vitastor/mon/lp-optimizer.js

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// Copyright (c) Vitaliy Filippov, 2019+
// License: VNPL-1.1 (see README.md for details)
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// Data distribution optimizer using linear programming (lp_solve)
const child_process = require('child_process');
const NO_OSD = 'Z';
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async function lp_solve(text)
{
const cp = child_process.spawn('lp_solve');
let stdout = '', stderr = '', finish_cb;
cp.stdout.on('data', buf => stdout += buf.toString());
cp.stderr.on('data', buf => stderr += buf.toString());
cp.on('exit', () => finish_cb && finish_cb());
cp.stdin.write(text);
cp.stdin.end();
if (cp.exitCode == null)
{
await new Promise(ok => finish_cb = ok);
}
if (!stdout.trim())
{
return null;
}
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let score = 0;
let vars = {};
for (const line of stdout.split(/\n/))
{
let m = /^(^Value of objective function: (-?[\d\.]+)|Actual values of the variables:)\s*$/.exec(line);
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if (m)
{
if (m[2])
{
score = m[2];
}
continue;
}
else if (/This problem is (infeasible|unbounded)/.exec(line))
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{
return null;
}
let [ k, v ] = line.trim().split(/\s+/, 2);
if (v)
{
vars[k] = v;
}
}
return { score, vars };
}
async function optimize_initial({ osd_tree, pg_count, pg_size = 3, pg_minsize = 2, max_combinations = 10000, parity_space = 1 })
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{
if (!pg_count || !osd_tree)
{
return null;
}
const all_weights = Object.assign({}, ...Object.values(osd_tree));
const total_weight = Object.values(all_weights).reduce((a, c) => Number(a) + Number(c), 0);
const all_pgs = Object.values(random_combinations(osd_tree, pg_size, max_combinations, parity_space > 1));
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const pg_per_osd = {};
for (const pg of all_pgs)
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{
for (let i = 0; i < pg.length; i++)
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{
const osd = pg[i];
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pg_per_osd[osd] = pg_per_osd[osd] || [];
pg_per_osd[osd].push((i >= pg_minsize ? parity_space+'*' : '')+"pg_"+pg.join("_"));
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}
}
const pg_effsize = Math.min(pg_minsize, Object.keys(osd_tree).length)
+ Math.max(0, Math.min(pg_size, Object.keys(osd_tree).length) - pg_minsize) * parity_space;
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let lp = '';
lp += "max: "+all_pgs.map(pg => 'pg_'+pg.join('_')).join(' + ')+";\n";
for (const osd in pg_per_osd)
{
if (osd !== NO_OSD)
{
let osd_pg_count = all_weights[osd]/total_weight*pg_effsize*pg_count;
lp += pg_per_osd[osd].join(' + ')+' <= '+osd_pg_count+';\n';
}
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}
for (const pg of all_pgs)
{
lp += 'pg_'+pg.join('_')+" >= 0;\n";
}
lp += "sec "+all_pgs.map(pg => 'pg_'+pg.join('_')).join(', ')+";\n";
const lp_result = await lp_solve(lp);
if (!lp_result)
{
console.log(lp);
throw new Error('Problem is infeasible or unbounded - is it a bug?');
}
const int_pgs = make_int_pgs(lp_result.vars, pg_count);
const eff = pg_list_space_efficiency(int_pgs, all_weights, pg_minsize, parity_space);
const res = {
score: lp_result.score,
weights: lp_result.vars,
int_pgs,
space: eff * pg_effsize,
total_space: total_weight,
};
return res;
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}
function make_int_pgs(weights, pg_count)
{
const total_weight = Object.values(weights).reduce((a, c) => Number(a) + Number(c), 0);
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let int_pgs = [];
let pg_left = pg_count;
let weight_left = total_weight;
for (const pg_name in weights)
{
let n = Math.round(weights[pg_name] / weight_left * pg_left);
for (let i = 0; i < n; i++)
{
int_pgs.push(pg_name.substr(3).split('_'));
}
weight_left -= weights[pg_name];
pg_left -= n;
}
return int_pgs;
}
function calc_intersect_weights(pg_size, pg_count, prev_weights, all_pgs)
{
const move_weights = {};
if ((1 << pg_size) < pg_count)
{
const intersect = {};
for (const pg_name in prev_weights)
{
const pg = pg_name.substr(3).split(/_/);
for (let omit = 1; omit < (1 << pg_size); omit++)
{
let pg_omit = [ ...pg ];
