Re: [PATCH] sched/cputime: make scale_stime() more precise

[Oleg Nesterov]

To simplify the review, see the code with this patch applied:

/*
 * Perform (stime * rtime) / total, but avoid multiplication overflow
 * by losing precision when the numbers are big.
 *
 * NOTE! currently the only user is cputime_adjust() and thus
 *
 *	stime < total && rtime > total
 *
 * this means that the end result is always precise and the additional
 * div64_u64_rem() inside the main loop is called at most once.
 */
static u64 scale_stime(u64 stime, u64 rtime, u64 total)
{
	u64 res = 0, div, rem;

	/* can stime * rtime overflow ? */
	while (ilog2(stime) + ilog2(rtime) > 62) {
		if (stime > rtime)
			swap(rtime, stime);

		if (rtime >= total) {
			/*
			 * (rtime * stime) / total is equal to
			 *
			 *	(rtime / total) * stime +
			 *	(rtime % total) * stime / total
			 *
			 * if nothing overflows. Can the 1st multiplication
			 * overflow? Yes, but we do not care: this can only
			 * happen if the end result can't fit in u64 anyway.
			 *
			 * So the code below does
			 *
			 *	res += (rtime / total) * stime;
			 *	rtime = rtime % total;
			 */
			div = div64_u64_rem(rtime, total, &rem);
			res += div * stime;
			rtime = rem;
			continue;
		}

		/* drop precision */
		rtime >>= 1;
		total >>= 1;
		if (!total)
			return res;
	}

	return res + div64_u64(stime * rtime, total);
}