Source file math.ml

(* gsl-ocaml - OCaml interface to GSL                       *)
(* Copyright (©) 2002-2012 - Olivier Andrieu                *)
(* Distributed under the terms of the GPL version 3         *)

let () = Error.init ()
let e = 2.71828182845904523536028747135 (* e *)
let log2e = 1.44269504088896340735992468100 (* log_2 (e) *)
let log10e = 0.43429448190325182765112891892 (* log_10 (e) *)
let sqrt2 = 1.41421356237309504880168872421 (* sqrt(2) *)
let sqrt1_2 = 0.70710678118654752440084436210 (* sqrt(1/2) *)
let sqrt3 = 1.73205080756887729352744634151 (* sqrt(3) *)
let pi = 3.14159265358979323846264338328 (* pi *)
let pi_2 = 1.57079632679489661923132169164 (* pi/2 *)
let pi_4 = 0.78539816339744830966156608458 (* pi/4 *)
let sqrtpi = 1.77245385090551602729816748334 (* sqrt(pi) *)
let i_2_sqrtpi = 1.12837916709551257389615890312 (* 2/sqrt(pi) *)
let i_1_pi = 0.31830988618379067153776752675 (* 1/pi *)
let i_2_pi = 0.63661977236758134307553505349 (* 2/pi *)
let ln10 = 2.30258509299404568401799145468 (* ln(10) *)
let ln2 = 0.69314718055994530941723212146 (* ln(2) *)
let lnpi = 1.14472988584940017414342735135 (* ln(pi) *)
let euler = 0.57721566490153286060651209008 (* Euler constant *)

let rec unsafe_pow_int x = function
  | 1 -> x
  | n when n mod 2 = 0 -> unsafe_pow_int (x *. x) (n / 2)
  | n -> x *. unsafe_pow_int x (pred n)

let pow_int x = function
  | 0 -> 1.
  | n when n > 0 -> unsafe_pow_int x n
  | _ -> invalid_arg "pow_int"

external log1p : float -> float = "ml_gsl_log1p" "gsl_log1p"
[@@unboxed] [@@noalloc]

external expm1 : float -> float = "ml_gsl_expm1" "gsl_expm1"
[@@unboxed] [@@noalloc]

external hypot : float -> float -> float = "ml_gsl_hypot" "gsl_hypot"
[@@unboxed] [@@noalloc]

external acosh : float -> float = "ml_gsl_acosh" "gsl_acosh"
[@@unboxed] [@@noalloc]

external asinh : float -> float = "ml_gsl_asinh" "gsl_asinh"
[@@unboxed] [@@noalloc]

external atanh : float -> float = "ml_gsl_atanh" "gsl_atanh"
[@@unboxed] [@@noalloc]

external fcmp : float -> float -> epsilon:float -> int = "ml_gsl_fcmp"