let intersect_count = pg_size;
for (let i = 0; i < pg_size; i++)
{
if (omit & (1 << i))
{
pg_omit[i] = '';
intersect_count--;
}
}
pg_omit = pg_omit.join(':');
intersect[pg_omit] = Math.max(intersect[pg_omit] || 0, intersect_count);
}
}
for (const pg of all_pgs)
{
let max_int = 0;
for (let omit = 1; omit < (1 << pg_size); omit++)
{
let pg_omit = [ ...pg ];
for (let i = 0; i < pg_size; i++)
{
if (omit & (1 << i))
{
pg_omit[i] = '';
}
}
pg_omit = pg_omit.join(':');
max_int = Math.max(max_int, intersect[pg_omit] || 0);
}
move_weights['pg_'+pg.join('_')] = pg_size-max_int;
}
}
else
{
const prev_pg_hashed = Object.keys(prev_weights).map(pg_name => pg_name.substr(3).split(/_/).reduce((a, c) => { a[c] = 1; return a; }, {}));
for (const pg of all_pgs)
{
if (!prev_weights['pg_'+pg.join('_')])
{
let max_int = 0;
for (const prev_hash in prev_pg_hashed)
{
const intersect_count = pg.reduce((a, osd) => a + (prev_hash[osd] ? 1 : 0), 0);
if (max_int < intersect_count)
{
max_int = intersect_count;
if (max_int >= pg_size)
{
break;
}
}
}
move_weights['pg_'+pg.join('_')] = pg_size-max_int;
}
}
}
return move_weights;
}
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function add_valid_previous(osd_tree, prev_weights, all_pgs)
{
// Add previous combinations that are still valid
const hosts = Object.keys(osd_tree).sort();
const host_per_osd = {};
for (const host in osd_tree)
{
for (const osd in osd_tree[host])
{
host_per_osd[osd] = host;
}
}
skip_pg: for (const pg_name in prev_weights)
{
const seen_hosts = {};
const pg = pg_name.substr(3).split(/_/);
for (const osd of pg)
{
if (!host_per_osd[osd] || seen_hosts[host_per_osd[osd]])
{
continue skip_pg;
}
seen_hosts[host_per_osd[osd]] = true;
}
if (!all_pgs[pg_name])
{
all_pgs[pg_name] = pg;
}
}
}
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// Try to minimize data movement
async function optimize_change({ prev_pgs: prev_int_pgs, osd_tree, pg_size = 3, pg_minsize = 2, max_combinations = 10000, parity_space = 1 })
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{
if (!osd_tree)
{
return null;
}
const pg_effsize = Math.min(pg_minsize, Object.keys(osd_tree).length)
+ Math.max(0, Math.min(pg_size, Object.keys(osd_tree).length) - pg_minsize) * parity_space;
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const pg_count = prev_int_pgs.length;
const prev_weights = {};
const prev_pg_per_osd = {};
for (const pg of prev_int_pgs)
{
const pg_name = 'pg_'+pg.join('_');
prev_weights[pg_name] = (prev_weights[pg_name]||0) + 1;
for (let i = 0; i < pg.length; i++)
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{
const osd = pg[i];
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prev_pg_per_osd[osd] = prev_pg_per_osd[osd] || [];
prev_pg_per_osd[osd].push([ pg_name, (i >= pg_minsize ? parity_space : 1) ]);
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}
}
// Get all combinations
let all_pgs = random_combinations(osd_tree, pg_size, max_combinations, parity_space > 1);
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add_valid_previous(osd_tree, prev_weights, all_pgs);
all_pgs = Object.values(all_pgs);
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const pg_per_osd = {};
for (const pg of all_pgs)
{
const pg_name = 'pg_'+pg.join('_');
for (let i = 0; i < pg.length; i++)
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{
const osd = pg[i];
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pg_per_osd[osd] = pg_per_osd[osd] || [];
pg_per_osd[osd].push([ pg_name, (i >= pg_minsize ? parity_space : 1) ]);
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}
}
// Penalize PGs based on their similarity to old PGs
const move_weights = calc_intersect_weights(pg_size, pg_count, prev_weights, all_pgs);
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// Calculate total weight - old PG weights
const all_pg_names = all_pgs.map(pg => 'pg_'+pg.join('_'));
const all_pgs_hash = all_pg_names.reduce((a, c) => { a[c] = true; return a; }, {});
const all_weights = Object.assign({}, ...Object.values(osd_tree));
const total_weight = Object.values(all_weights).reduce((a, c) => Number(a) + Number(c), 0);
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// Generate the LP problem
let lp = '';
lp += 'max: '+all_pg_names.map(pg_name => (
prev_weights[pg_name] ? `${pg_size+1}*add_${pg_name} - ${pg_size+1}*del_${pg_name}` : `${pg_size+1-move_weights[pg_name]}*${pg_name}`
