#ifdef __KERNEL__
# include <linux/string.h>
# include <linux/slab.h>
# include <linux/bug.h>
# include <linux/kernel.h>
# ifndef dprintk
# define dprintk(args...)
# endif
#else
# include <string.h>
# include <stdio.h>
# include <stdlib.h>
# include <assert.h>
# define BUG_ON(x) assert(!(x))
# define dprintk(args...) /* printf(args) */
# define kmalloc(x, f) malloc(x)
# define kfree(x) free(x)
#endif
#include <linux/crush/crush.h>
#include <linux/crush/hash.h>
#include "crush_ln_table.h"
/*
* Implement the core CRUSH mapping algorithm.
*/
/**
* crush_find_rule - find a crush_rule id for a given ruleset, type, and size.
* @map: the crush_map
* @ruleset: the storage ruleset id (user defined)
* @type: storage ruleset type (user defined)
* @size: output set size
*/
int crush_find_rule(const struct crush_map *map, int ruleset, int type, int size)
{
__u32 i;
for (i = 0; i < map->max_rules; i++) {
if (map->rules[i] &&
map->rules[i]->mask.ruleset == ruleset &&
map->rules[i]->mask.type == type &&
map->rules[i]->mask.min_size <= size &&
map->rules[i]->mask.max_size >= size)
return i;
}
return -1;
}
/*
* bucket choose methods
*
* For each bucket algorithm, we have a "choose" method that, given a
* crush input @x and replica position (usually, position in output set) @r,
* will produce an item in the bucket.
*/
/*
* Choose based on a random permutation of the bucket.
*
* We used to use some prime number arithmetic to do this, but it
* wasn't very random, and had some other bad behaviors. Instead, we
* calculate an actual random permutation of the bucket members.
* Since this is expensive, we optimize for the r=0 case, which
* captures the vast majority of calls.
*/
static int bucket_perm_choose(struct crush_bucket *bucket,
int x, int r)
{
unsigned int pr = r % bucket->size;
unsigned int i, s;
/* start a new permutation if @x has changed */
if (bucket->perm_x != (__u32)x || bucket->perm_n == 0) {
dprintk("bucket %d new x=%d\n", bucket->id, x);
bucket->perm_x = x;
/* optimize common r=0 case */
if (pr == 0) {
s = crush_hash32_3(bucket->hash, x, bucket->id, 0) %
bucket->size;
bucket->perm[0] = s;
bucket->perm_n = 0xffff; /* magic value, see below */
goto out;
}
for (i = 0; i < bucket->size; i++)
bucket->perm[i] = i;
bucket->perm_n = 0;
} else if (bucket->perm_n == 0xffff) {
/* clean up after the r=0 case above */
for (i = 1; i < bucket->size; i++)
bucket->perm[i] = i;
bucket->perm[bucket->perm[0]] = 0;
bucket->perm_n = 1;
}
/* calculate permutation up to pr */
for (i = 0; i < bucket->perm_n; i++)
dprintk(" perm_choose have %d: %d\n", i, bucket->perm[i]);
while (bucket->perm_n <= pr) {
unsigned int p = bucket->perm_n;
/* no point in swapping the final entry */
if (p < bucket->size - 1) {
i = crush_hash32_3(bucket->hash, x, bucket->id, p) %
(bucket->size - p);
if (i) {
unsigned int t = bucket->perm[p + i];
bucket->perm[p + i] = bucket->perm[p];
bucket->perm[p] = t;
}
dprintk(" perm_choose swap %d with %d\n", p, p+i);
}
bucket->perm_n++;
}
for (i = 0; i < bucket->size; i++)
dprintk(" perm_choose %d: %d\n", i, bucket->perm[i]);
s = bucket->perm[pr];
out:
dprintk(" perm_choose %d sz=%d x=%d r=%d (%d) s=%d\n", bucket->id,
bucket->size, x, r, pr, s);
