// SERVER-5044 Standard deviation expression operators

const t = db[jsTestName()];

function test(data, popExpected, sampExpected) {
    t.drop();
    assert.commandWorked(t.insert({})); // need one document to ensure we get output

    for (let i = 0; i < data.length; i++) assert.commandWorked(t.insert({num: data[i]}));

    let res = t
        .aggregate({
            $group: {
                _id: 1,
                pop: {$stdDevPop: "$num"},
                samp: {$stdDevSamp: "$num"},
            },
        })
        .next();

    if (popExpected === null) {
        assert.isnull(res.pop);
    } else {
        assert.close(res.pop, popExpected, "", 10 /*decimal places*/);
    }

    if (sampExpected === null) {
        assert.isnull(res.samp);
    } else {
        assert.close(res.samp, sampExpected, "", 10 /*decimal places*/);
    }
}

test([], null, null);
test([1], 0, null);
test([1, 1], 0, 0);

test(["a"], null, null);
test([1, "a"], 0, null);
test([1, "a", 1], 0, 0);

test([1, 2], 0.5, Math.sqrt(0.5));
test([1, 2, 3], Math.sqrt(2 / 3), 1);

// test from http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Example
test([4, 7, 13, 16], Math.sqrt(22.5), Math.sqrt(30));
test([1e8 + 4, 1e8 + 7, 1e8 + 13, 1e8 + 16], Math.sqrt(22.5), Math.sqrt(30));
test([1e9 + 4, 1e9 + 7, 1e9 + 13, 1e9 + 16], Math.sqrt(22.5), Math.sqrt(30));
test([1e10 + 4, 1e10 + 7, 1e10 + 13, 1e10 + 16], Math.sqrt(22.5), Math.sqrt(30));