1 // SPDX-License-Identifier: GPL-2.0 2 /* 3 * kernel/sched/loadavg.c 4 * 5 * This file contains the magic bits required to compute the global loadavg 6 * figure. Its a silly number but people think its important. We go through 7 * great pains to make it work on big machines and tickless kernels. 8 */ 9 10 /* 11 * Global load-average calculations 12 * 13 * We take a distributed and async approach to calculating the global load-avg 14 * in order to minimize overhead. 15 * 16 * The global load average is an exponentially decaying average of nr_running + 17 * nr_uninterruptible. 18 * 19 * Once every LOAD_FREQ: 20 * 21 * nr_active = 0; 22 * for_each_possible_cpu(cpu) 23 * nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible; 24 * 25 * avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n) 26 * 27 * Due to a number of reasons the above turns in the mess below: 28 * 29 * - for_each_possible_cpu() is prohibitively expensive on machines with 30 * serious number of CPUs, therefore we need to take a distributed approach 31 * to calculating nr_active. 32 * 33 * \Sum_i x_i(t) = \Sum_i x_i(t) - x_i(t_0) | x_i(t_0) := 0 34 * = \Sum_i { \Sum_j=1 x_i(t_j) - x_i(t_j-1) } 35 * 36 * So assuming nr_active := 0 when we start out -- true per definition, we 37 * can simply take per-CPU deltas and fold those into a global accumulate 38 * to obtain the same result. See calc_load_fold_active(). 39 * 40 * Furthermore, in order to avoid synchronizing all per-CPU delta folding 41 * across the machine, we assume 10 ticks is sufficient time for every 42 * CPU to have completed this task. 43 * 44 * This places an upper-bound on the IRQ-off latency of the machine. Then 45 * again, being late doesn't loose the delta, just wrecks the sample. 46 * 47 * - cpu_rq()->nr_uninterruptible isn't accurately tracked per-CPU because 48 * this would add another cross-CPU cacheline miss and atomic operation 49 * to the wakeup path. Instead we increment on whatever CPU the task ran 50 * when it went into uninterruptible state and decrement on whatever CPU 51 * did the wakeup. This means that only the sum of nr_uninterruptible over 52 * all CPUs yields the correct result. 53 * 54 * This covers the NO_HZ=n code, for extra head-aches, see the comment below. 55 */ 56 57 /* Variables and functions for calc_load */ 58 atomic_long_t calc_load_tasks; 59 unsigned long calc_load_update; 60 unsigned long avenrun[3]; 61 EXPORT_SYMBOL(avenrun); /* should be removed */ 62 63 /** 64 * get_avenrun - get the load average array 65 * @loads: pointer to dest load array 66 * @offset: offset to add 67 * @shift: shift count to shift the result left 68 * 69 * These values are estimates at best, so no need for locking. 70 */ 71 void get_avenrun(unsigned long *loads, unsigned long offset, int shift) 72 { 73 loads[0] = (avenrun[0] + offset) << shift; 74 loads[1] = (avenrun[1] + offset) << shift; 75 loads[2] = (avenrun[2] + offset) << shift; 76 } 77 78 long calc_load_fold_active(struct rq *this_rq, long adjust) 79 { 80 long nr_active, delta = 0; 81 82 nr_active = this_rq->nr_running - adjust; 83 nr_active += (int)this_rq->nr_uninterruptible; 84 85 if (nr_active != this_rq->calc_load_active) { 86 delta = nr_active - this_rq->calc_load_active; 87 this_rq->calc_load_active = nr_active; 88 } 89 90 return delta; 91 } 92 93 /** 94 * fixed_power_int - compute: x^n, in O(log n) time 95 * 96 * @x: base of the power 97 * @frac_bits: fractional bits of @x 98 * @n: power to raise @x to. 99 * 100 * By exploiting the relation between the definition of the natural power 101 * function: x^n := x*x*...*x (x multiplied by itself for n times), and 102 * the binary encoding of numbers used by computers: n := \Sum n_i * 2^i, 103 * (where: n_i \elem {0, 1}, the binary vector representing n), 104 * we find: x^n := x^(\Sum n_i * 2^i) := \Prod x^(n_i * 2^i), which is 105 * of course trivially computable in O(log_2 n), the length of our binary 106 * vector. 