update method instances

Author: heltonmc

src/besselj.jl

@@ -152,33 +152,36 @@ function besselj1(x::Float32)
 end
 
 function besselj(nu::Real, x::T) where T
+    isinteger(nu) && return besselj(Int(nu), x)
     abs_nu = abs(nu)
     abs_x = abs(x)
 
     Jnu = besselj_positive_args(abs_nu, abs_x)
+    if nu >= zero(T)
+        return x >= zero(T) ? Jnu : cispi(abs_nu)*Jnu
+    else
+        Ynu = bessely_positive_args(abs_nu, abs_x)
+        spi, cpi = sincospi(abs_nu)
+        out = cpi*Jnu - spi*Ynu
+        return x >= zero(T) ? out : out * cispi(nu)
+    end
+end
+
+function besselj(nu::Int, x::T) where T
+    abs_nu = abs(nu)
+    abs_x = abs(x)
+    sg = (iseven(Int(abs_nu)) ? 1 : -1)
 
+    Jnu = besselj_positive_args(abs_nu, abs_x)
     if nu >= zero(T)
-        if x >= zero(T)
-            return Jnu
-        else
-            if isinteger(abs_nu)
-                return Jnu * (iseven(Int(abs_nu)) ? 1 : -1)
-            else
-                return cispi(abs_nu)*Jnu
-            end
-        end
+        return x >= zero(T) ? Jnu : Jnu * sg
     else
         if x >= zero(T)
-            isinteger(nu) && return Jnu * (iseven(Int(abs_nu)) ? 1 : -1)
-            Ynu = bessely_positive_args(abs_nu, abs_x)
-            spi, cpi = sincospi(abs_nu)
-            return cpi*Jnu - spi*Ynu
+            return Jnu * sg
         else
             Ynu = bessely_positive_args(abs_nu, abs_x)
             spi, cpi = sincospi(abs_nu)
-            out = cpi*Jnu - spi*Ynu
-            isinteger(nu) && return out * (iseven(Int(abs_nu)) ? 1 : -1)
-            return cispi(nu)*out
+            return (cpi*Jnu - spi*Ynu) * sg
         end
     end
 end

src/bessely.jl

@@ -188,39 +188,35 @@ Bessel function of the first kind of order nu, ``J_{nu}(x)``.
 Nu must be real.
 """
 
-
 function bessely(nu::Real, x::T) where T
+    isinteger(nu) && return bessely(Int(nu), x)
     abs_nu = abs(nu)
     abs_x = abs(x)
 
     Ynu = bessely_positive_args(abs_nu, abs_x)
+    Jnu = besselj_positive_args(abs_nu, abs_x)
+    spi, cpi = sincospi(abs_nu)
+    if nu >= zero(T)
+        return x >= zero(T) ? Ynu : cispi(-nu)*Ynu + 2im*cpi*Jnu
+    else
+        return x >= zero(T) ? cpi*Ynu + spi*Jnu : cpi * (cispi(nu)*Ynu + 2im * cpi * Jnu) + spi * cispi(abs_nu) * Jnu
+    end
+end
+function bessely(nu::Int, x::T) where T
+    abs_nu = abs(nu)
+    abs_x = abs(x)
+    sg = (iseven(Int(abs_nu)) ? 1 : -1)
 
-    if nu > zero(T)
-        if x > zero(T)
-            return Ynu
-        else
-            Jnu = besselj_positive_args(abs_nu, abs_x)
-            return cispi(-nu)*Ynu + 2im*cospi(nu)*Jnu
-        end
+    Ynu = bessely_positive_args(abs_nu, abs_x)
+    if nu >= zero(T)
+        return x >= zero(T) ? Ynu : Ynu * sg + 2im * sg * besselj_positive_args(abs_nu, abs_x)
     elseif nu < zero(T)
-        if x > zero(T)
-            isinteger(nu) && return Ynu * (iseven(Int(abs_nu)) ? 1 : -1)
-            Jnu = besselj_positive_args(abs_nu, abs_x)
-            spi, cpi = sincospi(abs_nu)
-            return cpi*Ynu + spi*Jnu
-        else
-            Jnu = besselj_positive_args(abs_nu, abs_x)
-            isinteger(nu) && return Ynu + 2im * Jnu
-            spi, cpi = sincospi(abs_nu)
-            out = cpi * (cispi(nu)*Ynu + 2im * cpi * Jnu)
-            return out + spi * cispi(abs_nu) * Jnu
-        end
-    else
-        return -T(Inf)
+        return x > zero(T) ? Ynu * sg : Ynu + 2im * besselj_positive_args(abs_nu, abs_x)
     end
 end
 
 function bessely_positive_args(nu, x::T) where T
+    iszero(x) && return -T(Inf)
 
     # use forward recurrence if nu is an integer up until it becomes inefficient
     (isinteger(nu) && nu < 250) && return besselj_up_recurrence(x, bessely1(x), bessely0(x), 1, nu)[1]