diff --git a/compiler/lib/code.ml b/compiler/lib/code.ml
index 591cac4c1..d9fffb4ee 100644
--- a/compiler/lib/code.ml
+++ b/compiler/lib/code.ml
@@ -290,75 +290,79 @@ type constant =
   | NativeInt of nativeint
   | Tuple of int * constant array * array_or_not
 
-let rec constant_equal a b =
-  match a, b with
-  | String a, String b -> Some (String.equal a b)
-  | NativeString a, NativeString b -> Some (Native_string.equal a b)
-  | Tuple (ta, a, _), Tuple (tb, b, _) ->
-      if ta <> tb || Array.length a <> Array.length b
-      then Some false
-      else
-        let same = ref (Some true) in
-        for i = 0 to Array.length a - 1 do
-          match !same, constant_equal a.(i) b.(i) with
-          | None, _ -> ()
-          | _, None -> same := None
-          | Some s, Some c -> same := Some (s && c)
-        done;
-        !same
-  | Int a, Int b | Int32 a, Int32 b -> Some (Int32.equal a b)
-  | Int64 a, Int64 b -> Some (Int64.equal a b)
-  | NativeInt a, NativeInt b -> Some (Nativeint.equal a b)
-  | Float_array a, Float_array b -> Some (Array.equal Float.equal a b)
-  | Float a, Float b -> Some (Float.equal a b)
-  | String _, NativeString _ | NativeString _, String _ -> None
-  | Int _, Float _ | Float _, Int _ -> None
-  | Tuple ((0 | 254), _, _), Float_array _ -> None
-  | Float_array _, Tuple ((0 | 254), _, _) -> None
-  | ( Tuple _
-    , ( String _
-      | NativeString _
-      | Int64 _
-      | Int _
-      | Int32 _
-      | NativeInt _
-      | Float _
-      | Float_array _ ) ) -> Some false
-  | ( Float_array _
-    , ( String _
-      | NativeString _
-      | Int64 _
-      | Int _
-      | Int32 _
-      | NativeInt _
-      | Float _
-      | Tuple _ ) ) -> Some false
-  | ( String _
-    , (Int64 _ | Int _ | Int32 _ | NativeInt _ | Float _ | Tuple _ | Float_array _) ) ->
-      Some false
-  | ( NativeString _
-    , (Int64 _ | Int _ | Int32 _ | NativeInt _ | Float _ | Tuple _ | Float_array _) ) ->
-      Some false
-  | ( Int64 _
-    , ( String _
-      | NativeString _
-      | Int _
-      | Int32 _
-      | NativeInt _
-      | Float _
-      | Tuple _
-      | Float_array _ ) ) -> Some false
-  | Float _, (String _ | NativeString _ | Float_array _ | Int64 _ | Tuple (_, _, _)) ->
-      Some false
-  | ( (Int _ | Int32 _ | NativeInt _)
-    , (String _ | NativeString _ | Float_array _ | Int64 _ | Tuple (_, _, _)) ) ->
-      Some false
-  (* Note: the following cases should not occur when compiling to Javascript *)
-  | Int _, (Int32 _ | NativeInt _)
-  | Int32 _, (Int _ | NativeInt _)
-  | NativeInt _, (Int _ | Int32 _)
-  | (Int32 _ | NativeInt _), Float _
