[PATCH 3.10 09/13] jiffies: Fix timeval conversion to jiffies
From: Greg KroahHartman
Date: Tue Oct 07 2014  19:22:25 EST
3.10stable review patch. If anyone has any objections, please let me know.

From: Andrew Hunter <ahh@xxxxxxxxxx>
commit d78c9300c51d6ceed9f6d078d4e9366f259de28c upstream.
timeval_to_jiffies tried to round a timeval up to an integral number
of jiffies, but the logic for doing so was incorrect: intervals
corresponding to exactly N jiffies would become N+1. This manifested
itself particularly repeatedly stopping/starting an itimer:
setitimer(ITIMER_PROF, &val, NULL);
setitimer(ITIMER_PROF, NULL, &val);
would add a full tick to val, _even if it was exactly representable in
terms of jiffies_ (say, the result of a previous rounding.) Doing
this repeatedly would cause unbounded growth in val. So fix the math.
Here's what was wrong with the conversion: we essentially computed
(eliding seconds)
jiffies = usec * (NSEC_PER_USEC/TICK_NSEC)
by using scaling arithmetic, which took the best approximation of
NSEC_PER_USEC/TICK_NSEC with denominator of 2^USEC_JIFFIE_SC =
x/(2^USEC_JIFFIE_SC), and computed:
jiffies = (usec * x) >> USEC_JIFFIE_SC
and rounded this calculation up in the intermediate form (since we
can't necessarily exactly represent TICK_NSEC in usec.) But the
scaling arithmetic is a (very slight) *over*approximation of the true
value; that is, instead of dividing by (1 usec/ 1 jiffie), we
effectively divided by (1 usec/1 jiffie)epsilon (rounding
down). This would normally be fine, but we want to round timeouts up,
and we did so by adding 2^USEC_JIFFIE_SC  1 before the shift; this
would be fine if our division was exact, but dividing this by the
slightly smaller factor was equivalent to adding just _over_ 1 to the
final result (instead of just _under_ 1, as desired.)
In particular, with HZ=1000, we consistently computed that 10000 usec
was 11 jiffies; the same was true for any exact multiple of
TICK_NSEC.
We could possibly still round in the intermediate form, adding
something less than 2^USEC_JIFFIE_SC  1, but easier still is to
convert usec>nsec, round in nanoseconds, and then convert using
time*spec*_to_jiffies. This adds one constant multiplication, and is
not observably slower in microbenchmarks on recent x86 hardware.
Tested: the following program:
int main() {
struct itimerval zero = {{0, 0}, {0, 0}};
/* Initially set to 10 ms. */
struct itimerval initial = zero;
initial.it_interval.tv_usec = 10000;
setitimer(ITIMER_PROF, &initial, NULL);
/* Save and restore several times. */
for (size_t i = 0; i < 10; ++i) {
struct itimerval prev;
setitimer(ITIMER_PROF, &zero, &prev);
/* on old kernels, this goes up by TICK_USEC every iteration */
printf("previous value: %ld %ld %ld %ld\n",
prev.it_interval.tv_sec, prev.it_interval.tv_usec,
prev.it_value.tv_sec, prev.it_value.tv_usec);
setitimer(ITIMER_PROF, &prev, NULL);
}
return 0;
}
Cc: Thomas Gleixner <tglx@xxxxxxxxxxxxx>
Cc: Ingo Molnar <mingo@xxxxxxxxxx>
Cc: Paul Turner <pjt@xxxxxxxxxx>
Cc: Richard Cochran <richardcochran@xxxxxxxxx>
Cc: Prarit Bhargava <prarit@xxxxxxxxxx>
Reviewedby: Paul Turner <pjt@xxxxxxxxxx>
Reportedby: Aaron Jacobs <jacobsa@xxxxxxxxxx>
Signedoffby: Andrew Hunter <ahh@xxxxxxxxxx>
[jstultz: Tweaked to apply to 3.17rc]
Signedoffby: John Stultz <john.stultz@xxxxxxxxxx>
[bwh: Backported to 3.16: adjust filename]
Signedoffby: Ben Hutchings <ben@xxxxxxxxxxxxxxx>
Signedoffby: Greg KroahHartman <gregkh@xxxxxxxxxxxxxxxxxxx>

