556 lines
17 KiB
JavaScript
556 lines
17 KiB
JavaScript
// Copyright (c) Vitaliy Filippov, 2019+
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// License: VNPL-1.1 (see README.md for details)
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// Data distribution optimizer using linear programming (lp_solve)
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const child_process = require('child_process');
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const NO_OSD = 'Z';
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async function lp_solve(text)
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{
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const cp = child_process.spawn('lp_solve');
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let stdout = '', stderr = '', finish_cb;
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cp.stdout.on('data', buf => stdout += buf.toString());
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cp.stderr.on('data', buf => stderr += buf.toString());
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cp.on('exit', () => finish_cb && finish_cb());
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cp.stdin.write(text);
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cp.stdin.end();
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if (cp.exitCode == null)
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{
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await new Promise(ok => finish_cb = ok);
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}
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if (!stdout.trim())
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{
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return null;
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}
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let score = 0;
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let vars = {};
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for (const line of stdout.split(/\n/))
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{
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let m = /^(^Value of objective function: (-?[\d\.]+)|Actual values of the variables:)\s*$/.exec(line);
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if (m)
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{
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if (m[2])
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{
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score = m[2];
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}
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continue;
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}
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else if (/This problem is (infeasible|unbounded)/.exec(line))
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{
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return null;
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}
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let [ k, v ] = line.trim().split(/\s+/, 2);
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if (v)
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{
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vars[k] = v;
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}
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}
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return { score, vars };
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}
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// osd_weights = { [id]: weight }
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async function optimize_initial({ osd_weights, combinator, pg_count, pg_size = 3, pg_minsize = 2, parity_space = 1, ordered = false })
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{
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if (!pg_count || !osd_weights)
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{
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return null;
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}
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const total_weight = Object.values(osd_weights).reduce((a, c) => Number(a) + Number(c), 0);
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const all_pgs = Object.values(make_cyclic(combinator.random_combinations(), parity_space));
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const pg_per_osd = {};
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for (const pg of all_pgs)
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{
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for (let i = 0; i < pg.length; i++)
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{
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const osd = pg[i];
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pg_per_osd[osd] = pg_per_osd[osd] || [];
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pg_per_osd[osd].push((i >= pg_minsize ? parity_space+'*' : '')+"pg_"+pg.join("_"));
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}
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}
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let pg_effsize = all_pgs.reduce((a, c) => Math.max(a, c.filter(e => e != NO_OSD).length), 0);
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pg_effsize = Math.min(pg_minsize, pg_effsize) + Math.max(0, Math.min(pg_size, pg_effsize) - pg_minsize) * parity_space;
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let lp = '';
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lp += "max: "+all_pgs.map(pg => 'pg_'+pg.join('_')).join(' + ')+";\n";
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for (const osd in pg_per_osd)
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{
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if (osd !== NO_OSD)
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{
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let osd_pg_count = (osd_weights[osd]||0)/total_weight*pg_effsize*pg_count;
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lp += pg_per_osd[osd].join(' + ')+' <= '+osd_pg_count+';\n';
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}
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}
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for (const pg of all_pgs)
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{
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lp += 'pg_'+pg.join('_')+" >= 0;\n";
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}
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lp += "sec "+all_pgs.map(pg => 'pg_'+pg.join('_')).join(', ')+";\n";
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const lp_result = await lp_solve(lp);
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if (!lp_result)
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{
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console.log(lp);
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throw new Error('Problem is infeasible or unbounded - is it a bug?');
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}
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const int_pgs = make_int_pgs(lp_result.vars, pg_count, ordered);
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const eff = pg_list_space_efficiency(int_pgs, osd_weights, pg_minsize, parity_space);
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const res = {
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score: lp_result.score,
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weights: lp_result.vars,
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int_pgs,
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space: eff * pg_effsize,
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total_space: total_weight,
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};
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return res;
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}
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function make_cyclic(pgs, parity_space)
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{
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if (parity_space > 1)
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{
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for (const pg in pgs)
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{
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for (let i = 1; i < pg.size; i++)
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{
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const cyclic = [ ...pg.slice(i), ...pg.slice(0, i) ];
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pgs['pg_'+cyclic.join('_')] = cyclic;
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}
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}
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}
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return pgs;
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}
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function shuffle(array)
