@BEGIN_FROM_5_2_0@
 include Float
@END_FROM_5_2_0@
@BEGIN_BEFORE_5_2_0@

module Array = struct
  @BEGIN_FROM_4_08_0@
  include Float.Array
  @END_FROM_4_08_0@

  @BEGIN_BEFORE_4_08_0@

  type t = Stdcompat__init.floatarray

  include Stdcompat__array.Floatarray

  let unsafe_fill array offset len v =
    for i = offset to offset + len - 1 do
      unsafe_set array i v
    done

  let unsafe_blit src src_offset dst dst_offset len =
    for i = 0 to len - 1 do
      unsafe_set dst (dst_offset + i) (unsafe_get src (src_offset + i))
    done

  let make len v =
    let result = create len in
    unsafe_fill result 0 len v;
    result

  let init len f =
    let result = create len in
    for i = 0 to len - 1 do
      unsafe_set result i (f i)
    done;
    result

  let append a1 a2 =
    let l1 = length a1 in
    let l2 = length a2 in
    let result = create (l1 + l2) in
    unsafe_blit a1 0 result 0 l1;
    unsafe_blit a2 0 result l1 l2;
    result

  let concat l =
    let len = List.fold_left (fun acc a -> acc + length a) 0 l in
    let result = create len in
    let rec loop l i =
      match l with
      | [] -> ()
      | hd :: tl ->
          let len = length hd in
          unsafe_blit hd 0 result i len;
          loop tl (i + len) in
    loop l 0;
    result

  let check a offset len msg =
    if offset < 0 || len < 0 || offset + len < 0 || offset + len > length a then
      failwith msg

  let sub a offset len =
    check a offset len "Float.Array.sub";
    let result = create len in
    unsafe_blit a offset result 0 len;
    result

  let copy a =
    let len = length a in
    let result = create len in
    unsafe_blit a 0 result 0 len;
    result

  let fill a offset len v =
    check a offset len "Float.Array.fill";
    unsafe_fill a offset len v

  let blit src src_offset dst dst_offset len =
    check src src_offset len "Float.Array.blit";
    check dst dst_offset len "Float.Array.blit";
    unsafe_blit dst src_offset dst dst_offset len

  let to_list a =
    Stdcompat__list.init (length a) (unsafe_get a)

  let of_list l =
    let result = create (List.length l) in
    let rec fill i l =
      match l with
      | [] -> result
      | hd :: tl ->
          unsafe_set result i hd;
          fill (succ i) tl in
    fill 0 l

  let iter f a =
    for i = 0 to length a - 1 do
      f (unsafe_get a i)
    done

  let iteri f a =
    for i = 0 to length a - 1 do
      f i (unsafe_get a i)
    done

  let map f a =
    let len = length a in
    let result = create len in
    for i = 0 to len - 1 do
      unsafe_set result i (f (unsafe_get a i))
    done;
    result

  let mapi f a =
    let len = length a in
    let result = create len in
    for i = 0 to len - 1 do
      unsafe_set result i (f i (unsafe_get a i))
    done;
    result

  let fold_left f acc a =
    let len = length a in
    let rec aux i acc =
      if i < len then
        aux (succ i) (f acc (unsafe_get a i))
      else
        acc in
    aux 0 acc

  let fold_right f a acc =
    let len = length a in
    let rec aux i acc =
      if i > 0 then
        let j = pred i in
        aux j (f (unsafe_get a j) acc)
      else
        acc in
    aux len acc

  let iter2 f a b =
    let len = length a in
    if len <> length b then
      failwith "Float.Array.iter2";
    for i = 0 to len - 1 do
      f (unsafe_get a i) (unsafe_get b i)
    done

  let map2 f a b =
    let len = length a in
    if len <> length b then
      failwith "Float.Array.iter2";
    let result = create len in
    for i = 0 to len - 1 do
      unsafe_set result i (f (unsafe_get a i) (unsafe_get b i))
    done;
    result

  let for_all f a =
    let len = length a in
    let rec aux i =
      i >= len || f (unsafe_get a i) && aux (succ i) in
    aux 0

  let exists f a =
    let len = length a in
    let rec aux i =
      i < len && (f (unsafe_get a i) || aux (succ i)) in
    aux 0

  let mem x a =
    exists (fun y -> compare x y = 0) a

  let mem_ieee x a =
    exists (( = ) x) a

  let sort _p _a =
    failwith "unimplemented"

