module fvn_fnlib
use fvn_common
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! This module is a generic interface for fn library
! http://www.netlib.org/fn
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Elementary Functions
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Argument
interface carg
      real(4) function carg(z)
            complex(4) :: z
      end function carg
      real(8) function zarg(z)
            complex(8) :: z
      end function zarg
end interface carg

! Cubic root
interface cbrt
      real(4) function cbrt(x)
            real(4) :: x
      end function cbrt
      real(8) function dcbrt(x)
            real(8) :: x
      end function dcbrt
      complex(4) function ccbrt(z)
            complex(4) :: z
      end function ccbrt
      complex(8) function zcbrt(z)
            complex(8) :: z
      end function zcbrt
end interface cbrt

! (exp(x) -1)/x
interface exprl
      real(4) function exprel(x)
            real(4) :: x
      end function exprel
      real(8) function dexprl(x)
            real(8) :: x
      end function dexprl
      complex(4) function cexprl(z)
            complex(4) :: z
      end function cexprl
      complex(8) function zexprl(z)
            complex(8) :: z
      end function zexprl
end interface exprl

! log10 extension to complex arguments
interface log10
      complex(4) function clog10(z)
            complex(4) :: z
      end function clog10
      complex(8) function zlog10(z)
            complex(8) :: z
      end function zlog10
end interface log10 

! ln(x+1)
interface alnrel
      real(4) function alnrel(x)
            real(4) :: x
      end function alnrel
      real(8) function dlnrel(x)
            real(8) :: x
      end function dlnrel
      complex(4) function clnrel(z)
            complex(4) :: z
      end function clnrel
      complex(8) function zlnrel(z)
            complex(8) :: z
      end function zlnrel
end interface alnrel

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Elementary Functions
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Trigonometry
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Extension de la tangente aux arguments complexes
interface tan
      complex(4) function ctan(z)
            complex(4) :: z
      end function ctan
      complex(8) function ztan(z)
            complex(8) :: z
      end function ztan
end interface tan

! Cotangente
interface cot
      real(4) function cot(x)
            real(4) :: x
      end function cot
      real(8) function dcot(x)
            real(8) :: x
      end function dcot
      complex(4) function ccot(z)
            complex(4) :: z
      end function ccot
      complex(8) function zcot(z)
            complex(8) :: z
      end function zcot
end interface cot

! Sinus in degree
interface sindg
      real(4) function sindg(x)
            real(4) :: x
      end function sindg
      real(8) function dsindg(x)
            real(8) :: x
      end function dsindg
end interface sindg

! Cosinus in degree
interface cosdg
      real(4) function cosdg(x)
            real(4) :: x
      end function cosdg
      real(8) function dcosdg(x)
            real(8) :: x
      end function dcosdg
end interface cosdg


! Extension de l'arcsinus aux arguments complexes
interface asin
      complex(4) function casin(z)
            complex(4) :: z
      end function casin
      complex(8) function zasin(z)
            complex(8) :: z
      end function zasin
end interface asin

! Extension de l'arccosinus aux arguments complexes
interface acos
      complex(4) function cacos(z)
            complex(4) :: z
      end function cacos
      complex(8) function zacos(z)
            complex(8) :: z
      end function zacos
end interface acos

! Extension de l'arctangente aux arguments complexes
interface atan
      complex(4) function catan(z)
            complex(4) :: z
      end function catan
      complex(8) function zatan(z)
            complex(8) :: z
      end function zatan
end interface atan

! Extension de atan2 aux arguments complexes
interface atan2
      complex(4) function catan2(csn,ccs)
            complex(4) :: csn,ccs
      end function catan2
      complex(8) function zatan2(csn,ccs)
            complex(8) :: csn,ccs
      end function zatan2
end interface atan2


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Hyperbolic Trigonometry
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Extension du Sinus hyperbolique aux arguments complexes
interface sinh
      complex(4) function csinh(z)
            complex(4) :: z
      end function csinh
      complex(8) function zsinh(z)
            complex(8) :: z
      end function zsinh
end interface sinh

! Extension du Cosinus hyperbolique aux arguments complexes
interface cosh
      complex(4) function ccosh(z)
            complex(4) :: z
      end function ccosh
      complex(8) function zcosh(z)
            complex(8) :: z
      end function zcosh
end interface cosh

