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 #include "sched.h" 10 11 /* 12 * Global load-average calculations 13 * 14 * We take a distributed and async approach to calculating the global load-avg 15 * in order to minimize overhead. 16 * 17 * The global load average is an exponentially decaying average of nr_running + 18 * nr_uninterruptible. 19 * 20 * Once every LOAD_FREQ: 21 * 22 * nr_active = 0; 23 * for_each_possible_cpu(cpu) 24 * nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible; 25 * 26 * avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n) 27 * 28 * Due to a number of reasons the above turns in the mess below: 29 * 30 * - for_each_possible_cpu() is prohibitively expensive on machines with 31 * serious number of CPUs, therefore we need to take a distributed approach 32 * to calculating nr_active. 33 * 34 * \Sum_i x_i(t) = \Sum_i x_i(t) - x_i(t_0) | x_i(t_0) := 0 35 * = \Sum_i { \Sum_j=1 x_i(t_j) - x_i(t_j-1) } 36 * 37 * So assuming nr_active := 0 when we start out -- true per definition, we 38 * can simply take per-CPU deltas and fold those into a global accumulate 39 * to obtain the same result. See calc_load_fold_active(). 40 * 41 * Furthermore, in order to avoid synchronizing all per-CPU delta folding 42 * across the machine, we assume 10 ticks is sufficient time for every 43 * CPU to have completed this task. 44 * 45 * This places an upper-bound on the IRQ-off latency of the machine. Then 46 * again, being late doesn't loose the delta, just wrecks the sample. 47 * 48 * - cpu_rq()->nr_uninterruptible isn't accurately tracked per-CPU because 49 * this would add another cross-CPU cacheline miss and atomic operation 50 * to the wakeup path. Instead we increment on whatever CPU the task ran 51 * when it went into uninterruptible state and decrement on whatever CPU 52 * did the wakeup. This means that only the sum of nr_uninterruptible over 53 * all CPUs yields the correct result. 54 * 55 * This covers the NO_HZ=n code, for extra head-aches, see the comment below. 56 */ 57 58 /* Variables and functions for calc_load */ 59 atomic_long_t calc_load_tasks; 60 unsigned long calc_load_update; 61 unsigned long avenrun[3]; 62 EXPORT_SYMBOL(avenrun); /* should be removed */ 63 64 /** 65 * get_avenrun - get the load average array 66 * @loads: pointer to dest load array 67 * @offset: offset to add 68 * @shift: shift count to shift the result left 69 * 70 * These values are estimates at best, so no need for locking. 71 */ 72 void get_avenrun(unsigned long *loads, unsigned long offset, int shift) 73 { 74 loads[0] = (avenrun[0] + offset) << shift; 75 loads[1] = (avenrun[1] + offset) << shift; 76 loads[2] = (avenrun[2] + offset) << shift; 77 } 78 79 long calc_load_fold_active(struct rq *this_rq, long adjust) 80 { 81 long nr_active, delta = 0; 82 83 nr_active = this_rq->nr_running - adjust; 84 nr_active += (long)this_rq->nr_uninterruptible; 85 86 if (nr_active != this_rq->calc_load_active) { 87 delta = nr_active - this_rq->calc_load_active; 88 this_rq->calc_load_active = nr_active; 89 } 90 91 return delta; 92 } 93 94 /** 95 * fixed_power_int - compute: x^n, in O(log n) time 96 * 97 * @x: base of the power 98 * @frac_bits: fractional bits of @x 99 * @n: power to raise @x to. 100 * 101 * By exploiting the relation between the definition of the natural power 102 * function: x^n := x*x*...*x (x multiplied by itself for n times), and 103 * the binary encoding of numbers used by computers: n := \Sum n_i * 2^i, 104 * (where: n_i \elem {0, 1}, the binary vector representing n), 105 * we find: x^n := x^(\Sum n_i * 2^i) := \Prod x^(n_i * 2^i), which is 106 * of course trivially computable in O(log_2 n), the length of our binary 107 * vector. 