include/linux/jiffies.h  12 
kernel/time.c  54 ++++++++++++++++++++++++++
2 files changed, 30 insertions(+), 36 deletions()
 a/include/linux/jiffies.h
+++ b/include/linux/jiffies.h
@@ 254,23 +254,11 @@ extern unsigned long preset_lpj;
#define SEC_JIFFIE_SC (32  SHIFT_HZ)
#endif
#define NSEC_JIFFIE_SC (SEC_JIFFIE_SC + 29)
#define USEC_JIFFIE_SC (SEC_JIFFIE_SC + 19)
#define SEC_CONVERSION ((unsigned long)((((u64)NSEC_PER_SEC << SEC_JIFFIE_SC) +\
TICK_NSEC 1) / (u64)TICK_NSEC))
#define NSEC_CONVERSION ((unsigned long)((((u64)1 << NSEC_JIFFIE_SC) +\
TICK_NSEC 1) / (u64)TICK_NSEC))
#define USEC_CONVERSION \
 ((unsigned long)((((u64)NSEC_PER_USEC << USEC_JIFFIE_SC) +\
 TICK_NSEC 1) / (u64)TICK_NSEC))
/*
 * USEC_ROUND is used in the timeval to jiffie conversion. See there
 * for more details. It is the scaled resolution rounding value. Note
 * that it is a 64bit value. Since, when it is applied, we are already
 * in jiffies (albit scaled), it is nothing but the bits we will shift
 * off.
 */
#define USEC_ROUND (u64)(((u64)1 << USEC_JIFFIE_SC)  1)
/*
* The maximum jiffie value is (MAX_INT >> 1). Here we translate that
* into seconds. The 64bit case will overflow if we are not careful,
 a/kernel/time.c
+++ b/kernel/time.c
@@ 496,17 +496,20 @@ EXPORT_SYMBOL(usecs_to_jiffies);
* that a remainder subtract here would not do the right thing as the
* resolution values don't fall on second boundries. I.e. the line:
* nsec = nsec % TICK_NSEC; is NOT a correct resolution rounding.
+ * Note that due to the small error in the multiplier here, this
+ * rounding is incorrect for sufficiently large values of tv_nsec, but
+ * well formed timespecs should have tv_nsec < NSEC_PER_SEC, so we're
+ * OK.
*
* Rather, we just shift the bits off the right.
*
* The >> (NSEC_JIFFIE_SC  SEC_JIFFIE_SC) converts the scaled nsec
* value to a scaled second value.
*/
unsigned long
timespec_to_jiffies(const struct timespec *value)
+static unsigned long
+__timespec_to_jiffies(unsigned long sec, long nsec)
{
 unsigned long sec = value>tv_sec;
 long nsec = value>tv_nsec + TICK_NSEC  1;
+ nsec = nsec + TICK_NSEC  1;
if (sec >= MAX_SEC_IN_JIFFIES){
sec = MAX_SEC_IN_JIFFIES;
@@ 517,6 +520,13 @@ timespec_to_jiffies(const struct timespe
(NSEC_JIFFIE_SC  SEC_JIFFIE_SC))) >> SEC_JIFFIE_SC;
}
+
+unsigned long
+timespec_to_jiffies(const struct timespec *value)
+{
+ return __timespec_to_jiffies(value>tv_sec, value>tv_nsec);
+}
+
EXPORT_SYMBOL(timespec_to_jiffies);
void
@@ 533,31 +543,27 @@ jiffies_to_timespec(const unsigned long
}
EXPORT_SYMBOL(jiffies_to_timespec);
/* Same for "timeval"
+/*
+ * We could use a similar algorithm to timespec_to_jiffies (with a
+ * different multiplier for usec instead of nsec). But this has a
+ * problem with rounding: we can't exactly add TICK_NSEC  1 to the
+ * usec value, since it's not necessarily integral.
+ *
+ * We could instead round in the intermediate scaled representation
+ * (i.e. in units of 1/2^(large scale) jiffies) but that's also
+ * perilous: the scaling introduces a small positive error, which
+ * combined with a divisionroundingupward (i.e. adding 2^(scale)  1
+ * units to the intermediate before shifting) leads to accidental
+ * overflow and overestimates.
*
 * Well, almost. The problem here is that the real system resolution is
 * in nanoseconds and the value being converted is in micro seconds.
 * Also for some machines (those that use HZ = 1024, inparticular),
 * there is a LARGE error in the tick size in microseconds.

 * The solution we use is to do the rounding AFTER we convert the
 * microsecond part. Thus the USEC_ROUND, the bits to be shifted off.
 * Instruction wise, this should cost only an additional add with carry
 * instruction above the way it was done above.
+ * At the cost of one additional multiplication by a constant, just
+ * use the timespec implementation.
*/
unsigned long
timeval_to_jiffies(const struct timeval *value)
{
 unsigned long sec = value>tv_sec;
 long usec = value>tv_usec;

 if (sec >= MAX_SEC_IN_JIFFIES){
 sec = MAX_SEC_IN_JIFFIES;
 usec = 0;
 }
 return (((u64)sec * SEC_CONVERSION) +
 (((u64)usec * USEC_CONVERSION + USEC_ROUND) >>
 (USEC_JIFFIE_SC  SEC_JIFFIE_SC))) >> SEC_JIFFIE_SC;
+ return __timespec_to_jiffies(value>tv_sec,
+ value>tv_usec * NSEC_PER_USEC);
}
EXPORT_SYMBOL(timeval_to_jiffies);

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