  let stable_sort = sort

  let fast_sort = sort

  let to_seq a =
    let rec aux i () =
      if i < length a then
        let x = unsafe_get a i in
        Stdcompat__seq.Cons (x, aux (i + 1))
      else
        Stdcompat__seq.Nil in
    aux 0

  let to_seqi a =
    let rec aux i () =
      if i < length a then
        let x = unsafe_get a i in
        Stdcompat__seq.Cons ((i, x), aux (i + 1))
      else
        Stdcompat__seq.Nil in
    aux 0

  let of_rev_list l =
    let len = List.length l in
    let result = create len in
    let rec fill i l =
      match l with
      | [] -> result
      | hd :: tl ->
          unsafe_set result i hd;
          fill (pred i) tl in
    fill (len - 1) l

  let of_seq i =
    let l = Stdcompat__seq.fold_left (fun acc x -> x :: acc) [] i in
    of_rev_list l

  let map_to_array f a =
    Array.init (length a) (fun i -> f (unsafe_get a i))

  let map_from_array f a =
    init (Array.length a) (fun i -> f (Array.unsafe_get a i))

@END_BEFORE_4_08_0@

  @BEGIN_BEFORE_5_1_0@
  let map_inplace f array =
    for i = 0 to length array - 1 do
      unsafe_set array i (f (unsafe_get array i))
    done

  let mapi_inplace f array =
    for i = 0 to length array - 1 do
      unsafe_set array i (f i (unsafe_get array i))
    done

  let rec find_opt_from index f array =
    if index < length array then
      let v = unsafe_get array index in
      if f v then
        Some v
      else
        find_opt_from (succ index) f array
    else
      None

  let find_opt f array =
    find_opt_from 0 f array

  let rec find_index_from index p array =
    if index < length array then
      if p (unsafe_get array index) then
        Some index
      else
        find_index_from (succ index) p array
    else
      None

  let find_index p array =
    find_index_from 0 p array

  let rec find_map_from index f array =
    if index < length array then
      match f (unsafe_get array index) with
      | None -> find_map_from (succ index) f array
      | some -> some
    else
      None

  let find_map f array =
    find_map_from 0 f array

  let rec find_mapi_from index f array =
    if index < length array then
      match f index (unsafe_get array index) with
      | None -> find_mapi_from (succ index) f array
      | some -> some
    else
      None

  let find_mapi f array =
    find_mapi_from 0 f array
  @END_BEFORE_5_1_0@

  let make_matrix m n x =
    Array.init m (fun _ -> make n x)

  let init_matrix m n f =
    Array.init m (fun i -> init n (fun j -> f i j))
  
  let shuffle ~rand array =
    for i = length array - 1 downto 0 do
      let j = rand (i + 1) in
      let tmp = unsafe_get array i in
      unsafe_set array i (get array j);
      unsafe_set array j tmp
    done
end

module ArrayLabels = struct
  @BEGIN_FROM_4_08_0@
  include Float.ArrayLabels
  @END_FROM_4_08_0@
  @BEGIN_BEFORE_4_08_0@
  include Float.Array