return bucket->items[s];
}
/* uniform */
static int bucket_uniform_choose(struct crush_bucket_uniform *bucket,
int x, int r)
{
return bucket_perm_choose(&bucket->h, x, r);
}
/* list */
static int bucket_list_choose(struct crush_bucket_list *bucket,
int x, int r)
{
int i;
for (i = bucket->h.size-1; i >= 0; i--) {
__u64 w = crush_hash32_4(bucket->h.hash,x, bucket->h.items[i],
r, bucket->h.id);
w &= 0xffff;
dprintk("list_choose i=%d x=%d r=%d item %d weight %x "
"sw %x rand %llx",
i, x, r, bucket->h.items[i], bucket->item_weights[i],
bucket->sum_weights[i], w);
w *= bucket->sum_weights[i];
w = w >> 16;
/*dprintk(" scaled %llx\n", w);*/
if (w < bucket->item_weights[i])
return bucket->h.items[i];
}
dprintk("bad list sums for bucket %d\n", bucket->h.id);
return bucket->h.items[0];
}
/* (binary) tree */
static int height(int n)
{
int h = 0;
while ((n & 1) == 0) {
h++;
n = n >> 1;
}
return h;
}
static int left(int x)
{
int h = height(x);
return x - (1 << (h-1));
}
static int right(int x)
{
int h = height(x);
return x + (1 << (h-1));
}
static int terminal(int x)
{
return x & 1;
}
static int bucket_tree_choose(struct crush_bucket_tree *bucket,
int x, int r)
{
int n;
__u32 w;
__u64 t;
/* start at root */
n = bucket->num_nodes >> 1;
while (!terminal(n)) {
int l;
/* pick point in [0, w) */
w = bucket->node_weights[n];
t = (__u64)crush_hash32_4(bucket->h.hash, x, n, r,
bucket->h.id) * (__u64)w;
t = t >> 32;
/* descend to the left or right? */
l = left(n);
if (t < bucket->node_weights[l])
n = l;
else
n = right(n);
}
return bucket->h.items[n >> 1];
}
/* straw */
static int bucket_straw_choose(struct crush_bucket_straw *bucket,
int x, int r)
{
__u32 i;
int high = 0;
__u64 high_draw = 0;
__u64 draw;
for (i = 0; i < bucket->h.size; i++) {
draw = crush_hash32_3(bucket->h.hash, x, bucket->h.items[i], r);
draw &= 0xffff;
draw *= bucket->straws[i];
if (i == 0 || draw > high_draw) {
high = i;
high_draw = draw;
}
}
return bucket->h.items[high];
}
// compute 2^44*log2(input+1)
uint64_t crush_ln(unsigned xin)
{
unsigned x=xin, x1;
int iexpon, index1, index2;
uint64_t RH, LH, LL, xl64, result;
x++;
// normalize input
iexpon = 15;
while(!(x&0x18000)) { x<<=1; iexpon--; }
index1 = (x>>8)<<1;
// RH ~ 2^56/index1
RH = __RH_LH_tbl[index1 - 256];
// LH ~ 2^48 * log2(index1/256)
LH = __RH_LH_tbl[index1 + 1 - 256];
// RH*x ~ 2^48 * (2^15 + xf), xf<2^8
xl64 = (int64_t)x * RH;
xl64 >>= 48;
x1 = xl64;
result = iexpon;
result <<= (12 + 32);
index2 = x1 & 0xff;
// LL ~ 2^48*log2(1.0+index2/2^15)
LL = __LL_tbl[index2];
LH = LH + LL;
LH >>= (48-12 - 32);
result += LH;
return result;
}
/*
* straw2
*
* for reference, see:
*
* http://en.wikipedia.org/wiki/Exponential_distribution#Distribution_of_the_minimum_of_exponential_random_variables
*
*/
static int bucket_straw2_choose(struct crush_bucket_straw2 *bucket,
int x, int r)
{
unsigned i, high = 0;
unsigned u;
unsigned w;
__s64 ln, draw, high_draw = 0;
for (i = 0; i < bucket->h.size; i++) {
w = bucket->item_weights[i];
if (w) {
u = crush_hash32_3(bucket->h.hash, x,
bucket->h.items[i], r);
u &= 0xffff;
/*
* for some reason slightly less than 0x10000 produces
* a slightly more accurate distribution... probably a
* rounding effect.
