Fix unsigned/signed issues.

4 files changed, 92 insertions, 97 deletions

diff --git a/src/common/Coquplib.v b/src/common/Coquplib.v
index b8a02d2..5de1e7c 100644
--- a/src/common/Coquplib.v
+++ b/src/common/Coquplib.v
@@ -69,45 +69,52 @@ Ltac kill_bools :=
 
 Ltac unfold_constants :=
   repeat match goal with
-         | [ _ : _ |- context[Integers.Ptrofs.modulus] ] =>
+         | [ |- context[Integers.Ptrofs.modulus] ] =>
            replace Integers.Ptrofs.modulus with 4294967296 by reflexivity
          | [ H : context[Integers.Ptrofs.modulus] |- _ ] =>
            replace Integers.Ptrofs.modulus with 4294967296 in H by reflexivity
 
-         | [ _ : _ |- context[Integers.Ptrofs.min_signed] ] =>
+         | [ |- context[Integers.Ptrofs.min_signed] ] =>
            replace Integers.Ptrofs.min_signed with (-2147483648) by reflexivity
          | [ H : context[Integers.Ptrofs.min_signed] |- _ ] =>
            replace Integers.Ptrofs.min_signed with (-2147483648) in H by reflexivity
 
-         | [ _ : _ |- context[Integers.Ptrofs.max_signed] ] =>
+         | [ |- context[Integers.Ptrofs.max_signed] ] =>
            replace Integers.Ptrofs.max_signed with 2147483647 by reflexivity
          | [ H : context[Integers.Ptrofs.max_signed] |- _ ] =>
            replace Integers.Ptrofs.max_signed with 2147483647 in H by reflexivity
 
-         | [ _ : _ |- context[Integers.Ptrofs.max_unsigned] ] =>
+         | [ |- context[Integers.Ptrofs.max_unsigned] ] =>
            replace Integers.Ptrofs.max_unsigned with 4294967295 by reflexivity
          | [ H : context[Integers.Ptrofs.max_unsigned] |- _ ] =>
            replace Integers.Ptrofs.max_unsigned with 4294967295 in H by reflexivity
 
-         | [ _ : _ |- context[Integers.Int.modulus] ] =>
+         | [ |- context[Integers.Int.modulus] ] =>
            replace Integers.Int.modulus with 4294967296 by reflexivity
          | [ H : context[Integers.Int.modulus] |- _ ] =>
            replace Integers.Int.modulus with 4294967296 in H by reflexivity
 
-         | [ _ : _ |- context[Integers.Int.min_signed] ] =>
+         | [ |- context[Integers.Int.min_signed] ] =>
            replace Integers.Int.min_signed with (-2147483648) by reflexivity
          | [ H : context[Integers.Int.min_signed] |- _ ] =>
            replace Integers.Int.min_signed with (-2147483648) in H by reflexivity
 
-         | [ _ : _ |- context[Integers.Int.max_signed] ] =>
+         | [ |- context[Integers.Int.max_signed] ] =>
            replace Integers.Int.max_signed with 2147483647 by reflexivity
          | [ H : context[Integers.Int.max_signed] |- _ ] =>
            replace Integers.Int.max_signed with 2147483647 in H by reflexivity
 
-         | [ _ : _ |- context[Integers.Int.max_unsigned] ] =>
+         | [ |- context[Integers.Int.max_unsigned] ] =>
            replace Integers.Int.max_unsigned with 4294967295 by reflexivity
          | [ H : context[Integers.Int.max_unsigned] |- _ ] =>
            replace Integers.Int.max_unsigned with 4294967295 in H by reflexivity
+
+         | [ |- context[Integers.Ptrofs.unsigned (Integers.Ptrofs.repr ?x) ] ] =>
+           match (eval compute in (0 <=? x)) with
+           | true => replace (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr x))
+                    with x by reflexivity
+           | false => idtac
+           end
          end.
 
