diff --git a/src/lib/frontend/d_cnf.ml b/src/lib/frontend/d_cnf.ml
index 7ab12cb451..37b9710b47 100644
--- a/src/lib/frontend/d_cnf.ml
+++ b/src/lib/frontend/d_cnf.ml
@@ -295,7 +295,7 @@ let fpa_builtins =
     | _ -> assert false
   in
   let fpa_rounding_mode, rounding_modes, add_rounding_modes =
-    builtin_enum Fpa_rounding.fpa_rounding_mode
+    builtin_enum (Fpa_rounding.fpa_rounding_mode ())
   in
   let float_cst =
     let ty = DT.(arrow [int; int; fpa_rounding_mode; real] real) in
@@ -429,11 +429,18 @@ let fpa_builtins =
       | Builtin _ -> `Not_found
     end
 
+(** Concatenation of builtins handlers. *)
+(* let (++) bt1 bt2 =
+ *   fun a b ->
+ *   match bt1 a b with
+ *   | `Not_found -> bt2 a b
+ *   | res -> res *)
+
 let builtins =
   fun _st (lang : Typer.lang) ->
   match lang with
   | `Logic Alt_ergo -> fpa_builtins
-  | `Logic (Smtlib2 _) -> bv_builtins
+  | `Logic (Smtlib2 _) -> (* fpa_builtins ++ *) bv_builtins
   | _ -> fun _ _ -> `Not_found
 
 (** Translates dolmen locs to Alt-Ergo's locs *)
diff --git a/src/lib/frontend/typechecker.ml b/src/lib/frontend/typechecker.ml
index fe21034b8f..551bc7d71b 100644
--- a/src/lib/frontend/typechecker.ml
+++ b/src/lib/frontend/typechecker.ml
@@ -284,7 +284,7 @@ module Env = struct
       c = { tt_desc = TTconst (Tint n); tt_ty = Ty.Tint} ;
       annot = new_id () ;
     } in
-    let rm = Fpa_rounding.fpa_rounding_mode in
+    let rm = Fpa_rounding.fpa_rounding_mode () in
     let mode m =
       let h = find_builtin_cstr rm m in
       {
@@ -298,10 +298,12 @@ module Env = struct
     let float prec exp mode x =
       TTapp (Symbols.Op Float, [prec; exp; mode; x])
     in
+    let nte = Fpa_rounding.string_of_rounding_mode NearestTiesToEven in
+    let tname = Fpa_rounding.fpa_rounding_mode_type_name () in
     let float32 = float (int "24") (int "149") in
-    let float32d = float32 (mode "NearestTiesToEven") in
+    let float32d = float32 (mode nte) in
     let float64 = float (int "53") (int "1074") in
-    let float64d = float64 (mode "NearestTiesToEven") in
+    let float64d = float64 (mode nte) in
     let op n op profile =
       MString.add n @@ `Term (Symbols.Op op, profile, Other)
     in
@@ -312,8 +314,11 @@ module Env = struct
     let any = Ty.fresh_tvar in
     let env = {
       env with
-      types = Types.add_builtin env.types "fpa_rounding_mode" rm ;
-      builtins = add_builtin_enum Fpa_rounding.fpa_rounding_mode env.builtins;
+      types = Types.add_builtin env.types tname rm ;
+      builtins =
+        add_builtin_enum
+          (Fpa_rounding.fpa_rounding_mode ())
+          env.builtins;
     } in
     let builtins =
       env.builtins
diff --git a/src/lib/structures/expr.ml b/src/lib/structures/expr.ml
index e1e79add4e..6a6e2c9420 100644
--- a/src/lib/structures/expr.ml
+++ b/src/lib/structures/expr.ml
@@ -2819,7 +2819,7 @@ let const_view t =
         Fmt.failwith "error when trying to convert %a to an int" Z.pp_print n
     end
   | { f = Op (Constr c); ty; _ }
-    when Ty.equal ty Fpa_rounding.fpa_rounding_mode ->
+    when Ty.equal ty (Fpa_rounding.fpa_rounding_mode ()) ->
     RoundingMode (Fpa_rounding.rounding_mode_of_hs c)
   | _ -> Fmt.failwith "unsupported constant: %a" print t
 
diff --git a/src/lib/structures/fpa_rounding.ml b/src/lib/structures/fpa_rounding.ml
index cdd67d3a5c..894427a17e 100644
--- a/src/lib/structures/fpa_rounding.ml
+++ b/src/lib/structures/fpa_rounding.ml
@@ -33,64 +33,104 @@ module Hs = Hstring
 module Q = Numbers.Q
 module Z = Numbers.Z
 
