mz_storage_operators/

persist_source.rs

// Copyright Materialize, Inc. and contributors. All rights reserved.
//
// Use of this software is governed by the Business Source License
// included in the LICENSE file.
//
// As of the Change Date specified in that file, in accordance with
// the Business Source License, use of this software will be governed
// by the Apache License, Version 2.0.

//! A source that reads from an a persist shard.

use differential_dataflow::consolidation::ConsolidatingContainerBuilder;
use std::borrow::Cow;
use std::collections::VecDeque;
use std::convert::Infallible;
use std::fmt::Debug;
use std::future::Future;
use std::hash::Hash;
use std::sync::Arc;

use differential_dataflow::lattice::Lattice;
use futures::{StreamExt, future::Either};
use mz_expr::{
    ColumnSpecs, Eval, EvalError, Interpretable, Interpreter, MfpPlan, OptimizableExpr, ResultSpec,
    UnmaterializableFunc,
};
use mz_ore::cast::CastFrom;
use mz_ore::collections::CollectionExt;
use mz_ore::str::redact;
use mz_persist_client::cache::PersistClientCache;
use mz_persist_client::cfg::{PersistConfig, RetryParameters};
use mz_persist_client::fetch::{ExchangeableBatchPart, ShardSourcePart};
use mz_persist_client::fetch::{FetchedBlob, FetchedPart};
use mz_persist_client::operators::shard_source::{
    ErrorHandler, FilterResult, SnapshotMode, shard_source,
};
use mz_persist_client::stats::STATS_AUDIT_PANIC;
use mz_persist_types::Codec64;
use mz_persist_types::codec_impls::UnitSchema;
use mz_persist_types::columnar::{ColumnEncoder, Schema};
use mz_repr::{
    Datum, DatumVec, Diff, GlobalId, RelationDesc, ReprRelationType, Row, RowArena, Timestamp,
};
use mz_storage_types::StorageDiff;
use mz_storage_types::controller::{CollectionMetadata, TxnsCodecRow};
use mz_storage_types::errors::DataflowError;
use mz_storage_types::sources::SourceData;
use mz_storage_types::stats::RelationPartStats;
use mz_timely_util::builder_async::{
    Event, OperatorBuilder as AsyncOperatorBuilder, PressOnDropButton,
};
use mz_timely_util::probe::ProbeNotify;
use mz_txn_wal::operator::{TxnsContext, TxnsProgress};
use serde::{Deserialize, Serialize};
use timely::container::{CapacityContainerBuilder, PushInto};
use timely::dataflow::channels::pact::Pipeline;
use timely::dataflow::operators::generic::OutputBuilder;
use timely::dataflow::operators::generic::builder_rc::OperatorBuilder;
use timely::dataflow::operators::{Capability, Leave};
use timely::dataflow::operators::{CapabilitySet, ConnectLoop, Feedback};
use timely::dataflow::{Scope, Stream, StreamVec};
use timely::order::TotalOrder;
use timely::progress::Antichain;
use timely::progress::Timestamp as TimelyTimestamp;
use timely::progress::timestamp::PathSummary;
use timely::scheduling::Activator;
use timely::{ContainerBuilder, PartialOrder};
use tokio::sync::mpsc::UnboundedSender;
use tracing::{error, trace};

use crate::metrics::BackpressureOperatorMetrics;

/// This opaque token represents progress within a timestamp, allowing finer-grained frontier
/// progress than would otherwise be possible.
///
/// This is "opaque" since we'd like to reserve the right to change the definition in the future
/// without downstreams being able to rely on the precise representation. (At the moment, this
/// is a simple batch counter, though we may change it to eg. reflect progress through the keyspace
/// in the future.)
#[derive(
    Copy,
    Clone,
    PartialEq,
    Default,
    Eq,
    PartialOrd,
    Ord,
    Debug,
    Serialize,
    Deserialize,
    Hash,
    columnar::Columnar
)]
// Derive ordering on the generated `SubtimeReference` too: the paged merge
// batcher sorts the `(Timestamp, Subtime)` time and so requires `Ref: Ord`.
#[columnar(derive(PartialEq, Eq, PartialOrd, Ord))]
pub struct Subtime(u64);