107 */ 108 static unsigned long 109 fixed_power_int(unsigned long x, unsigned int frac_bits, unsigned int n) 110 { 111 unsigned long result = 1UL << frac_bits; 112 113 if (n) { 114 for (;;) { 115 if (n & 1) { 116 result *= x; 117 result += 1UL << (frac_bits - 1); 118 result >>= frac_bits; 119 } 120 n >>= 1; 121 if (!n) 122 break; 123 x *= x; 124 x += 1UL << (frac_bits - 1); 125 x >>= frac_bits; 126 } 127 } 128 129 return result; 130 } 131 132 /* 133 * a1 = a0 * e + a * (1 - e) 134 * 135 * a2 = a1 * e + a * (1 - e) 136 * = (a0 * e + a * (1 - e)) * e + a * (1 - e) 137 * = a0 * e^2 + a * (1 - e) * (1 + e) 138 * 139 * a3 = a2 * e + a * (1 - e) 140 * = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e) 141 * = a0 * e^3 + a * (1 - e) * (1 + e + e^2) 142 * 143 * ... 144 * 145 * an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1) [1] 146 * = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e) 147 * = a0 * e^n + a * (1 - e^n) 148 * 149 * [1] application of the geometric series: 150 * 151 * n 1 - x^(n+1) 152 * S_n := \Sum x^i = ------------- 153 * i=0 1 - x 154 */ 155 unsigned long 156 calc_load_n(unsigned long load, unsigned long exp, 157 unsigned long active, unsigned int n) 158 { 159 return calc_load(load, fixed_power_int(exp, FSHIFT, n), active); 160 } 161 162 #ifdef CONFIG_NO_HZ_COMMON 163 /* 164 * Handle NO_HZ for the global load-average. 165 * 166 * Since the above described distributed algorithm to compute the global 167 * load-average relies on per-CPU sampling from the tick, it is affected by 168 * NO_HZ. 169 * 170 * The basic idea is to fold the nr_active delta into a global NO_HZ-delta upon 171 * entering NO_HZ state such that we can include this as an 'extra' CPU delta 172 * when we read the global state. 173 * 174 * Obviously reality has to ruin such a delightfully simple scheme: 175 * 176 * - When we go NO_HZ idle during the window, we can negate our sample 177 * contribution, causing under-accounting. 178 * 179 * We avoid this by keeping two NO_HZ-delta counters and flipping them 180 * when the window starts, thus separating old and new NO_HZ load. 181 * 182 * The only trick is the slight shift in index flip for read vs write. 183 * 184 * 0s 5s 10s 15s 185 * +10 +10 +10 +10 186 * |-|-----------|-|-----------|-|-----------|-| 187 * r:0 0 1 1 0 0 1 1 0 188 * w:0 1 1 0 0 1 1 0 0 189 * 190 * This ensures we'll fold the old NO_HZ contribution in this window while 191 * accumulating the new one. 192 * 193 * - When we wake up from NO_HZ during the window, we push up our 194 * contribution, since we effectively move our sample point to a known 195 * busy state. 196 * 197 * This is solved by pushing the window forward, and thus skipping the 198 * sample, for this CPU (effectively using the NO_HZ-delta for this CPU which 199 * was in effect at the time the window opened). This also solves the issue 200 * of having to deal with a CPU having been in NO_HZ for multiple LOAD_FREQ 201 * intervals. 202 * 203 * When making the ILB scale, we should try to pull this in as well. 204 */ 205 static atomic_long_t calc_load_nohz[2]; 206 static int calc_load_idx; 207 208 static inline int calc_load_write_idx(void) 209 { 210 int idx = calc_load_idx; 211 212 /* 213 * See calc_global_nohz(), if we observe the new index, we also 214 * need to observe the new update time. 215 */ 216 smp_rmb(); 217 218 /* 219 * If the folding window started, make sure we start writing in the 220 * next NO_HZ-delta. 221 */ 222 if (!time_before(jiffies, READ_ONCE(calc_load_update))) 223 idx++; 224 225 return idx & 1; 226 } 227 228 static inline int calc_load_read_idx(void) 229 { 230 return calc_load_idx & 1; 231 } 232 233 static void calc_load_nohz_fold(struct rq *rq) 234 { 235 long delta; 236 237 delta = calc_load_fold_active(rq, 0); 238 if (delta) { 239 int idx = calc_load_write_idx(); 240 241 atomic_long_add(delta, &calc_load_nohz[idx]); 242 } 243 } 244 245 void calc_load_nohz_start(void) 246 { 247 /* 248 * We're going into NO_HZ mode, if there's any pending delta, fold it 249 * into the pending NO_HZ delta. 250 */ 251 calc_load_nohz_fold(this_rq()); 252 } 253 254 /* 255 * Keep track of the load for NOHZ_FULL, must be called between 256 * calc_load_nohz_{start,stop}(). 