sched/cputime: Improve cputime_adjust()

People report that utime and stime from /proc/<pid>/stat become very
wrong when the numbers are big enough, especially if you watch these
counters incrementally.

Specifically, the current implementation of: stime*rtime/total,
results in a saw-tooth function on top of the desired line, where the
teeth grow in size the larger the values become. IOW, it has a
relative error.

The result is that, when watching incrementally as time progresses
(for large values), we'll see periods of pure stime or utime increase,
irrespective of the actual ratio we're striving for.

Replace scale_stime() with a math64.h helper: mul_u64_u64_div_u64()
that is far more accurate. This also allows architectures to override
the implementation -- for instance they can opt for the old algorithm
if this new one turns out to be too expensive for them.

Signed-off-by: Oleg Nesterov <[e-mail]>
Signed-off-by: Peter Zijlstra (Intel) <[e-mail]>
Link: https://lkml.kernel.org/r/[e-mail]

arch/x86/include/asm/div64.h

···
 #else
 # include <asm-generic/div64.h>
 
-static inline u64 mul_u64_u32_div(u64 a, u32 mul, u32 div)
+/*
+ * Will generate an #DE when the result doesn't fit u64, could fix with an
+ * __ex_table[] entry when it becomes an issue.
+ */
+static inline u64 mul_u64_u64_div_u64(u64 a, u64 mul, u64 div)
 {
 	u64 q;
 
 	asm ("mulq %2; divq %3" : "=a" (q)
-				: "a" (a), "rm" ((u64)mul), "rm" ((u64)div)
+				: "a" (a), "rm" (mul), "rm" (div)
 				: "rdx");
 
 	return q;
+}
+#define mul_u64_u64_div_u64 mul_u64_u64_div_u64
+
+static inline u64 mul_u64_u32_div(u64 a, u32 mul, u32 div)
+{
+	return mul_u64_u64_div_u64(a, mul, div);
 }
 #define mul_u64_u32_div	mul_u64_u32_div
 

include/linux/math64.h

···
 }
 #endif /* mul_u64_u32_div */
 
+u64 mul_u64_u64_div_u64(u64 a, u64 mul, u64 div);
+
 #define DIV64_U64_ROUND_UP(ll, d)	\
 	({ u64 _tmp = (d); div64_u64((ll) + _tmp - 1, _tmp); })
 

kernel/sched/cputime.c

···
 }
 
 /*
- * Perform (stime * rtime) / total, but avoid multiplication overflow by
- * losing precision when the numbers are big.
- */
-static u64 scale_stime(u64 stime, u64 rtime, u64 total)
-{
-	u64 scaled;
-
-	for (;;) {
-		/* Make sure "rtime" is the bigger of stime/rtime */
-		if (stime > rtime)
-			swap(rtime, stime);
-
-		/* Make sure 'total' fits in 32 bits */
-		if (total >> 32)
-			goto drop_precision;
-
-		/* Does rtime (and thus stime) fit in 32 bits? */
-		if (!(rtime >> 32))
-			break;
-
-		/* Can we just balance rtime/stime rather than dropping bits? */
-		if (stime >> 31)
-			goto drop_precision;
-
-		/* We can grow stime and shrink rtime and try to make them both fit */
-		stime <<= 1;
-		rtime >>= 1;
-		continue;
-
-drop_precision:
-		/* We drop from rtime, it has more bits than stime */
-		rtime >>= 1;
-		total >>= 1;
-	}
-
-	/*
-	 * Make sure gcc understands that this is a 32x32->64 multiply,
-	 * followed by a 64/32->64 divide.
-	 */
-	scaled = div_u64((u64) (u32) stime * (u64) (u32) rtime, (u32)total);
-	return scaled;
-}
-
-/*
  * Adjust tick based cputime random precision against scheduler runtime
  * accounting.
  *
···
 		goto update;
 	}
 
-	stime = scale_stime(stime, rtime, stime + utime);
+	stime = mul_u64_u64_div_u64(stime, rtime, stime + utime);
 
 update:
 	/*

lib/math/div64.c

···
 	return __iter_div_u64_rem(dividend, divisor, remainder);
 }
 EXPORT_SYMBOL(iter_div_u64_rem);
+
+#ifndef mul_u64_u64_div_u64
+u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
+{
+	u64 res = 0, div, rem;
+	int shift;
+
+	/* can a * b overflow ? */
+	if (ilog2(a) + ilog2(b) > 62) {
+		/*
+		 * (b * a) / c is equal to
+		 *
+		 *      (b / c) * a +
+		 *      (b % c) * a / c
+		 *
+		 * 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 = (b / c) * a;
+		 *      b = b % c;
+		 */
+		div = div64_u64_rem(b, c, &rem);
+		res = div * a;
+		b = rem;
+
+		shift = ilog2(a) + ilog2(b) - 62;
+		if (shift > 0) {
+			/* drop precision */
+			b >>= shift;
+			c >>= shift;
+			if (!c)
+				return res;
+		}
+	}
+
+	return res + div64_u64(a * b, c);
+}
+#endif