Fix BigFloat support by generalizing procf type constraint

The `procf` function had a hardcoded `s::Float64` type constraint that
caused a MethodError when using BigFloat with λ >= 6 (which uses the
ad_rand algorithm). Changed to `s::Real` to support arbitrary precision.

Added BigFloat tests to prevent regression.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

Author: claude

src/PoissonRandom.jl

@@ -82,7 +82,7 @@ function ad_rand(rng::AbstractRNG, λ::Real)
 end
 
 # Procedure F
-function procf(λ::Real, K::Int, s::Float64)
+function procf(λ::Real, K::Int, s::Real)
     # can be pre-computed, but does not seem to affect performance
     INV_SQRT_2PI = inv(sqrt(2pi))
     ω = INV_SQRT_2PI / s

test/runtests.jl

@@ -89,3 +89,27 @@ println("testing mixed random sampler")
 for λ in [5.0, 10.0, 15.0, 20.0, 30.0]
     test_samples(pois_rand, Distributions.Poisson(λ), n_tsamples)
 end
+
+@testset "BigFloat support" begin
+    @testset "count_rand with BigFloat (λ < 6)" begin
+        for _ in 1:100
+            result = pois_rand(BigFloat(3.0))
+            @test result isa Integer
+            @test result >= 0
+        end
+    end
+    @testset "ad_rand with BigFloat (λ >= 6)" begin
+        for _ in 1:100
+            result = pois_rand(BigFloat(15.0))
+            @test result isa Integer
+            @test result >= 0
+        end
+    end
+    @testset "statistical validity with BigFloat" begin
+        n = 10000
+        λ = BigFloat(10.0)
+        samples = [pois_rand(λ) for _ in 1:n]
+        sample_mean = mean(samples)
+        @test abs(sample_mean - Float64(λ)) < 3 * sqrt(Float64(λ))
+    end
+end