sched/fair: Optimize and clean up sched averages

index b8a33ab..e803f11 100644
@@ -2603,6 +2603,15 @@ static const u32 runnable_avg_yN_sum[] = {
 };
 
 /*
+ * Precomputed \Sum y^k { 1<=k<=n, where n%32=0). Values are rolled down to
+ * lower integers.
+ */
+static const u32 __accumulated_sum_N32[] = {
+	    0, 23371, 35056, 40899, 43820, 45281,
+	46011, 46376, 46559, 46650, 46696, 46719,
+};
+
+/*
  * Approximate:
  *   val * y^n,    where y^32 ~= 0.5 (~1 scheduling period)
  */

@@ -2650,14 +2659,9 @@ static u32 __compute_runnable_contrib(u64 n)
 	else if (unlikely(n >= LOAD_AVG_MAX_N))
 		return LOAD_AVG_MAX;
 
-	/* Compute \Sum k^n combining precomputed values for k^i, \Sum k^j */
-	do {
-		contrib /= 2; /* y^LOAD_AVG_PERIOD = 1/2 */
-		contrib += runnable_avg_yN_sum[LOAD_AVG_PERIOD];
-
-		n -= LOAD_AVG_PERIOD;
-	} while (n > LOAD_AVG_PERIOD);
-
+	/* Since n < LOAD_AVG_MAX_N, n/LOAD_AVG_PERIOD < 11 */
+	contrib = __accumulated_sum_N32[n/LOAD_AVG_PERIOD];
+	n %= LOAD_AVG_PERIOD;
 	contrib = decay_load(contrib, n);
 	return contrib + runnable_avg_yN_sum[n];
 }

index e803f11..2b83b4c 100644
@@ -660,13 +660,15 @@ static int select_idle_sibling(struct task_struct *p, int cpu);
 static unsigned long task_h_load(struct task_struct *p);
 
 /*
- * We choose a half-life close to 1 scheduling period.
- * Note: The tables runnable_avg_yN_inv and runnable_avg_yN_sum are
- * dependent on this value.
+ * Note: everything in sched average calculation, including
+ * __decay_inv_multiply_N, __accumulated_sum_N, __accumulated_sum_N32,
+ * SCHED_AVG_MAX, and SCHED_AVG_MAX_N, is dependent on and only on
+ * (1) exponential decay, (2) a period of 1024*1024ns (~1ms), and (3)
+ * a half-life of 32 periods.
  */
-#define LOAD_AVG_PERIOD 32
-#define LOAD_AVG_MAX 47742 /* maximum possible load avg */
-#define LOAD_AVG_MAX_N 345 /* number of full periods to produce LOAD_AVG_MAX */
+#define SCHED_AVG_HALFLIFE 32	/* number of periods as a half-life */
+#define SCHED_AVG_MAX 47742	/* maximum possible sched avg */
+#define SCHED_AVG_MAX_N 345	/* number of full periods to produce SCHED_AVG_MAX */
 
 /* Give new sched_entity start runnable values to heavy its load in infant time */
 void init_entity_runnable_average(struct sched_entity *se)

@@ -681,7 +683,7 @@ void init_entity_runnable_average(struct sched_entity *se)
 	 */
 	sa->period_contrib = 1023;
 	sa->load_avg = scale_load_down(se->load.weight);
-	sa->load_sum = sa->load_avg * LOAD_AVG_MAX;
+	sa->load_sum = sa->load_avg * SCHED_AVG_MAX;
 	/*
 	 * At this point, util_avg won't be used in select_task_rq_fair anyway
 	 */

@@ -731,7 +733,7 @@ void post_init_entity_util_avg(struct sched_entity *se)
 		} else {
 			sa->util_avg = cap;
 		}
-		sa->util_sum = sa->util_avg * LOAD_AVG_MAX;
+		sa->util_sum = sa->util_avg * SCHED_AVG_MAX;
 	}
 }
 

@@ -1834,7 +1836,7 @@ static u64 numa_get_avg_runtime(struct task_struct *p, u64 *period)
 		*period = now - p->last_task_numa_placement;
 	} else {
 		delta = p->se.avg.load_sum / p->se.load.weight;
-		*period = LOAD_AVG_MAX;
+		*period = SCHED_AVG_MAX;
 	}
 
 	p->last_sum_exec_runtime = runtime;

@@ -2583,7 +2585,7 @@ static inline void update_cfs_shares(struct cfs_rq *cfs_rq)
 
 #ifdef CONFIG_SMP
 /* Precomputed fixed inverse multiplies for multiplication by y^n */
-static const u32 runnable_avg_yN_inv[] = {
+static const u32 __decay_inv_multiply_N[] = {
 	0xffffffff, 0xfa83b2da, 0xf5257d14, 0xefe4b99a, 0xeac0c6e6, 0xe5b906e6,
 	0xe0ccdeeb, 0xdbfbb796, 0xd744fcc9, 0xd2a81d91, 0xce248c14, 0xc9b9bd85,
 	0xc5672a10, 0xc12c4cc9, 0xbd08a39e, 0xb8fbaf46, 0xb504f333, 0xb123f581,

@@ -2596,7 +2598,7 @@ static const u32 runnable_avg_yN_inv[] = {
  * Precomputed \Sum y^k { 1<=k<=n }.  These are floor(true_value) to prevent
  * over-estimates when re-combining.
  */
-static const u32 runnable_avg_yN_sum[] = {
+static const u32 __accumulated_sum_N[] = {
 	    0, 1002, 1982, 2941, 3880, 4798, 5697, 6576, 7437, 8279, 9103,
 	 9909,10698,11470,12226,12966,13690,14398,15091,15769,16433,17082,
 	17718,18340,18949,19545,20128,20698,21256,21802,22336,22859,23371,

@@ -2612,16 +2614,18 @@ static const u32 __accumulated_sum_N32[] = {
 };
 
 /*
- * Approximate:
- *   val * y^n,    where y^32 ~= 0.5 (~1 scheduling period)
+ * val * y^n, where y^m ~= 0.5
+ *
+ * n is the number of periods past; a period is ~1ms
+ * m is called half-life in exponential decay; here it is SCHED_AVG_HALFLIFE=32.
  */
-static __always_inline u64 decay_load(u64 val, u64 n)
+static __always_inline u64 __decay_sum(u64 val, u64 n)
 {
 	unsigned int local_n;
 
 	if (!n)
 		return val;
-	else if (unlikely(n > LOAD_AVG_PERIOD * 63))
+	else if (unlikely(n > SCHED_AVG_HALFLIFE * 63))
 		return 0;
 
 	/* after bounds checking we can collapse to 32-bit */

@@ -2634,36 +2638,36 @@ static __always_inline u64 decay_load(u64 val, u64 n)
 	 *
 	 * To achieve constant time decay_load.
 	 */
-	if (unlikely(local_n >= LOAD_AVG_PERIOD)) {
-		val >>= local_n / LOAD_AVG_PERIOD;
-		local_n %= LOAD_AVG_PERIOD;
+	if (unlikely(local_n >= SCHED_AVG_HALFLIFE)) {
+		val >>= local_n / SCHED_AVG_HALFLIFE;
+		local_n %= SCHED_AVG_HALFLIFE;
 	}
 
-	val = mul_u64_u32_shr(val, runnable_avg_yN_inv[local_n], 32);
+	val = mul_u64_u32_shr(val, __decay_inv_multiply_N[local_n], 32);
 	return val;
 }
 
 /*
- * For updates fully spanning n periods, the contribution to runnable
- * average will be: \Sum 1024*y^n
+ * For updates fully spanning n periods, the accumulated contribution
+ * will be: \Sum 1024*y^n.
  *
- * We can compute this reasonably efficiently by combining:
- *   y^PERIOD = 1/2 with precomputed \Sum 1024*y^n {for  n <PERIOD}
+ * We can compute this efficiently by combining:
+ * y^32 = 1/2 with precomputed \Sum 1024*y^n   (where n < 32)
  */
-static u32 __compute_runnable_contrib(u64 n)
+static u32 __accumulate_sum(u64 n)
 {
 	u32 contrib = 0;
 
-	if (likely(n <= LOAD_AVG_PERIOD))
-		return runnable_avg_yN_sum[n];
-	else if (unlikely(n >= LOAD_AVG_MAX_N))
-		return LOAD_AVG_MAX;
+	if (likely(n <= SCHED_AVG_HALFLIFE))
+		return __accumulated_sum_N[n];
+	else if (unlikely(n >= SCHED_AVG_MAX_N))
+		return SCHED_AVG_MAX;
 
-	/* Since n < LOAD_AVG_MAX_N, n/LOAD_AVG_PERIOD < 11 */
-	contrib = __accumulated_sum_N32[n/LOAD_AVG_PERIOD];
-	n %= LOAD_AVG_PERIOD;
-	contrib = decay_load(contrib, n);
-	return contrib + runnable_avg_yN_sum[n];
+	/* Since n < SCHED_AVG_MAX_N, n/SCHED_AVG_HALFLIFE < 11 */
+	contrib = __accumulated_sum_N32[n/SCHED_AVG_HALFLIFE];
+	n %= SCHED_AVG_HALFLIFE;
+	contrib = __decay_sum(contrib, n);
+	return contrib + __accumulated_sum_N[n];
 }
 
