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The C operator <= defines a perfectly fine total ordering on the set of
values representable in a long. However, unlike its namesake in the
integers, it is not translation invariant, meaning that we do not have
"b <= c" iff "a+b <= a+c" for all a,b,c.
This means that it is always wrong to try to boil down the relationship
between two longs to a question about the sign of their difference,
because the resulting relation [a LEQ b iff a-b <= 0] is neither
anti-symmetric or transitive. The former is due to -LONG_MIN==LONG_MIN
(take any two a,b with a-b = LONG_MIN; then a LEQ b and b LEQ a, but a !=
b). The latter can either be seen observing that x LEQ x+1 for all x,
implying x LEQ x+1 LEQ x+2 ... LEQ x-1 LEQ x; or more directly with the
simple example a=LONG_MIN, b=0, c=1, for which a-b < 0, b-c < 0, but a-c >
0.
Note that it makes absolutely no difference that a transmogrying bijection
has been applied before the comparison is done. In fact, had the
obfuscation not been done, one could probably not observe the bug
(assuming all values being compared always lie in one half of the address
space, the mathematical value of a-b is always representable in a long).
As it stands, one can easily obtain three file descriptors exhibiting the
non-transitivity of kcmp().
Side note 1: I can't see that ensuring the MSB of the multiplier is
set serves any purpose other than obfuscating the obfuscating code.
Side note 2:
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <fcntl.h>
#include <unistd.h>
#include <assert.h>
#include <sys/syscall.h>
enum kcmp_type {
KCMP_FILE,
KCMP_VM,
KCMP_FILES,
KCMP_FS,
KCMP_SIGHAND,
KCMP_IO,
KCMP_SYSVSEM,
KCMP_TYPES,
};
pid_t pid;
int kcmp(pid_t pid1, pid_t pid2, int type,
unsigned long idx1, unsigned long idx2)
{
return syscall(SYS_kcmp, pid1, pid2, type, idx1, idx2);
}
int cmp_fd(int fd1, int fd2)
{
int c = kcmp(pid, pid, KCMP_FILE, fd1, fd2);
if (c < 0) {
perror("kcmp");
exit(1);
}
assert(0 <= c && c < 3);
return c;
}
int cmp_fdp(const void *a, const void *b)
{
static const int normalize[] = {0, -1, 1};
return normalize[cmp_fd(*(int*)a, *(int*)b)];
}
#define MAX 100 /* This is plenty; I've seen it trigger for MAX==3 */
int main(int argc, char *argv[])
{
int r, s, count = 0;
int REL[3] = {0,0,0};
int fd[MAX];
pid = getpid();
while (count < MAX) {
r = open("/dev/null", O_RDONLY);
if (r < 0)
break;
fd[count++] = r;
}
printf("opened %d file descriptors\n", count);
for (r = 0; r < count; ++r) {
for (s = r+1; s < count; ++s) {
REL[cmp_fd(fd[r], fd[s])]++;
}
}
printf("== %d\t< %d\t> %d\n", REL[0], REL[1], REL[2]);
qsort(fd, count, sizeof(fd[0]), cmp_fdp);
memset(REL, 0, sizeof(REL));
for (r = 0; r < count; ++r) {
for (s = r+1; s < count; ++s) {
REL[cmp_fd(fd[r], fd[s])]++;
}
}
printf("== %d\t< %d\t> %d\n", REL[0], REL[1], REL[2]);
return (REL[0] + REL[2] != 0);
}
Signed-off-by: Rasmus Villemoes <linux@rasmusvillemoes.dk>
Reviewed-by: Cyrill Gorcunov <gorcunov@openvz.org>
"Eric W. Biederman" <ebiederm@xmission.com>
Cc: <stable@vger.kernel.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
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