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// Copyright 2024 The Fuchsia Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
//! Sampling rate and aggregation intervals.
use itertools::Itertools;
use num::Integer;
use std::fmt::{self, Debug, Display, Formatter};
use std::marker::PhantomData;
use std::num::NonZeroUsize;
use std::{cmp, iter};
use crate::experimental::clock::{Duration, DurationExt as _, Quanta, QuantaExt as _, Tick};
use crate::experimental::series::interpolation::InterpolationState;
use crate::experimental::series::statistic::{Statistic, StatisticExt as _};
use crate::experimental::series::Fill;
use crate::experimental::Vec1;
/// An interval that has elapsed during a [`Tick`].
///
/// [`Tick`]: crate::experimental::clock::Tick;
#[derive(Clone, Copy, Debug, Eq, Hash, PartialEq)]
pub struct ElapsedInterval {
/// The number of fill (interpolated) samples required prior to computing the aggregation of
/// the interval.
fill_sample_count: Option<NonZeroUsize>,
}
impl ElapsedInterval {
/// Fills the given [`Statistic`] with interpolated samples using the given
/// [interpolation][`Interpolation`] and then computes the aggregation for the interval.
///
/// [`Interpolation`]: crate::experimental::series::interpolation::Interpolation
/// [`Statistic`]: crate::experimental::series::statistic::Statistic
fn interpolate_and_get_aggregation<F, P>(
self,
statistic: &mut F,
interpolation: &mut P,
) -> Result<Option<F::Aggregation>, F::Error>
where
F: Statistic,
P: InterpolationState<F::Aggregation, FillSample = F::Sample>,
{
let ElapsedInterval { fill_sample_count } = self;
self::fill_non_zero_with(statistic, fill_sample_count, || interpolation.sample())?;
Ok(statistic.get_aggregation_and_reset().inspect(|aggregation| {
interpolation.fold_aggregation(aggregation.clone());
}))
}
}
/// An interval that has been reached but **not** elapsed by a [`Tick`].
///
/// [`Tick`]: crate::experimental::clock::Tick;
#[derive(Clone, Copy, Debug, Eq, Hash, PartialEq)]
pub struct PendingInterval<T> {
/// The number of fill (interpolated) samples required prior to folding the observed sample.
fill_sample_count: Option<NonZeroUsize>,
/// The sample observed during the tick.
sample: T,
}
impl<T> PendingInterval<T> {
/// Folds the observed sample into the given [`Statistic`] using the given
/// [interpolation][`Interpolation`].
///
/// [`Interpolation`]: crate::experimental::series::interpolation::Interpolation
/// [`Statistic`]: crate::experimental::series::statistic::Statistic
fn fold<F, P>(self, statistic: &mut F, interpolation: &mut P) -> Result<(), F::Error>
where
T: Clone,
F: Statistic<Sample = T>,
P: InterpolationState<F::Aggregation, FillSample = T>,
{
let PendingInterval { fill_sample_count, sample } = self;
self::fill_non_zero_with(statistic, fill_sample_count, || interpolation.sample())?;
statistic.fold(sample.clone())?;
interpolation.fold_sample(sample);
Ok(())
}
}
// A pending interval has no observed sample (`PhantomData<T>` instead of `T`) when an
// interpolation (rather than a fold) is requested.
impl<T> PendingInterval<PhantomData<T>> {
/// Fills the given [`Statistic`] with interpolated samples using the given
/// [interpolation][`Interpolation`].
///
/// [`Interpolation`]: crate::experimental::series::interpolation::Interpolation
/// [`Statistic`]: crate::experimental::series::statistic::Statistic
fn interpolate<F, P>(self, statistic: &mut F, interpolation: &mut P) -> Result<(), F::Error>
where
T: Clone,
F: Statistic<Sample = T>,
P: InterpolationState<F::Aggregation, FillSample = T>,
{
let PendingInterval { fill_sample_count, .. } = self;
self::fill_non_zero_with(statistic, fill_sample_count, || interpolation.sample())
}
}
/// The expiration of [`SamplingInterval`]s intersected by a [`Tick`].