 #if (SCHED_LOAD_SHIFT - SCHED_LOAD_RESOLUTION) != 10 || SCHED_CAPACITY_SHIFT != 10

@@ -2673,35 +2677,35 @@ static u32 __compute_runnable_contrib(u64 n)
 #define cap_scale(v, s) ((v)*(s) >> SCHED_CAPACITY_SHIFT)
 
 /*
- * We can represent the historical contribution to runnable average as the
- * coefficients of a geometric series.  To do this we sub-divide our runnable
- * history into segments of approximately 1ms (1024us); label the segment that
- * occurred N-ms ago p_N, with p_0 corresponding to the current period, e.g.
+ * We can represent the historical contribution to sched average as the
+ * coefficients of a geometric series.  To do this we divide the history
+ * into segments of approximately 1ms (1024*1024ns); label the segment that
+ * occurred N-1024us ago p_N, with p_0 corresponding to the current period, e.g.
  *
  * [<- 1024us ->|<- 1024us ->|<- 1024us ->| ...
  *      p0            p1           p2
  *     (now)       (~1ms ago)  (~2ms ago)
  *
- * Let u_i denote the fraction of p_i that the entity was runnable.
+ * Let u_i denote the fraction of p_i whose state (runnable/running) we count.
  *
  * We then designate the fractions u_i as our co-efficients, yielding the
- * following representation of historical load:
+ * following representation of a sched metric:
  *   u_0 + u_1*y + u_2*y^2 + u_3*y^3 + ...
  *
- * We choose y based on the with of a reasonably scheduling period, fixing:
- *   y^32 = 0.5
+ * We choose y based on a half-life of 32 periods (which is ~32ms):
+ *   y^32 = 0.5 => y = (0.5)^(1/32)
  *
- * This means that the contribution to load ~32ms ago (u_32) will be weighted
- * approximately half as much as the contribution to load within the last ms
- * (u_0).
+ * where 32 is the number of periods that a past period's contribution is
+ * halved. This means that the impact of a period every ~32ms ago will be
+ * as much as 50% of the previous value.
  *
  * When a period "rolls over" and we have new u_0`, multiplying the previous
  * sum again by y is sufficient to update:
- *   load_avg = u_0` + y*(u_0 + u_1*y + u_2*y^2 + ... )
- *            = u_0 + u_1*y + u_2*y^2 + ... [re-labeling u_i --> u_{i+1}]
+ *   avg = u_0` + y*(u_0 + u_1*y + u_2*y^2 + ... )
+ *       = u_0 + u_1*y + u_2*y^2 + ... [re-labeling u_i --> u_{i+1}]
  */
 static __always_inline int
-__update_load_avg(u64 now, int cpu, struct sched_avg *sa,
+__update_sched_avg(u64 now, int cpu, struct sched_avg *sa,
 		  unsigned long weight, int running, struct cfs_rq *cfs_rq)
 {
 	u64 delta, scaled_delta, periods;

@@ -2762,15 +2766,15 @@ __update_load_avg(u64 now, int cpu, struct sched_avg *sa,
 		periods = delta / 1024;
 		delta %= 1024;
 
-		sa->load_sum = decay_load(sa->load_sum, periods + 1);
+		sa->load_sum = __decay_sum(sa->load_sum, periods + 1);
 		if (cfs_rq) {
 			cfs_rq->runnable_load_sum =
-				decay_load(cfs_rq->runnable_load_sum, periods + 1);
+				__decay_sum(cfs_rq->runnable_load_sum, periods + 1);
 		}
-		sa->util_sum = decay_load((u64)(sa->util_sum), periods + 1);
+		sa->util_sum = __decay_sum((u64)(sa->util_sum), periods + 1);
 
 		/* Efficiently calculate \sum (1..n_period) 1024*y^i */
-		contrib = __compute_runnable_contrib(periods);
+		contrib = __accumulate_sum(periods);
 		contrib = cap_scale(contrib, scale_freq);
 		if (weight) {
 			sa->load_sum += weight * contrib;

@@ -2794,12 +2798,12 @@ __update_load_avg(u64 now, int cpu, struct sched_avg *sa,
 	sa->period_contrib += delta;
 
 	if (decayed) {
-		sa->load_avg = div_u64(sa->load_sum, LOAD_AVG_MAX);
+		sa->load_avg = div_u64(sa->load_sum, SCHED_AVG_MAX);
 		if (cfs_rq) {
 			cfs_rq->runnable_load_avg =
-				div_u64(cfs_rq->runnable_load_sum, LOAD_AVG_MAX);
+				div_u64(cfs_rq->runnable_load_sum, SCHED_AVG_MAX);
 		}
-		sa->util_avg = sa->util_sum / LOAD_AVG_MAX;
+		sa->util_avg = sa->util_sum / SCHED_AVG_MAX;
 	}
 
 	return decayed;

@@ -2867,8 +2871,8 @@ void set_task_rq_fair(struct sched_entity *se,
 		p_last_update_time = prev->avg.last_update_time;
 		n_last_update_time = next->avg.last_update_time;
 #endif
-		__update_load_avg(p_last_update_time, cpu_of(rq_of(prev)),
-				  &se->avg, 0, 0, NULL);
+		__update_sched_avg(p_last_update_time, cpu_of(rq_of(prev)),
+				   &se->avg, 0, 0, NULL);
 		se->avg.last_update_time = n_last_update_time;
 	}
 }

@@ -2909,7 +2913,7 @@ static inline void cfs_rq_util_change(struct cfs_rq *cfs_rq)
 
 /* Group cfs_rq's load_avg is used for task_h_load and update_cfs_share */
 static inline int
-update_cfs_rq_load_avg(u64 now, struct cfs_rq *cfs_rq, bool update_freq)
+update_cfs_rq_sched_avg(u64 now, struct cfs_rq *cfs_rq, bool update_freq)
 {
 	struct sched_avg *sa = &cfs_rq->avg;
 	int decayed, removed_load = 0, removed_util = 0;

@@ -2917,18 +2921,18 @@ update_cfs_rq_load_avg(u64 now, struct cfs_rq *cfs_rq, bool update_freq)
 	if (atomic_long_read(&cfs_rq->removed_load_avg)) {
 		s64 r = atomic_long_xchg(&cfs_rq->removed_load_avg, 0);
 		sa->load_avg = max_t(long, sa->load_avg - r, 0);
-		sa->load_sum = max_t(s64, sa->load_sum - r * LOAD_AVG_MAX, 0);
+		sa->load_sum = max_t(s64, sa->load_sum - r * SCHED_AVG_MAX, 0);
 		removed_load = 1;
 	}
 
 	if (atomic_long_read(&cfs_rq->removed_util_avg)) {
 		long r = atomic_long_xchg(&cfs_rq->removed_util_avg, 0);
 		sa->util_avg = max_t(long, sa->util_avg - r, 0);
-		sa->util_sum = max_t(s32, sa->util_sum - r * LOAD_AVG_MAX, 0);
+		sa->util_sum = max_t(s32, sa->util_sum - r * SCHED_AVG_MAX, 0);
 		removed_util = 1;
 	}
 
-	decayed = __update_load_avg(now, cpu_of(rq_of(cfs_rq)), sa,
+	decayed = __update_sched_avg(now, cpu_of(rq_of(cfs_rq)), sa,
 		scale_load_down(cfs_rq->load.weight), cfs_rq->curr != NULL, cfs_rq);
 
 #ifndef CONFIG_64BIT

@@ -2943,7 +2947,7 @@ update_cfs_rq_load_avg(u64 now, struct cfs_rq *cfs_rq, bool update_freq)
 }
 
 /* Update task and its cfs_rq load average */
-static inline void update_load_avg(struct sched_entity *se, int update_tg)
+static inline void update_sched_avg(struct sched_entity *se, int update_tg)
 {
 	struct cfs_rq *cfs_rq = cfs_rq_of(se);
 	u64 now = cfs_rq_clock_task(cfs_rq);

@@ -2954,15 +2958,15 @@ static inline void update_load_avg(struct sched_entity *se, int update_tg)
 	 * Track task load average for carrying it to new CPU after migrated, and
 	 * track group sched_entity load average for task_h_load calc in migration
 	 */
-	__update_load_avg(now, cpu, &se->avg,
-			  se->on_rq * scale_load_down(se->load.weight),
-			  cfs_rq->curr == se, NULL);
+	__update_sched_avg(now, cpu, &se->avg,
+			   se->on_rq * scale_load_down(se->load.weight),
+			   cfs_rq->curr == se, NULL);
 
-	if (update_cfs_rq_load_avg(now, cfs_rq, true) && update_tg)
+	if (update_cfs_rq_sched_avg(now, cfs_rq, true) && update_tg)
 		update_tg_load_avg(cfs_rq, 0);
 }
 