*
* the natural log lookup table maps [0,0xffff]
* (corresponding to real numbers [1/0x10000, 1] to
* [0, 0xffffffffffff] (corresponding to real numbers
* [-11.090355,0]).
*/
ln = crush_ln(u) - 0x1000000000000ll;
/*
* divide by 16.16 fixed-point weight. note
* that the ln value is negative, so a larger
* weight means a larger (less negative) value
* for draw.
*/
draw = div64_s64(ln, w);
} else {
draw = S64_MIN;
}
if (i == 0 || draw > high_draw) {
high = i;
high_draw = draw;
}
}
return bucket->h.items[high];
}
static int crush_bucket_choose(struct crush_bucket *in, int x, int r)
{
dprintk(" crush_bucket_choose %d x=%d r=%d\n", in->id, x, r);
BUG_ON(in->size == 0);
switch (in->alg) {
case CRUSH_BUCKET_UNIFORM:
return bucket_uniform_choose((struct crush_bucket_uniform *)in,
x, r);
case CRUSH_BUCKET_LIST:
return bucket_list_choose((struct crush_bucket_list *)in,
x, r);
case CRUSH_BUCKET_TREE:
return bucket_tree_choose((struct crush_bucket_tree *)in,
x, r);
case CRUSH_BUCKET_STRAW:
return bucket_straw_choose((struct crush_bucket_straw *)in,
x, r);
case CRUSH_BUCKET_STRAW2:
return bucket_straw2_choose((struct crush_bucket_straw2 *)in,
x, r);
default:
dprintk("unknown bucket %d alg %d\n", in->id, in->alg);
return in->items[0];
}
}
/*
* true if device is marked "out" (failed, fully offloaded)
* of the cluster
*/
static int is_out(const struct crush_map *map,
const __u32 *weight, int weight_max,
int item, int x)
{
if (item >= weight_max)
return 1;
if (weight[item] >= 0x10000)
return 0;
if (weight[item] == 0)
return 1;
if ((crush_hash32_2(CRUSH_HASH_RJENKINS1, x, item) & 0xffff)
< weight[item])
return 0;
return 1;
}
/**
* crush_choose_firstn - choose numrep distinct items of given type
* @map: the crush_map
* @bucket: the bucket we are choose an item from
* @x: crush input value
* @numrep: the number of items to choose
* @type: the type of item to choose
* @out: pointer to output vector
* @outpos: our position in that vector
* @out_size: size of the out vector
* @tries: number of attempts to make
* @recurse_tries: number of attempts to have recursive chooseleaf make
* @local_retries: localized retries
* @local_fallback_retries: localized fallback retries
* @recurse_to_leaf: true if we want one device under each item of given type (chooseleaf instead of choose)
* @vary_r: pass r to recursive calls
* @out2: second output vector for leaf items (if @recurse_to_leaf)
* _r: r value passed from the parent
*/
static int crush_choose_firstn(const struct crush_map *map,
struct crush_bucket *bucket,
const __u32 *weight, int weight_max,
int x, int numrep, int type,
int *out, int outpos,
int out_size,
unsigned int tries,
unsigned int recurse_tries,
unsigned int local_retries,
unsigned int local_fallback_retries,
int recurse_to_leaf,
unsigned int vary_r,
int *out2,
int parent_r)
{
int rep;
unsigned int ftotal, flocal;
int retry_descent, retry_bucket, skip_rep;
struct crush_bucket *in = bucket;
int r;
int i;
int item = 0;
int itemtype;
int collide, reject;
int count = out_size;
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",
recurse_to_leaf ? "_LEAF" : "",
bucket->id, x, outpos, numrep,
tries, recurse_tries, local_retries, local_fallback_retries,
parent_r);
for (rep = outpos; rep < numrep && count > 0 ; rep++) {
/* keep trying until we get a non-out, non-colliding item */
ftotal = 0;
skip_rep = 0;
do {
retry_descent = 0;
in = bucket; /* initial bucket */
