interlace => ApproxFunBase.interlace (#738)

* interlace => ApproxFunBase.interlace

* test for the fix Fourier with BigFloat coefficients

* test Fourier BigFloat

Author: flob92

src/Extras/fftGeneric.jl

@@ -116,8 +116,8 @@ function *(::TransformPlan{T,Fourier{D,R},false},x::AbstractVector{T}) where {T<
     v = fft(x)
     rmul!(v,convert(T,2)/l)
     v[1] /= 2
-    mod(l,2) == 1 ? interlace(real(v[1:n]),-imag(v[2:n])) :
-      [interlace(real(v[1:n]),-imag(v[2:n]));-real(v[n+1])/2]
+    mod(l,2) == 1 ? ApproxFunBase.interlace(real(v[1:n]),-imag(v[2:n])) :
+      [ApproxFunBase.interlace(real(v[1:n]),-imag(v[2:n]));-real(v[n+1])/2]
 end
 
 function *(::ITransformPlan{T,Fourier{D,R},false},x::AbstractVector{T}) where {T<:BigFloat,D,R}

test/NumberTypeTest.jl

@@ -21,6 +21,21 @@ using ApproxFun, ApproxFunOrthogonalPolynomials, Test
         @test norm(single_double_err) < 10eps(Float64)
     end
 
+	@testset "BigFloat constructor (Fourier)" begin
+		f = exp ∘ cos
+		double_f = Fun(f,
+		  Fourier(Interval(Float64(0),2*Float64(π))))
+		big_f = Fun(f,
+		  Fourier(Interval(BigFloat(0),2*BigFloat(π))))
+		@test ncoefficients(double_f) <= ncoefficients(big_f)
+
+		@test eltype(coefficients(double_f)) == Float64
+		@test eltype(coefficients(big_f)) == BigFloat
+
+		double_big_err = coefficients(double_f) - coefficients(big_f)[1:ncoefficients(double_f)]
+		@test norm(double_big_err) < 10eps(Float64)
+	end
+
     @testset "BigFloat roots" begin
         a = Fun(ChebyshevInterval{BigFloat}(),BigFloat[1,2,3])
         # 12 is some bound on how accurately the polynomial can be evaluated