3 # include <linux/string.h>
4 # include <linux/slab.h>
5 # include <linux/bug.h>
6 # include <linux/kernel.h>
8 # define dprintk(args...)
15 # define BUG_ON(x) assert(!(x))
16 # define dprintk(args...) /* printf(args) */
17 # define kmalloc(x, f) malloc(x)
18 # define kfree(x) free(x)
21 #include <linux/crush/crush.h>
22 #include <linux/crush/hash.h>
23 #include "crush_ln_table.h"
26 * Implement the core CRUSH mapping algorithm.
30 * crush_find_rule - find a crush_rule id for a given ruleset, type, and size.
32 * @ruleset: the storage ruleset id (user defined)
33 * @type: storage ruleset type (user defined)
34 * @size: output set size
36 int crush_find_rule(const struct crush_map *map, int ruleset, int type, int size)
40 for (i = 0; i < map->max_rules; i++) {
42 map->rules[i]->mask.ruleset == ruleset &&
43 map->rules[i]->mask.type == type &&
44 map->rules[i]->mask.min_size <= size &&
45 map->rules[i]->mask.max_size >= size)
53 * bucket choose methods
55 * For each bucket algorithm, we have a "choose" method that, given a
56 * crush input @x and replica position (usually, position in output set) @r,
57 * will produce an item in the bucket.
61 * Choose based on a random permutation of the bucket.
63 * We used to use some prime number arithmetic to do this, but it
64 * wasn't very random, and had some other bad behaviors. Instead, we
65 * calculate an actual random permutation of the bucket members.
66 * Since this is expensive, we optimize for the r=0 case, which
67 * captures the vast majority of calls.
69 static int bucket_perm_choose(struct crush_bucket *bucket,
72 unsigned int pr = r % bucket->size;
75 /* start a new permutation if @x has changed */
76 if (bucket->perm_x != (__u32)x || bucket->perm_n == 0) {
77 dprintk("bucket %d new x=%d\n", bucket->id, x);
80 /* optimize common r=0 case */
82 s = crush_hash32_3(bucket->hash, x, bucket->id, 0) %
85 bucket->perm_n = 0xffff; /* magic value, see below */
89 for (i = 0; i < bucket->size; i++)
92 } else if (bucket->perm_n == 0xffff) {
93 /* clean up after the r=0 case above */
94 for (i = 1; i < bucket->size; i++)
96 bucket->perm[bucket->perm[0]] = 0;
100 /* calculate permutation up to pr */
101 for (i = 0; i < bucket->perm_n; i++)
102 dprintk(" perm_choose have %d: %d\n", i, bucket->perm[i]);
103 while (bucket->perm_n <= pr) {
104 unsigned int p = bucket->perm_n;
105 /* no point in swapping the final entry */
106 if (p < bucket->size - 1) {
107 i = crush_hash32_3(bucket->hash, x, bucket->id, p) %
110 unsigned int t = bucket->perm[p + i];
111 bucket->perm[p + i] = bucket->perm[p];
114 dprintk(" perm_choose swap %d with %d\n", p, p+i);
118 for (i = 0; i < bucket->size; i++)
119 dprintk(" perm_choose %d: %d\n", i, bucket->perm[i]);
121 s = bucket->perm[pr];
123 dprintk(" perm_choose %d sz=%d x=%d r=%d (%d) s=%d\n", bucket->id,
124 bucket->size, x, r, pr, s);
125 return bucket->items[s];
129 static int bucket_uniform_choose(struct crush_bucket_uniform *bucket,
132 return bucket_perm_choose(&bucket->h, x, r);
136 static int bucket_list_choose(struct crush_bucket_list *bucket,
141 for (i = bucket->h.size-1; i >= 0; i--) {
142 __u64 w = crush_hash32_4(bucket->h.hash,x, bucket->h.items[i],
145 dprintk("list_choose i=%d x=%d r=%d item %d weight %x "
147 i, x, r, bucket->h.items[i], bucket->item_weights[i],
148 bucket->sum_weights[i], w);
149 w *= bucket->sum_weights[i];
151 /*dprintk(" scaled %llx\n", w);*/
152 if (w < bucket->item_weights[i])
153 return bucket->h.items[i];
156 dprintk("bad list sums for bucket %d\n", bucket->h.id);
157 return bucket->h.items[0];
162 static int height(int n)
165 while ((n & 1) == 0) {
172 static int left(int x)
175 return x - (1 << (h-1));
178 static int right(int x)
181 return x + (1 << (h-1));
184 static int terminal(int x)
