add tests

Author: heltonmc

src/bessely.jl

@@ -317,7 +317,7 @@ function bessely_positive_args(nu, x::T) where T
 
     # at this point x > 19.0 (for Float64) and fairly close to nu
     # shift nu down and use the debye expansion for Hankel function (valid x > nu) then use forward recurrence
-    nu_shift = floor(nu) - ceil(Int, -1.5 + x + Base.Math._approx_cbrt(-411*x))
+    nu_shift = ceil(nu) - floor(Int, -1.5 + x + Base.Math._approx_cbrt(-411*x)) + 4
     v2 = nu - maximum((nu_shift, modf(nu)[1] + 1))
     return besselj_up_recurrence(x, imag(hankel_debye(v2, x)), imag(hankel_debye(v2 - 1, x)), v2, nu)[1]
 end

src/sphericalbessel.jl

@@ -67,7 +67,7 @@ end
 # if (x<nu) we can use forward recurrence from sphericalbesselj_recurrence and
 # then use a continued fraction approach. However, for largish orders (>60) the
 # continued fraction is slower converging and more efficient to use other methods
-function sphericalbesselj_recurrence(nu::Integer, x)
+function sphericalbesselj_recurrence(nu::Integer, x::T) where T
     if x >= nu
         # forward recurrence if stable
         xinv = inv(x)

test/sphericalbessel_test.jl

@@ -0,0 +1,20 @@
+# test very small inputs
+x = 1e-15
+@test Bessels.sphericalbesselj(0, x) ≈ SpecialFunctions.sphericalbesselj(0, x)
+@test Bessels.sphericalbesselj(1, x) ≈ SpecialFunctions.sphericalbesselj(1, x)
+@test Bessels.sphericalbesselj(5.5, x) ≈ SpecialFunctions.sphericalbesselj(5.5, x)
+@test Bessels.sphericalbesselj(10, x) ≈ SpecialFunctions.sphericalbesselj(10, x)
+@test Bessels.sphericalbessely(0, x) ≈ SpecialFunctions.sphericalbessely(0, x)
+@test Bessels.sphericalbessely(1, x) ≈ SpecialFunctions.sphericalbessely(1, x)
+@test Bessels.sphericalbessely(5.5, x) ≈ SpecialFunctions.sphericalbessely(5.5, x)
+@test Bessels.sphericalbessely(10, x) ≈ SpecialFunctions.sphericalbessely(10, x)
+
+for x in 0.5:1.0:100.0, v in [0, 1, 5.5, 10]
+    @test isapprox(Bessels.sphericalbesselj(v, x), SpecialFunctions.sphericalbesselj(v, x), rtol=1e-12)
+    @test isapprox(Bessels.sphericalbessely(v, x), SpecialFunctions.sphericalbessely(v, x), rtol=1e-12)
+end
+
+for x in 5.5:4.0:160.0, v in [20, 25.0, 32.4, 40.0, 45.12, 50.0, 55.2, 60.124, 70.23, 75.0, 80.0, 92.3, 100.0, 120.0]
+    @test isapprox(Bessels.sphericalbesselj(v, x), SpecialFunctions.sphericalbesselj(v, x), rtol=3e-12)
+    @test isapprox(Bessels.sphericalbessely(v, x), SpecialFunctions.sphericalbessely(v, x), rtol=3e-12)
+end