108 */ 109 static unsigned long 110 fixed_power_int(unsigned long x, unsigned int frac_bits, unsigned int n) 111 { 112 unsigned long result = 1UL << frac_bits; 113 114 if (n) { 115 for (;;) { 116 if (n & 1) { 117 result *= x; 118 result += 1UL << (frac_bits - 1); 119 result >>= frac_bits; 120 } 121 n >>= 1; 122 if (!n) 123 break; 124 x *= x; 125 x += 1UL << (frac_bits - 1); 126 x >>= frac_bits; 127 } 128 } 129 130 return result; 131 } 132 133 /* 134 * a1 = a0 * e + a * (1 - e) 135 * 136 * a2 = a1 * e + a * (1 - e) 137 * = (a0 * e + a * (1 - e)) * e + a * (1 - e) 138 * = a0 * e^2 + a * (1 - e) * (1 + e) 139 * 140 * a3 = a2 * e + a * (1 - e) 141 * = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e) 142 * = a0 * e^3 + a * (1 - e) * (1 + e + e^2) 143 * 144 * ... 145 * 146 * an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1) [1] 147 * = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e) 148 * = a0 * e^n + a * (1 - e^n) 149 * 150 * [1] application of the geometric series: 151 * 152 * n 1 - x^(n+1) 153 * S_n := \Sum x^i = ------------- 154 * i=0 1 - x 155 */ 156 unsigned long 157 calc_load_n(unsigned long load, unsigned long exp, 158 unsigned long active, unsigned int n) 159 { 160 return calc_load(load, fixed_power_int(exp, FSHIFT, n), active); 161 } 162 163 #ifdef CONFIG_NO_HZ_COMMON 164 /* 165 * Handle NO_HZ for the global load-average. 166 * 167 * Since the above described distributed algorithm to compute the global 168 * load-average relies on per-CPU sampling from the tick, it is affected by 169 * NO_HZ. 170 * 171 * The basic idea is to fold the nr_active delta into a global NO_HZ-delta upon 172 * entering NO_HZ state such that we can include this as an 'extra' CPU delta 173 * when we read the global state. 174 * 175 * Obviously reality has to ruin such a delightfully simple scheme: 176 * 177 * - When we go NO_HZ idle during the window, we can negate our sample 178 * contribution, causing under-accounting. 179 * 180 * We avoid this by keeping two NO_HZ-delta counters and flipping them 181 * when the window starts, thus separating old and new NO_HZ load. 182 * 183 * The only trick is the slight shift in index flip for read vs write. 184 * 185 * 0s 5s 10s 15s 186 * +10 +10 +10 +10 187 * |-|-----------|-|-----------|-|-----------|-| 188 * r:0 0 1 1 0 0 1 1 0 189 * w:0 1 1 0 0 1 1 0 0 190 * 191 * This ensures we'll fold the old NO_HZ contribution in this window while 192 * accumlating the new one. 193 * 194 * - When we wake up from NO_HZ during the window, we push up our 195 * contribution, since we effectively move our sample point to a known 196 * busy state. 197 * 198 * This is solved by pushing the window forward, and thus skipping the 199 * sample, for this CPU (effectively using the NO_HZ-delta for this CPU which 200 * was in effect at the time the window opened). This also solves the issue 201 * of having to deal with a CPU having been in NO_HZ for multiple LOAD_FREQ 202 * intervals. 203 * 204 * When making the ILB scale, we should try to pull this in as well. 205 */ 206 static atomic_long_t calc_load_nohz[2]; 207 static int calc_load_idx; 208 209 static inline int calc_load_write_idx(void) 210 { 211 int idx = calc_load_idx; 212 213 /* 214 * See calc_global_nohz(), if we observe the new index, we also 215 * need to observe the new update time. 216 */ 217 smp_rmb(); 218 219 /* 220 * If the folding window started, make sure we start writing in the 221 * next NO_HZ-delta. 222 */ 223 if (!time_before(jiffies, READ_ONCE(calc_load_update))) 224 idx++; 225 226 return idx & 1; 227 } 228 229 static inline int calc_load_read_idx(void) 230 { 231 return calc_load_idx & 1; 232 } 233 234 static void calc_load_nohz_fold(struct rq *rq) 235 { 236 long delta; 237 238 delta = calc_load_fold_active(rq, 0); 239 if (delta) { 240 int idx = calc_load_write_idx(); 241 242 atomic_long_add(delta, &calc_load_nohz[idx]); 243 } 244 } 245 246 void calc_load_nohz_start(void) 247 { 248 /* 249 * We're going into NO_HZ mode, if there's any pending delta, fold it 250 * into the pending NO_HZ delta. 251 */ 252 calc_load_nohz_fold(this_rq()); 253 } 254 255 /* 256 * Keep track of the load for NOHZ_FULL, must be called between 257 * calc_load_nohz_{start,stop}(). 