(** All utilities which should be included in all source files are defined here *)

(** {1 Functions from libm} *)

external erf_float : float -> float = "erf_float_bytecode" "erf_float"
  [@@unboxed] [@@noalloc]
  (** Error function [erf] from [libm] *)

external erfc_float : float -> float = "erfc_float_bytecode" "erfc_float"
  [@@unboxed] [@@noalloc]
  (** Complementary error function [erfc] from [libm] *)

external gamma_float : float -> float = "gamma_float_bytecode" "gamma_float"
  [@@unboxed] [@@noalloc]
  (** Gamma function [gamma] from [libm] *)



(** {1 General functions} *)

val fact : int -> float
(** Factorial function.
  @raise Invalid_argument for negative arguments or arguments >100.
  *)

val pow : float -> int -> float
(** Fast implementation of the power function for small integer powers *)

val chop : float -> (unit -> float) -> float
(** In [chop a f], evaluate [f] only if the absolute value of [a] is larger
  than {!Constants.epsilon}, and return [a *. f ()].
  *)



(** {1 Functions related to the Boys function} *)

val incomplete_gamma : alpha:float -> float -> float
(** {{:https://en.wikipedia.org/wiki/Incomplete_gamma_function}
    Lower incomplete gamma function}
   @raise Failure when the calculation doesn't converge.
  *)

val boys_function : maxm:int -> float -> float array
(** {{:https://link.springer.com/article/10.1007/s10910-005-9023-3}
    Generalized Boys function}.
  @param maxm Maximum total angular momentum.
  *)


(** {1 Extension of the Array module} *)

val array_sum : float array -> float
(** Returns the sum of all the elements of the array *)

val array_product : float array -> float
(** Returns the product of all the elements of the array *)


(** {1 Linear algebra } *)

val diagonalize_symm : Lacaml.D.mat -> Lacaml.D.mat * Lacaml.D.vec
(** Diagonalize a symmetric matrix. Returns the eigenvectors and the eigenvalues. *)

val xt_o_x : o:Lacaml.D.mat -> x:Lacaml.D.mat -> Lacaml.D.mat
(** Computes X{^T}.O.X *)