)).join(' + ')+';\n';
lp += all_pg_names
.map(pg_name => (prev_weights[pg_name] ? `add_${pg_name} - del_${pg_name}` : `${pg_name}`))
.join(' + ')+' = '+(pg_count
- Object.keys(prev_weights).reduce((a, old_pg_name) => (a + (all_pgs_hash[old_pg_name] ? prev_weights[old_pg_name] : 0)), 0)
)+';\n';
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for (const osd in pg_per_osd)
{
if (osd !== NO_OSD)
{
const osd_sum = (pg_per_osd[osd]||[]).map(([ pg_name, space ]) => (
prev_weights[pg_name] ? `${space} * add_${pg_name} - ${space} * del_${pg_name}` : `${space} * ${pg_name}`
)).join(' + ');
const rm_osd_pg_count = (prev_pg_per_osd[osd]||[])
.reduce((a, [ old_pg_name, space ]) => (a + (all_pgs_hash[old_pg_name] ? space : 0)), 0);
const osd_pg_count = all_weights[osd]*pg_effsize/total_weight*pg_count - rm_osd_pg_count;
lp += osd_sum + ' <= ' + osd_pg_count + ';\n';
}
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}
let pg_vars = [];
for (const pg_name of all_pg_names)
{
if (prev_weights[pg_name])
{
pg_vars.push(`add_${pg_name}`, `del_${pg_name}`);
// Can't add or remove less than zero
lp += `add_${pg_name} >= 0;\n`;
lp += `del_${pg_name} >= 0;\n`;
// Can't remove more than the PG already has
lp += `add_${pg_name} - del_${pg_name} >= -${prev_weights[pg_name]};\n`;
}
else
{
pg_vars.push(pg_name);
lp += `${pg_name} >= 0;\n`;
}
}
lp += 'sec '+pg_vars.join(', ')+';\n';
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// Solve it
const lp_result = await lp_solve(lp);
if (!lp_result)
{
console.log(lp);
throw new Error('Problem is infeasible or unbounded - is it a bug?');
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}
// Generate the new distribution
const weights = { ...prev_weights };
for (const k in prev_weights)
{
if (!all_pgs_hash[k])
{
delete weights[k];
}
}
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for (const k in lp_result.vars)
{
if (k.substr(0, 4) === 'add_')
{
weights[k.substr(4)] = (weights[k.substr(4)] || 0) + Number(lp_result.vars[k]);
}
else if (k.substr(0, 4) === 'del_')
{
weights[k.substr(4)] = (weights[k.substr(4)] || 0) - Number(lp_result.vars[k]);
}
else if (k.substr(0, 3) === 'pg_')
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{
weights[k] = Number(lp_result.vars[k]);
}
}
for (const k in weights)
{
if (!weights[k])
{
delete weights[k];
}
}
const int_pgs = make_int_pgs(weights, pg_count);
// Align them with most similar previous PGs
const new_pgs = align_pgs(prev_int_pgs, int_pgs);
let differs = 0, osd_differs = 0;
for (let i = 0; i < pg_count; i++)
{
if (new_pgs[i].join('_') != prev_int_pgs[i].join('_'))
{
differs++;
}
for (let j = 0; j < pg_size; j++)
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{
if (new_pgs[i][j] != prev_int_pgs[i][j])
{
osd_differs++;
}
}
}
return {
prev_pgs: prev_int_pgs,
score: lp_result.score,
weights,
int_pgs: new_pgs,
differs,
osd_differs,
space: pg_effsize * pg_list_space_efficiency(new_pgs, all_weights, pg_minsize, parity_space),
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total_space: total_weight,
};
}
function print_change_stats(retval, detailed)
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{
const new_pgs = retval.int_pgs;
const prev_int_pgs = retval.prev_pgs;
if (prev_int_pgs)
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{
if (detailed)
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{
for (let i = 0; i < new_pgs.length; i++)
{
if (new_pgs[i].join('_') != prev_int_pgs[i].join('_'))
{
console.log("pg "+i+": "+prev_int_pgs[i].join(' ')+" -> "+new_pgs[i].join(' '));
}
}
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}
console.log(
"Data movement: "+retval.differs+" pgs, "+
retval.osd_differs+" pg*osds = "+Math.round(retval.osd_differs / prev_int_pgs.length / 3 * 10000)/100+" %"
);
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}
console.log(
"Total space (raw): "+Math.round(retval.space*100)/100+" TB, space efficiency: "+
Math.round(retval.space/(retval.total_space||1)*10000)/100+" %"
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);
}
function align_pgs(prev_int_pgs, int_pgs)
{
const aligned_pgs = [];
put_aligned_pgs(aligned_pgs, int_pgs, prev_int_pgs, (pg) => [ pg.join(':') ]);
put_aligned_pgs(aligned_pgs, int_pgs, prev_int_pgs, (pg) => [ pg[0]+'::'+pg[2], ':'+pg[1]+':'+pg[2], pg[0]+':'+pg[1]+':' ]);