-  | Float _, (Int32 _ | NativeInt _) -> None
+module Constant = struct
+  type t = constant
+
+  let rec ocaml_equal a b =
+    match a, b with
+    | String a, String b -> Some (String.equal a b)
+    | NativeString a, NativeString b -> Some (Native_string.equal a b)
+    | Tuple (ta, a, _), Tuple (tb, b, _) ->
+        if ta <> tb || Array.length a <> Array.length b
+        then Some false
+        else
+          let same = ref (Some true) in
+          for i = 0 to Array.length a - 1 do
+            match !same, ocaml_equal a.(i) b.(i) with
+            | None, _ -> ()
+            | _, None -> same := None
+            | Some s, Some c -> same := Some (s && c)
+          done;
+          !same
+    | Int a, Int b | Int32 a, Int32 b -> Some (Int32.equal a b)
+    | Int64 a, Int64 b -> Some (Int64.equal a b)
+    | NativeInt a, NativeInt b -> Some (Nativeint.equal a b)
+    | Float_array a, Float_array b -> Some (Array.equal Float.ieee_equal a b)
+    | Float a, Float b -> Some (Float.ieee_equal a b)
+    | String _, NativeString _ | NativeString _, String _ -> None
+    | Int _, Float _ | Float _, Int _ -> None
+    | Tuple ((0 | 254), _, _), Float_array _ -> None
+    | Float_array _, Tuple ((0 | 254), _, _) -> None
+    | ( Tuple _
+      , ( String _
+        | NativeString _
+        | Int64 _
+        | Int _
+        | Int32 _
+        | NativeInt _
+        | Float _
+        | Float_array _ ) ) -> Some false
+    | ( Float_array _
+      , ( String _
+        | NativeString _
+        | Int64 _
+        | Int _
+        | Int32 _
+        | NativeInt _
+        | Float _
+        | Tuple _ ) ) -> Some false
+    | ( String _
+      , (Int64 _ | Int _ | Int32 _ | NativeInt _ | Float _ | Tuple _ | Float_array _) ) ->
+        Some false
+    | ( NativeString _
+      , (Int64 _ | Int _ | Int32 _ | NativeInt _ | Float _ | Tuple _ | Float_array _) ) ->
+        Some false
+    | ( Int64 _
+      , ( String _
+        | NativeString _
+        | Int _
+        | Int32 _
+        | NativeInt _
+        | Float _
+        | Tuple _
+        | Float_array _ ) ) -> Some false
+    | Float _, (String _ | NativeString _ | Float_array _ | Int64 _ | Tuple (_, _, _)) ->
+        Some false
+    | ( (Int _ | Int32 _ | NativeInt _)
+      , (String _ | NativeString _ | Float_array _ | Int64 _ | Tuple (_, _, _)) ) ->
+        Some false
+    (* Note: the following cases should not occur when compiling to Javascript *)
+    | Int _, (Int32 _ | NativeInt _)
+    | Int32 _, (Int _ | NativeInt _)
+    | NativeInt _, (Int _ | Int32 _)
+    | (Int32 _ | NativeInt _), Float _
+    | Float _, (Int32 _ | NativeInt _) -> None
+end
 