! Extension de la tangente hyperbolique aux arguments complexes
interface tanh
      complex(4) function ctanh(z)
            complex(4) :: z
      end function ctanh
      complex(8) function ztanh(z)
            complex(8) :: z
      end function ztanh
end interface tanh

! Arc sinus hyperbolique
interface asinh
      real(4) function asinh(x)
            real(4) :: x
      end function asinh
      real(8) function dasinh(x)
            real(8) :: x
      end function dasinh
      complex(4) function casinh(z)
            complex(4) :: z
      end function casinh
      complex(8) function zasinh(z)
            complex(8) :: z
      end function zasinh
end interface asinh

! Arc cosinus hyperbolique
interface acosh
      real(4) function acosh(x)
            real(4) :: x
      end function acosh
      real(8) function dacosh(x)
            real(8) :: x
      end function dacosh
      complex(4) function cacosh(z)
            complex(4) :: z
      end function cacosh
      complex(8) function zacosh(z)
            complex(8) :: z
      end function zacosh
end interface acosh

! Arc tangente hyperbolique
interface atanh
      real(4) function atanh(x)
            real(4) :: x
      end function atanh
      real(8) function datanh(x)
            real(8) :: x
      end function datanh
      complex(4) function catanh(z)
            complex(4) :: z
      end function catanh
      complex(8) function zatanh(z)
            complex(8) :: z
      end function zatanh
end interface atanh

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Trigonometry
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Exponential integral and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Exponential integral ei(x)
interface ei
      real(4) function ei(x)
            real(4) :: x
      end function ei
      real(8) function dei(x)
            real(8) :: x
      end function dei
end interface ei

! Exponential integral e1(x)
interface e1
      real(4) function e1(x)
            real(4) :: x
      end function e1
      real(8) function de1(x)
            real(8) :: x
      end function de1
end interface e1

!!!!!!!!!!!!!!!
! MISSING ENE
!!!!!!!!!!!!!!!

! Logarithm integral
interface ali
      real(4) function ali(x)
            real(4) :: x
      end function ali
      real(8) function dli(x)
            real(8) :: x
      end function dli
end interface ali

! Sine integral
interface si
      real(4) function si(x)
            real(4) :: x
      end function si
      real(8) function dsi(x)
            real(8) :: x
      end function dsi
end interface si

! Cosine integral
interface ci
      real(4) function ci(x)
            real(4) :: x
      end function ci
      real(8) function dci(x)
            real(8) :: x
      end function dci
end interface ci

! Cosine integral alternate definition
interface cin
      real(4) function cin(x)
            real(4) :: x
      end function cin
      real(8) function dcin(x)
            real(8) :: x
      end function dcin
end interface cin

! Hyperbolic sine integral
interface shi
      real(4) function shi(x)
            real(4) :: x
      end function shi
      real(8) function dshi(x)
            real(8) :: x
      end function dshi
end interface shi

! Hyperbolic cosine integral
interface chi
      real(4) function chi(x)
            real(4) :: x
      end function chi
      real(8) function dchi(x)
            real(8) :: x
      end function dchi
end interface chi

! Hyperbolic cosine integral alternate definition
interface cinh
      real(4) function cinh(x)
            real(4) :: x
      end function cinh
      real(8) function dcinh(x)
            real(8) :: x
      end function dcinh
end interface cinh

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Exponential integral and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!



!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Gamma family
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! No generic interface for fac and binom but we still
! define their prototypes
! Factorial
interface
      real(4) function fac(n)
            integer(4) :: n
      end function fac
      real(8) function dfac(n)
            integer(4) :: n
      end function dfac
! Binomial coefficient
      real(4) function binom(n,m)
            integer(4) :: n,m
      end function binom
      real(8) function dbinom(n,m)
            integer(4) :: n,m
      end function dbinom
end interface

! Gamma function
interface gamma
      real(4) function gamma(x)
            real(4) :: x
      end function gamma
      real(8) function dgamma(x)
            real(8) :: x
      end function dgamma
      complex(4) function cgamma(z)
            complex(4) :: z
      end function cgamma
      complex(8) function zgamma(z)
            complex(8) :: z
      end function zgamma
end interface gamma