  let init i ~f = init i f

  let sub a ~pos ~len = sub a pos len

  let fill a ~pos ~len v = fill a pos len v

  let blit ~src ~src_pos ~dst ~dst_pos ~len = blit src src_pos dst dst_pos len

  let iter ~f a = iter f a

  let iteri ~f a = iteri f a

  let map ~f a = map f a

  let mapi ~f a = mapi f a

  let fold_left ~f ~init a = fold_left f init a

  let fold_right ~f a ~init = fold_right f a init

  let iter2 ~f a = iter2 f a

  let map2 ~f a = map2 f a

  let for_all ~f a = for_all f a

  let exists ~f a = exists f a

  let mem v ~set = mem v set

  let mem_ieee v ~set = mem_ieee v set

  let sort ~cmp a = sort cmp a

  let stable_sort ~cmp a = stable_sort cmp a

  let fast_sort ~cmp a = fast_sort cmp a

  let map_to_array ~f a = map_to_array f a

  let map_from_array ~f a = map_from_array f a
  @END_BEFORE_4_08_0@

  @BEGIN_BEFORE_5_1_0@
  let map_inplace ~f a = Array.map_inplace f a

  let mapi_inplace ~f a = Array.mapi_inplace f a

  let find_opt ~f a = Array.find_opt f a

  let find_index ~f a = Array.find_index f a

  let find_map ~f a = Array.find_map f a

  let find_mapi ~f a = Array.find_mapi f a
  @END_BEFORE_5_1_0@

  let make_matrix ~dimx ~dimy v = Array.make_matrix dimx dimy v

  let init_matrix ~dimx ~dimy ~f = Array.init_matrix dimx dimy f

  let shuffle ~rand a = Array.shuffle rand a
end

@BEGIN_FROM_4_07_0@
 include (Float : module type of Float with module Array := Array and module ArrayLabels := ArrayLabels)
@END_FROM_4_07_0@
@END_BEFORE_5_2_0@
@BEGIN_BEFORE_4_07_0@
type fpclass = Pervasives.fpclass =
  | FP_normal 
  | FP_subnormal 
  | FP_zero 
  | FP_infinite 
  | FP_nan 
(** @since 4.07.0:
    type fpclass = Pervasives.fpclass =
      | FP_normal 
      | FP_subnormal 
      | FP_zero 
      | FP_infinite 
      | FP_nan 
 *)
type t = float

let infinity = Pervasives.infinity

let neg_infinity = Pervasives.neg_infinity

let nan = Pervasives.nan

@BEGIN_FROM_4_03_0@
let pi = 0x1.921fb54442d18p+1
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
let pi = 4. *. atan 1.
@END_BEFORE_4_03_0@

let max_float = Pervasives.max_float

let min_float = Pervasives.min_float

let epsilon = Pervasives.epsilon_float

let of_string_opt = Stdcompat__pervasives.float_of_string_opt

let to_string = Pervasives.string_of_float

external compare : float -> float -> int = "%compare"

let equal x y = compare x y = 0

let hash = Hashtbl.hash

@BEGIN_FROM_4_03_0@
external hypot : float -> float -> float = "caml_hypot_float" "caml_hypot"
[@@unboxed ][@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_4_00_0@
external hypot :
  float -> float -> float = "caml_hypot_float" "caml_hypot" "float"
@END_FROM_4_00_0@
@BEGIN_BEFORE_4_00_0@
let hypot = Stdcompat__pervasives.hypot
@END_BEFORE_4_00_0@

@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external expm1 : float -> float = "caml_expm1_float" "caml_expm1"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_12_0@
external expm1 : float -> float = "caml_expm1_float" "caml_expm1" "float"
@END_FROM_3_12_0@
@BEGIN_BEFORE_3_12_0@
let expm1 = Stdcompat__pervasives.expm1
@END_BEFORE_3_12_0@

@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external log1p : float -> float = "caml_log1p_float" "caml_log1p"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_12_0@
external log1p : float -> float = "caml_log1p_float" "caml_log1p" "float"
@END_FROM_3_12_0@
@BEGIN_BEFORE_3_12_0@
let log1p = Stdcompat__pervasives.log1p
@END_BEFORE_3_12_0@

@END_BEFORE_4_03_0@

external neg : float -> float = "%negfloat"

external add : float -> float -> float = "%addfloat"

external sub : float -> float -> float = "%subfloat"

external mul : float -> float -> float = "%mulfloat"

external div : float -> float -> float = "%divfloat"

@BEGIN_FROM_4_03_0@
external rem : float -> float -> float = "caml_fmod_float" "fmod"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external rem : float -> float -> float = "caml_fmod_float" "fmod" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external rem : float -> float -> float = "fmod_float" "fmod" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

external abs : float -> float = "%absfloat"

external of_int : int -> float = "%floatofint"

external to_int : float -> int = "%intoffloat"

@BEGIN_FROM_3_08_0@
external of_string : string -> float = "caml_float_of_string"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external of_string : string -> float = "float_of_string"
@END_BEFORE_3_08_0@