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{
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for (let i = array.length - 1, j, x; i > 0; i--)
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{
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j = Math.floor(Math.random() * (i + 1));
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x = array[i];
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array[i] = array[j];
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array[j] = x;
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}
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}
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function make_int_pgs(weights, pg_count, round_robin)
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{
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const total_weight = Object.values(weights).reduce((a, c) => Number(a) + Number(c), 0);
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let int_pgs = [];
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let pg_left = pg_count;
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let weight_left = total_weight;
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for (const pg_name in weights)
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{
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let cur_pg = pg_name.substr(3).split('_');
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let n = Math.round(weights[pg_name] / weight_left * pg_left);
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for (let i = 0; i < n; i++)
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{
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int_pgs.push([ ...cur_pg ]);
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if (round_robin)
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{
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cur_pg.push(cur_pg.shift());
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}
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}
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weight_left -= weights[pg_name];
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pg_left -= n;
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}
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shuffle(int_pgs);
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return int_pgs;
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}
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function calc_intersect_weights(old_pg_size, pg_size, pg_count, prev_weights, all_pgs, ordered)
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{
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const move_weights = {};
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if ((1 << old_pg_size) < pg_count)
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{
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const intersect = {};
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for (const pg_name in prev_weights)
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{
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const pg = pg_name.substr(3).split(/_/);
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for (let omit = 1; omit < (1 << old_pg_size); omit++)
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{
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let pg_omit = [ ...pg ];
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let intersect_count = old_pg_size;
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for (let i = 0; i < old_pg_size; i++)
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{
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if (omit & (1 << i))
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{
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pg_omit[i] = '';
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intersect_count--;
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}
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}
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if (!ordered)
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pg_omit = pg_omit.filter(n => n).sort();
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pg_omit = pg_omit.join(':');
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intersect[pg_omit] = Math.max(intersect[pg_omit] || 0, intersect_count);
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}
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}
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for (const pg of all_pgs)
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{
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let max_int = 0;
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for (let omit = 1; omit < (1 << pg_size); omit++)
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{
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let pg_omit = [ ...pg ];
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for (let i = 0; i < pg_size; i++)
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{
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if (omit & (1 << i))
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pg_omit[i] = '';
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}
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if (!ordered)
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pg_omit = pg_omit.filter(n => n).sort();
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pg_omit = pg_omit.join(':');
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max_int = Math.max(max_int, intersect[pg_omit] || 0);
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}
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move_weights['pg_'+pg.join('_')] = pg_size-max_int;
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}
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}
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else
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{
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const prev_pg_hashed = Object.keys(prev_weights).map(pg_name => pg_name
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.substr(3).split(/_/).reduce((a, c, i) => { a[c] = i+1; return a; }, {}));
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for (const pg of all_pgs)
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{
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if (!prev_weights['pg_'+pg.join('_')])
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{
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let max_int = 0;
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for (const prev_hash of prev_pg_hashed)
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{
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const intersect_count = ordered
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? pg.reduce((a, osd, i) => a + (prev_hash[osd] == 1+i ? 1 : 0), 0)
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: pg.reduce((a, osd, i) => a + (prev_hash[osd] ? 1 : 0), 0);
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if (max_int < intersect_count)
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{
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max_int = intersect_count;
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if (max_int >= pg_size)
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{
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break;
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}
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}
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}
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move_weights['pg_'+pg.join('_')] = pg_size-max_int;
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}
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}
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}
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return move_weights;
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}
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// Try to minimize data movement
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async function optimize_change({ prev_pgs: prev_int_pgs, osd_weights, combinator, pg_size = 3, pg_minsize = 2, parity_space = 1, ordered = false })
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{
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if (!osd_weights)
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{
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return null;
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}
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// FIXME: use parity_chunks with parity_space instead of pg_minsize
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let all_pgs = make_cyclic(combinator.random_combinations(), parity_space);
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let pg_effsize = Object.values(all_pgs).reduce((a, c) => Math.max(a, c.filter(e => e != NO_OSD).length), 0);
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pg_effsize = Math.min(pg_minsize, pg_effsize) + Math.max(0, Math.min(pg_size, pg_effsize) - pg_minsize) * parity_space;