 Ltac simplify := unfold_constants; simpl in *;
diff --git a/src/common/IntegerExtra.v b/src/common/IntegerExtra.v
index 5f06e26..ec1fb07 100644
--- a/src/common/IntegerExtra.v
+++ b/src/common/IntegerExtra.v
@@ -105,10 +105,10 @@ Module PtrofsExtra.
       (m | Ptrofs.modulus) ->
       Ptrofs.signed x mod m = 0 ->
       Ptrofs.signed y mod m = 0 ->
-      (Ptrofs.signed (Ptrofs.add x y)) mod m = 0.
+      (Ptrofs.unsigned (Ptrofs.add x y)) mod m = 0.
   Proof.
     intros. unfold Ptrofs.add.
-    rewrite Ptrofs.signed_repr_eq.
+    rewrite Ptrofs.unsigned_repr_eq.
 
     repeat match goal with
            | [ _ : _ |- context[if ?x then _ else _] ] => destruct x
@@ -118,21 +118,23 @@ Module PtrofsExtra.
            end; try (simplify; lia); ptrofs_mod_tac m.
   Qed.
 
-  Lemma mul_divs :
+  Lemma mul_divu :
     forall x y,
-      0 <= Ptrofs.signed y ->
-      0 < Ptrofs.signed x ->
-      Ptrofs.signed y mod Ptrofs.signed x = 0 ->
-      (Integers.Ptrofs.mul x (Integers.Ptrofs.divs y x)) = y.
+      0 < Ptrofs.unsigned x ->
+      Ptrofs.unsigned y mod Ptrofs.unsigned x = 0 ->
+      (Integers.Ptrofs.mul x (Integers.Ptrofs.divu y x)) = y.
   Proof.
     intros.
 
-    pose proof (Ptrofs.mods_divs_Euclid y x).
-    pose proof (Zquot.Zrem_Zmod_zero (Ptrofs.signed y) (Ptrofs.signed x)).
-    apply <- H3 in H1; try lia; clear H3.
-    unfold Ptrofs.mods in H2.
-    rewrite H1 in H2.
-    replace (Ptrofs.repr 0) with (Ptrofs.zero) in H2 by reflexivity.
+    assert (x <> Ptrofs.zero).
+    { intro.
+      rewrite H1 in H.
+      replace (Ptrofs.unsigned Ptrofs.zero) with 0 in H by reflexivity.
+      lia. }
+
+    exploit (Ptrofs.modu_divu_Euclid y x); auto; intros.
+    unfold Ptrofs.modu in H2. rewrite H0 in H2.
+    replace (Ptrofs.repr 0) with Ptrofs.zero in H2 by reflexivity.
     rewrite Ptrofs.add_zero in H2.
     rewrite Ptrofs.mul_commut.
     congruence.
diff --git a/src/translation/HTLgen.v b/src/translation/HTLgen.v
index 54ad77a..59fb70a 100644
--- a/src/translation/HTLgen.v
+++ b/src/translation/HTLgen.v
@@ -280,32 +280,36 @@ Definition translate_condition (c : Op.condition) (args : list reg) : mon expr :
   | _, _ => error (Errors.msg "Htlgen: condition instruction not implemented: other")
   end.
 
-Definition check_address_parameter (p : Z) : bool :=
+Definition check_address_parameter_signed (p : Z) : bool :=
   Z.eqb (Z.modulo p 4) 0
   && Z.leb Integers.Ptrofs.min_signed p
   && Z.leb p Integers.Ptrofs.max_signed.
 