! Reciprocal of gamma function
interface gamr
      real(4) function gamr(x)
            real(4) :: x
      end function gamr
      real(8) function dgamr(x)
            real(8) :: x
      end function dgamr
      complex(4) function cgamr(z)
            complex(4) :: z
      end function cgamr
      complex(8) function zgamr(z)
            complex(8) :: z
      end function zgamr
end interface gamr

! natural log of abs(gamma)
interface alngam
      real(4) function alngam(x)
            real(4) :: x
      end function alngam
      real(8) function dlngam(x)
            real(8) :: x
      end function dlngam
      complex(4) function clngam(z)
            complex(4) :: z
      end function clngam
      complex(8) function zlngam(z)
            complex(8) :: z
      end function zlngam
end interface alngam

! log abs gamma and sign
interface algams
      subroutine algams(x,algam,sgngam)
            real(4) :: x
      end subroutine algams
      subroutine dlgams(x,algam,sgngam)
            real(8) :: x
      end subroutine dlgams
end interface algams

! Incomplete gamma function
interface gami
      real(4) function gami(a,x)
            real(4) :: a,x
      end function gami
      real(8) function dgami(a,x)
            real(8) :: a,x
      end function dgami
end interface gami

! Complementary incomplete gamma function
interface gamic
      real(4) function gamic(a,x)
            real(4) :: a,x
      end function gamic
      real(8) function dgamic(a,x)
            real(8) :: a,x
      end function dgamic
end interface gamic

! Tricomi's incomplete gamma function
interface gamit
      real(4) function gamit(a,x)
            real(4) :: a,x
      end function gamit
      real(8) function dgamit(a,x)
            real(8) :: a,x
      end function dgamit
end interface gamit

! Psi function
interface psi
      real(4) function psi(x)
            real(4) :: x
      end function psi
      real(8) function dpsi(x)
            real(8) :: x
      end function dpsi
      complex(4) function cpsi(z)
            complex(4) :: z
      end function cpsi
      complex(8) function zpsi(z)
            complex(8) :: z
      end function zpsi
end interface psi

! Pochhammer
interface poch
      real(4) function poch(a,x)
            real(4) :: a,x
      end function poch
      real(8) function dpoch(a,x)
            real(8) :: a,x
      end function dpoch
end interface poch

! Pochhammer first order
interface poch1
      real(4) function poch1(a,x)
            real(4) :: a,x
      end function poch1
      real(8) function dpoch1(a,x)
            real(8) :: a,x
      end function dpoch1
end interface poch1

! Beta function
interface beta
      real(4) function beta(a,b)
            real(4) :: a,b
      end function beta
      real(8) function dbeta(a,b)
            real(8) :: a,b
      end function dbeta
      complex(4) function cbeta(a,b)
            complex(4) :: a,b
      end function cbeta
      complex(8) function zbeta(a,b)
            complex(8) :: a,b
      end function zbeta
end interface beta

! natural log of beta
interface albeta
      real(4) function albeta(a,b)
            real(4) :: a,b
      end function albeta
      real(8) function dlbeta(a,b)
            real(8) :: a,b
      end function dlbeta
      complex(4) function clbeta(a,b)
            complex(4) :: a,b
      end function clbeta
      complex(8) function zlbeta(a,b)
            complex(8) :: a,b
      end function zlbeta
end interface albeta

! Incomplete beta function
interface betai
      real(4) function betai(x,pin,qin)
            real(4) :: x,pin,qin
      end function betai
      real(8) function dbetai(x,pin,qin)
            real(8) :: x,pin,qin
      end function dbetai
end interface betai

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Gamma family
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!



!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Error function and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Error function
interface erf
      real(4) function erf(x)
            real(4) :: x
      end function erf
      real(8) function derf(x)
            real(8) :: x
      end function derf
end interface erf

! Complementary error function
interface erfc
      real(4) function erfc(x)
            real(4) :: x
      end function erfc
      real(8) function derfc(x)
            real(8) :: x
      end function derfc
end interface erfc

!!!!!!!!!!!
! MISSING ERFCE
! MISSING CERFI
! MISSING ERFI
! MISSING ERFCI
!!!!!!!!!!!!!!

