2 files changed, 140 insertions, 12 deletions

diff --git a/kernel/sched.c b/kernel/sched.c
index dc91a4d09ac3..6b7c26a1a097 100644
--- a/kernel/sched.c
+++ b/kernel/sched.c
@@ -3119,6 +3119,15 @@ static long calc_load_fold_active(struct rq *this_rq)
         return delta;
 }
 
+static unsigned long
+calc_load(unsigned long load, unsigned long exp, unsigned long active)
+{
+        load *= exp;
+        load += active * (FIXED_1 - exp);
+        load += 1UL << (FSHIFT - 1);
+        return load >> FSHIFT;
+}
+
 #ifdef CONFIG_NO_HZ
 /*
  * For NO_HZ we delay the active fold to the next LOAD_FREQ update.
@@ -3148,6 +3157,128 @@ static long calc_load_fold_idle(void)
 
         return delta;
 }
+
+/**
+ * fixed_power_int - compute: x^n, in O(log n) time
+ *
+ * @x:         base of the power
+ * @frac_bits: fractional bits of @x
+ * @n:         power to raise @x to.
+ *
+ * By exploiting the relation between the definition of the natural power
+ * function: x^n := x*x*...*x (x multiplied by itself for n times), and
+ * the binary encoding of numbers used by computers: n := \Sum n_i * 2^i,
+ * (where: n_i \elem {0, 1}, the binary vector representing n),
+ * we find: x^n := x^(\Sum n_i * 2^i) := \Prod x^(n_i * 2^i), which is
+ * of course trivially computable in O(log_2 n), the length of our binary
+ * vector.
+ */
+static unsigned long
+fixed_power_int(unsigned long x, unsigned int frac_bits, unsigned int n)
+{
+        unsigned long result = 1UL << frac_bits;
+
+        if (n) for (;;) {
+                if (n & 1) {
+                        result *= x;
+                        result += 1UL << (frac_bits - 1);
+                        result >>= frac_bits;
+                }
+                n >>= 1;
+                if (!n)
+                        break;
+                x *= x;
+                x += 1UL << (frac_bits - 1);
+                x >>= frac_bits;
+        }
+
+        return result;
+}
+
+/*
+ * a1 = a0 * e + a * (1 - e)
+ *
+ * a2 = a1 * e + a * (1 - e)
+ *    = (a0 * e + a * (1 - e)) * e + a * (1 - e)
+ *    = a0 * e^2 + a * (1 - e) * (1 + e)
+ *
+ * a3 = a2 * e + a * (1 - e)
+ *    = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e)
+ *    = a0 * e^3 + a * (1 - e) * (1 + e + e^2)
+ *
+ *  ...
+ *
+ * an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1) [1]
+ *    = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e)
+ *    = a0 * e^n + a * (1 - e^n)
+ *
+ * [1] application of the geometric series:
+ *
+ *              n         1 - x^(n+1)
+ *     S_n := \Sum x^i = -------------
+ *             i=0          1 - x
+ */
+static unsigned long
+calc_load_n(unsigned long load, unsigned long exp,
+            unsigned long active, unsigned int n)
+{
+
+        return calc_load(load, fixed_power_int(exp, FSHIFT, n), active);
+}
+
+/*
+ * NO_HZ can leave us missing all per-cpu ticks calling
+ * calc_load_account_active(), but since an idle CPU folds its delta into
+ * calc_load_tasks_idle per calc_load_account_idle(), all we need to do is fold
+ * in the pending idle delta if our idle period crossed a load cycle boundary.
+ *
+ * Once we've updated the global active value, we need to apply the exponential
+ * weights adjusted to the number of cycles missed.
+ */
+static void calc_global_nohz(unsigned long ticks)
+{
+        long delta, active, n;
+
+        if (time_before(jiffies, calc_load_update))
+                return;
+
+        /*
+         * If we crossed a calc_load_update boundary, make sure to fold
+         * any pending idle changes, the respective CPUs might have
+         * missed the tick driven calc_load_account_active() update
+         * due to NO_HZ.
+         */
+        delta = calc_load_fold_idle();
+        if (delta)
+                atomic_long_add(delta, &calc_load_tasks);
+
+        /*
+         * If we were idle for multiple load cycles, apply them.
+         */
+        if (ticks >= LOAD_FREQ) {
+                n = ticks / LOAD_FREQ;
+
+                active = atomic_long_read(&calc_load_tasks);
+                active = active > 0 ? active * FIXED_1 : 0;
+
+                avenrun[0] = calc_load_n(avenrun[0], EXP_1, active, n);
+                avenrun[1] = calc_load_n(avenrun[1], EXP_5, active, n);
+                avenrun[2] = calc_load_n(avenrun[2], EXP_15, active, n);
+
+                calc_load_update += n * LOAD_FREQ;
+        }
+
+        /*
+         * Its possible the remainder of the above division also crosses
+         * a LOAD_FREQ period, the regular check in calc_global_load()
+         * which comes after this will take care of that.
+         *
+         * Consider us being 11 ticks before a cycle completion, and us
+         * sleeping for 4*LOAD_FREQ + 22 ticks, then the above code will
+         * age us 4 cycles, and the test in calc_global_load() will
+         * pick up the final one.
+         */
+}
 #else
 static void calc_load_account_idle(struct rq *this_rq)
 {
@@ -3157,6 +3288,10 @@ static inline long calc_load_fold_idle(void)
 {
         return 0;
 }
+
+static void calc_global_nohz(unsigned long ticks)
+{
+}
 #endif
 
 /**
@@ -3174,24 +3309,17 @@ void get_avenrun(unsigned long *loads, unsigned long offset, int shift)
         loads[2] = (avenrun[2] + offset) << shift;
 }
 
-static unsigned long
-calc_load(unsigned long load, unsigned long exp, unsigned long active)
-{
-        load *= exp;
-        load += active * (FIXED_1 - exp);
-        return load >> FSHIFT;
-}
-
 /*
  * calc_load - update the avenrun load estimates 10 ticks after the
  * CPUs have updated calc_load_tasks.
  */
-void calc_global_load(void)
+void calc_global_load(unsigned long ticks)
 {
-        unsigned long upd = calc_load_update + 10;
         long active;
 
-        if (time_before(jiffies, upd))
+        calc_global_nohz(ticks);
+
+        if (time_before(jiffies, calc_load_update + 10))
                 return;
 
         active = atomic_long_read(&calc_load_tasks);
diff --git a/kernel/timer.c b/kernel/timer.c
index 68a9ae7679b7..7bd715fda974 100644
--- a/kernel/timer.c
+++ b/kernel/timer.c
@@ -1319,7 +1319,7 @@ void do_timer(unsigned long ticks)
 {
         jiffies_64 += ticks;
         update_wall_time();
-        calc_global_load();
+        calc_global_load(ticks);
 }
 
 #ifdef __ARCH_WANT_SYS_ALARM