+Definition check_address_parameter_unsigned (p : Z) : bool :=
+  Z.eqb (Z.modulo p 4) 0
+  && Z.leb p Integers.Ptrofs.max_unsigned.
+
 Definition translate_eff_addressing (a: Op.addressing) (args: list reg) : mon expr :=
   match a, args with (* TODO: We should be more methodical here; what are the possibilities?*)
   | Op.Aindexed off, r1::nil =>
-    if (check_address_parameter off)
+    if (check_address_parameter_signed off)
     then ret (boplitz Vadd r1 off)
     else error (Errors.msg "Veriloggen: translate_eff_addressing address misaligned")
   | Op.Ascaled scale offset, r1::nil =>
-    if (check_address_parameter scale) && (check_address_parameter offset)
+    if (check_address_parameter_signed scale) && (check_address_parameter_signed offset)
     then ret (Vbinop Vadd (boplitz Vmul r1 scale) (Vlit (ZToValue 32 offset)))
     else error (Errors.msg "Veriloggen: translate_eff_addressing address misaligned")
   | Op.Aindexed2 offset, r1::r2::nil =>
-    if (check_address_parameter offset)
+    if (check_address_parameter_signed offset)
     then ret (Vbinop Vadd (Vvar r1) (boplitz Vadd r2 offset))
     else error (Errors.msg "Veriloggen: translate_eff_addressing address misaligned")
   | Op.Aindexed2scaled scale offset, r1::r2::nil => (* Typical for dynamic array addressing *)
-    if (check_address_parameter scale) && (check_address_parameter offset)
+    if (check_address_parameter_signed scale) && (check_address_parameter_signed offset)
     then ret (Vbinop Vadd (boplitz Vadd r1 offset) (boplitz Vmul r2 scale))
     else error (Errors.msg "Veriloggen: translate_eff_addressing address misaligned")
   | Op.Ainstack a, nil => (* We need to be sure that the base address is aligned *)
     let a := Integers.Ptrofs.unsigned a in
-    if (check_address_parameter a)
+    if (check_address_parameter_unsigned a)
     then ret (Vlit (ZToValue 32 a))
     else error (Errors.msg "Veriloggen: translate_eff_addressing address misaligned")
   | _, _ => error (Errors.msg "Veriloggen: translate_eff_addressing unsuported addressing")
@@ -392,19 +396,19 @@ Definition translate_arr_access (mem : AST.memory_chunk) (addr : Op.addressing)
            (args : list reg) (stack : reg) : mon expr :=
   match mem, addr, args with (* TODO: We should be more methodical here; what are the possibilities?*)
   | Mint32, Op.Aindexed off, r1::nil =>
-    if (check_address_parameter off)
-    then ret (Vvari stack (Vbinop Vdiv (boplitz Vadd r1 off) (Vlit (ZToValue 32 4))))
+    if (check_address_parameter_signed off)
+    then ret (Vvari stack (Vbinop Vdivu (boplitz Vadd r1 off) (Vlit (ZToValue 32 4))))
     else error (Errors.msg "HTLgen: translate_arr_access address misaligned")
   | Mint32, Op.Aindexed2scaled scale offset, r1::r2::nil => (* Typical for dynamic array addressing *)
-    if (check_address_parameter scale) && (check_address_parameter offset)
+    if (check_address_parameter_signed scale) && (check_address_parameter_signed offset)
     then ret (Vvari stack
-                    (Vbinop Vdiv
+                    (Vbinop Vdivu
                             (Vbinop Vadd (boplitz Vadd r1 offset) (boplitz Vmul r2 scale))
                             (ZToValue 32 4)))
     else error (Errors.msg "HTLgen: translate_arr_access address misaligned")
   | Mint32, Op.Ainstack a, nil => (* We need to be sure that the base address is aligned *)
-    let a := Integers.Ptrofs.signed a in
-    if (check_address_parameter a)
+    let a := Integers.Ptrofs.unsigned a in
+    if (check_address_parameter_unsigned a)
     then ret (Vvari stack (Vlit (ZToValue 32 (a / 4))))
     else error (Errors.msg "HTLgen: eff_addressing misaligned stack offset")
   | _, _, _ => error (Errors.msg "HTLgen: translate_arr_access unsuported addressing")
diff --git a/src/translation/HTLgenproof.v b/src/translation/HTLgenproof.v
index 1e16398..eb9ff7a 100644
--- a/src/translation/HTLgenproof.v
+++ b/src/translation/HTLgenproof.v
@@ -594,17 +594,17 @@ Section CORRECTNESS.
         invert H8.
         clear H0. clear H6.
 
-        unfold check_address_parameter in *. simplify.
+        unfold check_address_parameter_signed in *;
+        unfold check_address_parameter_unsigned in *; simplify.
 
         remember (Integers.Ptrofs.add (Integers.Ptrofs.repr (valueToZ asr # r0))
                                       (Integers.Ptrofs.of_int (Integers.Int.repr z))) as OFFSET.
 
