ash,hush: fix a thinko about 2^64-1 factorization

function                                             old     new   delta
next_random                                          113     119      +6

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

diff --git a/shell/random.c b/shell/random.c
index fc2dfc26d90ad204e5521ccac007f92eec3315eb..5d3620516a329fad26e45227138f6cb775464fbf 100644 (file)
--- a/shell/random.c
+++ b/shell/random.c
@@ -80,7 +80,6 @@ next_random(random_t *rnd)
        rnd->galois_LFSR = 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
@@ -102,11 +101,19 @@ next_random(random_t *rnd)
         *         dab_filltree|  32
         *         dab_monobit2|  12
         */
+ again:
        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);
+       /*
+        * Period 2^64-1 = 2^32+1 * 2^32-1 has a common divisor with Galois LFSR.
+        * By skipping two possible states (0x1 and 0x2) we reduce period to
+        * 2^64-3 = 13 * 3889 * 364870227143809 which has no common divisors:
+        */
+       if (rnd->xs64_y == 0 && rnd->xs64_x <= 2)
+               goto again;
 
-       /* Combined LCG + Galois LFSR have 2^32 * 2^32-1 period.
+       /* Combined LCG + Galois LFSR rng has 2^32 * 2^32-1 period.
         * Strength:
         * individually, both are extremely weak cryptographycally;
         * when combined, they fail the following "dieharder -g 200 -a" tests:
@@ -118,9 +125,8 @@ next_random(random_t *rnd)
         *         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.
+        * 2^32 * 2^32-1 * 2^64-3
+        * which is about 2^128, or in base 10 ~3.40*10^38.
         * Strength of the combination:
         * passes all "dieharder -g 200 -a" tests.
         *