 type loc =
   | No
diff --git a/compiler/lib/code.mli b/compiler/lib/code.mli
index 6e8f0d0bd..1c107d75e 100644
--- a/compiler/lib/code.mli
+++ b/compiler/lib/code.mli
@@ -150,6 +150,8 @@ module Native_string : sig
   val of_string : string -> t
 
   val of_bytestring : string -> t
+
+  val equal : t -> t -> bool
 end
 
 type int_kind =
@@ -168,7 +170,13 @@ type constant =
   | NativeInt of nativeint  (** Only produced when compiling to WebAssembly. *)
   | Tuple of int * constant array * array_or_not
 
-val constant_equal : constant -> constant -> bool option
+module Constant : sig
+  type t = constant
+
+  val ocaml_equal : t -> t -> bool option
+  (** Guaranteed equality in terms of OCaml [(=)]: if [constant_equal a b =
+    Some v], then [Poly.(=) a b = v]. This is used for optimization purposes. *)
+end
 
 type loc =
   | No
diff --git a/compiler/lib/driver.ml b/compiler/lib/driver.ml
index 8882829f1..bb4ce4aaf 100644
--- a/compiler/lib/driver.ml
+++ b/compiler/lib/driver.ml
@@ -241,9 +241,9 @@ let gen_missing js missing =
         , ( ECond
               ( EBin
                   ( NotEqEq
-                  , dot (EVar (ident Constant.global_object_)) prim
+                  , dot (EVar (ident Global_constant.global_object_)) prim
                   , EVar (ident_s "undefined") )
-              , dot (EVar (ident Constant.global_object_)) prim
+              , dot (EVar (ident Global_constant.global_object_)) prim
               , EFun
                   ( None
                   , fun_
@@ -364,7 +364,7 @@ let link' ~export_runtime ~standalone ~link (js : Javascript.statement_list) :
                (EBin
                   ( Eq
                   , dot
-                      (EVar (ident Constant.global_object_))
+                      (EVar (ident Global_constant.global_object_))
                       (Utf8_string.of_string_exn "jsoo_runtime")
                   , EObj all ))
            , N )
@@ -375,7 +375,7 @@ let link' ~export_runtime ~standalone ~link (js : Javascript.statement_list) :
                      (EVar (ident (Utf8_string.of_string_exn "Object")))
                      (Utf8_string.of_string_exn "assign"))
                   [ dot
-                      (EVar (ident Constant.global_object_))
+                      (EVar (ident Global_constant.global_object_))
                       (Utf8_string.of_string_exn "jsoo_runtime")
                   ; EObj all
                   ]
@@ -404,7 +404,7 @@ let link' ~export_runtime ~standalone ~link (js : Javascript.statement_list) :
                          ; rest = None
                          }
                      , ( dot
-                           (EVar (ident Constant.global_object_))
+                           (EVar (ident Global_constant.global_object_))
                            (Utf8_string.of_string_exn "jsoo_runtime")
                        , N ) )
                  ] )
@@ -510,27 +510,30 @@ let pack ~wrap_with_fun ~standalone { Linker.runtime_code = js; always_required_
       o#get_free
     in
     let export_shim js =
-      if J.IdentSet.mem (J.ident Constant.exports_) freenames
+      if J.IdentSet.mem (J.ident Global_constant.exports_) freenames
       then
         if should_export wrap_with_fun
-        then var Constant.exports_ (J.EObj []) :: js
+        then var Global_constant.exports_ (J.EObj []) :: js
         else
           let export_node =
             let s =
               Printf.sprintf
                 {|((typeof module === 'object' && module.exports) || %s)|}
-                Constant.global_object
+                Global_constant.global_object
             in
             let lex = Parse_js.Lexer.of_string s in
             Parse_js.parse_expr lex
           in
-          var Constant.exports_ export_node :: js
+          var Global_constant.exports_ export_node :: js
       else js
     in
     let old_global_object_shim js =
-      if J.IdentSet.mem (J.ident Constant.old_global_object_) freenames
+      if J.IdentSet.mem (J.ident Global_constant.old_global_object_) freenames
       then
-        var Constant.old_global_object_ (J.EVar (J.ident Constant.global_object_)) :: js
+        var
+          Global_constant.old_global_object_
+          (J.EVar (J.ident Global_constant.global_object_))
+        :: js
       else js
     in
 
@@ -544,14 +547,15 @@ let pack ~wrap_with_fun ~standalone { Linker.runtime_code = js; always_required_
         then expr (J.EStr (Utf8_string.of_string_exn "use strict")) :: js
         else js
       in
-      f [ J.ident Constant.global_object_ ] js
+      f [ J.ident Global_constant.global_object_ ] js
     in
     match wrap_with_fun with
     | `Anonymous -> expr (mk efun)
     | `Named name ->
         let name = Utf8_string.of_string_exn name in
         mk (sfun (J.ident name))
-    | `Iife -> expr (J.call (mk efun) [ J.EVar (J.ident Constant.global_object_) ] J.N)
+    | `Iife ->
+        expr (J.call (mk efun) [ J.EVar (J.ident Global_constant.global_object_) ] J.N)
   in
   let always_required_js =
     (* consider adding a comments in the generated file with original
diff --git a/compiler/lib/eval.ml b/compiler/lib/eval.ml
index d8a4e48e2..5892f8dc1 100644
--- a/compiler/lib/eval.ml
+++ b/compiler/lib/eval.ml
@@ -66,14 +66,15 @@ let float_unop (l : constant list) (f : float -> float) : constant option =
   | [ Int i ] -> Some (Float (f (Int32.to_float i)))
   | _ -> None
 
+let bool' b = Int (if b then 1l else 0l)
+
+let bool b = Some (bool' b)
+
 let float_binop_bool l f =
   match float_binop_aux l f with
-  | Some true -> Some (Int 1l)
-  | Some false -> Some (Int 0l)
+  | Some b -> bool b
   | None -> None
 
-let bool b = Some (Int (if b then 1l else 0l))
-
 let eval_prim ~target x =
   match x with
   | Not, [ Int i ] -> bool Int32.(i = 0l)
@@ -255,16 +256,51 @@ let the_cont_of info x (a : cont array) =
       | _ -> None)
     x
 