impl PartialOrder for Subtime {
    fn less_equal(&self, other: &Self) -> bool {
        self.0.less_equal(&other.0)
    }
}

impl TotalOrder for Subtime {}

impl PathSummary<Subtime> for Subtime {
    fn results_in(&self, src: &Subtime) -> Option<Subtime> {
        self.0.results_in(&src.0).map(Subtime)
    }

    fn followed_by(&self, other: &Self) -> Option<Self> {
        self.0.followed_by(&other.0).map(Subtime)
    }
}

impl TimelyTimestamp for Subtime {
    type Summary = Subtime;

    fn minimum() -> Self {
        Subtime(0)
    }
}

impl columnation::Columnation for Subtime {
    type InnerRegion = columnation::CopyRegion<Subtime>;
}

impl differential_dataflow::lattice::Lattice for Subtime {
    fn join(&self, other: &Self) -> Self {
        Subtime(std::cmp::max(self.0, other.0))
    }
    fn meet(&self, other: &Self) -> Self {
        Subtime(std::cmp::min(self.0, other.0))
    }
}

impl differential_dataflow::lattice::Maximum for Subtime {
    fn maximum() -> Self {
        Subtime(u64::MAX)
    }
}

impl Subtime {
    /// The smallest non-zero summary for the opaque timestamp type.
    pub const fn least_summary() -> Self {
        Subtime(1)
    }
}

/// The scalar expression type of a source's [`MfpPlan`]: anything the plan can
/// evaluate per row and the filter-pushdown interpreter can summarize per part.
pub trait PlanExpr: OptimizableExpr + Eval + Interpretable + Send + Sync + 'static {}
impl<X: OptimizableExpr + Eval + Interpretable + Send + Sync + 'static> PlanExpr for X {}

/// Creates a new source that reads from a persist shard, distributing the work
/// of reading data to all timely workers.
///
/// Returns the shard's rows in `CB`'s containers and its errors in a stream of their own.
///
/// All times emitted will have been [advanced by] the given `as_of` frontier.
/// All updates at times greater or equal to `until` will be suppressed.
/// The `map_filter_project` argument, if supplied, may be partially applied,
/// and any un-applied part of the argument will be left behind in the argument.
///
/// Users of this function have the ability to apply flow control to the output
/// to limit the in-flight data (measured in bytes) it can emit. The flow control
/// input is a timely stream that communicates the frontier at which the data
/// emitted from by this source have been dropped.
///
/// **Note:** Because this function is reading batches from `persist`, it is working
/// at batch granularity. In practice, the source will be overshooting the target
/// flow control upper by an amount that is related to the size of batches.
///
/// If no flow control is desired an empty stream whose frontier immediately advances
/// to the empty antichain can be used. An easy easy of creating such stream is by
/// using [`timely::dataflow::operators::generic::operator::empty`].
///
/// [advanced by]: differential_dataflow::lattice::Lattice::advance_by
pub fn persist_source<'scope, E, CB, X>(
    scope: Scope<'scope, mz_repr::Timestamp>,
    source_id: GlobalId,
    persist_clients: Arc<PersistClientCache>,
    txns_ctx: &TxnsContext,
    metadata: CollectionMetadata,
    read_schema: Option<RelationDesc>,
    as_of: Option<Antichain<Timestamp>>,
    snapshot_mode: SnapshotMode,
    until: Antichain<Timestamp>,
    map_filter_project: Option<&mut MfpPlan<X>>,
    max_inflight_bytes: Option<usize>,
    start_signal: impl Future<Output = ()> + Send + 'static,
    error_handler: ErrorHandler,
) -> (
    Stream<'scope, mz_repr::Timestamp, CB::Container>,
    StreamVec<'scope, mz_repr::Timestamp, (E, Timestamp, Diff)>,
    Vec<PressOnDropButton>,
)
where
    E: timely::ExchangeData + Ord + Clone + Debug + From<DataflowError> + From<EvalError>,
    CB: ContainerBuilder + PushInto<(Row, mz_repr::Timestamp, Diff)>,
    CB::Container: Clone,
    X: PlanExpr,
{
    let mut tokens = vec![];
    let name = source_id.to_string();

