-----------------------------------------------------------------------------
{- |
Module      :  GSL.Special
Copyright   :  (c) Alberto Ruiz 2006
License     :  GPL-style

Maintainer  :  Alberto Ruiz (aruiz at um dot es)
Stability   :  provisional
Portability :  uses ffi

Wrappers for selected special functions.

<http://www.gnu.org/software/gsl/manual/html_node/Special-Functions.html#Special-Functions>
-}
-----------------------------------------------------------------------------

module GSL.Special (
  module GSL.Special.Airy
, module GSL.Special.Bessel
, module GSL.Special.Clausen
, module GSL.Special.Coulomb
, module GSL.Special.Coupling
, module GSL.Special.Dawson
, module GSL.Special.Debye
, module GSL.Special.Dilog
, module GSL.Special.Elementary
, module GSL.Special.Ellint
, module GSL.Special.Erf
, module GSL.Special.Exp
, module GSL.Special.Expint
, module GSL.Special.Fermi_dirac
, module GSL.Special.Gamma
, module GSL.Special.Gegenbauer
, module GSL.Special.Hyperg
, module GSL.Special.Laguerre
, module GSL.Special.Lambert
, module GSL.Special.Legendre
, module GSL.Special.Log
, module GSL.Special.Pow_int
, module GSL.Special.Psi
, module GSL.Special.Synchrotron
, module GSL.Special.Trig
, module GSL.Special.Zeta
)
where

import Foreign
import GSL.Special.Internal
import GSL.Special.Airy
import GSL.Special.Bessel
import GSL.Special.Clausen
import GSL.Special.Coulomb
import GSL.Special.Coupling
import GSL.Special.Dawson
import GSL.Special.Debye
import GSL.Special.Dilog
import GSL.Special.Elementary
import GSL.Special.Ellint
import GSL.Special.Erf
import GSL.Special.Exp
import GSL.Special.Expint
import GSL.Special.Fermi_dirac
import GSL.Special.Gamma
import GSL.Special.Gegenbauer
import GSL.Special.Hyperg
import GSL.Special.Laguerre
import GSL.Special.Lambert
import GSL.Special.Legendre
import GSL.Special.Log
import GSL.Special.Pow_int
import GSL.Special.Psi
import GSL.Special.Synchrotron
import GSL.Special.Trig
import GSL.Special.Zeta


-------------------- simple functions --------------------------

{- | The error function (/gsl_sf_erf/), defined as 2\/ \\sqrt \\pi * \int\_0\^t \\exp -t\^2 dt.

@> erf 1.5
0.9661051464753108@

-}
foreign import ccall "gsl-aux.h gsl_sf_erf" erf :: Double -> Double

{- | The Gaussian probability density function (/gsl_sf_erf_Z/), defined as (1\/\\sqrt\{2\\pi\}) \\exp(-x\^2\/2).

>> erf_Z 1.5
>0.12951759566589172

-}
foreign import ccall "gsl-aux.h gsl_sf_erf_Z" erf_Z :: Double -> Double

-------------------- functions returning sf_result -------------

{- | The regular cylindrical Bessel function of zeroth order, J_0(x). This is
   the example in the GSL manual, returning the value of the function and
   the error term: 

@\> bessel_J0_e 5.0
(-0.1775967713143383,1.9302109579684196e-16)@

-}
bessel_J0_e :: Double -> (Double,Double)
bessel_J0_e x = createSFR "bessel_J0_e" (gsl_sf_bessel_J0_e x)
foreign import ccall "gsl-aux.h gsl_sf_bessel_J0_e" gsl_sf_bessel_J0_e :: Double -> Ptr Double -> IO Int

-------------------- functions returning sf_result_e10 -------------

{- | (From the GSL manual) \"This function computes the exponential \exp(x) using the @gsl_sf_result_e10@ type to return a result with extended range. This function may be useful if the value of \exp(x) would overflow the numeric range of double\". 

For example:

@\> exp_e10_e 30.0
(1.0686474581524432,1.4711818964275088e-14,13)@

@\> exp 30.0
1.0686474581524463e13@

-}
exp_e10_e :: Double -> (Double,Int,Double)
exp_e10_e x = createSFR_E10 "exp_e10_e" (gsl_sf_exp_e10_e x)
foreign import ccall "gsl-aux.h gsl_sf_exp_e10_e" gsl_sf_exp_e10_e :: Double -> Ptr Double -> IO Int