Fix type instability in logdet(::Matrix{Complex64})

Ref: #10188

1. Adds pi*im in a type stable fashion when there are an odd number of
pivots

2. Uses mod2pi instead of mod(_, 2pi)

base/linalg/lu.jl

@@ -142,9 +142,12 @@ end
 
 function logdet{T<:Complex,S}(A::LU{T,S})
  n = chksquare(A)
- s = sum(log(diag(A.factors))) + (bool(sum(A.ipiv .!= 1:n) % 2) ? complex(0,pi) : 0)
+ s = sum(log(diag(A.factors)))
+ if bool(sum(A.ipiv .!= 1:n) % 2)
+ s = Complex(real(s), imag(s)+π)
+ end
  r, a = reim(s)
- a = pi-mod(pi-a,2pi) #Take principal branch with argument (-pi,pi]
+ a = π-mod2pi(π-a) #Take principal branch with argument (-pi,pi]
  complex(r,a)
 end
 

test/linalg/lu.jl

@@ -0,0 +1 @@
+@test logdet(Complex64[1.0f0 0.5f0; 0.5f0 -1.0f0]) === 0.22314355f0 + 3.1415927f0im

test/runtests.jl

@@ -34,7 +34,7 @@ end
 if "linalg" in tests
  # specifically selected case
  filter!(x -> x != "linalg", tests)
- prepend!(tests, ["linalg1", "linalg2", "linalg3", "linalg4", "linalg/lapack", "linalg/triangular", "linalg/tridiag", "linalg/pinv", "linalg/givens"])
+ prepend!(tests, ["linalg1", "linalg2", "linalg3", "linalg4", "linalg/lapack", "linalg/triangular", "linalg/tridiag", "linalg/pinv", "linalg/givens", "linalg/lu"])
 end
 
 net_required_for = ["socket", "parallel"]