         (** Read bounds assumption *)
-        assert (0 <= Integers.Ptrofs.signed OFFSET) as READ_BOUND_LOW by admit.
-        assert (Integers.Ptrofs.signed OFFSET < f.(RTL.fn_stacksize)) as READ_BOUND_HIGH by admit.
+        assert (Integers.Ptrofs.unsigned OFFSET < f.(RTL.fn_stacksize)) as READ_BOUND_HIGH by admit.
 
         (** Modular preservation proof *)
-        assert (Integers.Ptrofs.signed OFFSET mod 4 = 0) as MOD_PRESERVE.
+        assert (Integers.Ptrofs.unsigned OFFSET mod 4 = 0) as MOD_PRESERVE.
         { rewrite HeqOFFSET.
           apply PtrofsExtra.add_mod; simplify; try lia.
           exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *)
@@ -617,34 +617,28 @@ Section CORRECTNESS.
         (** Normalisation proof *)
         assert (Integers.Ptrofs.repr
                   (4 * Integers.Ptrofs.unsigned
-                         (Integers.Ptrofs.divs OFFSET (Integers.Ptrofs.repr 4))) = OFFSET)
+                         (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4))) = OFFSET)
           as NORMALISE.
         { replace 4 with (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr 4)) at 1 by reflexivity.
           rewrite <- PtrofsExtra.mul_unsigned.
-          apply PtrofsExtra.mul_divs; auto.
-          rewrite Integers.Ptrofs.signed_repr; simplify; lia. }
+          apply PtrofsExtra.mul_divu; simplify; auto; lia. }
 
         (** Normalised bounds proof *)
         assert (0 <=
-                Integers.Ptrofs.unsigned (Integers.Ptrofs.divs OFFSET (Integers.Ptrofs.repr 4))
+                Integers.Ptrofs.unsigned (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4))
                 < (RTL.fn_stacksize f / 4))
         as NORMALISE_BOUND.
         { split.
           apply Integers.Ptrofs.unsigned_range_2.
-          assert (forall x y, Integers.Ptrofs.divs x y = Integers.Ptrofs.divs x y ) by reflexivity.
-          unfold Integers.Ptrofs.divs at 2 in H0.
+          assert (forall x y, Integers.Ptrofs.divu x y = Integers.Ptrofs.divu x y ) by reflexivity.
+          unfold Integers.Ptrofs.divu at 2 in H0.
           rewrite H0. clear H0.
           rewrite Integers.Ptrofs.unsigned_repr; simplify.
-          rewrite Integers.Ptrofs.signed_repr; simplify; try lia.
-          rewrite Z.quot_div_nonneg; try (rewrite <- HeqOFFSET; assumption); try lia.
           apply Zmult_lt_reg_r with (p := 4); try lia.
           repeat rewrite ZLib.div_mul_undo; try lia.
-          rewrite Integers.Ptrofs.signed_repr.
-          rewrite Z.quot_div_nonneg; try (rewrite <- HeqOFFSET; assumption); try lia.
           split.
-          apply Z.div_pos; try (rewrite <- HeqOFFSET; assumption); try lia.
-          apply Z.div_le_upper_bound; simplify; try (rewrite <- HeqOFFSET; lia); try lia.
-          simplify; lia. }
+          apply Z.div_pos; try lia; apply Integers.Ptrofs.unsigned_range_2.
+          apply Z.div_le_upper_bound; lia. }
 
         inversion NORMALISE_BOUND as [ NORMALISE_BOUND_LOW NORMALISE_BOUND_HIGH ];
         clear NORMALISE_BOUND.
@@ -687,7 +681,7 @@ Section CORRECTNESS.
         setoid_rewrite Integers.Ptrofs.add_zero_l in H7.
 
         specialize (H7 (Integers.Ptrofs.unsigned
-                          (Integers.Ptrofs.divs
+                          (Integers.Ptrofs.divu
                              OFFSET
                              (Integers.Ptrofs.repr 4)))).
 