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const pg_count = prev_int_pgs.length;
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const prev_weights = {};
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const prev_pg_per_osd = {};
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for (const pg of prev_int_pgs)
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{
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const pg_name = 'pg_'+pg.join('_');
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prev_weights[pg_name] = (prev_weights[pg_name]||0) + 1;
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for (let i = 0; i < pg.length; i++)
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{
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const osd = pg[i];
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prev_pg_per_osd[osd] = prev_pg_per_osd[osd] || [];
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prev_pg_per_osd[osd].push([ pg_name, (i >= pg_minsize ? parity_space : 1) ]);
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}
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}
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const old_pg_size = prev_int_pgs[0].length;
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// Get all combinations
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if (old_pg_size == pg_size)
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{
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const still_valid = combinator.check_combinations(Object.keys(prev_weights).map(pg_name => pg_name.substr(3).split('_')));
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for (const pg of still_valid)
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{
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all_pgs['pg_'+pg.join('_')] = pg;
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}
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}
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all_pgs = Object.values(all_pgs);
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const pg_per_osd = {};
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for (const pg of all_pgs)
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{
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const pg_name = 'pg_'+pg.join('_');
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for (let i = 0; i < pg.length; i++)
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{
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const osd = pg[i];
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pg_per_osd[osd] = pg_per_osd[osd] || [];
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pg_per_osd[osd].push([ pg_name, (i >= pg_minsize ? parity_space : 1) ]);
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}
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}
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// Penalize PGs based on their similarity to old PGs
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const move_weights = calc_intersect_weights(old_pg_size, pg_size, pg_count, prev_weights, all_pgs, ordered);
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// Calculate total weight - old PG weights
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const all_pg_names = all_pgs.map(pg => 'pg_'+pg.join('_'));
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const all_pgs_hash = all_pg_names.reduce((a, c) => { a[c] = true; return a; }, {});
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const total_weight = Object.values(osd_weights).reduce((a, c) => Number(a) + Number(c), 0);
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// Generate the LP problem
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let lp = '';
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lp += 'max: '+all_pg_names.map(pg_name => (
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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}`
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)).join(' + ')+';\n';
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for (const osd in pg_per_osd)
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{
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if (osd !== NO_OSD)
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{
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const osd_sum = (pg_per_osd[osd]||[]).map(([ pg_name, space ]) => (
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prev_weights[pg_name] ? `${space} * add_${pg_name} - ${space} * del_${pg_name}` : `${space} * ${pg_name}`
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)).join(' + ');
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const rm_osd_pg_count = (prev_pg_per_osd[osd]||[])
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.reduce((a, [ old_pg_name, space ]) => (a + (all_pgs_hash[old_pg_name] ? space : 0)), 0);
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const osd_pg_count = (osd_weights[osd]||0)*pg_effsize/total_weight*pg_count - rm_osd_pg_count;
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lp += osd_sum + ' <= ' + osd_pg_count + ';\n';
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}
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}
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let pg_vars = [];
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for (const pg_name of all_pg_names)
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{
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if (prev_weights[pg_name])
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{
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pg_vars.push(`add_${pg_name}`, `del_${pg_name}`);
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// Can't add or remove less than zero
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lp += `add_${pg_name} >= 0;\n`;
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lp += `del_${pg_name} >= 0;\n`;
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// Can't remove more than the PG already has
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lp += `add_${pg_name} - del_${pg_name} >= -${prev_weights[pg_name]};\n`;
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}
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else
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{
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pg_vars.push(pg_name);
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lp += `${pg_name} >= 0;\n`;
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}
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}
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lp += 'sec '+pg_vars.join(', ')+';\n';
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// Solve it
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const lp_result = await lp_solve(lp);
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if (!lp_result)
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{
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console.log(lp);
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throw new Error('Problem is infeasible or unbounded - is it a bug?');
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}
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// Generate the new distribution
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const weights = { ...prev_weights };
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for (const k in prev_weights)
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{
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if (!all_pgs_hash[k])
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{
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delete weights[k];
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}
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}
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for (const k in lp_result.vars)
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{
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if (k.substr(0, 4) === 'add_')
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{
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weights[k.substr(4)] = (weights[k.substr(4)] || 0) + Number(lp_result.vars[k]);
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}
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else if (k.substr(0, 4) === 'del_')
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{
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weights[k.substr(4)] = (weights[k.substr(4)] || 0) - Number(lp_result.vars[k]);
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}
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else if (k.substr(0, 3) === 'pg_')
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{
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weights[k] = Number(lp_result.vars[k]);
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}
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}
