE), meet z2 (binary r z1 AST_DIVIDE))
+        if is_only_zero z1 || is_only_zero z2 then
+                if has_zero r then
+                        z1, z2
+                else raise Absurd
+        else
+          let z2' = meet z2 (three_part r z1 AST_DIVIDE) in
+          let z1' = meet z1 (three_part r z2 AST_DIVIDE) in
+          if has_zero r then
+            ( (if has_zero z1' then join z1' (const Z.zero) else z1'),
+              if has_zero z2' then join z2' (const Z.zero) else z2' )
+          else (z1', z2')
     | AST_DIVIDE ->
         (meet z1 (binary r z2 AST_MULTIPLY), meet z2 (binary z1 r AST_DIVIDE))
     | AST_MODULO -> (z1, z2)
 
-
   let print fmt z =
     Format.pp_print_string fmt "[";
     Z.pp_print fmt z.lower;