    let outer = scope.clone();
    let (ok_stream, err_stream) =
        scope.scoped(&format!("granular_backpressure({})", source_id), |scope| {
            let (flow_control, flow_control_probe) = match max_inflight_bytes {
                Some(max_inflight_bytes) => {
                    let series = &persist_clients.metrics().backpressure;
                    let backpressure_metrics = BackpressureOperatorMetrics::new(
                        series.emitted_bytes.clone(),
                        series.last_backpressured_bytes.clone(),
                        series.retired_bytes.clone(),
                    );

                    let probe = mz_timely_util::probe::Handle::default();
                    let progress_stream = mz_timely_util::probe::source(
                        scope.clone(),
                        format!("decode_backpressure_probe({source_id})"),
                        probe.clone(),
                    );
                    let flow_control = FlowControl {
                        progress_stream,
                        max_inflight_bytes,
                        summary: (Default::default(), Subtime::least_summary()),
                        metrics: Some(backpressure_metrics),
                    };
                    (Some(flow_control), Some(probe))
                }
                None => (None, None),
            };

            // Our default listen sleeps are tuned for the case of a shard that is
            // written once a second, but txn-wal allows these to be lazy.
            // Override the tuning to reduce crdb load. The pubsub fallback
            // responsibility is then replaced by manual "one state" wakeups in the
            // txns_progress operator.
            let cfg = Arc::clone(&persist_clients.cfg().configs);
            let subscribe_sleep = match metadata.txns_shard {
                Some(_) => Some(move || mz_txn_wal::operator::txns_data_shard_retry_params(&cfg)),
                None => None,
            };

            let filter_plan = map_filter_project.as_ref().map(|p| (*p).clone());
            let (cfg, fetched, source_tokens) = fetch_parts(
                outer,
                scope,
                source_id,
                Arc::clone(&persist_clients),
                metadata.clone(),
                read_schema,
                as_of.clone(),
                snapshot_mode,
                until.clone(),
                filter_plan,
                flow_control,
                subscribe_sleep,
                start_signal,
                error_handler,
            );
            tokens.extend(source_tokens);

            let (ok_stream, err_stream) = decode_and_mfp::<E, mz_repr::Timestamp, CB, X>(
                cfg,
                fetched,
                &name,
                until.clone(),
                map_filter_project,
                |time| time.0,
            );

            // The handle's frontier is the meet of what its clones report, so both streams
            // have to feed it for backpressure to retire the right bytes.
            let (ok_stream, err_stream) = match flow_control_probe {
                Some(probe) => (
                    ok_stream.probe_notify_with(vec![probe.clone()]),
                    err_stream.probe_notify_with(vec![probe]),
                ),
                None => (ok_stream, err_stream),
            };

            (ok_stream.leave(outer), err_stream.leave(outer))
        });

    // If a txns_shard was provided, then this shard is in the txn-wal
    // system. This means the "logical" upper may be ahead of the "physical"
    // upper. Render dataflow operators that pass through the inputs and
    // translate the progress frontiers as necessary.
    let (ok_stream, err_stream) = match metadata.txns_shard {
        Some(txns_shard) => {
            let (progress, remap_token) = TxnsProgress::new::<SourceData, (), i64, TxnsCodecRow, _>(
                outer,
                &name,
                txns_ctx,
                move || {
                    let (c, l) = (
                        Arc::clone(&persist_clients),
                        metadata.persist_location.clone(),
                    );
                    async move { c.open(l).await.expect("location is valid") }
                },
                txns_shard,
                metadata.data_shard,
                as_of
                    .expect("as_of is provided for table sources")
                    .into_option()
                    .expect("shard is not closed"),
                Arc::new(metadata.relation_desc),
                Arc::new(UnitSchema),
            );
            let (ok_stream, ok_token) = progress.translate(ok_stream, until.clone());
            let (err_stream, err_token) = progress.translate(err_stream, until);
            tokens.extend([remap_token, ok_token, err_token]);
            (ok_stream, err_stream)
        }
        None => (ok_stream, err_stream),
    };

    (ok_stream, err_stream, tokens)
}

type RefinedScope<'scope, T> = Scope<'scope, (T, Subtime)>;