-static void attach_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
+static void attach_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
 {
 	if (!sched_feat(ATTACH_AGE_LOAD))
 		goto skip_aging;

@@ -2972,8 +2976,8 @@ static void attach_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *s
 	 * have aged the average right before clearing @last_update_time.
 	 */
 	if (se->avg.last_update_time) {
-		__update_load_avg(cfs_rq->avg.last_update_time, cpu_of(rq_of(cfs_rq)),
-				  &se->avg, 0, 0, NULL);
+		__update_sched_avg(cfs_rq->avg.last_update_time, cpu_of(rq_of(cfs_rq)),
+				   &se->avg, 0, 0, NULL);
 
 		/*
 		 * XXX: we could have just aged the entire load away if we've been

@@ -2991,11 +2995,11 @@ skip_aging:
 	cfs_rq_util_change(cfs_rq);
 }
 
-static void detach_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
+static void detach_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
 {
-	__update_load_avg(cfs_rq->avg.last_update_time, cpu_of(rq_of(cfs_rq)),
-			  &se->avg, se->on_rq * scale_load_down(se->load.weight),
-			  cfs_rq->curr == se, NULL);
+	__update_sched_avg(cfs_rq->avg.last_update_time, cpu_of(rq_of(cfs_rq)),
+			   &se->avg, se->on_rq * scale_load_down(se->load.weight),
+			   cfs_rq->curr == se, NULL);
 
 	cfs_rq->avg.load_avg = max_t(long, cfs_rq->avg.load_avg - se->avg.load_avg, 0);
 	cfs_rq->avg.load_sum = max_t(s64,  cfs_rq->avg.load_sum - se->avg.load_sum, 0);

@@ -3007,7 +3011,7 @@ static void detach_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *s
 
 /* Add the load generated by se into cfs_rq's load average */
 static inline void
-enqueue_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
+enqueue_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
 {
 	struct sched_avg *sa = &se->avg;
 	u64 now = cfs_rq_clock_task(cfs_rq);

@@ -3015,18 +3019,18 @@ enqueue_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
 
 	migrated = !sa->last_update_time;
 	if (!migrated) {
-		__update_load_avg(now, cpu_of(rq_of(cfs_rq)), sa,
-			se->on_rq * scale_load_down(se->load.weight),
-			cfs_rq->curr == se, NULL);
+		__update_sched_avg(now, cpu_of(rq_of(cfs_rq)), sa,
+				   se->on_rq * scale_load_down(se->load.weight),
+				   cfs_rq->curr == se, NULL);
 	}
 
-	decayed = update_cfs_rq_load_avg(now, cfs_rq, !migrated);
+	decayed = update_cfs_rq_sched_avg(now, cfs_rq, !migrated);
 
 	cfs_rq->runnable_load_avg += sa->load_avg;
 	cfs_rq->runnable_load_sum += sa->load_sum;
 
 	if (migrated)
-		attach_entity_load_avg(cfs_rq, se);
+		attach_entity_sched_avg(cfs_rq, se);
 
 	if (decayed || migrated)
 		update_tg_load_avg(cfs_rq, 0);

@@ -3034,9 +3038,9 @@ enqueue_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
 
 /* Remove the runnable load generated by se from cfs_rq's runnable load average */
 static inline void
-dequeue_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
+dequeue_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
 {
-	update_load_avg(se, 1);
+	update_sched_avg(se, 1);
 
 	cfs_rq->runnable_load_avg =
 		max_t(long, cfs_rq->runnable_load_avg - se->avg.load_avg, 0);

@@ -3069,7 +3073,7 @@ static inline u64 cfs_rq_last_update_time(struct cfs_rq *cfs_rq)
  * Task first catches up with cfs_rq, and then subtract
  * itself from the cfs_rq (task must be off the queue now).
  */
-void remove_entity_load_avg(struct sched_entity *se)
+void remove_entity_sched_avg(struct sched_entity *se)
 {
 	struct cfs_rq *cfs_rq = cfs_rq_of(se);
 	u64 last_update_time;

@@ -3083,7 +3087,8 @@ void remove_entity_load_avg(struct sched_entity *se)
 
 	last_update_time = cfs_rq_last_update_time(cfs_rq);
 
-	__update_load_avg(last_update_time, cpu_of(rq_of(cfs_rq)), &se->avg, 0, 0, NULL);
+	__update_sched_avg(last_update_time, cpu_of(rq_of(cfs_rq)),
+			   &se->avg, 0, 0, NULL);
 	atomic_long_add(se->avg.load_avg, &cfs_rq->removed_load_avg);
 	atomic_long_add(se->avg.util_avg, &cfs_rq->removed_util_avg);
 }

@@ -3102,17 +3107,17 @@ static int idle_balance(struct rq *this_rq);
 
 #else /* CONFIG_SMP */
 
-static inline void update_load_avg(struct sched_entity *se, int update_tg) {}
+static inline void update_sched_avg(struct sched_entity *se, int update_tg) {}
 static inline void
-enqueue_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se) {}
+enqueue_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se) {}
 static inline void
-dequeue_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se) {}
-static inline void remove_entity_load_avg(struct sched_entity *se) {}
+dequeue_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se) {}
+static inline void remove_entity_sched_avg(struct sched_entity *se) {}
 
 static inline void
-attach_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se) {}
+attach_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se) {}
 static inline void
-detach_entity_load_avg(struct cfs_rq *cfs_rq, struct sched_entity *se) {}
+detach_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se) {}
 
 static inline int idle_balance(struct rq *rq)
 {

@@ -3272,7 +3277,7 @@ enqueue_entity(struct cfs_rq *cfs_rq, struct sched_entity *se, int flags)
 	if (renorm && !curr)
 		se->vruntime += cfs_rq->min_vruntime;
 
-	enqueue_entity_load_avg(cfs_rq, se);
+	enqueue_entity_sched_avg(cfs_rq, se);
 	account_entity_enqueue(cfs_rq, se);
 	update_cfs_shares(cfs_rq);
 

@@ -3351,7 +3356,7 @@ dequeue_entity(struct cfs_rq *cfs_rq, struct sched_entity *se, int flags)
 	 * Update run-time statistics of the 'current'.
 	 */
 	update_curr(cfs_rq);
-	dequeue_entity_load_avg(cfs_rq, se);
+	dequeue_entity_sched_avg(cfs_rq, se);
 
 	if (schedstat_enabled())
 		update_stats_dequeue(cfs_rq, se, flags);

@@ -3431,7 +3436,7 @@ set_next_entity(struct cfs_rq *cfs_rq, struct sched_entity *se)
 		if (schedstat_enabled())
 			update_stats_wait_end(cfs_rq, se);
 		__dequeue_entity(cfs_rq, se);
-		update_load_avg(se, 1);
+		update_sched_avg(se, 1);
 	}
 
 	update_stats_curr_start(cfs_rq, se);

@@ -3535,7 +3540,7 @@ static void put_prev_entity(struct cfs_rq *cfs_rq, struct sched_entity *prev)
 		/* Put 'current' back into the tree. */
 		__enqueue_entity(cfs_rq, prev);
 		/* in !on_rq case, update occurred at dequeue */
-		update_load_avg(prev, 0);
+		update_sched_avg(prev, 0);
 	}
 	cfs_rq->curr = NULL;
 }

@@ -3551,7 +3556,7 @@ entity_tick(struct cfs_rq *cfs_rq, struct sched_entity *curr, int queued)
 	/*
 	 * Ensure that runnable average is periodically updated.
 	 */
-	update_load_avg(curr, 1);
+	update_sched_avg(curr, 1);
 	update_cfs_shares(cfs_rq);
 
 #ifdef CONFIG_SCHED_HRTICK

@@ -4424,7 +4429,7 @@ enqueue_task_fair(struct rq *rq, struct task_struct *p, int flags)
 		if (cfs_rq_throttled(cfs_rq))
 			break;
 
-		update_load_avg(se, 1);
+		update_sched_avg(se, 1);
 		update_cfs_shares(cfs_rq);
 	}
 

@@ -4484,7 +4489,7 @@ static void dequeue_task_fair(struct rq *rq, struct task_struct *p, int flags)
 		if (cfs_rq_throttled(cfs_rq))
 			break;
 
-		update_load_avg(se, 1);
+		update_sched_avg(se, 1);
 		update_cfs_shares(cfs_rq);
 	}
 

@@ -5370,7 +5375,7 @@ static void migrate_task_rq_fair(struct task_struct *p)
 	 * will result in the wakee task is less decayed, but giving the wakee more
 	 * load sounds not bad.
 	 */
-	remove_entity_load_avg(&p->se);
+	remove_entity_sched_avg(&p->se);
 
 	/* Tell new CPU we are migrated */
 	p->se.avg.last_update_time = 0;

@@ -5381,7 +5386,7 @@ static void migrate_task_rq_fair(struct task_struct *p)
 
 static void task_dead_fair(struct task_struct *p)
 {
-	remove_entity_load_avg(&p->se);
+	remove_entity_sched_avg(&p->se);
 }
 #endif /* CONFIG_SMP */
 

