Add complex random normals.

base/random.jl

@@ -1123,7 +1123,10 @@ const ziggurat_exp_r      = 7.6971174701310497140446280481
 Generate a normally-distributed random number of type `T` with mean 0 and standard deviation 1.
 Optionally generate an array of normally-distributed random numbers.
 The `Base` module currently provides an implementation for the types
-`Float16`, `Float32`, and `Float64` (the default).
+`Float16`, `Float32`, `Float64` (the default), `Complex32`, `Complex64`, and `Complex128`.
+When the type argument is complex, the values returned are drawn from the circularly symmetric
+complex normal distribution.
+.
 """
 @inline function randn(rng::AbstractRNG=GLOBAL_RNG)
     @inbounds begin
@@ -1224,6 +1227,14 @@ let Floats = Union{Float16,Float32,Float64}
             $randfun(                                dims::Integer...               ) = $randfun(GLOBAL_RNG, Float64, dims...)
         end
     end
+
+    for (T,SQRT_HALF) in ((Float64, 0.7071067811865475),
+                          (Float32, 0.70710677f0),
+                          (Float16, 0.70710677f0))
+        @inline function randn(rng::AbstractRNG, ::Type{Complex{T}})
+            Complex{T}(SQRT_HALF*randn(rng, T), SQRT_HALF*randn(rng, T))
+        end
+    end
 end
 
 ## random UUID generation

doc/stdlib/numbers.rst

@@ -602,7 +602,7 @@ As ``BigInt`` represents unbounded integers, the interval must be specified (e.g
 
    .. Docstring generated from Julia source
 
-   Generate a normally-distributed random number of type ``T`` with mean 0 and standard deviation 1. Optionally generate an array of normally-distributed random numbers. The ``Base`` module currently provides an implementation for the types ``Float16``\ , ``Float32``\ , and ``Float64`` (the default).
+   Generate a normally-distributed random number of type ``T`` with mean 0 and standard deviation 1. Optionally generate an array of normally-distributed random numbers. The ``Base`` module currently provides an implementation for the types ``Float16``\ , ``Float32``\ , ``Float64`` (the default), ``Complex32``\ , ``Complex64``\ , and ``Complex128``\ . When the type argument is complex, the values returned are drawn from the circularly symmetric complex normal distribution. .
 
 .. function:: randn!([rng], A::AbstractArray) -> A
 

test/random.jl

@@ -13,6 +13,7 @@ srand(0); rand(); x = rand(384)
 @test(typeof(rand(false:true)) === Bool)
 @test(typeof(rand(Char)) === Char)
 @test length(randn(4, 5)) == 20
+@test length(randn(Complex128, 4, 5)) == 20
 @test length(bitrand(4, 5)) == 20
 
 @test rand(MersenneTwister()) == 0.8236475079774124
@@ -59,6 +60,10 @@ A = zeros(2, 2)
 randn!(MersenneTwister(42), A)
 @test A == [-0.5560268761463861  0.027155338009193845;
             -0.444383357109696  -0.29948409035891055]
+B = zeros(Complex128, 2)
+randn!(MersenneTwister(42), B)
+@test B == [Complex128(-0.5560268761463861,-0.444383357109696),
+            Complex128(0.027155338009193845,-0.29948409035891055)] * 0.7071067811865475
 
 for T in (Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128, BigInt,
           Float16, Float32, Float64, Rational{Int})
@@ -300,8 +305,9 @@ end
 
 # test all rand APIs
 for rng in ([], [MersenneTwister()], [RandomDevice()])
-    types = [Base.BitInteger_types..., Bool, Float16, Float32, Float64, Char]
     ftypes = [Float16, Float32, Float64]
+    cftypes = [ftypes..., Complex32, Complex64, Complex128]
+    types = [Base.BitInteger_types..., ftypes..., Bool, Char]
     b2 = big(2)
     u3 = UInt(3)
     for f in [rand, randn, randexp]
@@ -310,7 +316,7 @@ for rng in ([], [MersenneTwister()], [RandomDevice()])
         f(rng..., 2, 3)               ::Array{Float64, 2}
         f(rng..., b2, u3)             ::Array{Float64, 2}
         f(rng..., (2, 3))             ::Array{Float64, 2}
-        for T in (f === rand ? types : ftypes)
+        for T in (f === rand ? types : f === randn ? cftypes : ftypes)
             a0 = f(rng..., T)         ::T
             a1 = f(rng..., T, 5)      ::Vector{T}
             a2 = f(rng..., T, 2, 3)   ::Array{T, 2}
@@ -324,7 +330,7 @@ for rng in ([], [MersenneTwister()], [RandomDevice()])
         end
     end
     for f! in [rand!, randn!, randexp!]
-        for T in (f! === rand! ? types : ftypes)
+        for T in (f! === rand! ? types : f! === randn! ? cftypes : ftypes)
             X = T == Bool ? T[0,1] : T[0,1,2]
             for A in (Array{T}(5), Array{T}(2, 3))
                 f!(rng..., A)                    ::typeof(A)