Safety for poisson random calls

[SamuelBrand1]

Hi everyone,

Base Julia can't convert large floats into Int type using floor or round etc. This creates a problem for sampling from Poisson's with a large mean because this is used in fast polyalgo for Poisson sampling.

e.g.

using Distributions
log_μ = 48.0 #Plausible value in a log-scale random walk with a Poisson link
d = Poisson(exp(log_μ))
 rand(d)

ERROR: InexactError: trunc(Int64, 7.016735912097631e20) Stacktrace: [1] trunc @ ./float.jl:905 [inlined] [2] floor @ ./float.jl:383 [inlined] [3] PoissonADSampler @ ~/.julia/packages/Distributions/oGEEM/src/samplers/poisson.jl:54 [inlined] [4] PoissonADSampler @ ~/.julia/packages/Distributions/oGEEM/src/samplers/poisson.jl:49 [inlined] [5] sampler @ ~/.julia/packages/Distributions/oGEEM/src/univariate/discrete/poisson.jl:144 [inlined] [6] rand(rng::Random.TaskLocalRNG, d::Poisson{Float64}) @ Distributions ~/.julia/packages/Distributions/oGEEM/src/univariate/discrete/poisson.jl:148 [7] rand(::Poisson{Float64}) @ Distributions ~/.julia/packages/Distributions/oGEEM/src/genericrand.jl:22 [8] top-level scope @ REPL[18]:1

Now this would not be problematic, because the logpdf calls are not affected but for some reason a rand call comes into using Turing at inference time (not sure why...).

Is there any chance of a safer version of the Poisson/Negative Binomial that can detect if round(BigInt, ... should be used?