@@ -6262,7 +6267,7 @@ static void update_blocked_averages(int cpu)
 		if (throttled_hierarchy(cfs_rq))
 			continue;
 
-		if (update_cfs_rq_load_avg(cfs_rq_clock_task(cfs_rq), cfs_rq, true))
+		if (update_cfs_rq_sched_avg(cfs_rq_clock_task(cfs_rq), cfs_rq, true))
 			update_tg_load_avg(cfs_rq, 0);
 	}
 	raw_spin_unlock_irqrestore(&rq->lock, flags);

@@ -6323,7 +6328,7 @@ static inline void update_blocked_averages(int cpu)
 
 	raw_spin_lock_irqsave(&rq->lock, flags);
 	update_rq_clock(rq);
-	update_cfs_rq_load_avg(cfs_rq_clock_task(cfs_rq), cfs_rq, true);
+	update_cfs_rq_sched_avg(cfs_rq_clock_task(cfs_rq), cfs_rq, true);
 	raw_spin_unlock_irqrestore(&rq->lock, flags);
 }
 

@@ -8357,7 +8362,7 @@ static void detach_task_cfs_rq(struct task_struct *p)
 	}
 
 	/* Catch up with the cfs_rq and remove our load when we leave */
-	detach_entity_load_avg(cfs_rq, se);
+	detach_entity_sched_avg(cfs_rq, se);
 }
 
 static void attach_task_cfs_rq(struct task_struct *p)

@@ -8374,7 +8379,7 @@ static void attach_task_cfs_rq(struct task_struct *p)
 #endif
 
 	/* Synchronize task with its cfs_rq */
-	attach_entity_load_avg(cfs_rq, se);
+	attach_entity_sched_avg(cfs_rq, se);
 
 	if (!vruntime_normalized(p))
 		se->vruntime += cfs_rq->min_vruntime;

@@ -8513,7 +8518,7 @@ void unregister_fair_sched_group(struct task_group *tg)
 
 	for_each_possible_cpu(cpu) {
 		if (tg->se[cpu])
-			remove_entity_load_avg(tg->se[cpu]);
+			remove_entity_sched_avg(tg->se[cpu]);
 
 		/*
 		 * Only empty task groups can be destroyed; so we can speculatively

index 2b83b4c..34ccaa3 100644
@@ -2619,18 +2619,13 @@ static const u32 __accumulated_sum_N32[] = {
  * n is the number of periods past; a period is ~1ms
  * m is called half-life in exponential decay; here it is SCHED_AVG_HALFLIFE=32.
  */
-static __always_inline u64 __decay_sum(u64 val, u64 n)
+static __always_inline u64 __decay_sum(u64 val, u32 n)
 {
-	unsigned int local_n;
-
 	if (!n)
 		return val;
 	else if (unlikely(n > SCHED_AVG_HALFLIFE * 63))
 		return 0;
 
-	/* after bounds checking we can collapse to 32-bit */
-	local_n = n;
-
 	/*
 	 * As y^PERIOD = 1/2, we can combine
 	 *    y^n = 1/2^(n/PERIOD) * y^(n%PERIOD)

@@ -2638,12 +2633,12 @@ static __always_inline u64 __decay_sum(u64 val, u64 n)
 	 *
 	 * To achieve constant time decay_load.
 	 */
-	if (unlikely(local_n >= SCHED_AVG_HALFLIFE)) {
-		val >>= local_n / SCHED_AVG_HALFLIFE;
-		local_n %= SCHED_AVG_HALFLIFE;
+	if (unlikely(n >= SCHED_AVG_HALFLIFE)) {
+		val >>= n / SCHED_AVG_HALFLIFE;
+		n %= SCHED_AVG_HALFLIFE;
 	}
 
-	val = mul_u64_u32_shr(val, __decay_inv_multiply_N[local_n], 32);
+	val = mul_u64_u32_shr(val, __decay_inv_multiply_N[n], 32);
 	return val;
 }
 

@@ -2654,7 +2649,7 @@ static __always_inline u64 __decay_sum(u64 val, u64 n)
  * We can compute this efficiently by combining:
  * y^32 = 1/2 with precomputed \Sum 1024*y^n   (where n < 32)
  */
-static u32 __accumulate_sum(u64 n)
+static u32 __accumulate_sum(u32 n)
 {
 	u32 contrib = 0;
 

@@ -2708,8 +2703,8 @@ static __always_inline int
 __update_sched_avg(u64 now, int cpu, struct sched_avg *sa,
 		  unsigned long weight, int running, struct cfs_rq *cfs_rq)
 {
-	u64 delta, scaled_delta, periods;
-	u32 contrib;
+	u64 delta, scaled_delta;
+	u32 contrib, periods;
 	unsigned int delta_w, scaled_delta_w, decayed = 0;
 	unsigned long scale_freq, scale_cpu;
 

@@ -2762,7 +2757,11 @@ __update_sched_avg(u64 now, int cpu, struct sched_avg *sa,
 
 		delta -= delta_w;
 
-		/* Figure out how many additional periods this update spans */
+		/*
+		 * Figure out how many additional periods this update spans.
+		 * A period is 1024*1024ns or ~1ms, so a 32bit integer can hold
+		 * approximately a maximum of 49 (=2^32/1000/3600/24) days.
+		 */
 		periods = delta / 1024;
 		delta %= 1024;
 

index 56b7d4b..42515b6 100644
@@ -2527,7 +2527,7 @@ static __always_inline u64 decay_load(u64 val, u64 n)
 
 	if (!n)
 		return val;
-	else if (unlikely(n > LOAD_AVG_PERIOD * 63))
+	else if (unlikely(n > LOAD_AVG_MAX_N))
 		return 0;
 
 	/* after bounds checking we can collapse to 32-bit */

index 34ccaa3..a060ef2 100644
@@ -2649,7 +2649,7 @@ static __always_inline u64 __decay_sum(u64 val, u32 n)
  * We can compute this efficiently by combining:
  * y^32 = 1/2 with precomputed \Sum 1024*y^n   (where n < 32)
  */
-static u32 __accumulate_sum(u32 n)
+static __always_inline u32 __accumulate_sum(u32 n)
 {
 	u32 contrib = 0;
 

index a060ef2..495e5f0 100644
@@ -668,7 +668,7 @@ static unsigned long task_h_load(struct task_struct *p);
  */
 #define SCHED_AVG_HALFLIFE 32	/* number of periods as a half-life */
 #define SCHED_AVG_MAX 47742	/* maximum possible sched avg */
-#define SCHED_AVG_MAX_N 345	/* number of full periods to produce SCHED_AVG_MAX */
+#define SCHED_AVG_MAX_N 347	/* number of full periods to produce SCHED_AVG_MAX */
 
 /* Give new sched_entity start runnable values to heavy its load in infant time */
 void init_entity_runnable_average(struct sched_entity *se)

@@ -2606,7 +2606,7 @@ static const u32 __accumulated_sum_N[] = {
 
 /*
  * Precomputed \Sum y^k { 1<=k<=n, where n%32=0). Values are rolled down to
- * lower integers.
+ * lower integers. Since n < SCHED_AVG_MAX_N, n/SCHED_AVG_HALFLIFE < 11
  */
 static const u32 __accumulated_sum_N32[] = {
 	    0, 23371, 35056, 40899, 43820, 45281,

@@ -2616,8 +2616,11 @@ static const u32 __accumulated_sum_N32[] = {
 /*
  * val * y^n, where y^m ~= 0.5
  *
- * n is the number of periods past; a period is ~1ms
+ * n is the number of periods past. A period is ~1ms, so a 32bit
+ * integer can hold approximately a maximum of 49 (=2^32/1000/3600/24) days.
+ *
  * m is called half-life in exponential decay; here it is SCHED_AVG_HALFLIFE=32.
+ *
  */
 static __always_inline u64 __decay_sum(u64 val, u32 n)
 {

@@ -2649,20 +2652,30 @@ static __always_inline u64 __decay_sum(u64 val, u32 n)
  * We can compute this efficiently by combining:
  * y^32 = 1/2 with precomputed \Sum 1024*y^n   (where n < 32)
  */
-static __always_inline u32 __accumulate_sum(u32 n)
+static __always_inline u32
+__accumulate_sum(u32 periods, u32 period_contrib, u32 remainder)
 {
-	u32 contrib = 0;
+	u32 contrib;
+
+	if (!periods)
+		return remainder - period_contrib;
 
-	if (likely(n <= SCHED_AVG_HALFLIFE))
-		return __accumulated_sum_N[n];
-	else if (unlikely(n >= SCHED_AVG_MAX_N))
+	if (unlikely(periods >= SCHED_AVG_MAX_N))
 		return SCHED_AVG_MAX;
 