+(* If [constant_js_equal a b = Some v], then [caml_js_equals a b = v]). *)
+let constant_js_equal a b =
+  match a, b with
+  | Int i, Int j -> Some (Int32.equal i j)
+  | Float a, Float b -> Some (Float.ieee_equal a b)
+  | NativeString a, NativeString b -> Some (Native_string.equal a b)
+  | String a, String b when Config.Flag.use_js_string () -> Some (String.equal a b)
+  | Int _, Float _ | Float _, Int _ -> None
+  (* All other values may be distinct objects and thus different by [caml_js_equals]. *)
+  | String _, _
+  | _, String _
+  | NativeString _, _
+  | _, NativeString _
+  | Float_array _, _
+  | _, Float_array _
+  | Int64 _, _
+  | _, Int64 _
+  | Tuple _, _
+  | _, Tuple _ -> None
+
 let eval_instr ~target info ((x, loc) as i) =
   match x with
-  | Let (x, Prim (Extern ("caml_js_equals" | "caml_equal"), [ y; z ])) -> (
+  | Let (x, Prim (Extern (("caml_equal" | "caml_notequal") as prim), [ y; z ])) -> (
+      match the_const_of info y, the_const_of info z with
+      | Some e1, Some e2 -> (
+          match Code.Constant.ocaml_equal e1 e2 with
+          | None -> [ i ]
+          | Some c ->
+              let c =
+                match prim with
+                | "caml_equal" -> c
+                | "caml_notequal" -> not c
+                | _ -> assert false
+              in
+              let c = Constant (bool' c) in
+              Flow.update_def info x c;
+              [ Let (x, c), loc ])
+      | _ -> [ i ])
+  | Let (x, Prim (Extern ("caml_js_equals" | "caml_js_strict_equals"), [ y; z ])) -> (
       match the_const_of info y, the_const_of info z with
       | Some e1, Some e2 -> (
-          match constant_equal e1 e2 with
+          match constant_js_equal e1 e2 with
           | None -> [ i ]
           | Some c ->
-              let c = if c then 1l else 0l in
-              let c = Constant (Int c) in
+              let c = Constant (bool' c) in
               Flow.update_def info x c;
               [ Let (x, c), loc ])
       | _ -> [ i ])
@@ -300,8 +336,7 @@ let eval_instr ~target info ((x, loc) as i) =
       match is_int ~target info y with
       | Unknown -> [ i ]
       | (Y | N) as b ->
-          let b = if Poly.(b = N) then 0l else 1l in
-          let c = Constant (Int b) in
+          let c = Constant (bool' Poly.(b = Y)) in
           Flow.update_def info x c;
           [ Let (x, c), loc ])
   | Let (x, Prim (Extern "%direct_obj_tag", [ y ])) -> (
diff --git a/compiler/lib/flow.ml b/compiler/lib/flow.ml
index f5e8193ea..1212e56f0 100644
--- a/compiler/lib/flow.ml
+++ b/compiler/lib/flow.ml
@@ -322,6 +322,28 @@ let the_def_of info x =
         x
   | Pc c -> Some (Constant c)
 
