support better float16, integer arguments

Author: heltonmc

src/besseli.jl

@@ -164,8 +164,12 @@ end
 
 Modified Bessel function of the second kind of order nu, ``I_{nu}(x)``.
 """
-function besseli(nu::Real, x::T) where T
-    isinteger(nu) && return besseli(Int(nu), x)
+besseli(nu::Real, x::Real) = _besseli(nu, float(x))
+
+besseli(nu, x::Float16) = Float16(_besseli(nu, Float32(x)))
+
+function _besseli(nu::Real, x::T) where T
+    isinteger(nu) && return _besseli(Int(nu), x)
     abs_nu = abs(nu)
     abs_x = abs(x)
 
@@ -187,7 +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
     abs_nu = abs(nu)
     abs_x = abs(x)
     sg = iseven(abs_nu) ? 1 : -1
@@ -225,7 +229,11 @@ end
 Scaled modified Bessel function of the first kind of order nu, ``I_{nu}(x)*e^{-x}``.
 Nu must be real.
 """
-function besselix(nu, x::T) where T <: Union{Float32, Float64}
+besselix(nu::Real, x::Real) = _besselix(nu, float(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)
     isone(nu) && return besseli1x(x)
 

src/besselj.jl

@@ -192,8 +192,18 @@ end
 ##### Generic routine for `besselj`
 #####
 
-function besselj(nu::Real, x::T) where T
-    isinteger(nu) && return besselj(Int(nu), x)
+"""
+    besselj(nu, x::T) where T <: Union{Float32, Float64}
+
+Bessel function of the first kind of order nu, ``J_{nu}(x)``.
+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)))
+
+function _besselj(nu::Real, x::T) where T <: Union{Float32, Float64}
+    isinteger(nu) && return _besselj(Int(nu), x)
     abs_nu = abs(nu)
     abs_x = abs(x)
 
@@ -218,7 +228,7 @@ function besselj(nu::Real, x::T) where T
     end
 end
 
-function besselj(nu::Integer, x::T) where T
+function _besselj(nu::Integer, x::T) where T
     abs_nu = abs(nu)
     abs_x = abs(x)
     sg = iseven(abs_nu) ? 1 : -1

src/besselk.jl

@@ -185,8 +185,12 @@ end
 
 Modified Bessel function of the second kind of order nu, ``K_{nu}(x)``.
 """
-function besselk(nu::Real, x::T) where T
-    isinteger(nu) && return besselk(Int(nu), x)
+besselk(nu::Real, x::Real) = _besselk(nu, float(x))
+
+besselk(nu, x::Float16) = Float16(_besselk(nu, Float32(x)))
+
+function _besselk(nu::Real, x::T) where T
+    isinteger(nu) && return _besselk(Int(nu), x)
     abs_nu = abs(nu)
     abs_x = abs(x)
 
@@ -197,7 +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
     abs_nu = abs(nu)
     abs_x = abs(x)
     sg = iseven(abs_nu) ? 1 : -1

src/bessely.jl

@@ -235,9 +235,13 @@ end
 Bessel function of the second kind of order nu, ``Y_{nu}(x)``.
 nu and x must be real where nu and x can be positive or negative.
 """
-function bessely(nu::Real, x::T) where T
+bessely(nu::Real, x::Real) = _bessely(nu, float(x))
+
+bessely(nu, x::Float16) = Float16(_bessely(nu, Float32(x)))
+
+function _bessely(nu::Real, x::T) where T <: Union{Float32, Float64}
     isnan(nu) || isnan(x) && return NaN
-    isinteger(nu) && return bessely(Int(nu), x)
+    isinteger(nu) && return _bessely(Int(nu), x)
     abs_nu = abs(nu)
     abs_x = abs(x)
 
@@ -260,7 +264,7 @@ function bessely(nu::Real, x::T) where T
         end
     end
 end
-function bessely(nu::Integer, x::T) where T
+function _bessely(nu::Integer, x::T) where T
     abs_nu = abs(nu)
     abs_x = abs(x)
     sg = iseven(abs_nu) ? 1 : -1