! Dawson's function
interface daws
      real(4) function daws(x)
            real(4) :: x
      end function daws
      real(8) function ddaws(x)
            real(8) :: x
      end function ddaws
end interface daws

!!!!!!!!!!!!!!!!!
! MISSING FRESC
! MISSING FRESS
!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Error function and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Bessel functions and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!J0(x)
interface bsj0
      real(4) function besj0(x)
            real(4) :: x
      end function besj0
      real(8) function dbesj0(x)
            real(8) :: x
      end function dbesj0
end interface bsj0

!J1(x)
interface bsj1
      real(4) function besj1(x)
            real(4) :: x
      end function besj1
      real(8) function dbesj1(x)
            real(8) :: x
      end function dbesj1
end interface bsj1

!Y0(x)
interface bsy0
      real(4) function besy0(x)
            real(4) :: x
      end function besy0
      real(8) function dbesy0(x)
            real(8) x
      end function dbesy0
end interface bsy0

!Y1(x)
interface bsy1
      real(4) function besy1(x)
            real(4) :: x
      end function besy1
      real(8) function dbesy1(x)
            real(8) x
      end function dbesy1
end interface bsy1

!I0(x)
interface bsi0
      real(4) function besi0(x)
            real(4) :: x
      end function besi0
      real(8) function dbesi0(x)
            real(8) x
      end function dbesi0
end interface bsi0

!I1(x)
interface bsi1
      real(4) function besi1(x)
            real(4) :: x
      end function besi1
      real(8) function dbesi1(x)
            real(8) x
      end function dbesi1
end interface bsi1

!K0(x)
interface bsk0
      real(4) function besk0(x)
            real(4) :: x
      end function besk0
      real(8) function dbesk0(x)
            real(8) x
      end function dbesk0
end interface bsk0

!K1(x)
interface bsk1
      real(4) function besk1(x)
            real(4) :: x
      end function besk1
      real(8) function dbesk1(x)
            real(8) x
      end function dbesk1
end interface bsk1

! Exponentially scaled I0
interface bsi0e
      real(4) function besi0e(x)
            real(4) :: x
      end function besi0e
      real(8) function dbsi0e(x)
            real(8) :: x
      end function dbsi0e
end interface bsi0e

! Exponentially scaled I1
interface bsi1e
      real(4) function besi1e(x)
            real(4) :: x
      end function besi1e
      real(8) function dbsi1e(x)
            real(8) :: x
      end function dbsi1e
end interface bsi1e

! Exponentially scaled K0
interface bsk0e
      real(4) function besk0e(x)
            real(4) :: x
      end function besk0e
      real(8) function dbsk0e(x)
            real(8) :: x
      end function dbsk0e
end interface bsk0e

! Exponentially scaled K1
interface bsk1e
      real(4) function besk1e(x)
            real(4) :: x
      end function besk1e
      real(8) function dbsk1e(x)
            real(8) :: x
      end function dbsk1e
end interface bsk1e

! nth order J
interface bsjn
      real(4) function besjn(n,x,factor,big)
            integer(4) :: n
            real(4) :: x
            integer(4), optional :: factor
            real(4), optional :: big
      end function besjn
      real(8) function dbesjn(n,x,factor,big)
            integer(4) :: n
            real(8) :: x
            integer(4), optional :: factor
            real(8), optional :: big
      end function dbesjn
end interface bsjn

! nth order Y
interface bsyn
      real(4) function besyn(n,x)
            integer(4) :: n
            real(4) :: x
      end function besyn
      real(8) function dbesyn(n,x)
            integer(4) :: n
            real(8) :: x
      end function dbesyn
end interface bsyn

! nth order I
interface bsin
      real(4) function besin(n,x,factor,big)
            integer(4) :: n
            real(4) :: x
            integer(4), optional :: factor
            real(4), optional :: big
      end function besin
      real(8) function dbesin(n,x,factor,big)
            integer(4) :: n
            real(8) :: x
            integer(4), optional :: factor
            real(8), optional :: big
      end function dbesin
end interface bsin

! nth order K
interface bskn
      real(4) function beskn(n,x)
            integer(4) :: n
            real(4) :: x
      end function beskn
      real(8) function dbeskn(n,x)
            integer(4) :: n
            real(8) :: x
      end function dbeskn
end interface bskn

!!!!!!!!!!!!!!!!!!!!!
! MISSING BSJNS
! MISSING BSINS
! MISSING BSJS
! MISSING BSYS
! MISSING BSIS
! MISSING BSIES
!!!!!!!!!!!!!!!!!!!!!