+(* If [constant_identical a b = true], then the two values cannot be
+   distinguished, i.e., they are not different objects (and [caml_js_equals a b
+   = true]) and if both are floats, they are bitwise equal. *)
+let constant_identical a b =
+  match a, b with
+  | Int i, Int j -> Int32.equal i j
+  | Float a, Float b -> Float.bitwise_equal a b
+  | NativeString a, NativeString b -> Native_string.equal a b
+  | String a, String b -> Config.Flag.use_js_string () && String.equal a b
+  | Int _, Float _ | Float _, Int _ -> false
+  (* All other values may be distinct objects and thus different by [caml_js_equals]. *)
+  | String _, _
+  | _, String _
+  | NativeString _, _
+  | _, NativeString _
+  | Float_array _, _
+  | _, Float_array _
+  | Int64 _, _
+  | _, Int64 _
+  | Tuple _, _
+  | _, Tuple _ -> false
+
 let the_const_of info x =
   match x with
   | Pv x ->
@@ -337,7 +359,7 @@ let the_const_of info x =
         None
         (fun u v ->
           match u, v with
-          | Some i, Some j when Poly.(Code.constant_equal i j = Some true) -> u
+          | Some i, Some j when constant_identical i j -> u
           | _ -> None)
         x
   | Pc c -> Some c
diff --git a/compiler/lib/generate.ml b/compiler/lib/generate.ml
index 58893caae..16ff54a5e 100644
--- a/compiler/lib/generate.ml
+++ b/compiler/lib/generate.ml
@@ -1861,7 +1861,7 @@ and compile_conditional st queue last loop_stack backs frontier interm =
         true, flush_all queue (throw_statement st.ctx cx k loc)
     | Stop ->
         let e_opt =
-          if st.ctx.Ctx.should_export then Some (s_var Constant.exports) else None
+          if st.ctx.Ctx.should_export then Some (s_var Global_constant.exports) else None
         in
         true, flush_all queue [ J.Return_statement e_opt, loc ]
     | Branch cont -> compile_branch st queue cont loop_stack backs frontier interm
@@ -2006,7 +2006,7 @@ let generate_shared_value ctx =
          | Some (v, _) ->
              [ ( J.V v
                , ( J.dot
-                     (s_var Constant.global_object)
+                     (s_var Global_constant.global_object)
                      (Utf8_string.of_string_exn "jsoo_runtime")
                  , J.N ) )
              ])
diff --git a/compiler/lib/constant.ml b/compiler/lib/global_constant.ml
similarity index 100%
rename from compiler/lib/constant.ml
rename to compiler/lib/global_constant.ml
diff --git a/compiler/lib/javascript.ml b/compiler/lib/javascript.ml
index 633d96a86..acd03eee3 100644
--- a/compiler/lib/javascript.ml
+++ b/compiler/lib/javascript.ml
@@ -112,14 +112,14 @@ end = struct
     | FP_infinite -> if Float.(v < 0.) then "-Infinity" else "Infinity"
     | FP_normal | FP_subnormal -> (
         let vint = int_of_float v in
-        if Float.equal (float_of_int vint) v
+        if Float.ieee_equal (float_of_int vint) v
         then Printf.sprintf "%d." vint
         else
           match
             find_smaller
               ~f:(fun prec ->
                 let s = float_to_string prec v in
-                if Float.equal v (float_of_string s) then Some s else None)
+                if Float.ieee_equal v (float_of_string s) then Some s else None)
               ~bad:0
               ~good:18
               ~good_s:"max"
diff --git a/compiler/lib/linker.ml b/compiler/lib/linker.ml
index d0a610d90..8195a7cb9 100644
--- a/compiler/lib/linker.ml
+++ b/compiler/lib/linker.ml
@@ -134,9 +134,9 @@ module Check = struct
     in
     let freename = StringSet.diff freename Reserved.keyword in
     let freename = StringSet.diff freename Reserved.provided in
-    let freename = StringSet.remove Constant.global_object freename in
+    let freename = StringSet.remove Global_constant.global_object freename in
     let freename = if has_flags then StringSet.remove "FLAG" freename else freename in
-    if StringSet.mem Constant.old_global_object freename && false
+    if StringSet.mem Global_constant.old_global_object freename && false
        (* Don't warn yet, we want to give a transition period where both
           "globalThis" and "joo_global_object" are allowed without extra
           noise *)
@@ -145,7 +145,7 @@ module Check = struct
         "warning: %s: 'joo_global_object' is being deprecated, please use `globalThis` \
          instead@."
         (loc pi);
-    let freename = StringSet.remove Constant.old_global_object freename in
+    let freename = StringSet.remove Global_constant.old_global_object freename in
     let defname = to_stringset free#get_def in
     if not (StringSet.mem name defname)
     then
diff --git a/compiler/lib/stdlib.ml b/compiler/lib/stdlib.ml
index f68e8cdb5..d5c7122c4 100644
--- a/compiler/lib/stdlib.ml
+++ b/compiler/lib/stdlib.ml
@@ -423,7 +423,11 @@ end
 module Float = struct
   type t = float
 