///
/// [`SamplingInterval`]: crate::experimental::series::SamplingInterval
/// [`Tick`]: crate::experimental::clock::Tick;
#[derive(Clone, Copy, Debug, Eq, Hash, PartialEq)]
pub enum IntervalExpiration<T> {
Elapsed(ElapsedInterval),
Pending(PendingInterval<T>),
}
impl<T> IntervalExpiration<T> {
pub(crate) fn fold_and_get_aggregation<F, P>(
self,
statistic: &mut F,
interpolation: &mut P,
) -> Result<Option<F::Aggregation>, F::Error>
where
T: Clone,
F: Statistic<Sample = T>,
P: InterpolationState<F::Aggregation, FillSample = T>,
{
match self {
IntervalExpiration::Elapsed(elapsed) => {
elapsed.interpolate_and_get_aggregation(statistic, interpolation)
}
IntervalExpiration::Pending(pending) => {
pending.fold(statistic, interpolation).map(|_| None)
}
}
}
}
impl<T> IntervalExpiration<PhantomData<T>> {
pub(crate) fn interpolate_and_get_aggregation<F, P>(
self,
statistic: &mut F,
interpolation: &mut P,
) -> Result<Option<F::Aggregation>, F::Error>
where
T: Clone,
F: Statistic<Sample = T>,
P: InterpolationState<F::Aggregation, FillSample = T>,
{
match self {
IntervalExpiration::Elapsed(elapsed) => {
elapsed.interpolate_and_get_aggregation(statistic, interpolation)
}
IntervalExpiration::Pending(pending) => {
pending.interpolate(statistic, interpolation).map(|_| None)
}
}
}
}
/// A time interval in which samples are folded into an aggregation.
///
/// Sampling intervals determine the timing of aggregations and interpolation in time series and
/// are defined by the following quantities:
///
/// 1. **Maximum sampling period.** This is the basic unit of time that defines the sampling
/// interval and represents the maximum duration in which a sample must be observed. For any
/// such duration in which no sample is observed, an interpolated sample is used instead. This
/// can also be thought of as its inverse: the minimum sampling frequency.
/// 2. **Sampling period count.** This is the number of sampling periods that form the sampling
/// interval. This determines the minimum number of samples (interpolated or otherwise) folded
/// into the aggregation for the sampling interval.
/// 3. **Capacity.** This is the number of sampling intervals (and therefore aggregations) that
/// must be stored to represent an aggregated series. This quantity is somewhat extrinsic to
/// the time interval itself, but determines its durability.
///
/// These quantities are concatenated into a shorthand to describe sampling intervals, formatted
/// as `capacity x sampling_period_count x maximum_sampling_period`. For example, a 10x2x5s
/// sampling interval persists 10 intervals formed from two maximum sampling period of 5s. In such
/// an interval, there is at least one sample every 5s, an aggregation every 10s, and at most 10
/// aggregations that represent a 100s period.
#[derive(Clone, Copy, Debug, Eq, Hash, PartialEq)]
pub struct SamplingInterval {
capacity: u32,
sampling_period_count: u32,
max_sampling_period: Quanta,
}
impl SamplingInterval {
pub(crate) fn new(
capacity: u32,
sampling_period_count: u32,
max_sampling_period: impl Into<Duration>,
) -> Self {
SamplingInterval {
capacity: cmp::max(1, capacity),
sampling_period_count: cmp::max(1, sampling_period_count),
max_sampling_period: cmp::max(1, max_sampling_period.into().into_quanta().abs()),
}
}
/// Gets the durability of the interval.
