Add v bound for half integer, and expand tests.

Author: cgeoga

src/besselk.jl

@@ -227,7 +227,7 @@ function besselk_positive_args(nu, x::T) where T <: Union{Float32, Float64}
     iszero(nu) && return besselk0(x)
 
     # check if nu is a half-integer:
-    isinteger(nu-1/2) && return besselk_vhalfint(nu, x)
+    besselk_vhalfint_check(nu, x) && return besselk_vhalfint(nu, x)
 
     # use uniform debye expansion if x or nu is large
     besselik_debye_cutoff(nu, x) && return besselk_large_orders(nu, x)
@@ -447,3 +447,5 @@ function besselk_vhalfint(v, x::T) where T
     end
     b1
 end
+besselk_vhalfint_check(nu, x) = isinteger(nu-1/2) && (nu < 41.5) #@inline?
+

test/besselk_test.jl

@@ -68,9 +68,9 @@ k1x_32 = besselk1x.(Float32.(x))
 @test besselk(100, 234.0) ≈ SpecialFunctions.besselk(100, 234.0)
 
 # test half-integer orders:
-for v in (-3/2, -1/2, 1/2, 3/2, 5/2, 7/2, 9/2)
-  @test besselk(v, 7.0) ≈ SpecialFunctions.besselk(v, 7.0)
-  @test besselk(Float32(v), Float32(7.0)) ≈ SpecialFunctions.besselk(Float32(v), Float32(7.0))
+for (v,x) in Iterators.product(-35/2:1.0:81/2, range(0.0, 30.0, length=51)[2:end])
+  @test besselk(v, x) ≈ SpecialFunctions.besselk(v, x)
+  @test besselk(Float32(v), Float32(x)) ≈ SpecialFunctions.besselk(Float32(v), Float32(x))
 end
 
 # test small arguments and order