258 */ 259 void calc_load_nohz_remote(struct rq *rq) 260 { 261 calc_load_nohz_fold(rq); 262 } 263 264 void calc_load_nohz_stop(void) 265 { 266 struct rq *this_rq = this_rq(); 267 268 /* 269 * If we're still before the pending sample window, we're done. 270 */ 271 this_rq->calc_load_update = READ_ONCE(calc_load_update); 272 if (time_before(jiffies, this_rq->calc_load_update)) 273 return; 274 275 /* 276 * We woke inside or after the sample window, this means we're already 277 * accounted through the nohz accounting, so skip the entire deal and 278 * sync up for the next window. 279 */ 280 if (time_before(jiffies, this_rq->calc_load_update + 10)) 281 this_rq->calc_load_update += LOAD_FREQ; 282 } 283 284 static long calc_load_nohz_read(void) 285 { 286 int idx = calc_load_read_idx(); 287 long delta = 0; 288 289 if (atomic_long_read(&calc_load_nohz[idx])) 290 delta = atomic_long_xchg(&calc_load_nohz[idx], 0); 291 292 return delta; 293 } 294 295 /* 296 * NO_HZ can leave us missing all per-CPU ticks calling 297 * calc_load_fold_active(), but since a NO_HZ CPU folds its delta into 298 * calc_load_nohz per calc_load_nohz_start(), all we need to do is fold 299 * in the pending NO_HZ delta if our NO_HZ period crossed a load cycle boundary. 300 * 301 * Once we've updated the global active value, we need to apply the exponential 302 * weights adjusted to the number of cycles missed. 303 */ 304 static void calc_global_nohz(void) 305 { 306 unsigned long sample_window; 307 long delta, active, n; 308 309 sample_window = READ_ONCE(calc_load_update); 310 if (!time_before(jiffies, sample_window + 10)) { 311 /* 312 * Catch-up, fold however many we are behind still 313 */ 314 delta = jiffies - sample_window - 10; 315 n = 1 + (delta / LOAD_FREQ); 316 317 active = atomic_long_read(&calc_load_tasks); 318 active = active > 0 ? active * FIXED_1 : 0; 319 320 avenrun[0] = calc_load_n(avenrun[0], EXP_1, active, n); 321 avenrun[1] = calc_load_n(avenrun[1], EXP_5, active, n); 322 avenrun[2] = calc_load_n(avenrun[2], EXP_15, active, n); 323 324 WRITE_ONCE(calc_load_update, sample_window + n * LOAD_FREQ); 325 } 326 327 /* 328 * Flip the NO_HZ index... 329 * 330 * Make sure we first write the new time then flip the index, so that 331 * calc_load_write_idx() will see the new time when it reads the new 332 * index, this avoids a double flip messing things up. 333 */ 334 smp_wmb(); 335 calc_load_idx++; 336 } 337 #else /* !CONFIG_NO_HZ_COMMON */ 338 339 static inline long calc_load_nohz_read(void) { return 0; } 340 static inline void calc_global_nohz(void) { } 341 342 #endif /* CONFIG_NO_HZ_COMMON */ 343 344 /* 345 * calc_load - update the avenrun load estimates 10 ticks after the 346 * CPUs have updated calc_load_tasks. 347 * 348 * Called from the global timer code. 349 */ 350 void calc_global_load(unsigned long ticks) 351 { 352 unsigned long sample_window; 353 long active, delta; 354 355 sample_window = READ_ONCE(calc_load_update); 356 if (time_before(jiffies, sample_window + 10)) 357 return; 358 359 /* 360 * Fold the 'old' NO_HZ-delta to include all NO_HZ CPUs. 361 */ 362 delta = calc_load_nohz_read(); 363 if (delta) 364 atomic_long_add(delta, &calc_load_tasks); 365 366 active = atomic_long_read(&calc_load_tasks); 367 active = active > 0 ? active * FIXED_1 : 0; 368 369 avenrun[0] = calc_load(avenrun[0], EXP_1, active); 370 avenrun[1] = calc_load(avenrun[1], EXP_5, active); 371 avenrun[2] = calc_load(avenrun[2], EXP_15, active); 372 373 WRITE_ONCE(calc_load_update, sample_window + LOAD_FREQ); 374 375 /* 376 * In case we went to NO_HZ for multiple LOAD_FREQ intervals 377 * catch up in bulk. 378 */ 379 calc_global_nohz(); 380 } 381 382 /* 383 * Called from scheduler_tick() to periodically update this CPU's 384 * active count. 385 */ 386 void calc_global_load_tick(struct rq *this_rq) 387 { 388 long delta; 389 390 if (time_before(jiffies, this_rq->calc_load_update)) 391 return; 392 393 delta = calc_load_fold_active(this_rq, 0); 394 if (delta) 395 atomic_long_add(delta, &calc_load_tasks); 396 397 this_rq->calc_load_update += LOAD_FREQ; 398 } 399