! K nu + k
interface bsks
      subroutine besks(xnu,x,nin,bk)
            real(4) :: xnu,x
            integer :: nin
            real(4), dimension(nin) :: bk
      end subroutine besks
      subroutine dbesks(xnu,x,nin,bk)
            real(8) :: xnu,x
            integer :: nin
            real(8), dimension(nin) :: bk
      end subroutine dbesks
end interface bsks

! Exponentially scaled K nu + k
interface bskes
      subroutine beskes(xnu,x,nin,bke)
            real(4) :: xnu,x
            integer :: nin
            real(4),dimension(nin) :: bke
      end subroutine beskes
      subroutine dbskes(xnu,x,nin,bke)
            real(8) :: xnu,x
            integer :: nin
            real(8),dimension(nin) :: bke
      end subroutine dbskes
end interface bskes

!!!!!!!!!!!!!!!!!!
! MISSING CBJS
! MISSING CBYS
! MISSING CBIS
!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Bessel functions and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Airy functions and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!ai(x)
interface ai
      real(4) function ai(x)
            real(4) :: x
      end function ai
      real(8) function dai(x)
            real(8) :: x
      end function dai
end interface ai

!bi(x)
interface bi
      real(4) function bi(x)
            real(4) :: x
      end function bi
      real(8) function dbi(x)
            real(8) :: x
      end function dbi
end interface bi

!ai'(x)
interface aid
      real(4) function aid(x)
            real(4) :: x
      end function aid
      real(8) function daid(x)
            real(8) :: x
      end function daid
end interface aid

!bi'(x)
interface bid
      real(4) function bid(x)
            real(4) :: x
      end function bid
      real(8) function dbid(x)
            real(8) :: x
      end function dbid
end interface bid

! Exponentially scaled Ai
interface aie
      real(4) function aie(x)
            real(4) :: x
      end function aie
      real(8) function daie(x)
            real(8) :: x
      end function daie
end interface aie

! Exponentially scaled Bi
interface bie
      real(4) function bie(x)
            real(4) :: x
      end function bie
      real(8) function dbie(x)
            real(8) :: x
      end function dbie
end interface bie

! Exponentially scaled Ai'(x)
interface aide
      real(4) function aide(x)
            real(4) :: x
      end function aide
      real(8) function daide(x)
            real(8) :: x
      end function daide
end interface aide

! Exponentially scaled Bi'(x)
interface bide
      real(4) function bide(x)
            real(4) :: x
      end function bide
      real(8) function dbide(x)
            real(8) :: x
      end function dbide
end interface bide

!!!!!!!!!!!!!!!!!!!!!!!
! MISSING CAI
! MISSING CBI
! MISSING CAID
! MISSING CBID
!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Airy functions and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Miscellanous functions 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Spence dilogarithm
interface spenc
      real(4) function spenc(x)
            real(4) :: x
      end function spenc
      real(8) function dspenc(x)
            real(8) :: x
      end function dspenc
end interface spenc

! Initialize a Chebyshev series
interface inits
      integer(4) function inits(os,nos,eta)
            real(4),dimension(nos) :: os
            integer(4) :: nos
            real(4) :: eta
      end function inits
      integer(4) function initds(dos,nos,eta)
            real(8),dimension(nos) :: dos
            integer(4) :: nos
            real(4) :: eta
      end function initds
end interface inits

! Evaluate a Chebyshev series
interface csevl
      real(4) function csevl(x,cs,n)
            real(4) :: x
            real(4),dimension(n) :: cs
            integer(4) :: n
      end function csevl
      real(8) function dcsevl(x,a,n)
            real(8) :: x
            real(8), dimension(n) :: a
            integer(4) :: n
      end function dcsevl
end interface csevl


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Miscellanous functions 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!





end module fvn_fnlib