-	/* Since n < SCHED_AVG_MAX_N, n/SCHED_AVG_HALFLIFE < 11 */
-	contrib = __accumulated_sum_N32[n/SCHED_AVG_HALFLIFE];
-	n %= SCHED_AVG_HALFLIFE;
-	contrib = __decay_sum(contrib, n);
-	return contrib + __accumulated_sum_N[n];
+	remainder += __decay_sum((u64)(1024 - period_contrib), periods);
+
+	periods -= 1;
+	if (likely(periods <= SCHED_AVG_HALFLIFE))
+		contrib = __accumulated_sum_N[periods];
+	else {
+		contrib = __accumulated_sum_N32[periods/SCHED_AVG_HALFLIFE];
+		periods %= SCHED_AVG_HALFLIFE;
+		contrib = __decay_sum(contrib, periods);
+		contrib += __accumulated_sum_N[periods];
+	}
+
+	return contrib + remainder;
 }
 
 #if (SCHED_LOAD_SHIFT - SCHED_LOAD_RESOLUTION) != 10 || SCHED_CAPACITY_SHIFT != 10

@@ -2671,6 +2684,55 @@ static __always_inline u32 __accumulate_sum(u32 n)
 
 #define cap_scale(v, s) ((v)*(s) >> SCHED_CAPACITY_SHIFT)
 
+static __always_inline u32 accumulate_sum(u64 delta, struct sched_avg *sa,
+	struct cfs_rq *cfs_rq, int cpu, unsigned long weight, int running)
+{
+	u32 contrib, periods;
+	unsigned long scale_freq, scale_cpu;
+
+	scale_freq = arch_scale_freq_capacity(NULL, cpu);
+	scale_cpu = arch_scale_cpu_capacity(NULL, cpu);
+
+	delta += sa->period_contrib;
+	periods = delta >> 10; /* A period is 1024us (~1ms) */
+
+	/*
+	 * Accumulating *_sum has two steps.
+	 *
+	 * Step 1: decay old *_sum if we crossed period boundaries.
+	 */
+	if (periods) {
+		sa->load_sum = __decay_sum(sa->load_sum, periods);
+		if (cfs_rq) {
+			cfs_rq->runnable_load_sum =
+				__decay_sum(cfs_rq->runnable_load_sum, periods);
+		}
+		sa->util_sum = __decay_sum((u64)(sa->util_sum), periods);
+	}
+
+	/*
+	 * Step 2: accumulate new *_sum since last_update_time. This at most has
+	 * three parts (at least one part): (1) remainder of incomplete last
+	 * period, (2) full periods since (1), and (3) incomplete current period.
+	 *
+	 * Fortunately, we can (and should) do all these three at once.
+	 */
+	delta %= 1024;
+	contrib = __accumulate_sum(periods, sa->period_contrib, delta);
+	sa->period_contrib = delta;
+
+	contrib = cap_scale(contrib, scale_freq);
+	if (weight) {
+		sa->load_sum += weight * contrib;
+		if (cfs_rq)
+			cfs_rq->runnable_load_sum += weight * contrib;
+	}
+	if (running)
+		sa->util_sum += contrib * scale_cpu;
+
+	return periods;
+}
+
 /*
  * We can represent the historical contribution to sched average as the
  * coefficients of a geometric series.  To do this we divide the history

@@ -2701,12 +2763,9 @@ static __always_inline u32 __accumulate_sum(u32 n)
  */
 static __always_inline int
 __update_sched_avg(u64 now, int cpu, struct sched_avg *sa,
-		  unsigned long weight, int running, struct cfs_rq *cfs_rq)
+		   unsigned long weight, int running, struct cfs_rq *cfs_rq)
 {
-	u64 delta, scaled_delta;
-	u32 contrib, periods;
-	unsigned int delta_w, scaled_delta_w, decayed = 0;
-	unsigned long scale_freq, scale_cpu;
+	u64 delta;
 
 	delta = now - sa->last_update_time;
 	/*

@@ -2727,85 +2786,27 @@ __update_sched_avg(u64 now, int cpu, struct sched_avg *sa,
 		return 0;
 	sa->last_update_time = now;
 
-	scale_freq = arch_scale_freq_capacity(NULL, cpu);
-	scale_cpu = arch_scale_cpu_capacity(NULL, cpu);
-
-	/* delta_w is the amount already accumulated against our next period */
-	delta_w = sa->period_contrib;
-	if (delta + delta_w >= 1024) {
-		decayed = 1;
-
-		/* how much left for next period will start over, we don't know yet */
-		sa->period_contrib = 0;
-
-		/*
-		 * Now that we know we're crossing a period boundary, figure
-		 * out how much from delta we need to complete the current
-		 * period and accrue it.
-		 */
-		delta_w = 1024 - delta_w;
-		scaled_delta_w = cap_scale(delta_w, scale_freq);
-		if (weight) {
-			sa->load_sum += weight * scaled_delta_w;
-			if (cfs_rq) {
-				cfs_rq->runnable_load_sum +=
-						weight * scaled_delta_w;
-			}
-		}
-		if (running)
-			sa->util_sum += scaled_delta_w * scale_cpu;
-
-		delta -= delta_w;
-
-		/*
-		 * Figure out how many additional periods this update spans.
-		 * A period is 1024*1024ns or ~1ms, so a 32bit integer can hold
-		 * approximately a maximum of 49 (=2^32/1000/3600/24) days.
-		 */
-		periods = delta / 1024;
-		delta %= 1024;
-
-		sa->load_sum = __decay_sum(sa->load_sum, periods + 1);
-		if (cfs_rq) {
-			cfs_rq->runnable_load_sum =
-				__decay_sum(cfs_rq->runnable_load_sum, periods + 1);
-		}
-		sa->util_sum = __decay_sum((u64)(sa->util_sum), periods + 1);
-
-		/* Efficiently calculate \sum (1..n_period) 1024*y^i */
-		contrib = __accumulate_sum(periods);
-		contrib = cap_scale(contrib, scale_freq);
-		if (weight) {
-			sa->load_sum += weight * contrib;
-			if (cfs_rq)
-				cfs_rq->runnable_load_sum += weight * contrib;
-		}
-		if (running)
-			sa->util_sum += contrib * scale_cpu;
-	}
-
-	/* Remainder of delta accrued against u_0` */
-	scaled_delta = cap_scale(delta, scale_freq);
-	if (weight) {
-		sa->load_sum += weight * scaled_delta;
-		if (cfs_rq)
-			cfs_rq->runnable_load_sum += weight * scaled_delta;
-	}
-	if (running)
-		sa->util_sum += scaled_delta * scale_cpu;
-
-	sa->period_contrib += delta;
+	/*
+	 * Now we know we crossed measurement unit boundaries. The *_avg
+	 * accrues by two steps:
+	 *
+	 * Step 1: accumulate *_sum since last_update_time. If we haven't
+	 * crossed period boundaries, finish.
+	 */
+	if (!accumulate_sum(delta, sa, cfs_rq, cpu, weight, running))
+		return 0;
 
-	if (decayed) {
-		sa->load_avg = div_u64(sa->load_sum, SCHED_AVG_MAX);
-		if (cfs_rq) {
-			cfs_rq->runnable_load_avg =
-				div_u64(cfs_rq->runnable_load_sum, SCHED_AVG_MAX);
-		}
-		sa->util_avg = sa->util_sum / SCHED_AVG_MAX;
+	/*
+	 * Step 2: update *_avg.
+	 */
+	sa->load_avg = div_u64(sa->load_sum, SCHED_AVG_MAX);
+	if (cfs_rq) {
+		cfs_rq->runnable_load_avg =
+			div_u64(cfs_rq->runnable_load_sum, SCHED_AVG_MAX);
 	}
+	sa->util_avg = sa->util_sum / SCHED_AVG_MAX;
 
-	return decayed;
+	return 1;
 }
 
 #ifdef CONFIG_FAIR_GROUP_SCHED

index ad9454d..33e7929 100644
@@ -937,9 +937,19 @@ enum cpu_idle_type {
 };
 
 /*
+ * Integer metrics need fixed point arithmetic, e.g., sched/fair
+ * has a few: load, load_avg, util_avg, freq, and capacity.
+ *
+ * We define a basic fixed point arithmetic range, and then formalize
+ * all these metrics based on that basic range.
+ */
+# define SCHED_FIXEDPOINT_SHIFT	10
+# define SCHED_FIXEDPOINT_SCALE	(1L << SCHED_FIXEDPOINT_SHIFT)
+
+/*
  * Increase resolution of cpu_capacity calculations
  */
-#define SCHED_CAPACITY_SHIFT	10
+#define SCHED_CAPACITY_SHIFT	SCHED_FIXEDPOINT_SHIFT
 #define SCHED_CAPACITY_SCALE	(1L << SCHED_CAPACITY_SHIFT)
 
 /*

@@ -1205,8 +1215,8 @@ struct load_weight {
  * 1) load_avg factors frequency scaling into the amount of time that a
  * sched_entity is runnable on a rq into its weight. For cfs_rq, it is the
  * aggregated such weights of all runnable and blocked sched_entities.
- * 2) util_avg factors frequency and cpu scaling into the amount of time
- * that a sched_entity is running on a CPU, in the range [0..SCHED_LOAD_SCALE].
+ * 2) util_avg factors frequency and cpu capacity scaling into the amount of time
+ * that a sched_entity is running on a CPU, in the range [0..SCHED_CAPACITY_SCALE].
  * For cfs_rq, it is the aggregated such times of all runnable and
  * blocked sched_entities.
  * The 64 bit load_sum can:

index 495e5f0..1a61137 100644
@@ -2678,10 +2678,6 @@ __accumulate_sum(u32 periods, u32 period_contrib, u32 remainder)
 	return contrib + remainder;
 }
 
