Use OCaml floating-point operations on 64 bits arch

C functions were used for floating-point arithmetic operations, by
fear of double rounding that could happen on old x87 on 32 bits
architecture. This commit uses OCaml floating-point operations on 64
bits architectures.

The following snippet is made 17% faster by this commit.

    From Coq Require Import Int63 BinPos PrimFloat.
    Definition foo n :=
      let eps := sub (next_up one) one in
      Pos.iter (fun x => add x eps) two n.
    Time Eval native_compute in foo 1000000000.

1 files changed, 95 insertions, 0 deletions

diff --git a/kernel/float64_common.mli b/kernel/float64_common.mli
new file mode 100644
index 0000000000..4fb1c114a5
--- /dev/null
+++ b/kernel/float64_common.mli
@@ -0,0 +1,95 @@
+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *         Copyright INRIA, CNRS and contributors             *)
+(* <O___,, * (see version control and CREDITS file for authors & dates) *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+(** [t] is currently implemented by OCaml's [float] type.
+
+Beware: NaNs have a sign and a payload, while they should be
+indistinguishable from Coq's perspective. *)
+type t = float
+
+(** Test functions for special values to avoid calling [classify] *)
+val is_nan : t -> bool
+val is_infinity : t -> bool
+val is_neg_infinity : t -> bool
+
+val of_string : string -> t
+
+(** Print a float exactly as an hexadecimal value (exact decimal
+ * printing would be possible but sometimes requires more than 700
+ * digits). *)
+val to_hex_string : t -> string
+
+(** Print a float as a decimal value. The printing is not exact (the
+ * real value printed is not always the given floating-point value),
+ * however printing is precise enough that forall float [f],
+ * [of_string (to_decimal_string f) = f].  *)
+val to_string : t -> string
+
+val compile : t -> string
+
+val of_float : float -> t
+
+(** Return [true] for "-", [false] for "+". *)
+val sign : t -> bool
+
+val opp : t -> t
+val abs : t -> t
+
+type float_comparison = FEq | FLt | FGt | FNotComparable
+
+val eq : t -> t -> bool
+
+val lt : t -> t -> bool
+
+val le : t -> t -> bool
+
+(** The IEEE 754 float comparison.
+ * NotComparable is returned if there is a NaN in the arguments *)
+val compare : t -> t -> float_comparison
+[@@ocaml.inline always]
+
+type float_class =
+  | PNormal | NNormal | PSubn | NSubn | PZero | NZero | PInf | NInf | NaN
+
+val classify : t -> float_class
+[@@ocaml.inline always]
+
+(** Link with integers *)
+val of_int63 : Uint63.t -> t
+[@@ocaml.inline always]
+
+val normfr_mantissa : t -> Uint63.t
+[@@ocaml.inline always]
+
+(** Shifted exponent extraction *)
+val eshift : int
+
+val frshiftexp : t -> t * Uint63.t (* float remainder, shifted exponent *)
+[@@ocaml.inline always]
+
+val ldshiftexp : t -> Uint63.t -> t
+[@@ocaml.inline always]
+
+val next_up : t -> t
+
+val next_down : t -> t
+
+(** Return true if two floats are equal.
+ * All NaN values are considered equal. *)
+val equal : t -> t -> bool
+[@@ocaml.inline always]
+
+val hash : t -> int
+
+(** Total order relation over float values. Behaves like [Pervasives.compare].*)
+val total_compare : t -> t -> int
+
+val is_float64 : Obj.t -> bool
+[@@ocaml.inline always]