189 static int bucket_tree_choose(struct crush_bucket_tree *bucket,
197 n = bucket->num_nodes >> 1;
199 while (!terminal(n)) {
201 /* pick point in [0, w) */
202 w = bucket->node_weights[n];
203 t = (__u64)crush_hash32_4(bucket->h.hash, x, n, r,
204 bucket->h.id) * (__u64)w;
207 /* descend to the left or right? */
209 if (t < bucket->node_weights[l])
215 return bucket->h.items[n >> 1];
221 static int bucket_straw_choose(struct crush_bucket_straw *bucket,
229 for (i = 0; i < bucket->h.size; i++) {
230 draw = crush_hash32_3(bucket->h.hash, x, bucket->h.items[i], r);
232 draw *= bucket->straws[i];
233 if (i == 0 || draw > high_draw) {
238 return bucket->h.items[high];
241 // compute 2^44*log2(input+1)
242 uint64_t crush_ln(unsigned xin)
245 int iexpon, index1, index2;
246 uint64_t RH, LH, LL, xl64, result;
252 while(!(x&0x18000)) { x<<=1; iexpon--; }
256 RH = __RH_LH_tbl[index1 - 256];
257 // LH ~ 2^48 * log2(index1/256)
258 LH = __RH_LH_tbl[index1 + 1 - 256];
260 // RH*x ~ 2^48 * (2^15 + xf), xf<2^8
261 xl64 = (int64_t)x * RH;
266 result <<= (12 + 32);
269 // LL ~ 2^48*log2(1.0+index2/2^15)
270 LL = __LL_tbl[index2];
284 * for reference, see:
286 * http://en.wikipedia.org/wiki/Exponential_distribution#Distribution_of_the_minimum_of_exponential_random_variables
290 static int bucket_straw2_choose(struct crush_bucket_straw2 *bucket,
293 unsigned i, high = 0;
296 __s64 ln, draw, high_draw = 0;
298 for (i = 0; i < bucket->h.size; i++) {
299 w = bucket->item_weights[i];
301 u = crush_hash32_3(bucket->h.hash, x,
302 bucket->h.items[i], r);
306 * for some reason slightly less than 0x10000 produces
307 * a slightly more accurate distribution... probably a
310 * the natural log lookup table maps [0,0xffff]
311 * (corresponding to real numbers [1/0x10000, 1] to
312 * [0, 0xffffffffffff] (corresponding to real numbers
315 ln = crush_ln(u) - 0x1000000000000ll;
318 * divide by 16.16 fixed-point weight. note
319 * that the ln value is negative, so a larger
320 * weight means a larger (less negative) value
323 draw = div64_s64(ln, w);
328 if (i == 0 || draw > high_draw) {
333 return bucket->h.items[high];
337 static int crush_bucket_choose(struct crush_bucket *in, int x, int r)
339 dprintk(" crush_bucket_choose %d x=%d r=%d\n", in->id, x, r);
340 BUG_ON(in->size == 0);
342 case CRUSH_BUCKET_UNIFORM:
343 return bucket_uniform_choose((struct crush_bucket_uniform *)in,
345 case CRUSH_BUCKET_LIST:
346 return bucket_list_choose((struct crush_bucket_list *)in,
348 case CRUSH_BUCKET_TREE:
349 return bucket_tree_choose((struct crush_bucket_tree *)in,
351 case CRUSH_BUCKET_STRAW:
352 return bucket_straw_choose((struct crush_bucket_straw *)in,
354 case CRUSH_BUCKET_STRAW2:
355 return bucket_straw2_choose((struct crush_bucket_straw2 *)in,
358 dprintk("unknown bucket %d alg %d\n", in->id, in->alg);
365 * true if device is marked "out" (failed, fully offloaded)
368 static int is_out(const struct crush_map *map,
369 const __u32 *weight, int weight_max,
372 if (item >= weight_max)
374 if (weight[item] >= 0x10000)
376 if (weight[item] == 0)
378 if ((crush_hash32_2(CRUSH_HASH_RJENKINS1, x, item) & 0xffff)
385 * crush_choose_firstn - choose numrep distinct items of given type
386 * @map: the crush_map
387 * @bucket: the bucket we are choose an item from
388 * @x: crush input value
389 * @numrep: the number of items to choose
390 * @type: the type of item to choose
391 * @out: pointer to output vector
392 * @outpos: our position in that vector
393 * @out_size: size of the out vector
394 * @tries: number of attempts to make
395 * @recurse_tries: number of attempts to have recursive chooseleaf make
396 * @local_retries: localized retries
397 * @local_fallback_retries: localized fallback retries