/// Creates a new source that reads from a persist shard, distributing the work
/// of reading data to all timely workers.
///
/// Returns the ok and error sides separately, both carrying the refined time.
///
/// All times emitted will have been [advanced by] the given `as_of` frontier.
///
/// [advanced by]: differential_dataflow::lattice::Lattice::advance_by
pub fn persist_source_core<'g, 'outer, E, X>(
    outer: Scope<'outer, mz_repr::Timestamp>,
    scope: RefinedScope<'g, mz_repr::Timestamp>,
    source_id: GlobalId,
    persist_clients: Arc<PersistClientCache>,
    metadata: CollectionMetadata,
    read_schema: Option<RelationDesc>,
    as_of: Option<Antichain<Timestamp>>,
    snapshot_mode: SnapshotMode,
    until: Antichain<Timestamp>,
    map_filter_project: Option<&mut MfpPlan<X>>,
    flow_control: Option<FlowControl<'g, RefinedTime>>,
    // If Some, an override for the default listen sleep retry parameters.
    listen_sleep: Option<impl Fn() -> RetryParameters + Send + 'static>,
    start_signal: impl Future<Output = ()> + Send + 'static,
    error_handler: ErrorHandler,
) -> (
    StreamVec<'g, RefinedTime, (Row, RefinedTime, Diff)>,
    StreamVec<'g, RefinedTime, (E, RefinedTime, Diff)>,
    Vec<PressOnDropButton>,
)
where
    E: timely::ExchangeData + Ord + Clone + Debug + From<DataflowError> + From<EvalError>,
    X: PlanExpr,
{
    let name = source_id.to_string();
    let filter_plan = map_filter_project.as_ref().map(|p| (*p).clone());
    let (cfg, fetched, token) = fetch_parts(
        outer,
        scope,
        source_id,
        persist_clients,
        metadata,
        read_schema,
        as_of,
        snapshot_mode,
        until.clone(),
        filter_plan,
        flow_control,
        listen_sleep,
        start_signal,
        error_handler,
    );
    let (oks, errs) = decode_and_mfp::<E, RefinedTime, RowVecBuilder<RefinedTime>, X>(
        cfg,
        fetched,
        &name,
        until,
        map_filter_project,
        |time| time,
    );
    (oks, errs, token)
}

/// Fetch the parts of a persist shard a dataflow needs, distributing the work of reading them
/// across all timely workers.
#[allow(clippy::needless_borrow)]
fn fetch_parts<'g, 'outer, X: PlanExpr>(
    outer: Scope<'outer, mz_repr::Timestamp>,
    scope: RefinedScope<'g, mz_repr::Timestamp>,
    source_id: GlobalId,
    persist_clients: Arc<PersistClientCache>,
    metadata: CollectionMetadata,
    read_schema: Option<RelationDesc>,
    as_of: Option<Antichain<Timestamp>>,
    snapshot_mode: SnapshotMode,
    until: Antichain<Timestamp>,
    // The MFP whose filter is pushed down into persist, if any.
    filter_plan: Option<MfpPlan<X>>,
    flow_control: Option<FlowControl<'g, RefinedTime>>,
    // If Some, an override for the default listen sleep retry parameters.
    listen_sleep: Option<impl Fn() -> RetryParameters + Send + 'static>,
    start_signal: impl Future<Output = ()> + Send + 'static,
    error_handler: ErrorHandler,
) -> (
    PersistConfig,
    StreamVec<'g, RefinedTime, FetchedBlob<SourceData, (), Timestamp, StorageDiff>>,
    Vec<PressOnDropButton>,
)
where
    X: PlanExpr,
{
    let cfg = persist_clients.cfg().clone();
    let name = source_id.to_string();

