Fix composite complex

Author: dannys4

src/algos.jl

@@ -9,11 +9,11 @@ end
 fft!(::AbstractVector{T}, ::AbstractVector{T}, ::Int, ::Int, ::Direction, ::AbstractFFTType, ::CallGraph{T}, ::Int) where {T} = nothing
 
 @inline function direction_sign(::FFT_BACKWARD)
-    1
+    1.
 end
 
 @inline function direction_sign(::FFT_FORWARD)
-    -1
+    -1.
 end
 
 function (g::CallGraph{T})(out::AbstractVector{T}, in::AbstractVector{U}, start_out::Int, start_in::Int, v::Direction, t::AbstractFFTType, idx::Int) where {T,U}
@@ -36,10 +36,10 @@ function fft!(out::AbstractVector{T}, in::AbstractVector{U}, start_out::Int, sta
     wj1 = one(T)
     tmp = g.workspace[idx]
     for j1 in 0:N1-1
-        wk2 = wj1;
+        wk2 = wj1
         g(tmp, in, N2*j1+1, start_in + j1*s_in, d, right.type, right_idx)
         j1 > 0 && for k2 in 1:N2-1
-            tmp[N2*j1 + k2] *= wk2
+            tmp[N2*j1 + k2 + 1] *= wk2
             wk2 *= wj1
         end
         wj1 *= w1
@@ -48,7 +48,6 @@ function fft!(out::AbstractVector{T}, in::AbstractVector{U}, start_out::Int, sta
     for k2 in 0:N2-1
         g(out, tmp, start_out + k2*s_out, k2+1, d, left.type, left_idx)
     end
-    out .+= 0
 end
 
 function fft!(out::AbstractVector{T}, in::AbstractVector{U}, start_out::Int, start_in::Int, d::Direction, ::Pow2FFT, g::CallGraph{T}, idx::Int) where {T,U}
@@ -124,7 +123,6 @@ function fft_dft!(out::AbstractVector{T}, in::AbstractVector{T}, N::Int, start_o
     out[start_out] = tmp
 
     wk = wkn = w = convert(T, cispi(direction_sign(d)*2/N))
-    
     @inbounds for d in 1:N-1
         tmp = in[start_in]
         @inbounds for k in 1:N-1

test/complex_backward.jl

@@ -3,5 +3,7 @@ using FFTA, Test
 @testset verbose = true "bfft 1D complex, size $N" for N in [8, 11, 15, 100]
     x = ones(ComplexF64, N)
     y = bfft(x)
-    @test y[1] ≈ N && y[2:end] ≈ 0*x[2:end] atol=1e-12
+    b1 = isapprox(y[1], N, atol=1e-12)
+    b2 = isapprox(y[2:end], 0*x[2:end], atol=1e-12)
+    @test b1 && b2
 end