+(** The five standard rounding modes of the SMTLIB.
+    Note that the SMTLIB defines these rounding modes to be the only
+    possible modes. *)
 type rounding_mode =
-  (* five standard/why3 fpa rounding modes *)
   | NearestTiesToEven
-  (*ne in Gappa: to nearest, tie breaking to even mantissas*)
-  | ToZero (* zr in Gappa: toward zero *)
-  | Up (* up in Gappa: toward plus infinity *)
-  | Down (* dn in Gappa: toward minus infinity *)
-  | NearestTiesToAway (* na : to nearest, tie breaking away from zero *)
-
-  (* additional Gappa rounding modes *)
-  | Aw (* aw in Gappa: away from zero **)
-  | Od (* od in Gappa: to odd mantissas *)
-  | No (* no in Gappa: to nearest, tie breaking to odd mantissas *)
-  | Nz (* nz in Gappa: to nearest, tie breaking toward zero *)
-  | Nd (* nd in Gappa: to nearest, tie breaking toward minus infinity *)
-  | Nu (* nu in Gappa: to nearest, tie breaking toward plus infinity *)
-
-let pp_rounding_mode ppf m =
-  Format.pp_print_string ppf @@
+  | ToZero
+  | Up
+  | Down
+  | NearestTiesToAway
+
+let string_of_rounding_mode_ae m =
   match m with
   | NearestTiesToEven -> "NearestTiesToEven"
   | ToZero -> "ToZero"
   | Up -> "Up"
   | Down -> "Down"
   | NearestTiesToAway -> "NearestTiesToAway"
-  | Aw -> "Aw"
-  | Od -> "Od"
-  | No -> "No"
-  | Nz -> "Nz"
-  | Nd -> "Nd"
-  | Nu -> "Nu"
-
-let fpa_rounding_mode, rounding_mode_of_hs =
-  let cstrs =
-    [ (* standards *)
-      NearestTiesToEven;
-      ToZero;
-      Up;
-      Down;
-      NearestTiesToAway;
-      (* non standards *)
-      Aw;
-      Od;
-      No;
-      Nz;
-      Nd;
-      Nu ]
-  in
+
+let string_of_rounding_mode_smt2 m =
+  match m with
+  | NearestTiesToEven -> "RNE"
+  | ToZero -> "RTZ"
+  | Up -> "RTP"
+  | Down -> "RTN"
+  | NearestTiesToAway -> "RNA"
+
+let cstrs =
+  [
+    NearestTiesToEven;
+    ToZero;
+    Up;
+    Down;
+    NearestTiesToAway;
+  ]
+
+let if_smt ~then_ ~else_ =
+  match Options.get_input_format () with
+  | None | Some Smtlib2 -> then_
+  | _ -> else_
+
+let typ_and_rounding pp tname =
   let h_cstrs =
-    List.map (fun c -> Hs.make (Format.asprintf "%a" pp_rounding_mode c)) cstrs
+    List.map (fun c -> Hs.make (pp c)) cstrs
   in
-  let ty = Ty.Tsum (Hs.make "fpa_rounding_mode", h_cstrs) in
+  let ty = Ty.Tsum (Hs.make tname, h_cstrs) in
   let table =
-    let table = Hashtbl.create 17 in
-    List.iter2 (Hashtbl.add table) h_cstrs cstrs;
+    let table = Hashtbl.create 5 in
+    List.iter2 (
+      fun key bnd ->
+        Hashtbl.add table key bnd
+    ) h_cstrs cstrs;
     table
   in
-  ty, Hashtbl.find table
+  ty,
+  (fun key -> match Hashtbl.find_opt table key with
+     | None ->
+       Fmt.failwith
+         "%a"
+         (fun fmt k ->
+            Format.pp_print_string fmt tname;
+            Hashtbl.iter (fun key _ -> Format.fprintf fmt "%a --" Hstring.print key) table;
+            Hstring.print fmt k
+         )
+         key
+     | Some res -> res)
+
+let ae_type_name = "fpa_rounding_mode"
+let smt2_type_name = "RoundingMode"
+
+let fpa_rounding_mode_ae, rounding_mode_of_hs_ae =
+  typ_and_rounding string_of_rounding_mode_ae ae_type_name
+
+let fpa_rounding_mode_smt, rounding_mode_of_hs_smt =
+  typ_and_rounding string_of_rounding_mode_smt2 smt2_type_name
+
+let rounding_mode_of_hs_smt hs =
+  Format.printf "rounding_mode_smt2@.";
+  rounding_mode_of_hs_smt hs
+
+let rounding_mode_of_hs_ae hs =
+  Format.printf "rounding_mode_ae@.";
+  rounding_mode_of_hs_ae hs
+
+let fpa_rounding_mode_type_name () =
+  if_smt ~then_:smt2_type_name ~else_:ae_type_name
+
+let fpa_rounding_mode () =
+  if_smt ~then_:fpa_rounding_mode_smt ~else_:fpa_rounding_mode_ae
+
+let rounding_mode_of_hs hs =
+  Format.pp_print_bool Format.std_formatter (if_smt ~then_:true ~else_:false);
+  if_smt ~then_:(rounding_mode_of_hs_smt) ~else_:(rounding_mode_of_hs_ae) hs
+
+
+let string_of_rounding_mode m =
+  if_smt
+    ~then_:(string_of_rounding_mode_smt2 m)
+    ~else_:(string_of_rounding_mode_ae m)
 