put_aligned_pgs(aligned_pgs, int_pgs, prev_int_pgs, (pg) => [ pg[0]+'::', ':'+pg[1]+':', '::'+pg[2] ]);
const free_slots = prev_int_pgs.map((pg, i) => !aligned_pgs[i] ? i : null).filter(i => i != null);
for (const pg of int_pgs)
{
if (!free_slots.length)
{
throw new Error("Can't place unaligned PG");
}
aligned_pgs[free_slots.shift()] = pg;
}
return aligned_pgs;
}
function put_aligned_pgs(aligned_pgs, int_pgs, prev_int_pgs, keygen)
{
let prev_indexes = {};
for (let i = 0; i < prev_int_pgs.length; i++)
{
for (let k of keygen(prev_int_pgs[i]))
{
prev_indexes[k] = prev_indexes[k] || [];
prev_indexes[k].push(i);
}
}
PG: for (let i = int_pgs.length-1; i >= 0; i--)
{
let pg = int_pgs[i];
let keys = keygen(int_pgs[i]);
for (let k of keys)
{
while (prev_indexes[k] && prev_indexes[k].length)
{
let idx = prev_indexes[k].shift();
if (!aligned_pgs[idx])
{
aligned_pgs[idx] = pg;
int_pgs.splice(i, 1);
continue PG;
}
}
}
}
}
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// Convert multi-level osd_tree = { level: number|string, id?: string, size?: number, children?: osd_tree }[]
// levels = { string: number }
// to a two-level osd_tree suitable for all_combinations()
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function flatten_tree(osd_tree, levels, failure_domain_level, osd_level, domains = {}, i = { i: 1 })
{
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osd_level = levels[osd_level] || osd_level;
failure_domain_level = levels[failure_domain_level] || failure_domain_level;
for (const node of osd_tree)
{
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if ((levels[node.level] || node.level) < failure_domain_level)
{
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flatten_tree(node.children||[], levels, failure_domain_level, osd_level, domains, i);
}
else
{
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domains['dom'+(i.i++)] = extract_osds([ node ], levels, osd_level);
}
}
return domains;
}
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function extract_osds(osd_tree, levels, osd_level, osds = {})
{
for (const node of osd_tree)
{
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if ((levels[node.level] || node.level) >= osd_level)
{
osds[node.id] = node.size;
}
else
{
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extract_osds(node.children||[], levels, osd_level, osds);
}
}
return osds;
}
// ordered = don't treat (x,y) and (y,x) as equal
function random_combinations(osd_tree, pg_size, count, ordered)
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{
let seed = 0x5f020e43;
let rng = () =>
{
seed ^= seed << 13;
seed ^= seed >> 17;
seed ^= seed << 5;
return seed + 2147483648;
};
const hosts = Object.keys(osd_tree).sort();
const osds = Object.keys(osd_tree).reduce((a, c) => { a[c] = Object.keys(osd_tree[c]).sort(); return a; }, {});
const r = {};
// Generate random combinations including each OSD at least once
for (let h = 0; h < hosts.length; h++)
{
for (let o = 0; o < osds[hosts[h]].length; o++)
{
const pg = [ osds[hosts[h]][o] ];
const cur_hosts = [ ...hosts ];
cur_hosts.splice(h, 1);
for (let i = 1; i < pg_size && i < hosts.length; i++)
{
const next_host = rng() % cur_hosts.length;
const next_osd = rng() % osds[cur_hosts[next_host]].length;
pg.push(osds[cur_hosts[next_host]][next_osd]);
cur_hosts.splice(next_host, 1);
}
const cyclic_pgs = [ pg ];
if (ordered)
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{
for (let i = 1; i < pg.size; i++)
{
cyclic_pgs.push([ ...pg.slice(i), ...pg.slice(0, i) ]);
}
}
for (const pg of cyclic_pgs)
{
while (pg.length < pg_size)
{
pg.push(NO_OSD);
}
r['pg_'+pg.join('_')] = pg;
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}
}
}
// Generate purely random combinations
while (count > 0)
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{
let host_idx = [];
const cur_hosts = [ ...hosts.map((h, i) => i) ];
const max_hosts = pg_size < hosts.length ? pg_size : hosts.length;
if (ordered)
{
for (let i = 0; i < max_hosts; i++)
{
const r = rng() % cur_hosts.length;
host_idx[i] = cur_hosts[r];
cur_hosts.splice(r, 1);
}
}
else
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{
for (let i = 0; i < max_hosts; i++)
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{
const r = rng() % (cur_hosts.length - (max_hosts - i - 1));
host_idx[i] = cur_hosts[r];
cur_hosts.splice(0, r+1);
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}