-#if (SCHED_LOAD_SHIFT - SCHED_LOAD_RESOLUTION) != 10 || SCHED_CAPACITY_SHIFT != 10
-#error "load tracking assumes 2^10 as unit"
-#endif
-
 #define cap_scale(v, s) ((v)*(s) >> SCHED_CAPACITY_SHIFT)
 
 static __always_inline u32 accumulate_sum(u64 delta, struct sched_avg *sa,

index 69da6fc..996a137 100644
@@ -54,18 +54,23 @@ static inline void cpu_load_update_active(struct rq *this_rq) { }
  * increased costs.
  */
 #if 0 /* BITS_PER_LONG > 32 -- currently broken: it increases power usage under light load  */
-# define SCHED_LOAD_RESOLUTION	10
-# define scale_load(w)		((w) << SCHED_LOAD_RESOLUTION)
-# define scale_load_down(w)	((w) >> SCHED_LOAD_RESOLUTION)
+# define SCHED_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT + SCHED_FIXEDPOINT_SHIFT)
+# define scale_load(w)		((w) << SCHED_FIXEDPOINT_SHIFT)
+# define scale_load_down(w)	((w) >> SCHED_FIXEDPOINT_SHIFT)
 #else
-# define SCHED_LOAD_RESOLUTION	0
+# define SCHED_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT)
 # define scale_load(w)		(w)
 # define scale_load_down(w)	(w)
 #endif
 
-#define SCHED_LOAD_SHIFT	(10 + SCHED_LOAD_RESOLUTION)
 #define SCHED_LOAD_SCALE	(1L << SCHED_LOAD_SHIFT)
 
+/*
+ * NICE_0's weight (visible to user) and its load (invisible to user) have
+ * independent ranges, but they should be well calibrated. We use scale_load()
+ * and scale_load_down(w) to convert between them, the following must be true:
+ * scale_load(sched_prio_to_weight[20]) == NICE_0_LOAD
+ */
 #define NICE_0_LOAD		SCHED_LOAD_SCALE
 #define NICE_0_SHIFT		SCHED_LOAD_SHIFT
 

index 1a61137..017a26a 100644
@@ -721,7 +721,7 @@ void post_init_entity_util_avg(struct sched_entity *se)
 {
 	struct cfs_rq *cfs_rq = cfs_rq_of(se);
 	struct sched_avg *sa = &se->avg;
-	long cap = (long)(scale_load_down(SCHED_LOAD_SCALE) - cfs_rq->avg.util_avg) / 2;
+	long cap = (long)(SCHED_CAPACITY_SCALE - cfs_rq->avg.util_avg) / 2;
 
 	if (cap > 0) {
 		if (cfs_rq->avg.util_avg != 0) {

@@ -7019,7 +7019,7 @@ static inline void calculate_imbalance(struct lb_env *env, struct sd_lb_stats *s
 	if (busiest->group_type == group_overloaded &&
 	    local->group_type   == group_overloaded) {
 		load_above_capacity = busiest->sum_nr_running *
-					SCHED_LOAD_SCALE;
+				      scale_load_down(NICE_0_LOAD);
 		if (load_above_capacity > busiest->group_capacity)
 			load_above_capacity -= busiest->group_capacity;
 		else

index 996a137..1a3be6f 100644
@@ -54,25 +54,25 @@ static inline void cpu_load_update_active(struct rq *this_rq) { }
  * increased costs.
  */
 #if 0 /* BITS_PER_LONG > 32 -- currently broken: it increases power usage under light load  */
-# define SCHED_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT + SCHED_FIXEDPOINT_SHIFT)
+# define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT + SCHED_FIXEDPOINT_SHIFT)
 # define scale_load(w)		((w) << SCHED_FIXEDPOINT_SHIFT)
 # define scale_load_down(w)	((w) >> SCHED_FIXEDPOINT_SHIFT)
 #else
-# define SCHED_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT)
+# define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT)
 # define scale_load(w)		(w)
 # define scale_load_down(w)	(w)
 #endif
 
-#define SCHED_LOAD_SCALE	(1L << SCHED_LOAD_SHIFT)
-
 /*
- * NICE_0's weight (visible to user) and its load (invisible to user) have
- * independent ranges, but they should be well calibrated. We use scale_load()
- * and scale_load_down(w) to convert between them, the following must be true:
- * scale_load(sched_prio_to_weight[20]) == NICE_0_LOAD
+ * Task weight (visible to user) and its load (invisible to user) have
+ * independent resolution, but they should be well calibrated. We use
+ * scale_load() and scale_load_down(w) to convert between them. The
+ * following must be true:
+ *
+ *  scale_load(sched_prio_to_weight[USER_PRIO(NICE_TO_PRIO(0))]) == NICE_0_LOAD
+ *
  */
-#define NICE_0_LOAD		SCHED_LOAD_SCALE
-#define NICE_0_SHIFT		SCHED_LOAD_SHIFT
+#define NICE_0_LOAD		(1L << NICE_0_LOAD_SHIFT)
 
 /*
  * Single value that decides SCHED_DEADLINE internal math precision.

@@ -861,7 +861,7 @@ DECLARE_PER_CPU(struct sched_domain *, sd_asym);
 struct sched_group_capacity {
 	atomic_t ref;
 	/*
-	 * CPU capacity of this group, SCHED_LOAD_SCALE being max capacity
+	 * CPU capacity of this group, SCHED_CAPACITY_SCALE being max capacity
 	 * for a single CPU.
 	 */
 	unsigned int capacity;

index 76ca86e9fc20..e1485710d1ec 100644
@@ -719,7 +719,7 @@ void post_init_entity_util_avg(struct sched_entity *se)
 {
 	struct cfs_rq *cfs_rq = cfs_rq_of(se);
 	struct sched_avg *sa = &se->avg;
-	long cap = (long)(scale_load_down(SCHED_LOAD_SCALE) - cfs_rq->avg.util_avg) / 2;
+	long cap = (long)(SCHED_CAPACITY_SCALE - cfs_rq->avg.util_avg) / 2;
 
 	if (cap > 0) {
 		if (cfs_rq->avg.util_avg != 0) {

@@ -7010,7 +7010,7 @@ static inline void calculate_imbalance(struct lb_env *env, struct sd_lb_stats *s
 	if (busiest->group_type == group_overloaded &&
 	    local->group_type   == group_overloaded) {
 		load_above_capacity = busiest->sum_nr_running *
-					SCHED_LOAD_SCALE;
+				      scale_load_down(NICE_0_LOAD);
 		if (load_above_capacity > busiest->group_capacity)
 			load_above_capacity -= busiest->group_capacity;
 		else

index ad83361f9e67..d24e91b0a722 100644
@@ -56,25 +56,25 @@ static inline void cpu_load_update_active(struct rq *this_rq) { }
  * increase coverage and consistency always enable it on 64bit platforms.
  */
 #ifdef CONFIG_64BIT
-# define SCHED_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT + SCHED_FIXEDPOINT_SHIFT)
+# define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT + SCHED_FIXEDPOINT_SHIFT)
 # define scale_load(w)		((w) << SCHED_FIXEDPOINT_SHIFT)
 # define scale_load_down(w)	((w) >> SCHED_FIXEDPOINT_SHIFT)
 #else
-# define SCHED_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT)
+# define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT)
 # define scale_load(w)		(w)
 # define scale_load_down(w)	(w)
 #endif
 
-#define SCHED_LOAD_SCALE	(1L << SCHED_LOAD_SHIFT)
-
 /*
- * NICE_0's weight (visible to users) and its load (invisible to users) have
- * independent ranges, but they should be well calibrated. We use scale_load()
- * and scale_load_down(w) to convert between them, and the following must be true:
- * scale_load(sched_prio_to_weight[20]) == NICE_0_LOAD
+ * Task weight (visible to users) and its load (invisible to users) have
+ * independent resolution, but they should be well calibrated. We use
+ * scale_load() and scale_load_down(w) to convert between them. The
+ * following must be true:
+ *
+ *  scale_load(sched_prio_to_weight[USER_PRIO(NICE_TO_PRIO(0))]) == NICE_0_LOAD
+ *
  */
-#define NICE_0_LOAD		SCHED_LOAD_SCALE
-#define NICE_0_SHIFT		SCHED_LOAD_SHIFT
+#define NICE_0_LOAD		(1L << NICE_0_LOAD_SHIFT)
 
 /*
  * Single value that decides SCHED_DEADLINE internal math precision.

