Special case Geometric(OneHalf()) (#1934)

* Special case Geometric(OneHalf())

* Remove OneHalf and branch at sample time

* Use 1//2 instead of 0.5

Author: LilithHafner

src/univariate/discrete/geometric.jl

@@ -136,7 +136,14 @@ cf(d::Geometric, t::Real) = laplace_transform(d, -t*im)
 
 ### Sampling
 
-rand(rng::AbstractRNG, d::Geometric) = floor(Int,-randexp(rng) / log1p(-d.p))
+# Inlining is required to hoist the d.p == 1//2 check when generating in bulk
+@inline function rand(rng::AbstractRNG, d::Geometric)
+    if d.p == 1//2
+        leading_zeros(rand(rng, UInt)) # This branch is a performance optimization
+    else
+        floor(Int,-randexp(rng) / log1p(-d.p))
+    end
+end
 
 ### Model Fitting