}
let pg = host_idx.map(h => osds[hosts[h]][rng() % osds[hosts[h]].length]);
while (pg.length < pg_size)
{
pg.push(NO_OSD);
}
r['pg_'+pg.join('_')] = pg;
count--;
}
return r;
}
// Super-stupid algorithm. Given the current OSD tree, generate all possible OSD combinations
// osd_tree = { failure_domain1: { osd1: size1, ... }, ... }
// ordered = return combinations without duplicates having different order
function all_combinations(osd_tree, pg_size, ordered, count)
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{
const hosts = Object.keys(osd_tree).sort();
const osds = Object.keys(osd_tree).reduce((a, c) => { a[c] = Object.keys(osd_tree[c]).sort(); return a; }, {});
while (hosts.length < pg_size)
{
osds[NO_OSD] = [ NO_OSD ];
hosts.push(NO_OSD);
}
let host_idx = [];
let osd_idx = [];
for (let i = 0; i < pg_size; i++)
{
host_idx.push(i);
osd_idx.push(0);
}
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const r = [];
while (!count || count < 0 || r.length < count)
{
r.push(host_idx.map((hi, i) => osds[hosts[hi]][osd_idx[i]]));
let inc = pg_size-1;
while (inc >= 0)
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{
osd_idx[inc]++;
if (osd_idx[inc] >= osds[hosts[host_idx[inc]]].length)
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{
osd_idx[inc] = 0;
inc--;
}
else
{
break;
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}
}
if (inc < 0)
{
// no osds left in the current host combination, select the next one
inc = pg_size-1;
same_again: while (inc >= 0)
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{
host_idx[inc]++;
for (let prev_host = 0; prev_host < inc; prev_host++)
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{
if (host_idx[prev_host] == host_idx[inc])
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{
continue same_again;
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}
}
if (host_idx[inc] < (ordered ? hosts.length-(pg_size-1-inc) : hosts.length))
{
while ((++inc) < pg_size)
{
host_idx[inc] = (ordered ? host_idx[inc-1]+1 : 0);
}
break;
}
else
{
inc--;
}
}
if (inc < 0)
{
break;
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}
}
}
return r;
}
function pg_weights_space_efficiency(weights, pg_count, osd_sizes)
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{
const per_osd = {};
for (const pg_name in weights)
{
for (const osd of pg_name.substr(3).split(/_/))
{
per_osd[osd] = (per_osd[osd]||0) + weights[pg_name];
}
}
return pg_per_osd_space_efficiency(per_osd, pg_count, osd_sizes);
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}
function pg_list_space_efficiency(pgs, osd_sizes, pg_minsize, parity_space)
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{
const per_osd = {};
for (const pg of pgs)
{
for (let i = 0; i < pg.length; i++)
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{
const osd = pg[i];
per_osd[osd] = (per_osd[osd]||0) + (i >= pg_minsize ? (parity_space||1) : 1);
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}
}
return pg_per_osd_space_efficiency(per_osd, pgs.length, osd_sizes);
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}
function pg_per_osd_space_efficiency(per_osd, pg_count, osd_sizes)
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{
// each PG gets randomly selected in 1/N cases
// & there are x PGs per OSD
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// => an OSD is selected in x/N cases
// => total space * x/N <= OSD size
// => total space <= OSD size * N/x
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let space;
for (let osd in per_osd)
{
if (osd in osd_sizes)
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{
const space_estimate = osd_sizes[osd] * pg_count / per_osd[osd];
if (space == null || space > space_estimate)
{
space = space_estimate;
}
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}
}
return space == null ? 0 : space;
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}
module.exports = {
NO_OSD,
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optimize_initial,
optimize_change,
print_change_stats,
pg_weights_space_efficiency,
pg_list_space_efficiency,
pg_per_osd_space_efficiency,
flatten_tree,
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lp_solve,
make_int_pgs,
align_pgs,
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random_combinations,
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all_combinations,
};