@BEGIN_FROM_4_03_0@
external classify_float :
  ((float)[@unboxed ]) -> fpclass = "caml_classify_float"
    "caml_classify_float_unboxed"[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external classify_float : float -> fpclass = "caml_classify_float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external classify_float : float -> fpclass = "classify_float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external pow : float -> float -> float = "caml_power_float" "pow"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external pow : float -> float -> float = "caml_power_float" "pow" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external pow : float -> float -> float = "power_float" "pow" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external sqrt : float -> float = "caml_sqrt_float" "sqrt"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external sqrt : float -> float = "caml_sqrt_float" "sqrt" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external sqrt : float -> float = "sqrt_float" "sqrt" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external exp : float -> float = "caml_exp_float" "exp"[@@unboxed ][@@noalloc
                                                                    ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external exp : float -> float = "caml_exp_float" "exp" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external exp : float -> float = "exp_float" "exp" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external log : float -> float = "caml_log_float" "log"[@@unboxed ][@@noalloc
                                                                    ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external log : float -> float = "caml_log_float" "log" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external log : float -> float = "log_float" "log" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external log10 : float -> float = "caml_log10_float" "log10"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external log10 : float -> float = "caml_log10_float" "log10" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external log10 : float -> float = "log10_float" "log10" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external cos : float -> float = "caml_cos_float" "cos"[@@unboxed ][@@noalloc
                                                                    ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external cos : float -> float = "caml_cos_float" "cos" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external cos : float -> float = "cos_float" "cos" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external sin : float -> float = "caml_sin_float" "sin"[@@unboxed ][@@noalloc
                                                                    ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external sin : float -> float = "caml_sin_float" "sin" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external sin : float -> float = "sin_float" "sin" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external tan : float -> float = "caml_tan_float" "tan"[@@unboxed ][@@noalloc
                                                                    ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external tan : float -> float = "caml_tan_float" "tan" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external tan : float -> float = "tan_float" "tan" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external acos : float -> float = "caml_acos_float" "acos"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external acos : float -> float = "caml_acos_float" "acos" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external acos : float -> float = "acos_float" "acos" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external asin : float -> float = "caml_asin_float" "asin"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external asin : float -> float = "caml_asin_float" "asin" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external asin : float -> float = "asin_float" "asin" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external atan : float -> float = "caml_atan_float" "atan"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external atan : float -> float = "caml_atan_float" "atan" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external atan : float -> float = "atan_float" "atan" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external atan2 : float -> float -> float = "caml_atan2_float" "atan2"
[@@unboxed ][@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external atan2 : float -> float -> float = "caml_atan2_float" "atan2" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external atan2 : float -> float -> float = "atan2_float" "atan2" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external cosh : float -> float = "caml_cosh_float" "cosh"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external cosh : float -> float = "caml_cosh_float" "cosh" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external cosh : float -> float = "cosh_float" "cosh" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external sinh : float -> float = "caml_sinh_float" "sinh"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external sinh : float -> float = "caml_sinh_float" "sinh" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external sinh : float -> float = "sinh_float" "sinh" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external tanh : float -> float = "caml_tanh_float" "tanh"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external tanh : float -> float = "caml_tanh_float" "tanh" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external tanh : float -> float = "tanh_float" "tanh" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external ceil : float -> float = "caml_ceil_float" "ceil"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external ceil : float -> float = "caml_ceil_float" "ceil" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external ceil : float -> float = "ceil_float" "ceil" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_4_03_0@
external floor : float -> float = "caml_floor_float" "floor"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external floor : float -> float = "caml_floor_float" "floor" "float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external floor : float -> float = "floor_float" "floor" "float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_3_08_0@
external frexp : float -> (float * int) = "caml_frexp_float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external frexp : float -> (float * int) = "frexp_float"
@END_BEFORE_3_08_0@

@BEGIN_FROM_4_03_0@
external ldexp :
  ((float)[@unboxed ]) -> ((int)[@untagged ]) -> ((float)[@unboxed ]) =
    "caml_ldexp_float" "caml_ldexp_float_unboxed"[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_3_08_0@
external ldexp : float -> int -> float = "caml_ldexp_float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external ldexp : float -> int -> float = "ldexp_float"
@END_BEFORE_3_08_0@
@END_BEFORE_4_03_0@

@BEGIN_FROM_3_08_0@
external modf : float -> (float * float) = "caml_modf_float"
@END_FROM_3_08_0@
@BEGIN_BEFORE_3_08_0@
external modf : float -> (float * float) = "modf_float"
@END_BEFORE_3_08_0@

@END_BEFORE_4_07_0@

@BEGIN_BEFORE_4_08_0@
let sign_of_bits bits =
  not (Stdcompat__int64.equal (Int64.shift_right_logical bits 63) Int64.zero)

let sign_bit x = 
  sign_of_bits (Int64.bits_of_float x)

let is_nan (x : float) =
  x <> x

let is_infinite x =
  1. /. x = 0.

let is_finite x =
  x -. x = 0.