@@ -699,11 +693,11 @@ Section CORRECTNESS.
 
         assert (Z.to_nat
                   (Integers.Ptrofs.unsigned
-                     (Integers.Ptrofs.divs
+                     (Integers.Ptrofs.divu
                         OFFSET
                         (Integers.Ptrofs.repr 4)))
                 =
-                valueToNat (vdivs (vplus asr # r0 (ZToValue 32 z) ?EQ2) (ZToValue 32 4) ?EQ1))
+                valueToNat (vdiv (vplus asr # r0 (ZToValue 32 z) ?EQ2) (ZToValue 32 4) ?EQ1))
           as EXPR_OK by admit.
         rewrite <- EXPR_OK.
         rewrite NORMALISE in I.
@@ -757,7 +751,7 @@ Section CORRECTNESS.
         rewrite Registers.Regmap.gss.
         unfold arr_stack_based_pointers in ASBP.
         specialize (ASBP (Integers.Ptrofs.unsigned
-                            (Integers.Ptrofs.divs OFFSET (Integers.Ptrofs.repr 4)))).
+                            (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4)))).
         exploit ASBP; auto; intros I.
 
         rewrite NORMALISE in I.
@@ -804,7 +798,8 @@ Section CORRECTNESS.
         invert H10. invert H12.
         clear H0. clear H6. clear H8.
 
-        unfold check_address_parameter in *. simplify.
+        unfold check_address_parameter_signed in *;
+        unfold check_address_parameter_unsigned in *; simplify.
 
         remember (Integers.Ptrofs.add (Integers.Ptrofs.repr (valueToZ asr # r0))
                                       (Integers.Ptrofs.of_int
@@ -812,11 +807,10 @@ Section CORRECTNESS.
                                                            (Integers.Int.repr z0)))) as OFFSET.
 
         (** Read bounds assumption *)
-        assert (0 <= Integers.Ptrofs.signed OFFSET) as READ_BOUND_LOW by admit.
-        assert (Integers.Ptrofs.signed OFFSET < f.(RTL.fn_stacksize)) as READ_BOUND_HIGH by admit.
+        assert (Integers.Ptrofs.unsigned OFFSET < f.(RTL.fn_stacksize)) as READ_BOUND_HIGH by admit.
 
         (** Modular preservation proof *)
-        assert (Integers.Ptrofs.signed OFFSET mod 4 = 0) as MOD_PRESERVE.
+        assert (Integers.Ptrofs.unsigned OFFSET mod 4 = 0) as MOD_PRESERVE.
         { rewrite HeqOFFSET.
           apply PtrofsExtra.add_mod; simplify; try lia.
           exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *)
@@ -835,34 +829,28 @@ Section CORRECTNESS.
         (** Normalisation proof *)
         assert (Integers.Ptrofs.repr
                   (4 * Integers.Ptrofs.unsigned
-                         (Integers.Ptrofs.divs OFFSET (Integers.Ptrofs.repr 4))) = OFFSET)
+                         (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4))) = OFFSET)
           as NORMALISE.
         { replace 4 with (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr 4)) at 1 by reflexivity.
           rewrite <- PtrofsExtra.mul_unsigned.
-          apply PtrofsExtra.mul_divs; auto.
-          rewrite Integers.Ptrofs.signed_repr; simplify; lia. }
+          apply PtrofsExtra.mul_divu; simplify; auto; lia. }
 