@@ -863,7 +863,7 @@ DECLARE_PER_CPU(struct sched_domain *, sd_asym);
 struct sched_group_capacity {
 	atomic_t ref;
 	/*
-	 * CPU capacity of this group, SCHED_LOAD_SCALE being max capacity
+	 * CPU capacity of this group, SCHED_CAPACITY_SCALE being max capacity
 	 * for a single CPU.
 	 */
 	unsigned int capacity;

index 33e7929..a7cddd6 100644
@@ -1211,18 +1211,56 @@ struct load_weight {
 };
 
 /*
- * The load_avg/util_avg accumulates an infinite geometric series.
- * 1) load_avg factors frequency scaling into the amount of time that a
- * sched_entity is runnable on a rq into its weight. For cfs_rq, it is the
- * aggregated such weights of all runnable and blocked sched_entities.
- * 2) util_avg factors frequency and cpu capacity scaling into the amount of time
- * that a sched_entity is running on a CPU, in the range [0..SCHED_CAPACITY_SCALE].
- * For cfs_rq, it is the aggregated such times of all runnable and
+ * The load_avg/util_avg accumulates an infinite geometric series
+ * (see __update_sched_avg() in kernel/sched/fair.c).
+ *
+ * [load_avg definition]
+ *
+ * load_avg = runnable% * scale_load_down(load)
+ *
+ * where runnable% is the time ratio that a sched_entity is runnable.
+ * For cfs_rq, it is the aggregated such load_avg of all runnable and
  * blocked sched_entities.
- * The 64 bit load_sum can:
- * 1) for cfs_rq, afford 4353082796 (=2^64/47742/88761) entities with
- * the highest weight (=88761) always runnable, we should not overflow
- * 2) for entity, support any load.weight always runnable
+ *
+ * load_avg may also take frequency scaling into account:
+ *
+ * load_avg = runnable% * scale_load_down(load) * freq%
+ *
+ * where freq% is the CPU frequency normalize to the highest frequency
+ *
+ * [util_avg definition]
+ *
+ * util_avg = running% * SCHED_CAPACITY_SCALE
+ *
+ * where running% is the time ratio that a sched_entity is running on
+ * a CPU. For cfs_rq, it is the aggregated such util_avg of all runnable
+ * and blocked sched_entities.
+ *
+ * util_avg may also factor frequency scaling and CPU capacity scaling:
+ *
+ * util_avg = running% * SCHED_CAPACITY_SCALE * freq% * capacity%
+ *
+ * where freq% is the same as above, and capacity% is the CPU capacity
+ * normalized to the greatest capacity (due to uarch differences, etc).
+ *
+ * N.B., the above ratios (runnable%, running%, freq%, and capacity%)
+ * themselves are in the range of [0, 1]. To do fixed point arithmetic,
+ * we therefore scale them to as large range as necessary. This is for
+ * example reflected by util_avg's SCHED_CAPACITY_SCALE.
+ *
+ * [Overflow issue]
+ *
+ * The 64bit load_sum can have 4353082796 (=2^64/47742/88761) entities
+ * with the highest load (=88761) always runnable on a single cfs_rq, we
+ * should not overflow as the number already hits PID_MAX_LIMIT.
+ *
+ * For all other cases (including 32bit kernel), struct load_weight's
+ * weight will overflow first before we do, because:
+ *
+ *    Max(load_avg) <= Max(load.weight)
+ *
+ * Then, it is the load_weight's responsibility to consider overflow
+ * issues.
  */
 struct sched_avg {
 	u64 last_update_time, load_sum;

index a7cddd6..b718cb0 100644
@@ -1216,7 +1216,7 @@ struct load_weight {
  *
  * [load_avg definition]
  *
- * load_avg = runnable% * scale_load_down(load)
+ * load_avg = runnable% * load
  *
  * where runnable% is the time ratio that a sched_entity is runnable.
  * For cfs_rq, it is the aggregated such load_avg of all runnable and

@@ -1224,7 +1224,7 @@ struct load_weight {
  *
  * load_avg may also take frequency scaling into account:
  *
- * load_avg = runnable% * scale_load_down(load) * freq%
+ * load_avg = runnable% * load * freq%
  *
  * where freq% is the CPU frequency normalize to the highest frequency
  *

@@ -1250,9 +1250,18 @@ struct load_weight {
  *
  * [Overflow issue]
  *
- * The 64bit load_sum can have 4353082796 (=2^64/47742/88761) entities
- * with the highest load (=88761) always runnable on a single cfs_rq, we
- * should not overflow as the number already hits PID_MAX_LIMIT.
+ * On 64bit kernel:
+ *
+ * When load has small fixed point range (SCHED_FIXEDPOINT_SHIFT), the
+ * 64bit load_sum can have 4353082796 (=2^64/47742/88761) tasks with
+ * the highest load (=88761) always runnable on a cfs_rq, we should
+ * not overflow as the number already hits PID_MAX_LIMIT.
+ *
+ * When load has large fixed point range (2*SCHED_FIXEDPOINT_SHIFT),
+ * the 64bit load_sum can have 4251057 (=2^64/47742/88761/1024) tasks
+ * with the highest load (=88761*1024) always runnable on ONE cfs_rq,
+ * we should be fine. Even if the overflow occurs at the end of day,
+ * at the time the load_avg won't be useful anyway in that situation.
  *
  * For all other cases (including 32bit kernel), struct load_weight's
  * weight will overflow first before we do, because:

index 017a26a..4487c2a 100644
@@ -682,7 +682,7 @@ void init_entity_runnable_average(struct sched_entity *se)
 	 * will definitely be update (after enqueue).
 	 */
 	sa->period_contrib = 1023;
-	sa->load_avg = scale_load_down(se->load.weight);
+	sa->load_avg = se->load.weight;
 	sa->load_sum = sa->load_avg * SCHED_AVG_MAX;
 	/*
 	 * At this point, util_avg won't be used in select_task_rq_fair anyway

@@ -2929,7 +2929,7 @@ update_cfs_rq_sched_avg(u64 now, struct cfs_rq *cfs_rq, bool update_freq)
 	}
 
 	decayed = __update_sched_avg(now, cpu_of(rq_of(cfs_rq)), sa,
-		scale_load_down(cfs_rq->load.weight), cfs_rq->curr != NULL, cfs_rq);
+				     cfs_rq->load.weight, cfs_rq->curr != NULL, cfs_rq);
 
 #ifndef CONFIG_64BIT
 	smp_wmb();

@@ -2954,8 +2954,7 @@ static inline void update_sched_avg(struct sched_entity *se, int update_tg)
 	 * Track task load average for carrying it to new CPU after migrated, and
 	 * track group sched_entity load average for task_h_load calc in migration
 	 */
-	__update_sched_avg(now, cpu, &se->avg,
-			   se->on_rq * scale_load_down(se->load.weight),
+	__update_sched_avg(now, cpu, &se->avg, se->on_rq * se->load.weight,
 			   cfs_rq->curr == se, NULL);
 
 	if (update_cfs_rq_sched_avg(now, cfs_rq, true) && update_tg)

@@ -2994,7 +2993,7 @@ skip_aging:
 static void detach_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
 {
 	__update_sched_avg(cfs_rq->avg.last_update_time, cpu_of(rq_of(cfs_rq)),
-			   &se->avg, se->on_rq * scale_load_down(se->load.weight),
+			   &se->avg, se->on_rq * se->load.weight,
 			   cfs_rq->curr == se, NULL);
 
 	cfs_rq->avg.load_avg = max_t(long, cfs_rq->avg.load_avg - se->avg.load_avg, 0);

@@ -3016,7 +3015,7 @@ enqueue_entity_sched_avg(struct cfs_rq *cfs_rq, struct sched_entity *se)
 	migrated = !sa->last_update_time;
 	if (!migrated) {
 		__update_sched_avg(now, cpu_of(rq_of(cfs_rq)), sa,
-				   se->on_rq * scale_load_down(se->load.weight),
+				   se->on_rq * se->load.weight,
 				   cfs_rq->curr == se, NULL);
 	}
 

@@ -7018,10 +7017,10 @@ static inline void calculate_imbalance(struct lb_env *env, struct sd_lb_stats *s
 	 */
 	if (busiest->group_type == group_overloaded &&
 	    local->group_type   == group_overloaded) {
-		load_above_capacity = busiest->sum_nr_running *
-				      scale_load_down(NICE_0_LOAD);
-		if (load_above_capacity > busiest->group_capacity)
-			load_above_capacity -= busiest->group_capacity;
+		load_above_capacity = busiest->sum_nr_running * NICE_0_LOAD;
+		if (load_above_capacity > scale_load(busiest->group_capacity))
+			load_above_capacity -=
+				scale_load(busiest->group_capacity);
 		else
 			load_above_capacity = ~0UL;
 	}

index c82ca6e..349d776 100644
@@ -698,12 +698,12 @@ static void set_load_weight(struct task_struct *p)
 	 * SCHED_IDLE tasks get minimal weight:
 	 */
 	if (idle_policy(p->policy)) {
-		load->weight = scale_load(WEIGHT_IDLEPRIO);
+		load->weight = user_to_kernel_load(WEIGHT_IDLEPRIO);
 		load->inv_weight = WMULT_IDLEPRIO;
 		return;
 	}
 