///
/// Durability is the maximum period of time represented by the aggregations of a sampling
/// interval. This is the time period for which it represents historical data.
pub fn durability(&self) -> Duration {
self.max_sampling_period() * (self.sampling_period_count * self.capacity)
}
/// Gets the duration of the interval (also known as the aggregation period).
pub fn duration(&self) -> Duration {
self.max_sampling_period() * self.sampling_period_count
}
/// Gets the maximum sampling period of the interval.
pub fn max_sampling_period(&self) -> Duration {
Duration::from_quanta(self.max_sampling_period)
}
pub(crate) fn capacity(&self) -> u32 {
self.capacity
}
/// Gets the [expirations][`IntervalExpiration`] of intervals intersected by the given
/// [`Tick`].
///
/// The given sample is always folded into exactly one pending interval that terminates the
/// sequence.
///
/// [`IntervalExpiration`]: crate::experimental::series::interval::IntervalExpiration
/// [`Tick`]: crate::experimental::clock::Tick;
pub(crate) fn fold_and_get_expirations<T>(
&self,
tick: Tick,
sample: T,
) -> impl Clone + Iterator<Item = IntervalExpiration<T>>
where
T: Clone,
{
let interval = self.max_sampling_period * Quanta::from(self.sampling_period_count);
let (start, end) = tick.quantize();
let start_has_sample = tick.start_has_sample(self.max_sampling_period);
// The intervals intersected by this `Tick` are constructed from three groups:
//
// - Zero or one _resumed_ intervals. Such an interval was previously the _pending_
// interval (see below), but has been elapsed by this `Tick`.
// - Zero or more _skipped_ intervals. Such intervals were never previously intersected,
// but are elapsed by this `Tick`.
// - Exactly one _pending_ interval. This is the interval intersected by the end
// timestamp of this `Tick`. There is always such an interval and this interval may
// have been pending previously.
//
// Note that all quantities here are technically periods or durations: start and end
// timestamps are durations from zero, for example. Divisions yield unitless quantities
// (counts).
//
// About the below calculation: Buckets are always aligned, so we can simply divide
// timestamps by an `interval` or `max_sampling_period` to find out whether they fall into
// the same interval or max_sampling_period.
//
// For example, if the interval is 60s, timestamps at 1s and 30s marks would both into
// the [0, 60) interval. OTOH, timestamp at 61s mark would fall into the [60, 120) interval.
// We see that `1 / 60 == 30 / 60` (integer division), whereas `1 / 60 != 61 / 60`.
let resumed_interval_has_elapsed = (end / interval) > (start / interval);
let num_skipped_intervals = (end / interval) - Integer::div_ceil(&start, &interval);
let pending_interval_fill_sample_count = if resumed_interval_has_elapsed {
// If the pending interval is a new one, simply calculate how many sampling periods
// it covers.
(end % interval) / self.max_sampling_period
} else {
// If the pending interval is an existing one, check how many sampling periods exist
// between start and end.
let num_elapsed_sampling_periods =
(end / self.max_sampling_period) - (start / self.max_sampling_period);
// Adjust the result based on whether the sampling period for the start timestamp
// already had a sample.
// This calculation can yield negative number if `start` and `end` are in the same
// sampling period, but we'll change it to 0 when cast to usize later on.
num_elapsed_sampling_periods - if start_has_sample { 1 } else { 0 }
};
itertools::chain!(
resumed_interval_has_elapsed.then(|| {
// Calculate how many sampling periods the remaining duration of the resumed
// interval covers. Adjust the result based on whether the sampling period for
// the start timestamp already had a sample.
let resumed_interval_remaining = interval - (start % interval);
let resumed_interval_fill_sample_count =
Integer::div_ceil(&resumed_interval_remaining, &self.max_sampling_period)
- if start_has_sample { 1 } else { 0 };
IntervalExpiration::Elapsed(ElapsedInterval {
fill_sample_count: NonZeroUsize::new(
usize::try_from(resumed_interval_fill_sample_count).unwrap_or(0),
),
})
}),
iter::repeat(IntervalExpiration::Elapsed(ElapsedInterval {
fill_sample_count: NonZeroUsize::new(
usize::try_from(self.sampling_period_count).unwrap_or(usize::MAX)
),
}))
.take(usize::try_from(num_skipped_intervals).unwrap_or(0)),
// The pending interval falls on the end timestamp and so includes the associated
// sample.
