fix allocation and readme

Author: heltonmc

README.md

@@ -145,21 +145,7 @@ In general, this provides a fast way to generate a sequence of Bessel functions
 julia> @btime besselj(0:100, 50.0)
   443.328 ns (2 allocations: 1.75 KiB)
 ```
-This function will allocate so it is recommended that you calculate the Bessel functions at the top level of your function outside any hot loop. For example,
-
-```julia
-function bessel_sequence(x, orders)
-    J_nu = besselj(orders, x)
-    out = zero(x)
-    for i in eachindex(J_nu)
-        out += sin(x*i)*J_nu[i]
-    end
-    return out
-end
-
-julia> bessel_sequence(10.2, 1:400)
-0.11404996570230919
-```
+This function will allocate so it is recommended that you calculate the Bessel functions at the top level of your function outside any hot loop.
 
 ### Support for negative arguments
 

src/besseli.jl

@@ -225,7 +225,8 @@ function _besseli(nu::AbstractRange, x::T) where T
     end
     if k > 1
         out[k] = _besseli(nu[k], x)
-        out[1:k+1] = besselk_down_recurrence!(out[1:k+1], x, nu[1:k+1])
+        tmp = @view out[1:k+1]
+        out[1:k+1] = besselk_down_recurrence!(tmp, x, nu[1:k+1])
         return out
     else
         return out

src/besselj.jl

@@ -279,7 +279,8 @@ function _besselj(nu::AbstractRange, x::T) where T
         end
         if k > 1
             out[k] = _besselj(nu[k], x)
-            out[1:k+1] = besselj_down_recurrence!(out[1:k+1], x, nu[1:k+1])
+            tmp = @view out[1:k+1]
+            besselj_down_recurrence!(tmp, x, nu[1:k+1])
             return out
         else
             return out

src/besselk.jl

@@ -235,7 +235,8 @@ function _besselk(nu::AbstractRange, x::T) where T
     end
     if k < len
         out[k] = _besselk(nu[k], x)
-        out[k-1:end] = besselk_up_recurrence!(out[k-1:end], x, nu[k-1:end])
+        tmp = @view out[k-1:end]
+        out[k-1:end] = besselk_up_recurrence!(tmp, x, nu[k-1:end])
         return out
     else
         return out