re-enable the 0-arg MersenneTwister() constructor

The arguments to `srand(rng, ...)` and `typeof(rng)(...)`
should mirror each-other, in particular
`srand(MersenneTwister(0))` and `MersenneTwister()` should
produce an equivalent object.
Also, `srand(::RandomDevice)` has been added for consistency,
which could be useful in generic code.

base/deprecated.jl

@@ -1307,9 +1307,6 @@ end
  end
 end
 
-# PR #16984
-@deprecate MersenneTwister() MersenneTwister(0)
-
 # #19635
 for fname in (:ones, :zeros)
  @eval @deprecate ($fname)(T::Type, arr) ($fname)(T, size(arr))

base/random.jl

@@ -59,6 +59,7 @@ end # os-test
  RandomDevice()
 
 Create a `RandomDevice` RNG object. Two such objects will always generate different streams of random numbers.
+The entropy is obtained from the operating system.
 """
 RandomDevice
 
@@ -85,16 +86,21 @@ mutable struct MersenneTwister <: AbstractRNG
  end
 end
 
-MersenneTwister(seed::Vector{UInt32}, state::DSFMT_state) =
+_MersenneTwister(seed=Vector{UInt32}(), state=DSFMT_state()) =
  MersenneTwister(seed, state, zeros(Float64, MTCacheLength), MTCacheLength)
 
 """
  MersenneTwister(seed)
+ MersenneTwister()
 
 Create a `MersenneTwister` RNG object. Different RNG objects can have their own seeds, which
 may be useful for generating different streams of random numbers.
+The `seed` may be a non-negative integer or a vector of `UInt32` integers.
+If no seed is provided, a random one is selected (using entropy from the system).
+See the [`srand`](@ref) function for reseeding an already existing `MersenneTwister` object.
 """
-MersenneTwister(seed) = srand(MersenneTwister(Vector{UInt32}(), DSFMT_state()), seed)
+MersenneTwister(seed) = srand(_MersenneTwister(), seed)
+MersenneTwister() = srand(_MersenneTwister())
 
 function copy!(dst::MersenneTwister, src::MersenneTwister)
  copy!(resize!(dst.seed, length(src.seed)), src.seed)
@@ -166,7 +172,7 @@ function randjump(mt::MersenneTwister, jumps::Integer, jumppoly::AbstractString)
  push!(mts, mt)
  for i in 1:jumps-1
  cmt = mts[end]
- push!(mts, MersenneTwister(copy(cmt.seed), dSFMT.dsfmt_jump(cmt.state, jumppoly)))
+ push!(mts, _MersenneTwister(copy(cmt.seed), dSFMT.dsfmt_jump(cmt.state, jumppoly)))
  end
  return mts
 end
@@ -219,11 +225,16 @@ end
  srand([rng=GLOBAL_RNG], seed) -> rng
  srand([rng=GLOBAL_RNG]) -> rng
 
-Reseed the random number generator. If a `seed` is provided, the RNG will give a
-reproducible sequence of numbers, otherwise Julia will get entropy from the system. For
-`MersenneTwister`, the `seed` may be a non-negative integer or a vector of `UInt32` integers.
-`RandomDevice` does not support seeding.
+Reseed the random number generator. If a `seed` is provided, the RNG
+will give a reproducible sequence of numbers.
+After the call to `srand`, `rng` is equivalent to a newly created object
+with the same parameters (e.g.
+`MersenneTwister(1) == srand(MersenneTwister(), 1)`).
 """
+function srand end
+
+srand(r::RandomDevice) = r
+
 srand(r::MersenneTwister) = srand(r, make_seed())
 srand(r::MersenneTwister, n::Integer) = srand(r, make_seed(n))
 

test/random.jl

@@ -37,8 +37,7 @@ A = zeros(UInt128, 2, 2)
 @test_throws BoundsError rand!(MersenneTwister(0), A, 5)
 
 # rand from AbstractArray
-let mt = MersenneTwister(0)
- srand(mt)
+let mt = MersenneTwister()
  @test rand(mt, 0:3:1000) in 0:3:1000
  @test issubset(rand!(mt, Array{Int}(100), 0:3:1000), 0:3:1000)
  coll = Any[2, UInt128(128), big(619), "string"]
@@ -377,7 +376,7 @@ function hist(X,n)
 end
 
 # test uniform distribution of floats
-for rng in [srand(MersenneTwister(0)), RandomDevice()]
+for rng in [MersenneTwister(), RandomDevice()]
  for T in [Float16,Float32,Float64]
  # array version
  counts = hist(rand(rng, T, 2000), 4)