    // N.B. `read_schema` may be a subset of the total columns for this shard.
    let read_desc = match read_schema {
        Some(desc) => desc,
        None => metadata.relation_desc,
    };

    let desc_transformer = match flow_control {
        Some(flow_control) => Some(move |scope, descs, chosen_worker| {
            let (stream, token) = backpressure(
                scope,
                &format!("backpressure({source_id})"),
                descs,
                flow_control,
                chosen_worker,
                None,
            );
            (stream, vec![token])
        }),
        None => None,
    };

    let metrics = Arc::clone(persist_clients.metrics());
    let filter_name = name.clone();
    // The `until` gives us an upper bound on the possible values of `mz_now` this query may see.
    // Ranges are inclusive, so it's safe to use the maximum timestamp as the upper bound when
    // `until ` is the empty antichain.
    let upper = until.as_option().cloned().unwrap_or(Timestamp::MAX);
    let (fetched, token) = shard_source(
        outer,
        scope,
        &name,
        move || {
            let (c, l) = (
                Arc::clone(&persist_clients),
                metadata.persist_location.clone(),
            );
            async move { c.open(l).await.unwrap() }
        },
        metadata.data_shard,
        as_of,
        snapshot_mode,
        until.clone(),
        desc_transformer,
        Arc::new(read_desc.clone()),
        Arc::new(UnitSchema),
        move |stats, frontier| {
            let Some(lower) = frontier.as_option().copied() else {
                // If the frontier has advanced to the empty antichain,
                // we'll never emit any rows from any part.
                return FilterResult::Discard;
            };

            if lower > upper {
                // The frontier timestamp is larger than the until of the dataflow:
                // anything from this part will necessarily be filtered out.
                return FilterResult::Discard;
            }

            let time_range =
                ResultSpec::value_between(Datum::MzTimestamp(lower), Datum::MzTimestamp(upper));
            if let Some(plan) = &filter_plan {
                let metrics = &metrics.pushdown.part_stats;
                let stats = RelationPartStats::new(&filter_name, metrics, &read_desc, stats);
                filter_result(&read_desc, time_range, stats, plan)
            } else {
                FilterResult::Keep
            }
        },
        listen_sleep,
        start_signal,
        error_handler,
    );
    (cfg, fetched, token)
}

fn filter_result<X: PlanExpr>(
    relation_desc: &RelationDesc,
    time_range: ResultSpec,
    stats: RelationPartStats,
    plan: &MfpPlan<X>,
) -> FilterResult {
    let arena = RowArena::new();
    let relation = ReprRelationType::from(relation_desc.typ());
    let mut ranges = ColumnSpecs::new(&relation, &arena);
    ranges.push_unmaterializable(UnmaterializableFunc::MzNow, time_range);

    let may_error = stats.err_count().map_or(true, |count| count > 0);

    // N.B. We may have pushed down column "demands" into Persist, so this
    // relation desc may have a different set of columns than the stats.
    for (pos, (idx, _, _)) in relation_desc.iter_all().enumerate() {
        let result_spec = stats.col_stats(idx, &arena);
        ranges.push_column(pos, result_spec);
    }
    let result = ranges.mfp_plan_filter(plan).range;
    let may_error = may_error || result.may_fail();
    let may_keep = result.may_contain(Datum::True);
    let may_skip = result.may_contain(Datum::False) || result.may_contain(Datum::Null);
    if relation_desc.len() == 0 && !may_error && !may_skip {
        let Ok(mut key) = <RelationDesc as Schema<SourceData>>::encoder(relation_desc) else {
            return FilterResult::Keep;
        };
        key.append(&SourceData(Ok(Row::default())));
        let key = key.finish();
        let Ok(mut val) = <UnitSchema as Schema<()>>::encoder(&UnitSchema) else {
            return FilterResult::Keep;
        };
        val.append(&());
        let val = val.finish();

        FilterResult::ReplaceWith {
            key: Arc::new(key),
            val: Arc::new(val),
        }
    } else if may_error || may_keep {
        FilterResult::Keep
    } else {
        FilterResult::Discard
    }
}

/// The time a decode operator's capabilities carry, refined with a [`Subtime`] so flow
/// control can pace parts within a millisecond.
type RefinedTime = (mz_repr::Timestamp, Subtime);

/// Ok-side container builder producing row vectors timestamped with `T`.
pub type RowVecBuilder<T> = ConsolidatingContainerBuilder<Vec<(Row, T, Diff)>>;

/// Err-side container builder.
type ErrBuilder<E, RT> = ConsolidatingContainerBuilder<Vec<(E, RT, Diff)>>;

