On Mon, 11 Feb 2019, Bruce Evans wrote:
On Sun, 10 Feb 2019, Conrad Meyer wrote:
Log:
Prevent overflow for usertime/systime in caclru1
...
+static uint64_t
+mul64_by_fraction(uint64_t a, uint64_t b, uint64_t c)
+{
+ /*
+ * Compute floor(a * (b / c)) without overflowing, (b / c) <= 1.0.
+ */
+ return ((a / c) * b + (a % c) * (b / c) + (a % c) * (b % c) / c);
+}
+
This is the slowest correct fix in the PR followup. kib predicted
that I wouldn't like it. It does 2 64-bit divmods (after optimization)
and many multiplications per call. Times 2 calls. clang will probably
inline this, giving only 3 64-bit divmods instead of 4.
Better version:
+ /*
+ * Subdivide tu. Combine avoiding overflow with reduction to 32-bit
+ * operands in the multiplications in the usual case of tu <=
+ * UINT32_MAX usec = 4294 seconds.
+ */
+ if (__predict_true(tu <= UINT32_MAX && tt <= UINT32_MAX)) {
+ uu = ((uint64_t)(uint32_t)tu * (uint32_t)ut) / tt;
+ su = ((uint64_t)(uint32_t)tu * (uint32_t)st) / tt;
+ } else {
+ q = tu / tt;
+ r = tu % tt;
+ uu = q * ut + (r * ut) / tt;
+ su = q * st + (r * st) / tt;
+ }
I didn't keep the part of your reply to my reply above where you said
that you tested over a number of years.
I also tested over fake years in a running kernel using a fake cpu_tick
freqency of 100000 times smaller.
Now I see that all versions still overflow after 388 days with stathz =
128 when tt exceeds UINT32_MAX. Then r can be 1 less than tt, and
ut and st can be the same as tt, so one operation is like sqaring tt
which overflows when tt is 1 more than UINT32_MAX.
There is a PR or 2 about this 388-day limit. I knew about it before I
knew about the 105-hour limit fixed in this commit.(
Uptimes of a few years are not preposterous, and cpu_idle threads usually
have system time of nearly the uptime, so the overflow occurs on most
systems after they have been up for 388 days.
I'm trying a fix with tt and r divided by 16 in some places. This should
work for 17 years with stathz = 128. The thread runtime is more than 388
days when this occurs, so no one would care about differences of even a few
days but losing precision in the seconds and microseconds parts is not so
good.
Bruce
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