         (** Normalised bounds proof *)
         assert (0 <=
-                Integers.Ptrofs.unsigned (Integers.Ptrofs.divs OFFSET (Integers.Ptrofs.repr 4))
+                Integers.Ptrofs.unsigned (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4))
                 < (RTL.fn_stacksize f / 4))
         as NORMALISE_BOUND.
         { split.
           apply Integers.Ptrofs.unsigned_range_2.
-          assert (forall x y, Integers.Ptrofs.divs x y = Integers.Ptrofs.divs x y ) by reflexivity.
-          unfold Integers.Ptrofs.divs at 2 in H0.
+          assert (forall x y, Integers.Ptrofs.divu x y = Integers.Ptrofs.divu x y ) by reflexivity.
+          unfold Integers.Ptrofs.divu at 2 in H0.
           rewrite H0. clear H0.
           rewrite Integers.Ptrofs.unsigned_repr; simplify.
-          rewrite Integers.Ptrofs.signed_repr; simplify; try lia.
-          rewrite Z.quot_div_nonneg; try (rewrite <- HeqOFFSET; assumption); try lia.
           apply Zmult_lt_reg_r with (p := 4); try lia.
           repeat rewrite ZLib.div_mul_undo; try lia.
-          rewrite Integers.Ptrofs.signed_repr.
-          rewrite Z.quot_div_nonneg; try (rewrite <- HeqOFFSET; assumption); try lia.
           split.
-          apply Z.div_pos; try (rewrite <- HeqOFFSET; assumption); try lia.
-          apply Z.div_le_upper_bound; simplify; try (rewrite <- HeqOFFSET; lia); try lia.
-          simplify; lia. }
+          apply Z.div_pos; try lia; apply Integers.Ptrofs.unsigned_range_2.
+          apply Z.div_le_upper_bound; lia. }
 
         inversion NORMALISE_BOUND as [ NORMALISE_BOUND_LOW NORMALISE_BOUND_HIGH ];
         clear NORMALISE_BOUND.
@@ -911,7 +899,7 @@ Section CORRECTNESS.
         setoid_rewrite Integers.Ptrofs.add_zero_l in H7.
 
         specialize (H7 (Integers.Ptrofs.unsigned
-                          (Integers.Ptrofs.divs
+                          (Integers.Ptrofs.divu
                              OFFSET
                              (Integers.Ptrofs.repr 4)))).
 
@@ -922,12 +910,12 @@ Section CORRECTNESS.
         intros I.
         assert (Z.to_nat
                   (Integers.Ptrofs.unsigned
-                     (Integers.Ptrofs.divs
+                     (Integers.Ptrofs.divu
                         OFFSET
                         (Integers.Ptrofs.repr 4)))
                 = valueToNat
-                    (vdivs (vplus (vplus asr # r0 (ZToValue 32 z0) ?EQ5)
-                                  (vmul asr # r1 (ZToValue 32 z) ?EQ6) ?EQ4) (ZToValue 32 4) ?EQ3))
+                    (vdiv (vplus (vplus asr # r0 (ZToValue 32 z0) ?EQ5)
+                                 (vmul asr # r1 (ZToValue 32 z) ?EQ6) ?EQ4) (ZToValue 32 4) ?EQ3))
           as EXPR_OK by admit.
         rewrite <- EXPR_OK.
         rewrite NORMALISE in I.
@@ -981,7 +969,7 @@ Section CORRECTNESS.
         rewrite Registers.Regmap.gss.
         unfold arr_stack_based_pointers in ASBP.
         specialize (ASBP (Integers.Ptrofs.unsigned
-                            (Integers.Ptrofs.divs OFFSET (Integers.Ptrofs.repr 4)))).
+                            (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4)))).
         exploit ASBP; auto; intros I.
 
         rewrite NORMALISE in I.
@@ -1001,7 +989,8 @@ Section CORRECTNESS.
         destruct (Archi.ptr64) eqn:ARCHI; simplify.
         rewrite ARCHI in H0. simplify.
 
-        unfold check_address_parameter in EQ; simplify.
+        unfold check_address_parameter_unsigned in *;
+        unfold check_address_parameter_signed in *; simplify.
 
         assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity.
         rewrite ZERO in H1. clear ZERO.
@@ -1010,43 +999,36 @@ Section CORRECTNESS.
         remember i0 as OFFSET.
 
         (** Read bounds assumption *)
-        assert (0 <= Integers.Ptrofs.signed OFFSET) as READ_BOUND_LOW by admit.
-        assert (Integers.Ptrofs.signed OFFSET < f.(RTL.fn_stacksize)) as READ_BOUND_HIGH by admit.
+        assert (Integers.Ptrofs.unsigned OFFSET < f.(RTL.fn_stacksize)) as READ_BOUND_HIGH by admit.
 
         (** Modular preservation proof *)
-        rename H8 into MOD_PRESERVE.
+        rename H0 into MOD_PRESERVE.
 
