Fix JuliaLang#11512 (disable computation for Complex BigInt/BigFloat …

…type)

We implement an explicit type checking and disable Complex{BigInt} and Complex{BigFloat}.
Currently only do for Bessel and Airy function.

base/special/bessel.jl

@@ -88,7 +88,17 @@ airybiprime(z) = airy(3,z)
 airy(k::Number, x::AbstractFloat) = oftype(x, real(airy(k, complex(x))))
 airy(k::Number, x::Real) = airy(k, float(x))
 airy(k::Number, z::Complex64) = Complex64(airy(k, Complex128(z)))
-airy(k::Number, z::Complex) = airy(convert(Int,k), Complex128(z))
+
+function airy{T}(k::Number, z::Complex{T})
+    if T === BigInt
+        throw(ArgumentError("Airy is currently not supported for type Complex{BigInt} (see #11512)"))
+    elseif T == BigFloat
+        throw(ArgumentError("Airy is currently not supported for type Complex{BigFloat} (see #11512)"))
+    else
+        airy(convert(Int,k), Complex128(z))
+    end
+end
+
 @vectorize_2arg Number airy
 
 function airyx(k::Int, z::Complex128)
@@ -370,7 +380,16 @@ for f in ("i", "ix", "j", "jx", "k", "kx", "y", "yx")
     bfn = symbol("bessel", f)
     @eval begin
         $bfn(nu::Real, z::Complex64) = Complex64($bfn(Float64(nu), Complex128(z)))
-        $bfn(nu::Real, z::Complex) = $bfn(Float64(nu), Complex128(z))
+        function $bfn{T}(nu::Real, z::Complex{T})
+            if T === BigInt
+                throw(ArgumentError("Bessel is currently not supported for type Complex{BigInt} (see #11512)"))
+            elseif T === BigFloat
+                throw(ArgumentError("Bessel is currently not supported for type Complex{BigFloat} (see #11512)"))
+            else
+               $bfn(Float64(nu), Complex128(z))
+            end
+        end
+
         $bfn(nu::Real, x::Integer) = $bfn(nu, Float64(x))
         @vectorize_2arg Number $bfn
     end

test/math.jl

@@ -314,7 +314,7 @@ end
 @test_throws Base.Math.AmosException airybi(200)
 @test_throws ArgumentError airy(5,one(Complex128))
 z = 1.8 + 1.0im
-for elty in [Complex64,Complex128, Complex{BigFloat}]
+for elty in [Complex64,Complex128]
     @test_approx_eq airy(convert(elty,1.8)) 0.0470362168668458052247
     z = convert(elty,z)
     @test_approx_eq airyx(z) airyx(0,z)
@@ -325,6 +325,11 @@ for elty in [Complex64,Complex128, Complex{BigFloat}]
     @test_throws ArgumentError airyx(5,z)
 end
 
+@test_throws ArgumentError airy(0, big(1im))
+@test_throws ArgumentError airy(0, big(1.0im))
+@test_throws ArgumentError airy(1, big(1im))
+@test_throws ArgumentError airy(1, big(1.0im))
+
 # bessely0, bessely1, besselj0, besselj1
 @test_approx_eq besselj0(Float32(2.0)) besselj0(Float64(2.0))
 @test_approx_eq besselj1(Float32(2.0)) besselj1(Float64(2.0))
@@ -339,6 +344,15 @@ end
 @test_approx_eq bessely0(2.0 + im) bessely(0, 2.0 + im)
 @test_approx_eq bessely1(2.0 + im) bessely(1, 2.0 + im)
 
+@test_throws ArgumentError besselj0(big(2im))
+@test_throws ArgumentError besselj0(big(2.0im))
+@test_throws ArgumentError besselj1(big(2im))
+@test_throws ArgumentError besselj1(big(2.0im))
+@test_throws ArgumentError bessely0(big(2im))
+@test_throws ArgumentError bessely0(big(2.0im))
+@test_throws ArgumentError bessely1(big(2im))
+@test_throws ArgumentError bessely1(big(2.0im))
+
 # besselh
 true_h133 = 0.30906272225525164362 - 0.53854161610503161800im
 @test_approx_eq besselh(3,1,3) true_h133