/// Decode fetched parts and apply `map_filter_project`, writing ok records into `CB`'s
/// containers and err records into a separate output.
///
/// `record_time` picks what a record stores for its time. A reader that does not distinguish
/// times within a millisecond passes `|time| time.0`, which drops the [`Subtime`] coordinate
/// the enclosing scope refines with: that coordinate exists to pace flow control and stays on
/// the capabilities, and keeping it in the records would force a re-encode to strip it later.
/// A reader that builds a collection in the refined scope needs it, and passes `|time| time`.
fn decode_and_mfp<'scope, E, RT, CB, X>(
    cfg: PersistConfig,
    fetched: StreamVec<'scope, RefinedTime, FetchedBlob<SourceData, (), Timestamp, StorageDiff>>,
    name: &str,
    until: Antichain<Timestamp>,
    mut map_filter_project: Option<&mut MfpPlan<X>>,
    record_time: fn(RefinedTime) -> RT,
) -> (
    Stream<'scope, RefinedTime, CB::Container>,
    StreamVec<'scope, RefinedTime, (E, RT, Diff)>,
)
where
    E: timely::ExchangeData + Ord + Clone + Debug + From<DataflowError> + From<EvalError>,
    RT: Ord + Clone + Debug + 'static,
    CB: ContainerBuilder + PushInto<(Row, RT, Diff)>,
    X: PlanExpr,
{
    let scope = fetched.scope();
    let mut builder = OperatorBuilder::new(
        format!("persist_source::decode_and_mfp({})", name),
        scope.clone(),
    );
    let operator_info = builder.operator_info();

    let mut fetched_input = builder.new_input(fetched, Pipeline);
    let (ok_output, ok_stream) = builder.new_output::<CB::Container>();
    let mut ok_output: OutputBuilder<_, CB> = OutputBuilder::from(ok_output);
    let (err_output, err_stream) = builder.new_output();
    let mut err_output: OutputBuilder<_, ErrBuilder<E, RT>> = OutputBuilder::from(err_output);

    let name = name.to_owned();
    // Extract the MFP if it exists; leave behind an identity MFP in that case.
    let map_filter_project = map_filter_project.as_mut().map(|mfp| mfp.take());

    builder.build(move |_caps| {
        // Acquire an activator to reschedule the operator when it has unfinished work.
        let activator = Activator::new(operator_info.address, scope.activations());
        let panic_on_audit_failure = STATS_AUDIT_PANIC.handle(&cfg);
        let mut pending_work = VecDeque::new();
        let mut datum_vec = DatumVec::new();
        let mut row_builder = Row::default();

        move |_frontier| {
            fetched_input.for_each(|time, data| {
                const EMPTY_STAMP: &str = "message stamped with no capabilities";
                // The scope is totally ordered, so the least of the message's capabilities
                // dominates the rest and alone suffices to hold the fetched parts.
                let capabilities = [
                    time.retain_least(0).expect(EMPTY_STAMP),
                    time.retain_least(1).expect(EMPTY_STAMP),
                ];
                let panic_on_audit_failure = panic_on_audit_failure.get();
                for blob in data.drain(..) {
                    pending_work.push_back(PendingWork {
                        panic_on_audit_failure,
                        capabilities: capabilities.clone(),
                        part: PendingPart::Unparsed(blob),
                    });
                }
            });

            // Get dyncfg values once per schedule to amortize the cost of loading the atomics.
            let yield_fuel = cfg.storage_source_decode_fuel();
            let mut work = 0;
            let mut ok_output = ok_output.activate();
            let mut err_output = err_output.activate();
            while let Some(front) = pending_work.front_mut() {
                if work >= yield_fuel {
                    break;
                }
                let cap_time = *front.capabilities[0].time();
                // A session per part: dropping it flushes the container builder, so a
                // container never mixes records from parts held at different capabilities.
                let mut ok_session = ok_output.session_with_builder(&front.capabilities[0]);
                let mut err_session = err_output.session_with_builder(&front.capabilities[1]);
                let done = decode_part(
                    &mut front.part,
                    front.panic_on_audit_failure,
                    cap_time,
                    &name,
                    &until,
                    map_filter_project.as_ref(),
                    &mut datum_vec,
                    &mut row_builder,
                    &mut work,
                    yield_fuel,
                    |record, time, diff| match record {
                        Ok(row) => ok_session.give((row.into_owned(), record_time(time), diff)),
                        Err(err) => err_session.give((err, record_time(time), diff)),
                    },
                );
                drop(ok_session);
                drop(err_session);
                if done {
                    pending_work.pop_front();
                }
            }
            if !pending_work.is_empty() {
                activator.activate();
            }
        }
    });