         (** Normalisation proof *)
         assert (Integers.Ptrofs.repr
                   (4 * Integers.Ptrofs.unsigned
-                         (Integers.Ptrofs.divs OFFSET (Integers.Ptrofs.repr 4))) = OFFSET)
+                         (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4))) = OFFSET)
           as NORMALISE.
         { replace 4 with (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr 4)) at 1 by reflexivity.
           rewrite <- PtrofsExtra.mul_unsigned.
-          apply PtrofsExtra.mul_divs; auto.
-          rewrite Integers.Ptrofs.signed_repr; simplify; lia. }
+          apply PtrofsExtra.mul_divu; simplify; auto; try lia. }
 
         (** Normalised bounds proof *)
         assert (0 <=
-                Integers.Ptrofs.unsigned (Integers.Ptrofs.divs OFFSET (Integers.Ptrofs.repr 4))
+                Integers.Ptrofs.unsigned (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4))
                 < (RTL.fn_stacksize f / 4))
         as NORMALISE_BOUND.
         { split.
           apply Integers.Ptrofs.unsigned_range_2.
-          assert (forall x y, Integers.Ptrofs.divs x y = Integers.Ptrofs.divs x y ) by reflexivity.
-          unfold Integers.Ptrofs.divs at 2 in H0.
+          assert (forall x y, Integers.Ptrofs.divu x y = Integers.Ptrofs.divu x y ) by reflexivity.
+          unfold Integers.Ptrofs.divu at 2 in H0.
           rewrite H0. clear H0.
           rewrite Integers.Ptrofs.unsigned_repr; simplify.
-          rewrite Integers.Ptrofs.signed_repr; simplify; try lia.
-          rewrite Z.quot_div_nonneg; try (rewrite <- HeqOFFSET; assumption); try lia.
           apply Zmult_lt_reg_r with (p := 4); try lia.
           repeat rewrite ZLib.div_mul_undo; try lia.
-          rewrite Integers.Ptrofs.signed_repr.
-          rewrite Z.quot_div_nonneg; try (rewrite <- HeqOFFSET; assumption); try lia.
           split.
-          apply Z.div_pos; try (rewrite <- HeqOFFSET; assumption); try lia.
-          apply Z.div_le_upper_bound; simplify; try (rewrite <- HeqOFFSET; lia); try lia.
-          simplify; lia. }
+          apply Z.div_pos; try lia; apply Integers.Ptrofs.unsigned_range_2.
+          apply Z.div_le_upper_bound; lia. }
 
         inversion NORMALISE_BOUND as [ NORMALISE_BOUND_LOW NORMALISE_BOUND_HIGH ];
         clear NORMALISE_BOUND.
@@ -1086,7 +1068,7 @@ Section CORRECTNESS.
         setoid_rewrite Integers.Ptrofs.add_zero_l in H7.
 
         specialize (H7 (Integers.Ptrofs.unsigned
-                          (Integers.Ptrofs.divs
+                          (Integers.Ptrofs.divu
                              OFFSET
                              (Integers.Ptrofs.repr 4)))).
 
@@ -1097,11 +1079,11 @@ Section CORRECTNESS.
         intros I.
         assert (Z.to_nat
                   (Integers.Ptrofs.unsigned
-                     (Integers.Ptrofs.divs
+                     (Integers.Ptrofs.divu
                         OFFSET
                         (Integers.Ptrofs.repr 4)))
                   =
-                  valueToNat (ZToValue 32 (Integers.Ptrofs.signed OFFSET / 4)))
+                  valueToNat (ZToValue 32 (Integers.Ptrofs.unsigned OFFSET / 4)))
           as EXPR_OK by admit.
         rewrite <- EXPR_OK.
         rewrite NORMALISE in I.
@@ -1155,7 +1137,7 @@ Section CORRECTNESS.
         rewrite Registers.Regmap.gss.
         unfold arr_stack_based_pointers in ASBP.
         specialize (ASBP (Integers.Ptrofs.unsigned
-                            (Integers.Ptrofs.divs OFFSET (Integers.Ptrofs.repr 4)))).
+                            (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4)))).
         exploit ASBP; auto; intros I.
 
         rewrite NORMALISE in I.