257 */ 258 void calc_load_nohz_remote(struct rq *rq) 259 { 260 calc_load_nohz_fold(rq); 261 } 262 263 void calc_load_nohz_stop(void) 264 { 265 struct rq *this_rq = this_rq(); 266 267 /* 268 * If we're still before the pending sample window, we're done. 269 */ 270 this_rq->calc_load_update = READ_ONCE(calc_load_update); 271 if (time_before(jiffies, this_rq->calc_load_update)) 272 return; 273 274 /* 275 * We woke inside or after the sample window, this means we're already 276 * accounted through the nohz accounting, so skip the entire deal and 277 * sync up for the next window. 278 */ 279 if (time_before(jiffies, this_rq->calc_load_update + 10)) 280 this_rq->calc_load_update += LOAD_FREQ; 281 } 282 283 static long calc_load_nohz_read(void) 284 { 285 int idx = calc_load_read_idx(); 286 long delta = 0; 287 288 if (atomic_long_read(&calc_load_nohz[idx])) 289 delta = atomic_long_xchg(&calc_load_nohz[idx], 0); 290 291 return delta; 292 } 293 294 /* 295 * NO_HZ can leave us missing all per-CPU ticks calling 296 * calc_load_fold_active(), but since a NO_HZ CPU folds its delta into 297 * calc_load_nohz per calc_load_nohz_start(), all we need to do is fold 298 * in the pending NO_HZ delta if our NO_HZ period crossed a load cycle boundary. 299 * 300 * Once we've updated the global active value, we need to apply the exponential 301 * weights adjusted to the number of cycles missed. 302 */ 303 static void calc_global_nohz(void) 304 { 305 unsigned long sample_window; 306 long delta, active, n; 307 308 sample_window = READ_ONCE(calc_load_update); 309 if (!time_before(jiffies, sample_window + 10)) { 310 /* 311 * Catch-up, fold however many we are behind still 312 */ 313 delta = jiffies - sample_window - 10; 314 n = 1 + (delta / LOAD_FREQ); 315 316 active = atomic_long_read(&calc_load_tasks); 317 active = active > 0 ? active * FIXED_1 : 0; 318 319 avenrun[0] = calc_load_n(avenrun[0], EXP_1, active, n); 320 avenrun[1] = calc_load_n(avenrun[1], EXP_5, active, n); 321 avenrun[2] = calc_load_n(avenrun[2], EXP_15, active, n); 322 323 WRITE_ONCE(calc_load_update, sample_window + n * LOAD_FREQ); 324 } 325 326 /* 327 * Flip the NO_HZ index... 328 * 329 * Make sure we first write the new time then flip the index, so that 330 * calc_load_write_idx() will see the new time when it reads the new 331 * index, this avoids a double flip messing things up. 332 */ 333 smp_wmb(); 334 calc_load_idx++; 335 } 336 #else /* !CONFIG_NO_HZ_COMMON */ 337 338 static inline long calc_load_nohz_read(void) { return 0; } 339 static inline void calc_global_nohz(void) { } 340 341 #endif /* CONFIG_NO_HZ_COMMON */ 342 343 /* 344 * calc_load - update the avenrun load estimates 10 ticks after the 345 * CPUs have updated calc_load_tasks. 346 * 347 * Called from the global timer code. 348 */ 349 void calc_global_load(void) 350 { 351 unsigned long sample_window; 352 long active, delta; 353 354 sample_window = READ_ONCE(calc_load_update); 355 if (time_before(jiffies, sample_window + 10)) 356 return; 357 358 /* 359 * Fold the 'old' NO_HZ-delta to include all NO_HZ CPUs. 360 */ 361 delta = calc_load_nohz_read(); 362 if (delta) 363 atomic_long_add(delta, &calc_load_tasks); 364 365 active = atomic_long_read(&calc_load_tasks); 366 active = active > 0 ? active * FIXED_1 : 0; 367 368 avenrun[0] = calc_load(avenrun[0], EXP_1, active); 369 avenrun[1] = calc_load(avenrun[1], EXP_5, active); 370 avenrun[2] = calc_load(avenrun[2], EXP_15, active); 371 372 WRITE_ONCE(calc_load_update, sample_window + LOAD_FREQ); 373 374 /* 375 * In case we went to NO_HZ for multiple LOAD_FREQ intervals 376 * catch up in bulk. 377 */ 378 calc_global_nohz(); 379 } 380 381 /* 382 * Called from scheduler_tick() to periodically update this CPU's 383 * active count. 384 */ 385 void calc_global_load_tick(struct rq *this_rq) 386 { 387 long delta; 388 389 if (time_before(jiffies, this_rq->calc_load_update)) 390 return; 391 392 delta = calc_load_fold_active(this_rq, 0); 393 if (delta) 394 atomic_long_add(delta, &calc_load_tasks); 395 396 this_rq->calc_load_update += LOAD_FREQ; 397 } 398