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for (const k in weights)
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{
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if (!weights[k])
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{
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delete weights[k];
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}
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}
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const int_pgs = make_int_pgs(weights, pg_count);
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// Align them with most similar previous PGs
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const new_pgs = align_pgs(prev_int_pgs, int_pgs);
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let differs = 0, osd_differs = 0;
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for (let i = 0; i < pg_count; i++)
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{
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if (new_pgs[i].join('_') != prev_int_pgs[i].join('_'))
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{
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differs++;
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}
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}
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if (ordered)
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{
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for (let i = 0; i < pg_count; i++)
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{
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for (let j = 0; j < pg_size; j++)
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{
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if (new_pgs[i][j] != prev_int_pgs[i][j])
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{
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osd_differs++;
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}
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}
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}
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}
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else
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{
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for (let i = 0; i < pg_count; i++)
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{
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const old_map = prev_int_pgs[i].reduce((a, c) => { a[c] = (a[c]|0) + 1; return a; }, {});
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for (let j = 0; j < pg_size; j++)
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{
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if ((0|old_map[new_pgs[i][j]]) > 0)
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{
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old_map[new_pgs[i][j]]--;
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}
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else
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{
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osd_differs++;
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}
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}
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}
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}
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return {
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prev_pgs: prev_int_pgs,
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score: lp_result.score,
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weights,
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int_pgs: new_pgs,
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differs,
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osd_differs,
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space: pg_effsize * pg_list_space_efficiency(new_pgs, osd_weights, pg_minsize, parity_space),
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total_space: total_weight,
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};
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}
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function print_change_stats(retval, detailed)
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{
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const new_pgs = retval.int_pgs;
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const prev_int_pgs = retval.prev_pgs;
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if (prev_int_pgs)
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{
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if (detailed)
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{
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for (let i = 0; i < new_pgs.length; i++)
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{
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if (new_pgs[i].join('_') != prev_int_pgs[i].join('_'))
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{
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console.log("pg "+i+": "+prev_int_pgs[i].join(' ')+" -> "+new_pgs[i].join(' '));
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}
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}
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}
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console.log(
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"Data movement: "+retval.differs+" pgs, "+
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retval.osd_differs+" pg*osds = "+Math.round(retval.osd_differs / prev_int_pgs.length / 3 * 10000)/100+" %"
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);
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}
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console.log(
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"Total space (raw): "+Math.round(retval.space*100)/100+" TB, space efficiency: "+
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Math.round(retval.space/(retval.total_space||1)*10000)/100+" %"
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);
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}
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function align_pgs(prev_int_pgs, int_pgs)
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{
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const aligned_pgs = [];
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put_aligned_pgs(aligned_pgs, int_pgs, prev_int_pgs, (pg) => [ pg.join(':') ]);
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put_aligned_pgs(aligned_pgs, int_pgs, prev_int_pgs, (pg) => [ pg[0]+'::'+pg[2], ':'+pg[1]+':'+pg[2], pg[0]+':'+pg[1]+':' ]);
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put_aligned_pgs(aligned_pgs, int_pgs, prev_int_pgs, (pg) => [ pg[0]+'::', ':'+pg[1]+':', '::'+pg[2] ]);
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const free_slots = prev_int_pgs.map((pg, i) => !aligned_pgs[i] ? i : null).filter(i => i != null);
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for (const pg of int_pgs)
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{
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if (!free_slots.length)
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{
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throw new Error("Can't place unaligned PG");
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}
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aligned_pgs[free_slots.shift()] = pg;
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}
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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;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
function pg_weights_space_efficiency(weights, pg_count, osd_sizes)
|
|
{
|
|
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);
|
|
}
|
|
|
|
function pg_list_space_efficiency(pgs, osd_sizes, pg_minsize, parity_space)
|
|
{
|
|
const per_osd = {};
|
|
for (const pg of pgs)
|
|
{
|
|
for (let i = 0; i < pg.length; i++)
|
|
{
|
|
const osd = pg[i];
|
|
per_osd[osd] = (per_osd[osd]||0) + (i >= pg_minsize ? (parity_space||1) : 1);
|
|
}
|
|
}
|
|
return pg_per_osd_space_efficiency(per_osd, pgs.length, osd_sizes);
|
|
}
|
|
|
|
function pg_per_osd_space_efficiency(per_osd, pg_count, osd_sizes)
|
|
{
|
|
// each PG gets randomly selected in 1/N cases
|
|
// & there are x PGs per OSD
|
|
// => an OSD is selected in x/N cases
|
|
// => total space * x/N <= OSD size
|
|
// => total space <= OSD size * N/x
|
|
let space;
|
|
for (let osd in per_osd)
|
|
{
|
|
if (osd in osd_sizes)
|
|
{
|
|
const space_estimate = osd_sizes[osd] * pg_count / per_osd[osd];
|
|
if (space == null || space > space_estimate)
|
|
{
|
|
space = space_estimate;
|
|
}
|
|
}
|
|
}
|
|
return space == null ? 0 : space;
|
|
}
|
|
|
|
module.exports = {
|
|
NO_OSD,
|
|
|
|
optimize_initial,
|
|
optimize_change,
|
|
print_change_stats,
|
|
pg_weights_space_efficiency,
|
|
pg_list_space_efficiency,
|
|
pg_per_osd_space_efficiency,
|
|
|
|
lp_solve,
|
|
make_int_pgs,
|
|
align_pgs,
|
|
};
|