/* choose through intervening buckets */
flocal = 0;
do {
collide = 0;
retry_bucket = 0;
r = rep + parent_r;
/* r' = r + f_total */
r += ftotal;
/* bucket choose */
if (in->size == 0) {
reject = 1;
goto reject;
}
if (local_fallback_retries > 0 &&
flocal >= (in->size>>1) &&
flocal > local_fallback_retries)
item = bucket_perm_choose(in, x, r);
else
item = crush_bucket_choose(in, x, r);
if (item >= map->max_devices) {
dprintk(" bad item %d\n", item);
skip_rep = 1;
break;
}
/* desired type? */
if (item < 0)
itemtype = map->buckets[-1-item]->type;
else
itemtype = 0;
dprintk(" item %d type %d\n", item, itemtype);
/* keep going? */
if (itemtype != type) {
if (item >= 0 ||
(-1-item) >= map->max_buckets) {
dprintk(" bad item type %d\n", type);
skip_rep = 1;
break;
}
in = map->buckets[-1-item];
retry_bucket = 1;
continue;
}
/* collision? */
for (i = 0; i < outpos; i++) {
if (out[i] == item) {
collide = 1;
break;
}
}
reject = 0;
if (!collide && recurse_to_leaf) {
if (item < 0) {
int sub_r;
if (vary_r)
sub_r = r >> (vary_r-1);
else
sub_r = 0;
if (crush_choose_firstn(map,
map->buckets[-1-item],
weight, weight_max,
x, outpos+1, 0,
out2, outpos, count,
recurse_tries, 0,
local_retries,
local_fallback_retries,
0,
vary_r,
NULL,
sub_r) <= outpos)
/* didn't get leaf */
reject = 1;
} else {
/* we already have a leaf! */
out2[outpos] = item;
}
}
if (!reject) {
/* out? */
if (itemtype == 0)
reject = is_out(map, weight,
weight_max,
item, x);
else
reject = 0;
}
reject:
if (reject || collide) {
ftotal++;
flocal++;
if (collide && flocal <= local_retries)
/* retry locally a few times */
retry_bucket = 1;
else if (local_fallback_retries > 0 &&
flocal <= in->size + local_fallback_retries)
/* exhaustive bucket search */
retry_bucket = 1;
else if (ftotal < tries)
/* then retry descent */
retry_descent = 1;
else
/* else give up */
skip_rep = 1;
dprintk(" reject %d collide %d "
"ftotal %u flocal %u\n",
reject, collide, ftotal,
flocal);
}
} while (retry_bucket);
} while (retry_descent);
if (skip_rep) {
dprintk("skip rep\n");
continue;
}
dprintk("CHOOSE got %d\n", item);
out[outpos] = item;
outpos++;
count--;
}
dprintk("CHOOSE returns %d\n", outpos);
return outpos;
}
/**
* crush_choose_indep: alternative breadth-first positionally stable mapping
*
*/
static void crush_choose_indep(const struct crush_map *map,
struct crush_bucket *bucket,
const __u32 *weight, int weight_max,
int x, int left, int numrep, int type,
int *out, int outpos,
unsigned int tries,
unsigned int recurse_tries,
int recurse_to_leaf,
int *out2,
int parent_r)
{
struct crush_bucket *in = bucket;
int endpos = outpos + left;
int rep;
unsigned int ftotal;
int r;
int i;
int item = 0;
int itemtype;
int collide;
dprintk("CHOOSE%s INDEP bucket %d x %d outpos %d numrep %d\n", recurse_to_leaf ? "_LEAF" : "",
bucket->id, x, outpos, numrep);
/* initially my result is undefined */
for (rep = outpos; rep < endpos; rep++) {
out[rep] = CRUSH_ITEM_UNDEF;
if (out2)
out2[rep] = CRUSH_ITEM_UNDEF;
}
for (ftotal = 0; left > 0 && ftotal < tries; ftotal++) {
for (rep = outpos; rep < endpos; rep++) {
if (out[rep] != CRUSH_ITEM_UNDEF)
continue;
in = bucket; /* initial bucket */
/* choose through intervening buckets */
for (;;) {
/* note: we base the choice on the position
* even in the nested call. that means that
* if the first layer chooses the same bucket
* in a different position, we will tend to
* choose a different item in that bucket.