Some(IntervalExpiration::Pending(PendingInterval {
fill_sample_count: NonZeroUsize::new(
usize::try_from(pending_interval_fill_sample_count).unwrap_or(0)
),
sample,
})),
)
}
}
impl Display for SamplingInterval {
fn fmt(&self, formatter: &mut Formatter<'_>) -> fmt::Result {
write!(
formatter,
"{}x{}x{}",
self.capacity,
self.sampling_period_count,
self.max_sampling_period.into_nearest_unit_display(),
)
}
}
/// One or more cooperative [`SamplingInterval`]s.
#[derive(Clone, Debug)]
pub struct SamplingProfile(Vec1<SamplingInterval>);
impl SamplingProfile {
fn from_sampling_intervals<I>(intervals: I) -> Self
where
Vec1<SamplingInterval>: From<I>,
{
SamplingProfile(intervals.into())
}
/// Constructs a highly granular sampling profile with high fidelity.
///
/// The minimum granularity is 10s and the maximum durability is 20m.
pub fn highly_granular() -> Self {
SamplingProfile::from_sampling_intervals([
// 720x1x10s
SamplingInterval::new(720, 1, Duration::from_seconds(10)),
// 3600x1x1m
SamplingInterval::new(3600, 1, Duration::from_minutes(1)),
])
}
/// Constructs a granular sampling profile with decently high fidelity.
pub fn granular() -> Self {
SamplingProfile::from_sampling_intervals([
// 720x1x10s
SamplingInterval::new(720, 1, Duration::from_seconds(10)),
// 600x1x1m
SamplingInterval::new(600, 1, Duration::from_minutes(1)),
// 360x1x5m
SamplingInterval::new(720, 1, Duration::from_minutes(5)),
])
}
/// Constructs a sampling profile with fidelity and durability that is applicable to most
/// metrics.
pub fn balanced() -> Self {
SamplingProfile::from_sampling_intervals([
// 120x1x10s
SamplingInterval::new(120, 1, Duration::from_seconds(10)),
// 120x1x1m
SamplingInterval::new(120, 1, Duration::from_minutes(1)),
// 120x1x5m
SamplingInterval::new(120, 1, Duration::from_minutes(5)),
// 120x1x30m
SamplingInterval::new(120, 1, Duration::from_minutes(30)),
])
}
/// Gets the minimum granularity of the profile.
pub fn granularity(&self) -> Duration {
self.0.iter().map(SamplingInterval::max_sampling_period).min().unwrap()
}
/// Gets the maximum durability of the profile.
pub fn durability(&self) -> Duration {
self.0.iter().map(SamplingInterval::durability).max().unwrap()
}
pub(crate) fn into_sampling_intervals(self) -> Vec1<SamplingInterval> {
self.0
}
}
impl Default for SamplingProfile {
fn default() -> Self {
SamplingProfile::balanced()
}
}
impl Display for SamplingProfile {
fn fmt(&self, formatter: &mut Formatter<'_>) -> fmt::Result {
use itertools::Position::{First, Last, Middle, Only};
// Avoid `join` and other sources of intermediate allocations.
