diff --git a/compiler/lib/stdlib.ml b/compiler/lib/stdlib.ml
index 42c2dd05cd..8cb2de2a4a 100644
--- a/compiler/lib/stdlib.ml
+++ b/compiler/lib/stdlib.ml
@@ -307,23 +307,25 @@ module Int32 = struct
 
   external equal : int32 -> int32 -> bool = "%equal"
 
-  let warn_overflow ~to_dec ~to_hex i i32 =
+  let warn_overflow name ~to_dec ~to_hex i i32 =
     warn
-      "Warning: integer overflow: integer 0x%s (%s) truncated to 0x%lx (%ld); the \
-       generated code might be incorrect.@."
+      "Warning: integer overflow: %s 0x%s (%s) truncated to 0x%lx (%ld); the generated \
+       code might be incorrect.@."
+      name
       (to_hex i)
       (to_dec i)
       i32
       i32
 
-  let convert_warning_on_overflow ~to_int32 ~of_int32 ~equal ~to_dec ~to_hex x =
+  let convert_warning_on_overflow name ~to_int32 ~of_int32 ~equal ~to_dec ~to_hex x =
     let i32 = to_int32 x in
     let x' = of_int32 i32 in
-    if not (equal x' x) then warn_overflow ~to_dec ~to_hex x i32;
+    if not (equal x' x) then warn_overflow name ~to_dec ~to_hex x i32;
     i32
 
   let of_nativeint_warning_on_overflow n =
     convert_warning_on_overflow
+      "native integer"
       ~to_int32:Nativeint.to_int32
       ~of_int32:Nativeint.of_int32
       ~equal:Nativeint.equal
diff --git a/compiler/lib/targetint.ml b/compiler/lib/targetint.ml
index 1d906e5ffe..5a79678e9e 100644
--- a/compiler/lib/targetint.ml
+++ b/compiler/lib/targetint.ml
@@ -122,6 +122,7 @@ let of_float_opt x =
 
 let of_int_warning_on_overflow i =
   Stdlib.Int32.convert_warning_on_overflow
+    "integer"
     ~to_int32:(fun i -> wrap_modulo (Int32.of_int i))
     ~of_int32:Int32.to_int
     ~equal:Int.equal
@@ -131,6 +132,7 @@ let of_int_warning_on_overflow i =
 
 let of_int32_warning_on_overflow n =
   Stdlib.Int32.convert_warning_on_overflow
+    "int32"
     ~to_int32:(fun i -> wrap_modulo i)
     ~of_int32:Fun.id
     ~equal:Int32.equal
@@ -140,6 +142,7 @@ let of_int32_warning_on_overflow n =
 
 let of_nativeint_warning_on_overflow n =
   Stdlib.Int32.convert_warning_on_overflow
+    "native integer"
     ~to_int32:(fun i -> wrap_modulo (Nativeint.to_int32 i))
     ~of_int32:Nativeint.of_int32
     ~equal:Nativeint.equal
diff --git a/compiler/tests-compiler/dune.inc b/compiler/tests-compiler/dune.inc
index 2e5db3e098..b1a61b3664 100644
--- a/compiler/tests-compiler/dune.inc
+++ b/compiler/tests-compiler/dune.inc
@@ -287,11 +287,11 @@
 (library
  ;; compiler/tests-compiler/gh1051.ml
  (name gh1051_15)
- (enabled_if true)
+ (enabled_if %{arch_sixtyfour})
  (modules gh1051)
  (libraries js_of_ocaml_compiler unix str jsoo_compiler_expect_tests_helper)
  (inline_tests
-  (enabled_if true)
+  (enabled_if %{arch_sixtyfour})
   (deps
    (file %{project_root}/compiler/bin-js_of_ocaml/js_of_ocaml.exe)
    (file %{project_root}/compiler/bin-jsoo_minify/jsoo_minify.exe)))
diff --git a/compiler/tests-compiler/gen-rules/gen.ml b/compiler/tests-compiler/gen-rules/gen.ml
index a74855765d..7a216c040a 100644
--- a/compiler/tests-compiler/gen-rules/gen.ml
+++ b/compiler/tests-compiler/gen-rules/gen.ml
@@ -47,14 +47,17 @@ let prefix : string =
 
 type enabled_if =
   | GE5
+  | B64
   | Any
 
 let lib_enabled_if = function
   | "obj" | "effects" -> GE5
+  | "gh1051" -> B64
   | _ -> Any
 