* this will involve more devices in data
* movement and tend to distribute the load.
*/
r = rep + parent_r;
/* be careful */
if (in->alg == CRUSH_BUCKET_UNIFORM &&
in->size % numrep == 0)
/* r'=r+(n+1)*f_total */
r += (numrep+1) * ftotal;
else
/* r' = r + n*f_total */
r += numrep * ftotal;
/* bucket choose */
if (in->size == 0) {
dprintk(" empty bucket\n");
break;
}
item = crush_bucket_choose(in, x, r);
if (item >= map->max_devices) {
dprintk(" bad item %d\n", item);
out[rep] = CRUSH_ITEM_NONE;
if (out2)
out2[rep] = CRUSH_ITEM_NONE;
left--;
break;
}
/* desired type? */
if (item < 0)
itemtype = map->buckets[-1-item]->type;
else
itemtype = 0;
dprintk(" item %d type %d\n", item, itemtype);
/* keep going? */
if (itemtype != type) {
if (item >= 0 ||
(-1-item) >= map->max_buckets) {
dprintk(" bad item type %d\n", type);
out[rep] = CRUSH_ITEM_NONE;
if (out2)
out2[rep] =
CRUSH_ITEM_NONE;
left--;
break;
}
in = map->buckets[-1-item];
continue;
}
/* collision? */
collide = 0;
for (i = outpos; i < endpos; i++) {
if (out[i] == item) {
collide = 1;
break;
}
}
if (collide)
break;
if (recurse_to_leaf) {
if (item < 0) {
crush_choose_indep(map,
map->buckets[-1-item],
weight, weight_max,
x, 1, numrep, 0,
out2, rep,
recurse_tries, 0,
0, NULL, r);
if (out2[rep] == CRUSH_ITEM_NONE) {
/* placed nothing; no leaf */
break;
}
} else {
/* we already have a leaf! */
out2[rep] = item;
}
}
/* out? */
if (itemtype == 0 &&
is_out(map, weight, weight_max, item, x))
break;
/* yay! */
out[rep] = item;
left--;
break;
}
}
}
for (rep = outpos; rep < endpos; rep++) {
if (out[rep] == CRUSH_ITEM_UNDEF) {
out[rep] = CRUSH_ITEM_NONE;
}
if (out2 && out2[rep] == CRUSH_ITEM_UNDEF) {
out2[rep] = CRUSH_ITEM_NONE;
}
}
}
/**
* crush_do_rule - calculate a mapping with the given input and rule
* @map: the crush_map
* @ruleno: the rule id
* @x: hash input
* @result: pointer to result vector
* @result_max: maximum result size
* @weight: weight vector (for map leaves)
* @weight_max: size of weight vector
* @scratch: scratch vector for private use; must be >= 3 * result_max
*/
int crush_do_rule(const struct crush_map *map,
int ruleno, int x, int *result, int result_max,
const __u32 *weight, int weight_max,
int *scratch)
{
int result_len;
int *a = scratch;
int *b = scratch + result_max;
int *c = scratch + result_max*2;
int recurse_to_leaf;
int *w;
int wsize = 0;
int *o;
int osize;
int *tmp;
struct crush_rule *rule;
__u32 step;
int i, j;
int numrep;
int out_size;
/*
* the original choose_total_tries value was off by one (it
* counted "retries" and not "tries"). add one.