398 * @recurse_to_leaf: true if we want one device under each item of given type (chooseleaf instead of choose)
399 * @vary_r: pass r to recursive calls
400 * @out2: second output vector for leaf items (if @recurse_to_leaf)
401 * @parent_r: r value passed from the parent
403 static int crush_choose_firstn(const struct crush_map *map,
404 struct crush_bucket *bucket,
405 const __u32 *weight, int weight_max,
406 int x, int numrep, int type,
407 int *out, int outpos,
410 unsigned int recurse_tries,
411 unsigned int local_retries,
412 unsigned int local_fallback_retries,
419 unsigned int ftotal, flocal;
420 int retry_descent, retry_bucket, skip_rep;
421 struct crush_bucket *in = bucket;
427 int count = out_size;
429 dprintk("CHOOSE%s bucket %d x %d outpos %d numrep %d tries %d recurse_tries %d local_retries %d local_fallback_retries %d parent_r %d\n",
430 recurse_to_leaf ? "_LEAF" : "",
431 bucket->id, x, outpos, numrep,
432 tries, recurse_tries, local_retries, local_fallback_retries,
435 for (rep = outpos; rep < numrep && count > 0 ; rep++) {
436 /* keep trying until we get a non-out, non-colliding item */
441 in = bucket; /* initial bucket */
443 /* choose through intervening buckets */
449 /* r' = r + f_total */
457 if (local_fallback_retries > 0 &&
458 flocal >= (in->size>>1) &&
459 flocal > local_fallback_retries)
460 item = bucket_perm_choose(in, x, r);
462 item = crush_bucket_choose(in, x, r);
463 if (item >= map->max_devices) {
464 dprintk(" bad item %d\n", item);
471 itemtype = map->buckets[-1-item]->type;
474 dprintk(" item %d type %d\n", item, itemtype);
477 if (itemtype != type) {
479 (-1-item) >= map->max_buckets) {
480 dprintk(" bad item type %d\n", type);
484 in = map->buckets[-1-item];
490 for (i = 0; i < outpos; i++) {
491 if (out[i] == item) {
498 if (!collide && recurse_to_leaf) {
502 sub_r = r >> (vary_r-1);
505 if (crush_choose_firstn(map,
506 map->buckets[-1-item],
512 local_fallback_retries,
517 /* didn't get leaf */
520 /* we already have a leaf! */
528 reject = is_out(map, weight,
536 if (reject || collide) {
540 if (collide && flocal <= local_retries)
541 /* retry locally a few times */
543 else if (local_fallback_retries > 0 &&
544 flocal <= in->size + local_fallback_retries)
545 /* exhaustive bucket search */
547 else if (ftotal < tries)
548 /* then retry descent */
553 dprintk(" reject %d collide %d "
554 "ftotal %u flocal %u\n",
555 reject, collide, ftotal,
558 } while (retry_bucket);
559 } while (retry_descent);
562 dprintk("skip rep\n");
566 dprintk("CHOOSE got %d\n", item);
572 dprintk("CHOOSE returns %d\n", outpos);
578 * crush_choose_indep: alternative breadth-first positionally stable mapping
581 static void crush_choose_indep(const struct crush_map *map,
582 struct crush_bucket *bucket,
583 const __u32 *weight, int weight_max,
584 int x, int left, int numrep, int type,
585 int *out, int outpos,
587 unsigned int recurse_tries,
592 struct crush_bucket *in = bucket;
593 int endpos = outpos + left;
602 dprintk("CHOOSE%s INDEP bucket %d x %d outpos %d numrep %d\n", recurse_to_leaf ? "_LEAF" : "",
603 bucket->id, x, outpos, numrep);
605 /* initially my result is undefined */
606 for (rep = outpos; rep < endpos; rep++) {
607 out[rep] = CRUSH_ITEM_UNDEF;
609 out2[rep] = CRUSH_ITEM_UNDEF;
612 for (ftotal = 0; left > 0 && ftotal < tries; ftotal++) {
613 for (rep = outpos; rep < endpos; rep++) {
614 if (out[rep] != CRUSH_ITEM_UNDEF)
617 in = bucket; /* initial bucket */
619 /* choose through intervening buckets */
621 /* note: we base the choice on the position
622 * even in the nested call. that means that
623 * if the first layer chooses the same bucket
624 * in a different position, we will tend to
625 * choose a different item in that bucket.
626 * this will involve more devices in data
627 * movement and tend to distribute the load.