-	load->weight = scale_load(sched_prio_to_weight[prio]);
+	load->weight = user_to_kernel_load(sched_prio_to_weight[prio]);
 	load->inv_weight = sched_prio_to_wmult[prio];
 }
 

@@ -8184,7 +8184,7 @@ static void cpu_cgroup_attach(struct cgroup_taskset *tset)
 static int cpu_shares_write_u64(struct cgroup_subsys_state *css,
 				struct cftype *cftype, u64 shareval)
 {
-	return sched_group_set_shares(css_tg(css), scale_load(shareval));
+	return sched_group_set_shares(css_tg(css), user_to_kernel_load(shareval));
 }
 
 static u64 cpu_shares_read_u64(struct cgroup_subsys_state *css,

@@ -8192,7 +8192,7 @@ static u64 cpu_shares_read_u64(struct cgroup_subsys_state *css,
 {
 	struct task_group *tg = css_tg(css);
 
-	return (u64) scale_load_down(tg->shares);
+	return (u64) kernel_to_user_load(tg->shares);
 }
 
 #ifdef CONFIG_CFS_BANDWIDTH

index 4487c2a..200f752 100644
@@ -189,7 +189,7 @@ static void __update_inv_weight(struct load_weight *lw)
 	if (likely(lw->inv_weight))
 		return;
 
-	w = scale_load_down(lw->weight);
+	w = kernel_to_user_load(lw->weight);
 
 	if (BITS_PER_LONG > 32 && unlikely(w >= WMULT_CONST))
 		lw->inv_weight = 1;

@@ -210,10 +210,14 @@ static void __update_inv_weight(struct load_weight *lw)
  *
  * Or, weight =< lw.weight (because lw.weight is the runqueue weight), thus
  * weight/lw.weight <= 1, and therefore our shift will also be positive.
+ *
+ * Note load.weight falls back to user load scale (i.e., NICE_0's load is
+ * 1024), instead of possibly increased kernel load scale (i.e., NICE_0's
+ * load is NICE_0_LOAD) due to multiplication and division efficiency.
  */
 static u64 __calc_delta(u64 delta_exec, unsigned long weight, struct load_weight *lw)
 {
-	u64 fact = scale_load_down(weight);
+	u64 fact = kernel_to_user_load(weight);
 	int shift = WMULT_SHIFT;
 
 	__update_inv_weight(lw);

@@ -7017,10 +7021,11 @@ static inline void calculate_imbalance(struct lb_env *env, struct sd_lb_stats *s
 	 */
 	if (busiest->group_type == group_overloaded &&
 	    local->group_type   == group_overloaded) {
+		unsigned long min_cpu_load =
+			busiest->group_capacity * NICE_0_LOAD / SCHED_CAPACITY_SCALE;
 		load_above_capacity = busiest->sum_nr_running * NICE_0_LOAD;
-		if (load_above_capacity > scale_load(busiest->group_capacity))
-			load_above_capacity -=
-				scale_load(busiest->group_capacity);
+		if (load_above_capacity > min_cpu_load)
+			load_above_capacity -= min_cpu_load;
 		else
 			load_above_capacity = ~0UL;
 	}

@@ -8574,7 +8579,8 @@ int sched_group_set_shares(struct task_group *tg, unsigned long shares)
 	if (!tg->se[0])
 		return -EINVAL;
 
-	shares = clamp(shares, scale_load(MIN_SHARES), scale_load(MAX_SHARES));
+	shares = clamp(shares, user_to_kernel_load(MIN_SHARES),
+		       user_to_kernel_load(MAX_SHARES));
 
 	mutex_lock(&shares_mutex);
 	if (tg->shares == shares)

index 1a3be6f..871da67 100644
@@ -55,22 +55,22 @@ static inline void cpu_load_update_active(struct rq *this_rq) { }
  */
 #if 0 /* BITS_PER_LONG > 32 -- currently broken: it increases power usage under light load  */
 # define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT + SCHED_FIXEDPOINT_SHIFT)
-# define scale_load(w)		((w) << SCHED_FIXEDPOINT_SHIFT)
-# define scale_load_down(w)	((w) >> SCHED_FIXEDPOINT_SHIFT)
+# define user_to_kernel_load(w)	((w) << SCHED_FIXEDPOINT_SHIFT)
+# define kernel_to_user_load(w)	((w) >> SCHED_FIXEDPOINT_SHIFT)
 #else
 # define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT)
-# define scale_load(w)		(w)
-# define scale_load_down(w)	(w)
+# define user_to_kernel_load(w)	(w)
+# define kernel_to_user_load(w)	(w)
 #endif
 
 /*
  * Task weight (visible to user) and its load (invisible to user) have
  * independent resolution, but they should be well calibrated. We use
- * scale_load() and scale_load_down(w) to convert between them. The
- * following must be true:
- *
- *  scale_load(sched_prio_to_weight[USER_PRIO(NICE_TO_PRIO(0))]) == NICE_0_LOAD
+ * user_to_kernel_load() and kernel_to_user_load(w) to convert between
+ * them. The following must be true:
  *
+ * user_to_kernel_load(sched_prio_to_weight[USER_PRIO(NICE_TO_PRIO(0))]) == NICE_0_LOAD
+ * kernel_to_user_load(NICE_0_LOAD) == sched_prio_to_weight[USER_PRIO(NICE_TO_PRIO(0))]
  */
 #define NICE_0_LOAD		(1L << NICE_0_LOAD_SHIFT)
 

index 871da67..5f66a2c 100644
@@ -42,37 +42,36 @@ static inline void cpu_load_update_active(struct rq *this_rq) { }
 #define NS_TO_JIFFIES(TIME)	((unsigned long)(TIME) / (NSEC_PER_SEC / HZ))
 
 /*
- * Increase resolution of nice-level calculations for 64-bit architectures.
- * The extra resolution improves shares distribution and load balancing of
- * low-weight task groups (eg. nice +19 on an autogroup), deeper taskgroup
- * hierarchies, especially on larger systems. This is not a user-visible change
- * and does not change the user-interface for setting shares/weights.
+ * Task weight (visible and set by user) and its load (invisible to user)
+ * can have independent ranges. We increase the scale of load for 64-bit
+ * architectures. The extra precision improves share distribution and
+ * load balancing of low-weight task groups (e.g., nice +19 on an autogroup),
+ * deeper taskgroup hierarchies, especially on larger systems. This is not
+ * a user-visible change and does not change the user-interface for setting
+ * shares/weights. We increase resolution only if we have enough bits to allow
+ * this increased precision (i.e., BITS_PER_LONG > 32). The costs for increasing
+ * resolution when BITS_PER_LONG <= 32 are pretty high and the returns do not
+ * justify the increased costs.
  *
- * We increase resolution only if we have enough bits to allow this increased
- * resolution (i.e. BITS_PER_LONG > 32). The costs for increasing resolution
- * when BITS_PER_LONG <= 32 are pretty high and the returns do not justify the
- * increased costs.
- */
-#if 0 /* BITS_PER_LONG > 32 -- currently broken: it increases power usage under light load  */
-# define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT + SCHED_FIXEDPOINT_SHIFT)
-# define user_to_kernel_load(w)	((w) << SCHED_FIXEDPOINT_SHIFT)
-# define kernel_to_user_load(w)	((w) >> SCHED_FIXEDPOINT_SHIFT)
-#else
-# define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT)
-# define user_to_kernel_load(w)	(w)
-# define kernel_to_user_load(w)	(w)
-#endif
-
-/*
- * Task weight (visible to user) and its load (invisible to user) have
- * independent resolution, but they should be well calibrated. We use
- * user_to_kernel_load() and kernel_to_user_load(w) to convert between
- * them. The following must be true:
+ * Therefore, the user load and kernel should be well expressed to make them
+ * easily exchanged. We use user_to_kernel_load() and kernel_to_user_load(w)
+ * to convert between them.
  *
+ * Following equations are a simple illustration of their relationship:
  * user_to_kernel_load(sched_prio_to_weight[USER_PRIO(NICE_TO_PRIO(0))]) == NICE_0_LOAD
  * kernel_to_user_load(NICE_0_LOAD) == sched_prio_to_weight[USER_PRIO(NICE_TO_PRIO(0))]
  */
-#define NICE_0_LOAD		(1L << NICE_0_LOAD_SHIFT)
+#if defined(CONFIG_64BIT) && defined(CONFIG_FAIR_GROUP_SCHED)
+#define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT + SCHED_FIXEDPOINT_SHIFT)
+#define user_to_kernel_load(w)	(w << SCHED_FIXEDPOINT_SHIFT)
+#define kernel_to_user_load(w)	(w >> SCHED_FIXEDPOINT_SHIFT)
+#else
+#define NICE_0_LOAD_SHIFT	(SCHED_FIXEDPOINT_SHIFT)
+#define user_to_kernel_load(w)	(w)
+#define kernel_to_user_load(w)	(w)
+#endif
+
+#define NICE_0_LOAD		(1UL << NICE_0_LOAD_SHIFT)
 
 /*
  * Single value that decides SCHED_DEADLINE internal math precision.