TamperMonkey log to local file

While developing a userscript for tampermonkey, how can I have it write logs to local files on my machine?

I want the userscript to run when visiting a website, e.g. stackoverflow.com, then I want the running userscript to store its logs permanently (e.g. in a file on my disk) instead of in the browser console that only lasts as long as the tab does.

I ended up using GM_setValue, GM_getValue, & co. as suggested in comments.

You need to grant them in the preamble:

// @grant GM_setValue
// @grant GM_getValue
// @grant GM_listValues
// @grant GM_deleteValue

I used this function to download it to disk on button click:

var saveData = (function () {
    var a = document.createElement("a");
    document.body.appendChild(a);
    a.style = "display: none";
    return function (data, fileName) {
        var blob = new Blob([data], {type: "octet/stream"});
        var url = window.URL.createObjectURL(blob);
        a.href = url;
        a.download = fileName;
        a.click();
        window.URL.revokeObjectURL(url);
    };
}());

let logs = GM_getValue('logs', null);
if (logs != null) {
    saveData(logs.join('\n'), 'logs.txt');
} else {
    alert('empty storage!');
}