fix type ambiguous

Author: heltonmc

src/besseli.jl

@@ -166,9 +166,9 @@ Modified Bessel function of the second kind of order nu, ``I_{nu}(x)``.
 """
 besseli(nu::Real, x::Real) = _besseli(nu, float(x))
 
-besseli(nu, x::Float16) = Float16(_besseli(nu, Float32(x)))
+_besseli(nu, x::Float16) = Float16(_besseli(nu, Float32(x)))
 
-function _besseli(nu::Real, x::T) where T
+function _besseli(nu, x::T) where T <: Union{Float32, Float64}
     isinteger(nu) && return _besseli(Int(nu), x)
     abs_nu = abs(nu)
     abs_x = abs(x)
@@ -191,7 +191,7 @@ function _besseli(nu::Real, x::T) where T
         end
     end
 end
-function _besseli(nu::Integer, x::T) where T
+function _besseli(nu::Integer, x::T) where T <: Union{Float32, Float64}
     abs_nu = abs(nu)
     abs_x = abs(x)
     sg = iseven(abs_nu) ? 1 : -1
@@ -231,7 +231,7 @@ Nu must be real.
 """
 besselix(nu::Real, x::Real) = _besselix(nu, float(x))
 
-besselix(nu, x::Float16) = Float16(_besselix(nu, Float32(x)))
+_besselix(nu, x::Float16) = Float16(_besselix(nu, Float32(x)))
 
 function _besselix(nu, x::T) where T <: Union{Float32, Float64}
     iszero(nu) && return besseli0x(x)

src/besselj.jl

@@ -200,9 +200,9 @@ nu and x must be real where nu and x can be positive or negative.
 """
 besselj(nu::Real, x::Real) = _besselj(nu, float(x))
 
-besselj(nu, x::Float16) = Float16(_besselj(nu, Float32(x)))
+_besselj(nu, x::Float16) = Float16(_besselj(nu, Float32(x)))
 
-function _besselj(nu::Real, x::T) where T <: Union{Float32, Float64}
+function _besselj(nu, x::T) where T <: Union{Float32, Float64}
     isinteger(nu) && return _besselj(Int(nu), x)
     abs_nu = abs(nu)
     abs_x = abs(x)
@@ -228,7 +228,7 @@ function _besselj(nu::Real, x::T) where T <: Union{Float32, Float64}
     end
 end
 
-function _besselj(nu::Integer, x::T) where T
+function _besselj(nu::Integer, x::T) where T <: Union{Float32, Float64}
     abs_nu = abs(nu)
     abs_x = abs(x)
     sg = iseven(abs_nu) ? 1 : -1

src/besselk.jl

@@ -187,9 +187,9 @@ Modified Bessel function of the second kind of order nu, ``K_{nu}(x)``.
 """
 besselk(nu::Real, x::Real) = _besselk(nu, float(x))
 
-besselk(nu, x::Float16) = Float16(_besselk(nu, Float32(x)))
+_besselk(nu, x::Float16) = Float16(_besselk(nu, Float32(x)))
 
-function _besselk(nu::Real, x::T) where T
+function _besselk(nu, x::T) where T <: Union{Float32, Float64}
     isinteger(nu) && return _besselk(Int(nu), x)
     abs_nu = abs(nu)
     abs_x = abs(x)
@@ -201,7 +201,7 @@ function _besselk(nu::Real, x::T) where T
         #return cispi(-abs_nu)*besselk_positive_args(abs_nu, abs_x) - besseli_positive_args(abs_nu, abs_x) * im * π
     end
 end
-function _besselk(nu::Integer, x::T) where T
+function _besselk(nu::Integer, x::T) where T <: Union{Float32, Float64}
     abs_nu = abs(nu)
     abs_x = abs(x)
     sg = iseven(abs_nu) ? 1 : -1

src/bessely.jl

@@ -237,9 +237,9 @@ nu and x must be real where nu and x can be positive or negative.
 """
 bessely(nu::Real, x::Real) = _bessely(nu, float(x))
 
-bessely(nu, x::Float16) = Float16(_bessely(nu, Float32(x)))
+_bessely(nu, x::Float16) = Float16(_bessely(nu, Float32(x)))
 
-function _bessely(nu::Real, x::T) where T <: Union{Float32, Float64}
+function _bessely(nu, x::T) where T <: Union{Float32, Float64}
     isnan(nu) || isnan(x) && return NaN
     isinteger(nu) && return _bessely(Int(nu), x)
     abs_nu = abs(nu)
@@ -264,7 +264,7 @@ function _bessely(nu::Real, x::T) where T <: Union{Float32, Float64}
         end
     end
 end
-function _bessely(nu::Integer, x::T) where T
+function _bessely(nu::Integer, x::T) where T <: Union{Float32, Float64}
     abs_nu = abs(nu)
     abs_x = abs(x)
     sg = iseven(abs_nu) ? 1 : -1

test/sphericalbessel_test.jl

@@ -33,8 +33,8 @@ x = 1e-15
 @test isnan(Bessels.sphericalbessely(4.0, NaN))
 
 # test Float16 types
-@test Bessels.sphericalbesselj(1.4, Float16(1.2)) isa Float16
-@test Bessels.sphericalbessely(1.4, Float16(1.2)) isa Float16
+@test Bessels.sphericalbesselj(Float16(1.4), Float16(1.2)) isa Float16
+@test Bessels.sphericalbessely(Float16(1.4), Float16(1.2)) isa Float16
 
 for x in 0.5:1.0:100.0, v in [0, 1, 5.5, 8.2, 10]
     @test isapprox(Bessels.sphericalbesselj(v, x), SpecialFunctions.sphericalbesselj(v, x), rtol=1e-12)