CCRandom: add an uniformity test

src/core/CCRandom.ml

@@ -192,3 +192,31 @@ let (<*>) f g st = f st (g st)
 let __default_state = Random.State.make_self_init ()
 
 let run ?(st=__default_state) g = g st
+
+let uniformity_test ?(size_hint=10) k rng st =
+  let histogram = Hashtbl.create size_hint in
+  let add x = let n = try Hashtbl.find histogram x with Not_found -> 0 in
+    Hashtbl.replace histogram x (n + 1) in
+  let () =
+    for _i = 0 to ( k - 1 ) do
+      add @@ rng st
+    done in
+  let cardinal = float_of_int @@ Hashtbl.length histogram in
+  let kf = float_of_int k in
+  (* average number of points assuming an uniform distribution *)
+  let average = kf /. cardinal in
+  (* The number of points is a sum of random variables with binomial distribution *)
+  let p = 1. /. cardinal in
+  (* The variance of a binomial distribution with average p is *)
+  let variance = p *. (1. -. p ) in
+  (* Central limit theorem: a confidence interval of 4σ provides a false positive rate
+     of 0.00634% *)
+  let confidence = 4. in
+  let std = confidence *. ( sqrt @@ kf *. variance ) in
+  let predicate _key n acc =
+    acc && abs_float (average -. float_of_int n) < std in
+  Hashtbl.fold predicate histogram true
+
+(*$T split_list
+  run ( uniformity_test 50_000 (split_list 10 ~len:3) )
+*)

src/core/CCRandom.mli

@@ -153,3 +153,11 @@ val (<*>) : ('a -> 'b) t -> 'a t -> 'b t
 
 val run : ?st:state -> 'a t -> 'a
 (** Using a random state (possibly the one in argument) run a generator *)
+
+(** {6 Random generator testing } *)
+
+val uniformity_test : ?size_hint:int -> int -> 'a t -> bool t
+(** [uniformity_test k rng] tests the uniformity of the random generator [rng] using
+    [k] samples.
+    @since 0.15
+*)