ash,hush: improve randomness of $RANDOM, add easy-ish way to test it

function                                             old     new   delta
next_random                                           68     113     +45
change_random                                        103     121     +18

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>

shell/random.c

@@ -6,17 +6,51 @@
  *
  * Licensed under GPLv2, see file LICENSE in this source tree.
  */
-#include "libbb.h"
+
-#include "random.h"
+/* For testing against dieharder, you need only random.{c,h}
+ * Howto:
+ * gcc -O2 -Wall -DRANDTEST random.c -o random
+ * ./random | dieharder -g 200 -a
+ */
+
+#if !defined RANDTEST
+
+# include "libbb.h"
+# include "random.h"
+# define RAND_BASH_MASK 0x7fff
+
+#else
+# include <stdint.h>
+# include <unistd.h>
+# include <stdio.h>
+# include <time.h>
+# define RAND_BASH_MASK 0xffffffff /* off */
+# define FAST_FUNC /* nothing */
+# define PUSH_AND_SET_FUNCTION_VISIBILITY_TO_HIDDEN /* nothing */
+# define POP_SAVED_FUNCTION_VISIBILITY /* nothing */
+# define monotonic_us() time(NULL)
+# include "random.h"
+#endif
 
 uint32_t FAST_FUNC
 next_random(random_t *rnd)
 {
-	/* Galois LFSR parameter */
+	/* Galois LFSR parameter:
-	/* Taps at 32 31 29 1: */
+	 * Taps at 32 31 29 1:
+	 */
 	enum { MASK = 0x8000000b };
 	/* Another example - taps at 32 31 30 10: */
-	/* MASK = 0x00400007 */
+	/* enum { MASK = 0x00400007 }; */
+
+	/* Xorshift parameters:
+	 * Choices for a,b,c: 10,13,10; 8,9,22; 2,7,3; 23,3,24
+	 * (given by algorithm author)
+	 */
+        enum {
+                a = 2,
+                b = 7,
+                c = 3,
+        };
 
 	uint32_t t;
 
@@ -27,18 +61,94 @@ next_random(random_t *rnd)
 		INIT_RANDOM_T(rnd, getpid(), monotonic_us());
 	}
 
-	/* LCG has period of 2^32 and alternating lowest bit */
+	/* LCG: period of 2^32, but quite weak:
+	 * bit 0 alternates beetween 0 and 1 (pattern of length 2)
+	 * bit 1 has a repeating pattern of length 4
+	 * bit 2 has a repeating pattern of length 8
+	 * etc...
+	 */
 	rnd->LCG = 1664525 * rnd->LCG + 1013904223;
-	/* Galois LFSR has period of 2^32-1 = 3 * 5 * 17 * 257 * 65537 */
+
+	/* Galois LFSR:
+	 * period of 2^32-1 = 3 * 5 * 17 * 257 * 65537.
+	 * Successive values are right-shifted one bit
+	 * and possibly xored with a sparse constant.
+	 */
 	t = (rnd->galois_LFSR << 1);
 	if (rnd->galois_LFSR < 0) /* if we just shifted 1 out of msb... */
 		t ^= MASK;
 	rnd->galois_LFSR = t;
-	/* Both are weak, combining them gives better randomness
-	 * and ~2^64 period. & 0x7fff is probably bash compat
-	 * for $RANDOM range. Combining with subtraction is
-	 * just for fun. + and ^ would work equally well. */
-	t = (t - rnd->LCG) & 0x7fff;
 
-	return t;
+	/* http://en.wikipedia.org/wiki/Xorshift
+	 * Period 2^64-1 = 3 * 715827883 * 2147483647
+	 * Moderately good statistical properties:
+	 * fails the following "dieharder -g 200 -a" tests:
+	 *       diehard_operm5|   0
+	 *         diehard_oqso|   0
+	 * diehard_count_1s_byt|   0
+	 *     diehard_3dsphere|   3
+	 *      diehard_squeeze|   0
+	 *         diehard_runs|   0
+	 *         diehard_runs|   0
+	 *        diehard_craps|   0
+	 *        diehard_craps|   0
+	 * rgb_minimum_distance|   3
+	 * rgb_minimum_distance|   4
+	 * rgb_minimum_distance|   5
+	 *     rgb_permutations|   3
+	 *     rgb_permutations|   4
+	 *     rgb_permutations|   5
+	 *         dab_filltree|  32
+	 *         dab_filltree|  32
+	 *         dab_monobit2|  12
+	 */
+	t = rnd->xs64_x ^ (rnd->xs64_x << a);
+	rnd->xs64_x = rnd->xs64_y;
+	rnd->xs64_y = rnd->xs64_y ^ (rnd->xs64_y >> c) ^ t ^ (t >> b);
+
+	/* Combined LCG + Galois LFSR have 2^32 * 2^32-1 period.
+	 * Strength:
+	 * individually, both are extremely weak cryptographycally;
+	 * when combined, they fail the following "dieharder -g 200 -a" tests:
+	 *     diehard_rank_6x8|   0
+	 *         diehard_oqso|   0
+	 *          diehard_dna|   0
+	 * diehard_count_1s_byt|   0
+	 *          rgb_bitdist|   2
+	 *         dab_monobit2|  12
+	 *
+	 * Combining them with xorshift-64 increases period to
+	 * 2^32 * 2^32-1 * 2^64-1 / 3
+	 * (2^32-1 and 2^64-1 have one common divisor 3, hence "/ 3" part),
+	 * which is about 2^128 / 3, or in base 10 ~1.13*10^38.
+	 * Strength of the combination:
+	 * passes all "dieharder -g 200 -a" tests.
+	 *
+	 * Combining with subtraction and addition is just for fun.
+	 * It does not add meaningful strength, could use xor operation instead.
+	 */
+	t = rnd->galois_LFSR - rnd->LCG + rnd->xs64_y;
+
+	/* bash compat $RANDOM range: */
+	return t & RAND_BASH_MASK;
 }
+
+#ifdef RANDTEST
+static random_t rnd;
+
+int main(int argc, char **argv)
+{
+	int i;
+	int buf[4096];
+
+	for (;;) {
+		for (i = 0; i < sizeof(buf) / sizeof(buf[0]); i++) {
+			buf[i] = next_random(&rnd);
+		}
+		write(1, buf, sizeof(buf));
+	}
+
+        return 0;
+}
+
+#endif

shell/random.h

@@ -12,16 +12,24 @@
 PUSH_AND_SET_FUNCTION_VISIBILITY_TO_HIDDEN
 
 typedef struct random_t {
-	/* Random number generators */
+	/* State of random number generators: */
-	int32_t galois_LFSR; /* Galois LFSR (fast but weak). signed! */
+
-	uint32_t LCG;        /* LCG (fast but weak) */
+	/* Galois LFSR (fast but weak) */
+	int32_t galois_LFSR; /* must be signed! */
+
+	/* LCG (fast but weak) */
+	uint32_t LCG;
+
+	/* 64-bit xorshift (fast, moderate strength) */
+	uint32_t xs64_x;
+	uint32_t xs64_y;
 } random_t;
 
 #define UNINITED_RANDOM_T(rnd) \
 	((rnd)->galois_LFSR == 0)
 
 #define INIT_RANDOM_T(rnd, nonzero, v) \
-	((rnd)->galois_LFSR = (nonzero), (rnd)->LCG = (v))
+	((rnd)->galois_LFSR = (rnd)->xs64_x = (nonzero), (rnd)->LCG = (rnd)->xs64_y = (v))
 
 #define CLEAR_RANDOM_T(rnd) \
 	((rnd)->galois_LFSR = 0)