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fvn_fnlib/fvn_fnlib.f90
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module fvn_fnlib
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! 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)
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complex(8) :: z |
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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
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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! No generic interface for fac and binom but we still ! define their prototypes |
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! Factorial |
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interface |
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real(4) function fac(n)
integer(4) :: n
end function fac
real(8) function dfac(n)
integer(4) :: n
end function dfac
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! Binomial coefficient |
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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
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! 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
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! 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
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!!!!!!!!!!!!!!!!!!!!!
! 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
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