Random: make statistical uniform tests fail less often (#52165)

We have a very basic test to check that a distribution might be uniform:
all the sampled elements should be unique, under certain conditions. But
these conditions allowed the tests to fail too often. So allow one
collision if the probability of such an event is too high.

Fix #52156.

---------

Co-authored-by: Kristoffer Carlsson <[email protected]>

Author: rfourquet

stdlib/Random/test/runtests.jl

@@ -16,15 +16,30 @@ using Random: jump_128, jump_192, jump_128!, jump_192!
 import Future # randjump
 
 function test_uniform(xs::AbstractArray{T}) where {T<:AbstractFloat}
-    if precision(T) >= precision(Float32) # TODO: refine
-        @test allunique(xs)
+    # TODO: refine
+    prec = isempty(xs) ? precision(T) : precision(first(xs))
+    proba_nocollision = prod((1.0 - i/2.0^prec for i=1:length(xs)-1), init=1.0) # rough estimate
+    xsu = Set(xs)
+    if (1.0 - proba_nocollision) < 2.0^-64
+        @test length(xsu) == length(xs)
+    elseif prec > 52 && length(xs) < 3000
+        # if proba of collisions is high enough, allow at most one collision;
+        # with the constraints on precision and length, more than one collision would happen
+        # with proba less than 2.0^-62
+        @test length(xsu) >= length(xs)-1
     end
     @test all(x -> zero(x) <= x < one(x), xs)
 end
 
-function test_uniform(xs::AbstractArray{T}) where {T<:Integer}
-    if !Base.hastypemax(T) || widen(typemax(T)) - widen(typemin(T)) >= 2^30 # TODO: refine
-        @test allunique(xs)
+function test_uniform(xs::AbstractArray{T}) where {T<:Base.BitInteger}
+    # TODO: refine
+    prec = 8*sizeof(T)
+    proba_nocollision = prod((1.0 - i/2.0^prec for i=1:length(xs)-1), init=1.0)
+    xsu = Set(xs)
+    if (1.0 - proba_nocollision) < 2.0^-64
+        @test length(xsu) == length(xs)
+    elseif prec > 52 && length(xs) < 3000
+        @test length(xsu) >= length(xs)-1
     end
 end