jiffies: Fix timeval conversion to jiffies

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: stable@vger.kernel.org
Cc: Thomas Gleixner <tglx@linutronix.de>
Cc: Ingo Molnar <mingo@redhat.com>
Cc: Paul Turner <pjt@google.com>
Cc: Richard Cochran <richardcochran@gmail.com>
Cc: Prarit Bhargava <prarit@redhat.com>
Reviewed-by: Paul Turner <pjt@google.com>
Reported-by: Aaron Jacobs <jacobsa@google.com>
Signed-off-by: Andrew Hunter <ahh@google.com>
[jstultz: Tweaked to apply to 3.17-rc]
Signed-off-by: John Stultz <john.stultz@linaro.org>

include/linux/jiffies.h

@@ -259,23 +259,11 @@ 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 64-bit 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 64-bit case will overflow if we are not careful,

kernel/time.c

@@ -487,17 +487,20 @@ 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;
@@ -508,6 +511,13 @@ timespec_to_jiffies(const struct timespec *value)
 		 (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
@@ -524,31 +534,27 @@ jiffies_to_timespec(const unsigned long jiffies, struct timespec *value)
 }
 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.
  *
- * 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, in-particular),
- * 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.
+ * 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 division-rounding-upward (i.e. adding 2^(scale) - 1
+ * units to the intermediate before shifting) leads to accidental
+ * overflow and overestimates.
+ *
+ * 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);