 (** Helper functions **)
 
@@ -160,9 +200,6 @@ let round_big_int (mode : rounding_mode) y =
     if Q.sign diff = 0 then z
     else if Q.compare diff half < 0 then z else Z.add z (signed_one y)
 
-  | Aw | Od | No | Nz | Nd | Nu -> assert false
-
-
 let to_mantissa_exp prec exp mode x =
   let sign_x = Q.sign x in
   assert ((sign_x = 0) == Q.equal x Q.zero);
diff --git a/src/lib/structures/fpa_rounding.mli b/src/lib/structures/fpa_rounding.mli
index 2aa00eada1..daf9c02bf0 100644
--- a/src/lib/structures/fpa_rounding.mli
+++ b/src/lib/structures/fpa_rounding.mli
@@ -29,26 +29,20 @@
 (**************************************************************************)
 
 type rounding_mode =
-  (* five standard/why3 fpa rounding modes *)
   | NearestTiesToEven
-  (*ne in Gappa: to nearest, tie breaking to even mantissas*)
-  | ToZero (* zr in Gappa: toward zero *)
-  | Up (* up in Gappa: toward plus infinity *)
-  | Down (* dn in Gappa: toward minus infinity *)
-  | NearestTiesToAway (* na : to nearest, tie breaking away from zero *)
+  | ToZero
+  | Up
+  | Down
+  | NearestTiesToAway
 
-  (* additional Gappa rounding modes *)
-  | Aw (* aw in Gappa: away from zero **)
-  | Od (* od in Gappa: to odd mantissas *)
-  | No (* no in Gappa: to nearest, tie breaking to odd mantissas *)
-  | Nz (* nz in Gappa: to nearest, tie breaking toward zero *)
-  | Nd (* nd in Gappa: to nearest, tie breaking toward minus infinity *)
-  | Nu (* nu in Gappa: to nearest, tie breaking toward plus infinity *)
+val fpa_rounding_mode_type_name : unit -> string
 
-val fpa_rounding_mode : Ty.t
+val fpa_rounding_mode : unit -> Ty.t
 
 val rounding_mode_of_hs : Hstring.t -> rounding_mode
 
+val string_of_rounding_mode : rounding_mode -> string
+
 (** Integer part of binary logarithm for NON-ZERO POSITIVE number **)
 val integer_log_2 : Numbers.Q.t -> int