632 if (in->alg == CRUSH_BUCKET_UNIFORM &&
633 in->size % numrep == 0)
634 /* r'=r+(n+1)*f_total */
635 r += (numrep+1) * ftotal;
637 /* r' = r + n*f_total */
638 r += numrep * ftotal;
642 dprintk(" empty bucket\n");
646 item = crush_bucket_choose(in, x, r);
647 if (item >= map->max_devices) {
648 dprintk(" bad item %d\n", item);
649 out[rep] = CRUSH_ITEM_NONE;
651 out2[rep] = CRUSH_ITEM_NONE;
658 itemtype = map->buckets[-1-item]->type;
661 dprintk(" item %d type %d\n", item, itemtype);
664 if (itemtype != type) {
666 (-1-item) >= map->max_buckets) {
667 dprintk(" bad item type %d\n", type);
668 out[rep] = CRUSH_ITEM_NONE;
675 in = map->buckets[-1-item];
681 for (i = outpos; i < endpos; i++) {
682 if (out[i] == item) {
690 if (recurse_to_leaf) {
692 crush_choose_indep(map,
693 map->buckets[-1-item],
699 if (out2[rep] == CRUSH_ITEM_NONE) {
700 /* placed nothing; no leaf */
704 /* we already have a leaf! */
711 is_out(map, weight, weight_max, item, x))
721 for (rep = outpos; rep < endpos; rep++) {
722 if (out[rep] == CRUSH_ITEM_UNDEF) {
723 out[rep] = CRUSH_ITEM_NONE;
725 if (out2 && out2[rep] == CRUSH_ITEM_UNDEF) {
726 out2[rep] = CRUSH_ITEM_NONE;
732 * crush_do_rule - calculate a mapping with the given input and rule
733 * @map: the crush_map
734 * @ruleno: the rule id
736 * @result: pointer to result vector
737 * @result_max: maximum result size
738 * @weight: weight vector (for map leaves)
739 * @weight_max: size of weight vector
740 * @scratch: scratch vector for private use; must be >= 3 * result_max
742 int crush_do_rule(const struct crush_map *map,
743 int ruleno, int x, int *result, int result_max,
744 const __u32 *weight, int weight_max,
749 int *b = scratch + result_max;
750 int *c = scratch + result_max*2;
757 struct crush_rule *rule;
763 * the original choose_total_tries value was off by one (it
764 * counted "retries" and not "tries"). add one.
766 int choose_tries = map->choose_total_tries + 1;
767 int choose_leaf_tries = 0;
769 * the local tries values were counted as "retries", though,
770 * and need no adjustment
772 int choose_local_retries = map->choose_local_tries;
773 int choose_local_fallback_retries = map->choose_local_fallback_tries;
775 int vary_r = map->chooseleaf_vary_r;
777 if ((__u32)ruleno >= map->max_rules) {
778 dprintk(" bad ruleno %d\n", ruleno);
782 rule = map->rules[ruleno];
787 for (step = 0; step < rule->len; step++) {
789 struct crush_rule_step *curstep = &rule->steps[step];
791 switch (curstep->op) {
792 case CRUSH_RULE_TAKE:
793 w[0] = curstep->arg1;
797 case CRUSH_RULE_SET_CHOOSE_TRIES:
798 if (curstep->arg1 > 0)
799 choose_tries = curstep->arg1;
802 case CRUSH_RULE_SET_CHOOSELEAF_TRIES:
803 if (curstep->arg1 > 0)
804 choose_leaf_tries = curstep->arg1;
807 case CRUSH_RULE_SET_CHOOSE_LOCAL_TRIES:
808 if (curstep->arg1 >= 0)
809 choose_local_retries = curstep->arg1;
812 case CRUSH_RULE_SET_CHOOSE_LOCAL_FALLBACK_TRIES:
813 if (curstep->arg1 >= 0)
814 choose_local_fallback_retries = curstep->arg1;
817 case CRUSH_RULE_SET_CHOOSELEAF_VARY_R:
818 if (curstep->arg1 >= 0)
819 vary_r = curstep->arg1;
822 case CRUSH_RULE_CHOOSELEAF_FIRSTN:
823 case CRUSH_RULE_CHOOSE_FIRSTN:
826 case CRUSH_RULE_CHOOSELEAF_INDEP:
827 case CRUSH_RULE_CHOOSE_INDEP:
833 CRUSH_RULE_CHOOSELEAF_FIRSTN ||
835 CRUSH_RULE_CHOOSELEAF_INDEP;
840 for (i = 0; i < wsize; i++) {
842 * see CRUSH_N, CRUSH_N_MINUS macros.
843 * basically, numrep <= 0 means relative to
844 * the provided result_max
846 numrep = curstep->arg1;
848 numrep += result_max;
855 if (choose_leaf_tries)
858 else if (map->chooseleaf_descend_once)
861 recurse_tries = choose_tries;
862 osize += crush_choose_firstn(
864 map->buckets[-1-w[i]],
872 choose_local_retries,
873 choose_local_fallback_retries,
879 out_size = ((numrep < (result_max-osize)) ?
880 numrep : (result_max-osize));
883 map->buckets[-1-w[i]],
890 choose_leaf_tries : 1,
899 /* copy final _leaf_ values to output set */
900 memcpy(o, c, osize*sizeof(*o));
902 /* swap o and w arrays */
910 case CRUSH_RULE_EMIT:
911 for (i = 0; i < wsize && result_len < result_max; i++) {
912 result[result_len] = w[i];
919 dprintk(" unknown op %d at step %d\n",