Date: Tue, 04 Feb 2003 14:43:57 +0100 From: Dag-Erling Smorgrav <des@ofug.org> To: "Andrey A. Chernov" <ache@nagual.pp.ru> Cc: David Schultz <dschultz@uclink.Berkeley.EDU>, Kris Kennaway <kris@obsecurity.org>, current@FreeBSD.ORG Subject: Re: rand() is broken Message-ID: <xzpwukgupnm.fsf@flood.ping.uio.no> In-Reply-To: <20030204131748.GA92510@nagual.pp.ru> ("Andrey A. Chernov"'s message of "Tue, 4 Feb 2003 16:17:48 %2B0300") References: <20030202070644.GA9987@rot13.obsecurity.org> <20030202090422.GA59750@nagual.pp.ru> <20030203002639.GB44914@HAL9000.homeunix.com> <20030203100002.GA73386@nagual.pp.ru> <20030204054020.GA2447@HAL9000.homeunix.com> <20030204094659.GA87303@nagual.pp.ru> <20030204115237.GA6483@HAL9000.homeunix.com> <xzpfzr4b3pw.fsf@flood.ping.uio.no> <20030204131006.GB92301@nagual.pp.ru> <20030204131748.GA92510@nagual.pp.ru>
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"Andrey A. Chernov" <ache@nagual.pp.ru> writes:
> There is one bug in your patch: 0 is still illegal, so my fix required.
I believe that's a feature. All linear congruence generator have a
fixed point. 0 is a far better fixed point than any other because it
is more "obviously unsuited" (for some values of "obviously") as a
seed value. (but see below)
> The next bug is that there is % RAND_MAX + 1, not % RAND_MAX.
No, using modulo 0x80000000 instead of modulo 0x7fffffff breaks the
algorithm. (but see below)
> The next is not the bug but portability thing alowing different RAND_MAX:
> you need to assign *ctx first and return it % RAND_MAX + 1 next, not
> assign *ctx % RAND_MAX + 1 like you currently does.
Changing RAND_MAX affects the algorithm in such a way that you should
not do so without giving serious thought to revising the algorithm
itself. In fact, RAND_MAX should be considered a characteristic of
the algorithm rather than a parameter that regulates it. For that
reason, and to make the algorithm more transparent to the reader, I've
replaced RAND_MAX with 0x7fffffff in the attached patch.
All that being said, adding 1 to *ctx before returning it (see patch)
adresses both of your objections: a seed of 0 will not cause the LCG
to get stuck, and the result of rand() will range between 0 and
RAND_MAX inclusive.
des@des ~/src% ./rndtest| head
2 0 1 7 1 7 f 2 5 3 f 6 a d 6 a 3 b 5 2 f 8 6 3 d 9 6 1 f 0 2 3
4 4 1 a f 3 b 5 4 2 a 6 f 0 0 6 9 5 1 7 c f 6 9 1 7 7 a 7 8 1 b
0 a c 7 a c 7 3 9 f 4 2 d 3 d 9 d 4 4 a 3 0 c f 7 6 2 5 9 2 3 7
5 b 7 7 f 9 9 b d 1 d c 5 2 b 6 7 c c 5 8 4 3 b 2 1 6 f 6 c 2 2
5 6 5 e a b b 8 e e 4 9 1 9 4 2 3 4 d b 3 5 3 a d 4 3 5 b 7 4 a
c 1 2 4 e 5 d 9 0 6 6 8 b 7 f 8 8 2 6 1 c d 1 c f f 0 9 1 3 4 c
5 6 8 b 8 9 a 8 5 d b 8 8 d 7 e 7 0 c 2 c 8 0 6 5 8 f 8 9 6 0 c
9 d 4 7 0 8 5 2 c b 8 e 5 f 5 c d 1 c c b 3 8 8 f f 1 2 a 5 c f
0 5 f 2 4 e 9 0 1 1 9 2 5 f 0 0 2 2 d f b f 7 0 2 a 2 4 7 a 2 f
9 0 f 1 c 8 e 2 f c f 2 8 c d 5 7 0 f 2 b a 2 a 4 d 8 b c 4 0 4
DES
--
Dag-Erling Smorgrav - des@ofug.org
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Content-Type: text/x-patch
Content-Disposition: attachment; filename=rand.diff
Index: lib/libc/stdlib/rand.c
===================================================================
RCS file: /home/ncvs/src/lib/libc/stdlib/rand.c,v
retrieving revision 1.11
diff -u -r1.11 rand.c
--- lib/libc/stdlib/rand.c 2 Feb 2003 14:27:51 -0000 1.11
+++ lib/libc/stdlib/rand.c 4 Feb 2003 13:33:30 -0000
@@ -52,7 +52,7 @@
#endif /* TEST */
static int
-do_rand(unsigned long *ctx)
+do_rand(uint32_t *ctx)
{
#ifdef USE_WEAK_SEEDING
/*
@@ -63,21 +63,23 @@
return ((*ctx = *ctx * 1103515245 + 12345) % ((u_long)RAND_MAX + 1));
#else /* !USE_WEAK_SEEDING */
/*
- * Compute x = (7^5 * x) mod (2^31 - 1)
- * wihout overflowing 31 bits:
- * (2^31 - 1) = 127773 * (7^5) + 2836
- * From "Random number generators: good ones are hard to find",
- * Park and Miller, Communications of the ACM, vol. 31, no. 10,
- * October 1988, p. 1195.
+ * New algorithm derived from
+ * The Laws of Cryptography: Pseudo-random Number Generation
+ * by Neal R. Wagner
+ * http://www.cs.utsa.edu/~wagner/laws/rng.html
+ * which itself is derived from work by Donald E. Knuth.
+ *
+ * This is a linear congruence generator using the equation
+ *
+ * x(n+1) = (k * x(n) + a) mod m
+ *
+ * where m is 2^31 - 1, k is 62089911 and a is 0.
*/
- long hi, lo, x;
+ uint64_t tmp;
- hi = *ctx / 127773;
- lo = *ctx % 127773;
- x = 16807 * lo - 2836 * hi;
- if (x <= 0)
- x += 0x7fffffff;
- return ((*ctx = x) % ((u_long)RAND_MAX + 1));
+ tmp = *ctx * 62089911;
+ *ctx = (uint32_t)(tmp % (uint64_t)0x7fffffff + 1);
+ return (*ctx);
#endif /* !USE_WEAK_SEEDING */
}
@@ -85,7 +87,7 @@
int
rand_r(unsigned int *ctx)
{
- u_long val = (u_long) *ctx;
+ uint32_t val = (uint32_t) *ctx;
int r = do_rand(&val);
*ctx = (unsigned int) val;
@@ -93,7 +95,7 @@
}
-static u_long next = 1;
+static uint32_t next = 1;
int
rand()
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