 let test_enabled_if = function
   | "obj" | "lazy" -> GE5
+  | "gh1051" -> B64
   | _ -> Any
 
 let () =
@@ -86,8 +89,10 @@ let () =
            (Hashtbl.hash prefix mod 100)
            (match lib_enabled_if basename with
            | Any -> "true"
-           | GE5 -> "(>= %{ocaml_version} 5)")
+           | GE5 -> "(>= %{ocaml_version} 5)"
+           | B64 -> "%{arch_sixtyfour}")
            basename
            (match test_enabled_if basename with
            | Any -> "true"
-           | GE5 -> "(>= %{ocaml_version} 5)"))
+           | GE5 -> "(>= %{ocaml_version} 5)"
+           | B64 -> "%{arch_sixtyfour}"))
diff --git a/compiler/tests-compiler/gh1051.ml b/compiler/tests-compiler/gh1051.ml
index 02045f8072..31030ffece 100644
--- a/compiler/tests-compiler/gh1051.ml
+++ b/compiler/tests-compiler/gh1051.ml
@@ -25,19 +25,21 @@ let%expect_test _ =
   Util.compile_and_run ~skip_modern:true prog;
   [%expect
     {|
-Warning: integer overflow: integer 0xffffffff (4294967295) truncated to 0xffffffff (-1); the generated code might be incorrect.
-ffffffff |}];
+    Warning: integer overflow: native integer 0xffffffff (4294967295) truncated to 0xffffffff (-1); the generated code might be incorrect.
+    ffffffff
+    |}];
   ()
 
 let%expect_test _ =
   Util.print_fun_decl (Util.compile_and_parse prog) None;
   [%expect
     {|
-    Warning: integer overflow: integer 0xffffffff (4294967295) truncated to 0xffffffff (-1); the generated code might be incorrect.
+    Warning: integer overflow: native integer 0xffffffff (4294967295) truncated to 0xffffffff (-1); the generated code might be incorrect.
     function caml_call2(f, a0, a1){
      return (f.l >= 0 ? f.l : f.l = f.length) == 2
              ? f(a0, a1)
              : runtime.caml_call_gen(f, [a0, a1]);
     }
-    //end |}];
+    //end
+    |}];
   ()
diff --git a/compiler/tests-compiler/pbt/test_int31.ml b/compiler/tests-compiler/pbt/test_int31.ml
index 26211f4cd4..37f72d354c 100644
--- a/compiler/tests-compiler/pbt/test_int31.ml
+++ b/compiler/tests-compiler/pbt/test_int31.ml
@@ -59,6 +59,8 @@ let%expect_test _ =
            i);
   [%expect ""]
 
+let sixty_four = Sys.int_size > 32
+
 let%expect_test _ =
   let i = Gen.(generate1 (no_shrink out_of_range_i32)) in
   let i_trunc = Int32.(shift_right (shift_left i 1) 1) in
@@ -66,14 +68,14 @@ let%expect_test _ =
   let output = [%expect.output] in
   let expected =
     Format.sprintf
-      "Warning: integer overflow: integer 0x%lx (%ld) truncated to 0x%lx (%ld); the \
+      "Warning: integer overflow: int32 0x%lx (%ld) truncated to 0x%lx (%ld); the \
        generated code might be incorrect.@."
       i
       i
       i_trunc
       i_trunc
   in
-  if not (String.equal output expected)
+  if sixty_four && not (String.equal output expected)
   then Format.printf "Unexpected output string@.%s@.Expected:@.%s@." output expected;
   [%expect ""]
 
@@ -91,7 +93,7 @@ let%expect_test _ =
       i_trunc
       i_trunc
   in
-  if not (String.equal output expected)
+  if sixty_four && not (String.equal output expected)
   then Format.printf "Unexpected output string@.%s@.Expected:@.%s@." output expected;
   [%expect ""]
 
@@ -102,14 +104,14 @@ let%expect_test _ =
   let output = [%expect.output] in
   let expected =
     Format.sprintf
-      "Warning: integer overflow: integer 0x%nx (%nd) truncated to 0x%lx (%ld); the \
-       generated code might be incorrect.@."
+      "Warning: integer overflow: native integer 0x%nx (%nd) truncated to 0x%lx (%ld); \
+       the generated code might be incorrect.@."
       i
       i
       i_trunc
       i_trunc
   in
-  if not (String.equal output expected)
+  if sixty_four && not (String.equal output expected)
   then Format.printf "Unexpected output string@.%s@.Expected:@.%s@." output expected;
   [%expect ""]