math.js

math.js

/* This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
 
/*globals onmessage */

¶

The probabilities function computes the likelihood of shipping all of N locales, given the likelihood of a single locale loclikely, the maximum number of string-frozen cycles, and the maximum number of locales maxloc.
```
function probabilities(loclikely, cycles, maxloc) {
    var locales, fails, c, rv = [[1]], _rv;
```
¶

The return value probs is a matrix, where each row consists of the likelyhood of shipping all of N locales, starting with 0, which always passes, thus the first column is 1.
```
    var probs = [[1]];
```

Without string freeze, the likelyhood is just the likelyhood of one locale to the power of N.

    for (locales=1; locales <= maxloc; ++locales) {
        probs[0][locales] = Math.pow(loclikely, locales);
    }

¶

generate string freeze cycles
```
    for (c=0; c < cycles; ++c) {
```

For each cycle, see how much we can recover. locales is the number of locales in the full release.

        probs[c+1] = [1];
        for (locales=1; locales <= maxloc; ++locales) {

¶

partition the 1: for fails out of locales locales failing, pick up how likely we can fix that remaining task with one cycle less
```
            probs[c+1][locales] = 0;
            for (fails=0; fails <=locales; ++fails) {
```

how likely is this case? p^(locales-fails)*(1-p)^(fails)*binomial(locales, fails)

                _rv = Math.pow(loclikely, locales-fails)
                    * Math.pow(1-loclikely, fails)
                    * binomial(locales, fails);

¶

and now compute how likely it is to fix the fails later and multiplicate that
```
                _rv *= probs[c][fails];
```

The likelyhood of success is the sum over all likelyhoods in the partitioned 1. Right?

                probs[c+1][locales] += _rv;
            }
        }
    }
    return probs;
}

var _bins = {};
function binomial(n, k) {
    if (n === 0) return 0;
    if (k === 0) return 1;
    if (_bins[n] === undefined) {
        _bins[n] = {};
    }
    else if (_bins[n][k] !== undefined) {
        return _bins[n][k];
    }
    var i, rv = 1;
    for (i = 1; i <= k; ++i) {
        rv = rv * (n - (k - i))/i;
    }
    _bins[n][k] = rv;
    return rv;
}

onmessage = function (event) {
    var params = event.data;
    postMessage(probabilities(params.likely, params.cycles, params.maxloc));
}