*/
int choose_tries = map->choose_total_tries + 1;
int choose_leaf_tries = 0;
/*
* the local tries values were counted as "retries", though,
* and need no adjustment
*/
int choose_local_retries = map->choose_local_tries;
int choose_local_fallback_retries = map->choose_local_fallback_tries;
int vary_r = map->chooseleaf_vary_r;
if ((__u32)ruleno >= map->max_rules) {
dprintk(" bad ruleno %d\n", ruleno);
return 0;
}
rule = map->rules[ruleno];
result_len = 0;
w = a;
o = b;
for (step = 0; step < rule->len; step++) {
int firstn = 0;
struct crush_rule_step *curstep = &rule->steps[step];
switch (curstep->op) {
case CRUSH_RULE_TAKE:
w[0] = curstep->arg1;
wsize = 1;
break;
case CRUSH_RULE_SET_CHOOSE_TRIES:
if (curstep->arg1 > 0)
choose_tries = curstep->arg1;
break;
case CRUSH_RULE_SET_CHOOSELEAF_TRIES:
if (curstep->arg1 > 0)
choose_leaf_tries = curstep->arg1;
break;
case CRUSH_RULE_SET_CHOOSE_LOCAL_TRIES:
if (curstep->arg1 >= 0)
choose_local_retries = curstep->arg1;
break;
case CRUSH_RULE_SET_CHOOSE_LOCAL_FALLBACK_TRIES:
if (curstep->arg1 >= 0)
choose_local_fallback_retries = curstep->arg1;
break;
case CRUSH_RULE_SET_CHOOSELEAF_VARY_R:
if (curstep->arg1 >= 0)
vary_r = curstep->arg1;
break;
case CRUSH_RULE_CHOOSELEAF_FIRSTN:
case CRUSH_RULE_CHOOSE_FIRSTN:
firstn = 1;
/* fall through */
case CRUSH_RULE_CHOOSELEAF_INDEP:
case CRUSH_RULE_CHOOSE_INDEP:
if (wsize == 0)
break;
recurse_to_leaf =
curstep->op ==
CRUSH_RULE_CHOOSELEAF_FIRSTN ||
curstep->op ==
CRUSH_RULE_CHOOSELEAF_INDEP;
/* reset output */
osize = 0;
for (i = 0; i < wsize; i++) {
/*
* see CRUSH_N, CRUSH_N_MINUS macros.
* basically, numrep <= 0 means relative to
* the provided result_max
*/
numrep = curstep->arg1;
if (numrep <= 0) {
numrep += result_max;
if (numrep <= 0)
continue;
}
j = 0;
if (firstn) {
int recurse_tries;
if (choose_leaf_tries)
recurse_tries =
choose_leaf_tries;
else if (map->chooseleaf_descend_once)
recurse_tries = 1;
else
recurse_tries = choose_tries;
osize += crush_choose_firstn(
map,
map->buckets[-1-w[i]],
weight, weight_max,
x, numrep,
curstep->arg2,
o+osize, j,
result_max-osize,
choose_tries,
recurse_tries,
choose_local_retries,
choose_local_fallback_retries,
recurse_to_leaf,
vary_r,
c+osize,
0);
} else {
out_size = ((numrep < (result_max-osize)) ?
numrep : (result_max-osize));
crush_choose_indep(
map,
map->buckets[-1-w[i]],
weight, weight_max,
x, out_size, numrep,
curstep->arg2,
o+osize, j,
choose_tries,
choose_leaf_tries ?
choose_leaf_tries : 1,
recurse_to_leaf,
c+osize,
0);
osize += out_size;
}
}
if (recurse_to_leaf)
/* copy final _leaf_ values to output set */
memcpy(o, c, osize*sizeof(*o));
/* swap o and w arrays */
tmp = o;
o = w;
w = tmp;
wsize = osize;
break;
case CRUSH_RULE_EMIT:
for (i = 0; i < wsize && result_len < result_max; i++) {
result[result_len] = w[i];
result_len++;
}
wsize = 0;
break;
default:
dprintk(" unknown op %d at step %d\n",
curstep->op, step);
break;
}
}
return result_len;
}