let trunc x =
  if sign_bit x then
    ceil x
  else
    floor x

let is_integer x =
  x = trunc x && is_finite x

let round x =
  if is_finite x then
    let ceil = ceil x in
    let floor = floor x in
    let o = compare (x -. floor) (ceil -. x) in
    if o < 0 then
      floor
    else if o > 0 then
      ceil
    else
      if sign_bit x then
        floor
      else
        ceil
  else
    x

let min_max_num x y =
  if is_nan x then (y, y)
  else if is_nan y then (x, x)
  else if x <= y && (sign_bit x || not (sign_bit y)) then (x, y)
  else (y, x)

let max_num x y =
  if is_nan x then y
  else if is_nan y then x
  else if x <= y && (sign_bit x || not (sign_bit y)) then y
  else x

let min_num x y =
  if is_nan x then y
  else if is_nan y then x
  else if x <= y && (sign_bit x || not (sign_bit y)) then x
  else y

let min_max x y =
  if is_nan x then (x, x)
  else if is_nan y then (y, y)
  else if x <= y && (sign_bit x || not (sign_bit y)) then (x, y)
  else (y, x)

let max x y =
  if is_nan x then x
  else if is_nan y then y
  else if x <= y && (sign_bit x || not (sign_bit y)) then y
  else x

let min x y =
  if is_nan x then x
  else if is_nan y then y
  else if x <= y && (sign_bit x || not (sign_bit y)) then x
  else y

@BEGIN_FROM_4_03_0@
external copy_sign :
  float -> float -> float = "caml_copysign_float" "caml_copysign"[@@unboxed ]
[@@noalloc ]
@END_FROM_4_03_0@
@BEGIN_BEFORE_4_03_0@
@BEGIN_FROM_4_00_0@
external copy_sign :
  float -> float -> float = "caml_copysign_float" "caml_copysign" "float"
@END_FROM_4_00_0@
@BEGIN_BEFORE_4_00_0@
let copy_sign = Stdcompat__pervasives.copysign
@END_BEFORE_4_00_0@
@END_BEFORE_4_03_0@

let pred_ x =
  let bits = Int64.bits_of_float x in
  if is_finite x then
    let bits' =
      if sign_of_bits bits then
        Int64.succ bits
      else
        Int64.pred bits in
    Int64.float_of_bits bits'
  else
    if sign_of_bits bits then
      x
    else
      Int64.float_of_bits (Int64.pred bits)

let succ_ x =
  let bits = Int64.bits_of_float x in
  if is_finite x then
    let bits' =
      if sign_of_bits bits then
        Int64.pred bits
      else
        Int64.succ bits in
    Int64.float_of_bits bits'
  else
    if sign_of_bits bits then
      Int64.float_of_bits (Int64.pred bits)
    else
      x

let next_after x y =
  if is_nan x || is_nan y then nan
  else
    let o = compare x y in
    if o < 0 then
      succ_ x
    else if o > 0 then
      pred_ x
    else
      y

let pred x =
  if is_nan x then
    x
  else
    pred_ x

let succ x =
  if is_nan x then
    x
  else
    succ_ x

let fma x y z =
  x *. y +. z

let minus_one = -1.

let one = 1.

let zero = 0.

@END_BEFORE_4_08_0@

@BEGIN_BEFORE_4_13_0@
let cbrt x =
  let res = exp ((1. /. 3.) *. log (abs x)) in
  if x >= 0. then
    res
  else
    -. res

let log2e = log 2.

let log2 x =
  log x /. log2e

let exp2 x =
  pow 2. x

let acosh x =
  log (x +. sqrt (x *. x -. 1.))

let asinh x =
  log (x +. sqrt (x *. x +. 1.))

let atanh x =
  0.5 *. log ((1. +. x) /. (1. -. x))

let erf x =
  (* from ocaml source floats.c, based on formula 7.1.26
     from the "Handbook of Mathematical Functions" by Abramowitz and Stegun. *)
  let a1 =  0.254829592 and a2 = -0.284496736 and a3 = 1.421413741
  and a4 = -1.453152027 and a5 = 1.061405429 and p = 0.3275911 in
  let x' = abs x in
  let t = 1. /. (1. +. p *. x') in
  let y =
    1. -. ((((a5 *. t +. a4) *. t +. a3) *. t +. a2) *. t +. a1) *.
      t *. exp (-. x' *. x') in
  if x >= 0. then y
  else -. y

let erfc x =
  1. -. erf x
@END_BEFORE_4_13_0@

@BEGIN_BEFORE_5_1_0@
let signaling_nan = nan

let quiet_nan = nan

let seeded_hash = Stdcompat__hashtbl.seeded_hash
@END_BEFORE_5_1_0@