-  let equal (a : float) (b : float) =
+  let equal (_ : float) (_ : float) = `Use_ieee_equal_or_bitwise_equal
+
+  let ieee_equal (a : float) (b : float) = Poly.equal a b
+
+  let bitwise_equal (a : float) (b : float) =
     Int64.equal (Int64.bits_of_float a) (Int64.bits_of_float b)
 
   (* Re-defined here to stay compatible with OCaml 4.02 *)
diff --git a/compiler/tests-compiler/dune.inc b/compiler/tests-compiler/dune.inc
index 5ab5836bf..f541039ba 100644
--- a/compiler/tests-compiler/dune.inc
+++ b/compiler/tests-compiler/dune.inc
@@ -359,6 +359,21 @@
  (preprocess
   (pps ppx_expect)))
 
+(library
+ ;; compiler/tests-compiler/gh1659.ml
+ (name gh1659_15)
+ (enabled_if true)
+ (modules gh1659)
+ (libraries js_of_ocaml_compiler unix str jsoo_compiler_expect_tests_helper)
+ (inline_tests
+  (enabled_if true)
+  (deps
+   (file %{project_root}/compiler/bin-js_of_ocaml/js_of_ocaml.exe)
+   (file %{project_root}/compiler/bin-jsoo_minify/jsoo_minify.exe)))
+ (flags (:standard -open Jsoo_compiler_expect_tests_helper))
+ (preprocess
+  (pps ppx_expect)))
+
 (library
  ;; compiler/tests-compiler/gh747.ml
  (name gh747_15)
diff --git a/compiler/tests-compiler/gh1659.ml b/compiler/tests-compiler/gh1659.ml
new file mode 100644
index 000000000..3607703f2
--- /dev/null
+++ b/compiler/tests-compiler/gh1659.ml
@@ -0,0 +1,62 @@
+let%expect_test _ =
+  let prog =
+    {|
+let f a b = a = b
+let () = Printf.printf "(0., 0.) = (-0., 0.) => %B\n" (f (0., 0.) (-0., 0.))
+let f a b = a = b
+let () = Printf.printf "0. = -0. => %B\n" (f 0. (-0.));;
+let f a b = a = b
+let nan1 = 0. /. 0.
+let nan2 = 0. /. 0.
+let () = Printf.printf "nan = nan => %B\n" (f nan1 nan2);;
+  |}
+  in
+  Util.compile_and_run prog;
+  [%expect
+    {|
+    (0., 0.) = (-0., 0.) => true
+    0. = -0. => true
+    nan = nan => false
+    |}]
+
+let%expect_test _ =
+  let prog =
+    {|
+external equals : 'a -> 'a -> bool = "caml_js_equals";;
+let () = Printf.printf "x = (0., 0.); x = x => %B\n" (let x = (0., 0.) in equals x x)
+let () = Printf.printf "(0., 0.) = (0., 0.) => %B\n" (equals (0., 0.) (0., 0.))
+let () = Printf.printf "0. = -0. => %B\n" (equals 0. (-0.));;
+let nan1 = 0. /. 0.
+let nan2 = 0. /. 0.
+let () = Printf.printf "nan = nan => %B\n" (equals nan1 nan2);;
+  |}
+  in
+  Util.compile_and_run prog;
+  [%expect
+    {|
+    x = (0., 0.); x = x => true
+    (0., 0.) = (0., 0.) => false
+    0. = -0. => true
+    nan = nan => false
+    |}]
+
+let%expect_test _ =
+  let prog =
+    {|
+external equals : 'a -> 'a -> bool = "caml_js_strict_equals";;
+let () = Printf.printf "x = (0., 0.); x = x => %B\n" (let x = (0., 0.) in equals x x)
+let () = Printf.printf "(0., 0.) = (0., 0.) => %B\n" (equals (0., 0.) (0., 0.))
+let () = Printf.printf "0. = -0. => %B\n" (equals 0. (-0.));;
+let nan1 = 0. /. 0.
+let nan2 = 0. /. 0.
+let () = Printf.printf "nan = nan => %B\n" (equals nan1 nan2);;
+  |}
+  in
+  Util.compile_and_run prog;
+  [%expect
+    {|
+    x = (0., 0.); x = x => true
+    (0., 0.) = (0., 0.) => false
+    0. = -0. => true
+    nan = nan => false
+    |}]