SpecialFunctions.jl

module SpecialFunctions

using IrrationalConstants:
    twoπ,
    halfπ,
    sqrtπ,
    sqrt2π,
    invπ,
    inv2π,
    invsqrt2,
    invsqrt2π,
    logtwo,
    logπ,
    log2π

import LogExpFunctions

using OpenLibm_jll
using OpenSpecFun_jll

export
    airyai,
    airyaiprime,
    airybi,
    airybiprime,
    airyaix,
    airyaiprimex,
    airybix,
    airybiprimex,
    besselh,
    besselhx,
    besseli,
    besselix,
    besselj,
    sphericalbesselj,
    besselj0,
    besselj1,
    besseljx,
    besselk,
    besselkx,
    bessely,
    sphericalbessely,
    bessely0,
    bessely1,
    besselyx,
    jinc,
    dawson,
    ellipk,
    ellipe,
    erf,
    erfc,
    erfcinv,
    erfcx,
    erfi,
    erfinv,
    logerf,
    logerfc,
    logerfcx,
    faddeeva,
    eta,
    digamma,
    invdigamma,
    polygamma,
    trigamma,
    gamma_inc,
    beta_inc,
    beta_inc_inv,
    gamma_inc_inv,
    ncbeta,
    ncF,
    hankelh1,
    hankelh1x,
    hankelh2,
    hankelh2x,
    zeta,
    expint,
    expinti,
    expintx,
    sinint,
    cosint,
    lbinomial

include("amos/AMOS.jl")
include("bessel.jl")
include("erf.jl")
include("ellip.jl")
include("expint.jl")
include("sincosint.jl")
include("logabsgamma/e_lgammaf_r.jl")
include("logabsgamma/e_lgamma_r.jl")
include("gamma.jl")
include("gamma_inc.jl")
include("betanc.jl")
include("beta_inc.jl")
if !isdefined(Base, :get_extension)
    include("../ext/SpecialFunctionsChainRulesCoreExt.jl")
end
include("deprecated.jl")

for f in (:digamma, :erf, :erfc, :erfcinv, :erfcx, :erfi, :erfinv, :logerfc, :logerfcx,
          :eta, :gamma, :invdigamma, :logfactorial, :lgamma, :trigamma, :ellipk, :ellipe)
    @eval $(f)(::Missing) = missing
end
for f in (:beta, :lbeta)
    @eval $(f)(::Number, ::Missing) = missing
    @eval $(f)(::Missing, ::Number) = missing
    @eval $(f)(::Missing, ::Missing) = missing
end
polygamma(m::Integer, x::Missing) = missing

 # In future just use `fastabs` from Base.Math
 # https://github.com/JuliaLang/julia/blob/93fb785831dcfcc442f82fab8746f0244c5274ae/base/special/trig.jl#L1057
if isdefined(Base.Math, :fastabs)
    import Base.Math: fastabs
else
    fastabs(x::Number) = abs(x)
    fastabs(x::Complex) = abs(real(x)) + abs(imag(x))
end

end # module