[m1el]

As a developer who doesn't use mathematical notation very often, I've had some difficulty reading it. From my understanding, the paper goes as follows:

2.1 Define FlameGraph

    Frame = something that identifies function/location in the code
    Stack = Vec<Frame>
    FlameGraph = Map<Stack, Real>
    FlameGraphPositive = Map<Stack, RealPositive>

2.2 Define FlameChart

    FlameChart = Vec<{ start: Real, flame_graph: FlameGraphPositive }>
    # such that the start values are strictly ordered
    fn to_flamegraph(flame_chart: FlameChart) -> FlameGraphPositive {
        flame_chart
            .map(|{ start, flame_graph }| flame_graph)
            .sum() 
    }

Personally, I think a better definition of FlameChart is:

    FlameChart = Vec<{ end_time: RealPositive, stack: Stack }>
    # such that sampling starts at 0 and Vec is strictly ordered by end_time
    fn to_flamegraph(flame_chart: FlameChart) -> FlameGraphPositive {
        let mut start = 0.0;
        flame_chart.map(|{ end_time, stack }| {
            let elapsed = end_time - start;
            start = end_time;
            FlameGraphPositive::from_stack(stack, elapsed)
        }).sum()
    }

3.1 Define diff

    # a,b: FlameGraphPositive
    fn diff(a, b) -> FlameGraph;
    # such that a + diff = b
    # diff: FlameGraph
    # add, sub: FlameGraphPositive
    fn to_positive(diff) -> { add, sub };
    # such that diff = add - sub

3.2 Define a naive diff metric

    # a,b: FlameGraphPositive
    fn diff_metric(a, b) -> RealPositive {
        diff(a, b).size() / (a.size() + b.size())
    }
    # diff_metric(a, b) \in [0, 1]^Real

3.3 Define a more sophisticated diff metric

Using Hotelling T^2 Test, the author defines a metric, which takes sampling variance into account, and allows to detect performance regression, even when the sampling profile is noisy. (you'd have to read the paper for the exact method)

The code for this test is here: https://github.com/P403n1x87/flamegraph-experiment/blob/04db... https://github.com/P403n1x87/flamegraph-experiment/blob/04db...