RFC: Adds random number generation for BigInts from GMP

[jiahao]

Introduces new type BigIntRand that initializes GMP RNG.

• gmp_randinit_default - initialize RNG (current default: Mersenne Twister)
• gmp_randseed_ui, gmp_randseed - sets random seed

Provides methods to generate random BigInts.

• rand(Range1{BigInt}) - wraps mpz_urandomm
• rand!(Range1, Array) - initializes a BigIntRand automatically and populates an array

Also adds low-level creation of BigInttype from constituent data elements.

Is this the right way to expose the RNG state from GMP?

[jiahao]

cc: @andrioni - This is as far as I got with random BigInts from our discussion in julia-dev.

[andrioni]

Why did you define a second constructor to BigInt?

[jiahao]

As you had pointed out, the seed in BigIntRand had to be unpacked to be allocated correctly. I put in the second constructor in case down the line extracting the seed as a BigInt might become desirable.

[andrioni]

Also, the methods don't follow the API you wrote here, nor the one on random.jl.

rand{T<:Integer}(randstate::BigIntRand,x::Range1{T<:Integer}) at gmp.jl:354
rand!{T<:Integer}(r::Range1{T<:Integer},A::Array{T<:Integer,N}) at gmp.jl:362

range.jl will also need changes, as BigInt ranges with length larger than typemax(Int) don't work:

julia> range = BigInt(1):BigInt("127138971893189187381")
ERROR: InexactError()
 in convert at gmp.jl:67
 in colon at range.jl:38

You also need to re-seed the functions someway, as rand!{T<:Integer}(r::Range1{T<:Integer},A::Array{T<:Integer,N}) doesn't work properly because it always get seeded with zeros.

[andrioni]

The problem of using this to extract the seed is that we can't control when the finalizer will be called, and this means it is possible for the seed to be freed while BigIntRand is still alive.