write!(
formatter,
"{}..{}: ",
self.granularity().into_quanta().into_nearest_unit_display(),
self.durability().into_quanta().into_nearest_unit_display(),
)?;
for interval in self.0.iter().with_position() {
match interval {
First(interval) | Middle(interval) => write!(formatter, "{} + ", interval),
Only(interval) | Last(interval) => write!(formatter, "{}", interval),
}?;
}
Ok(())
}
}
impl From<SamplingInterval> for SamplingProfile {
fn from(interval: SamplingInterval) -> Self {
SamplingProfile(Vec1::from_item(interval))
}
}
fn fill_non_zero_with<S, T, F>(
sampler: &mut S,
n: Option<NonZeroUsize>,
f: F,
) -> Result<(), S::Error>
where
S: Fill<T>,
F: FnOnce() -> T,
{
if let Some(n) = n {
sampler.fill(f(), n)
} else {
Ok(())
}
}
#[cfg(test)]
mod tests {
use super::*;
use std::sync::mpsc::{self, Receiver, Sender};
use crate::experimental::clock::{ObservationTime, Timestamp};
use crate::experimental::series::{Counter, Fill, Sampler};
const SAMPLE: u64 = 1337u64;
#[test]
fn sampling_interval_fold_and_get_expirations() {
let sampling_interval = SamplingInterval::new(120, 6, Duration::from_seconds(10));
let mut last = ObservationTime {
last_update_timestamp: Timestamp::from_nanos(71_000_000_000),
last_sample_timestamp: Timestamp::from_nanos(-1),
};
// Tick in the same sampling period that did not have a sample.
// (last sample at -1 nano)
let tick = last.tick(Timestamp::from_nanos(75_000_000_000), true).unwrap();
let expirations: Vec<_> =
sampling_interval.fold_and_get_expirations(tick, SAMPLE).collect();
assert_eq!(
expirations,
vec![IntervalExpiration::Pending(PendingInterval {
fill_sample_count: None,
sample: SAMPLE,
})]
);
// Tick in the same sampling period that already had a sample.
// (last sample at 75s)
let tick = last.tick(Timestamp::from_nanos(79_000_000_000), false).unwrap();
let expirations: Vec<_> =
sampling_interval.fold_and_get_expirations(tick, SAMPLE).collect();
assert_eq!(
expirations,
vec![IntervalExpiration::Pending(PendingInterval {
fill_sample_count: None,
sample: SAMPLE,
})]
);
// Tick to a new sampling period, but in the same interval. The sampling period
// at the start of the tick already had a sample.
let tick = last.tick(Timestamp::from_nanos(83_000_000_000), false).unwrap();
let expirations: Vec<_> =
sampling_interval.fold_and_get_expirations(tick, SAMPLE).collect();
assert_eq!(
expirations,
vec![IntervalExpiration::Pending(PendingInterval {
fill_sample_count: None,
sample: SAMPLE,
})]
);
// Tick to a new sampling period, but in the same interval. The sampling period
// at the start of the tick did not have a sample.
let tick = last.tick(Timestamp::from_nanos(91_000_000_000), true).unwrap();
let expirations: Vec<_> =
sampling_interval.fold_and_get_expirations(tick, SAMPLE).collect();
assert_eq!(
expirations,
vec![IntervalExpiration::Pending(PendingInterval {
fill_sample_count: NonZeroUsize::new(1),
sample: SAMPLE,
})]
);
// Tick to a new interval. The sampling period at the start of the tick already
// had a sample.
let tick = last.tick(Timestamp::from_nanos(133_000_000_000), false).unwrap();
let expirations: Vec<_> =
sampling_interval.fold_and_get_expirations(tick, SAMPLE).collect();
let expected = vec![
IntervalExpiration::Elapsed(ElapsedInterval {
fill_sample_count: NonZeroUsize::new(2),
}),
IntervalExpiration::Pending(PendingInterval {
fill_sample_count: NonZeroUsize::new(1),
sample: SAMPLE,
}),
];
assert_eq!(expirations, expected);
// Tick to a new interval. The sampling period at the start of the tick did not
// have a sample. Additionally, there are some skipped intervals in-between
let tick = last.tick(Timestamp::from_nanos(240_000_000_000), false).unwrap();
let expirations: Vec<_> =
sampling_interval.fold_and_get_expirations(tick, SAMPLE).collect();
let expected = vec![
IntervalExpiration::Elapsed(ElapsedInterval {
fill_sample_count: NonZeroUsize::new(5),
}),
IntervalExpiration::Elapsed(ElapsedInterval {
fill_sample_count: NonZeroUsize::new(6),
}),
IntervalExpiration::Pending(PendingInterval {
fill_sample_count: None,
sample: SAMPLE,
}),
];
assert_eq!(expirations, expected);
}
#[derive(Clone, Debug, PartialEq)]
enum MockStatisticCall {
// Though `n` is represented as `NonZeroUsize`, it is represented as `usize` here for more
// fluent expressions in assertions.
