1 ;;;; various RANDOM tests without side effects
3 ;;;; This software is part of the SBCL system. See the README file for
6 ;;;; While most of SBCL is derived from the CMU CL system, the test
7 ;;;; files (like this one) were written from scratch after the fork
10 ;;;; This software is in the public domain and is provided with
11 ;;;; absolutely no warranty. See the COPYING and CREDITS files for
12 ;;;; more information.
16 ;;; Tests in this file that rely on properties of the distribution of
17 ;;; the random numbers are designed to be fast and have a very low
18 ;;; probability of false positives, generally of the order of (expt 10 -60).
19 ;;; These tests are not intended to assure the statistical qualities of the
20 ;;; pseudo random number generator but to help find bugs in its and RANDOM's
23 ;; When the type of the argument of RANDOM is a set of integers, a
24 ;; DEFTRANSFORM triggered that simply generated (REM (RANDOM-CHUNK) NUM),
25 ;; which has two severe problems: The resulting distribution is very uneven
26 ;; for most arguments of RANDOM near the size of a random chunk and the
27 ;; RANDOM-CHUNK used was always 32 bits, even under 64 bit wordsize which
28 ;; yields even more disastrous distributions.
29 (with-test (:name (:random :integer :set-of-integers :distribution))
30 (let* ((high (floor (expt 2 33) 3))
32 (fun (compile nil `(lambda (x)
33 (random (if x ,high 10)))))
37 (when (>= (funcall fun t) mid)
39 ;; Half of the values of (RANDOM HIGH) should be >= MID, so we expect
40 ;; N1 to be binomially distributed such that this distribution can be
41 ;; approximated by a normal distribution with mean (/ N 2) and standard
42 ;; deviation (* (sqrt N) 1/2). The broken RANDOM we are testing here for
43 ;; yields (/ N 3) and (* (sqrt N) (sqrt 2/9)), respectively. We test if
44 ;; N1 is below the average of (/ N 3) and (/ N 2). With a value of N of
45 ;; 10000 this is more than 16 standard deviations away from the expected
46 ;; mean, which has a probability of occurring by chance of below
48 (when (< n1 (* n 5/12))
49 (error "bad RANDOM distribution: expected ~d, got ~d" (/ n 2) n1))))
51 (with-test (:name (:random :integer :set-of-integers :chunk-size))
52 (let* ((high (expt 2 64))
53 (fun (compile nil `(lambda (x)
54 (random (if x ,high 10)))))
58 (setf x (logior x (funcall fun t))))
59 ;; If RANDOM works correctly, x should be #b111...111 (64 ones)
60 ;; with a probability of 1 minus approximately (expt 2 -194).
61 (unless (= x (1- high))
62 (error "bad RANDOM distribution: ~16,16,'0r" x))))