Fill { sample: u64, n: usize },
Fold { sample: u64 },
Reset,
Aggregation,
}
#[derive(Clone, Debug)]
struct MockStatistic(Sender<MockStatisticCall>);
impl MockStatistic {
pub fn channel() -> (Self, Receiver<MockStatisticCall>) {
let (tx, rx) = mpsc::channel();
(Self(tx), rx)
}
}
impl Statistic for MockStatistic {
type Semantic = Counter;
type Sample = u64;
type Aggregation = u64;
fn reset(&mut self) {
self.0.send(MockStatisticCall::Reset).unwrap();
}
fn aggregation(&self) -> Option<Self::Aggregation> {
self.0.send(MockStatisticCall::Aggregation).unwrap();
Some(100)
}
}
impl Fill<u64> for MockStatistic {
fn fill(&mut self, sample: u64, n: NonZeroUsize) -> Result<(), Self::Error> {
// Tests assert against `n` as a `usize` instead of `NonZeroUsize`.
self.0.send(MockStatisticCall::Fill { sample, n: n.get() }).unwrap();
Ok(())
}
}
impl Sampler<u64> for MockStatistic {
type Error = ();
fn fold(&mut self, sample: u64) -> Result<(), Self::Error> {
self.0.send(MockStatisticCall::Fold { sample }).unwrap();
Ok(())
}
}
#[derive(Clone, Debug, PartialEq)]
enum MockInterpolationStateCall {
FoldSample { sample: u64 },
FoldAggregation { aggregation: u64 },
}
#[derive(Clone, Debug)]
struct MockInterpolationState(Vec<MockInterpolationStateCall>);
impl MockInterpolationState {
fn new() -> Self {
Self(vec![])
}
}
impl InterpolationState<u64> for MockInterpolationState {
type FillSample = u64;
fn sample(&self) -> Self::FillSample {
42u64
}
fn fold_sample(&mut self, sample: Self::FillSample) {
self.0.push(MockInterpolationStateCall::FoldSample { sample });
}
fn fold_aggregation(&mut self, sample: Self::FillSample) {
self.0.push(MockInterpolationStateCall::FoldAggregation { aggregation: sample });
}
}
#[test]
fn elapsed_interval_interpolate_and_get_aggregation() {
let interval = ElapsedInterval { fill_sample_count: NonZeroUsize::new(6) };
let (mut statistic, calls) = MockStatistic::channel();
let mut interpolation = MockInterpolationState::new();
let result = interval.interpolate_and_get_aggregation(&mut statistic, &mut interpolation);
assert!(result.is_ok());
assert_eq!(
calls.try_iter().collect::<Vec<_>>(),
&[
MockStatisticCall::Fill { sample: 42, n: 6 },
MockStatisticCall::Aggregation,
MockStatisticCall::Reset,
],
);
assert_eq!(
interpolation.0,
vec![MockInterpolationStateCall::FoldAggregation { aggregation: 100 }],
);
}
#[test]
fn pending_interval_fold() {
let interval = PendingInterval { fill_sample_count: NonZeroUsize::new(6), sample: 50u64 };
let (mut statistic, calls) = MockStatistic::channel();
let mut interpolation = MockInterpolationState::new();
let result = interval.fold(&mut statistic, &mut interpolation);
assert!(result.is_ok());
assert_eq!(
calls.try_iter().collect::<Vec<_>>(),
&[MockStatisticCall::Fill { sample: 42, n: 6 }, MockStatisticCall::Fold { sample: 50 }],
);
assert_eq!(interpolation.0, vec![MockInterpolationStateCall::FoldSample { sample: 50 }]);
}
}