    (ok_stream, err_stream)
}

/// Pending work to read from fetched parts
struct PendingWork {
    /// Whether to panic if a part fails an audit, or to just pass along the audited data.
    panic_on_audit_failure: bool,
    /// The time at which the work should happen, one capability per operator output.
    capabilities: [Capability<RefinedTime>; 2],
    /// Pending fetched part.
    part: PendingPart,
}

enum PendingPart {
    Unparsed(FetchedBlob<SourceData, (), Timestamp, StorageDiff>),
    Parsed {
        part: ShardSourcePart<SourceData, (), Timestamp, StorageDiff>,
    },
}

impl PendingPart {
    /// Returns the contained `FetchedPart`, first parsing it from a
    /// `FetchedBlob` if necessary.
    ///
    /// Also returns a bool, which is true if the part is known (from pushdown
    /// stats) to be free of `SourceData(Err(_))`s. It will be false if the part
    /// is known to contain errors or if it's unknown.
    fn part_mut(&mut self) -> &mut FetchedPart<SourceData, (), Timestamp, StorageDiff> {
        match self {
            PendingPart::Unparsed(x) => {
                *self = PendingPart::Parsed { part: x.parse() };
                // Won't recurse any further.
                self.part_mut()
            }
            PendingPart::Parsed { part } => &mut part.part,
        }
    }
}

/// Read `part`, apply the MFP, and hand every record to `give`, stopping once `work` reaches
/// `yield_fuel`. Returns whether the part is exhausted.
///
/// Records carry `cap_time` with its millisecond replaced by the record's own time, so the
/// caller must emit them at the capability `cap_time` came from.
fn decode_part<E, F, X>(
    part: &mut PendingPart,
    panic_on_audit_failure: bool,
    cap_time: RefinedTime,
    name: &str,
    until: &Antichain<Timestamp>,
    map_filter_project: Option<&MfpPlan<X>>,
    datum_vec: &mut DatumVec,
    row_builder: &mut Row,
    work: &mut usize,
    yield_fuel: usize,
    mut give: F,
) -> bool
where
    E: timely::ExchangeData + Ord + Clone + Debug + From<DataflowError> + From<EvalError>,
    F: FnMut(Result<Cow<'_, Row>, E>, RefinedTime, Diff),
    X: PlanExpr,
{
    let fetched_part = part.part_mut();
    let is_filter_pushdown_audit = fetched_part.is_filter_pushdown_audit();
    let mut row_buf = None;
    while let Some(((key, val), time, diff)) =
        fetched_part.next_with_storage(&mut row_buf, &mut None)
    {
        if until.less_equal(&time) {
            continue;
        }
        match (key, val) {
            (SourceData(Ok(row)), ()) => {
                if let Some(mfp) = map_filter_project {
                    // We originally accounted work as the number of outputs, to give downstream
                    // operators a chance to reduce down anything we've emitted. This mfp call
                    // might have a restrictive filter, which would have been counted as no
                    // work. However, in practice, we've been decode_and_mfp be a source of
                    // interactivity loss during rehydration, so we now also count each mfp
                    // evaluation against our fuel.
                    *work += 1;
                    let arena = mz_repr::RowArena::new();
                    let mut datums_local = datum_vec.borrow_with(&row);
                    for result in mfp.evaluate(
                        &mut datums_local,
                        &arena,
                        time,
                        diff.into(),
                        |time| !until.less_equal(time),
                        row_builder,
                    ) {
                        // Earlier we decided this Part doesn't need to be fetched, but to
                        // audit our logic we fetched it any way. If the MFP returned data it
                        // means our earlier decision to not fetch this part was incorrect.
                        if let Some(stats) = &is_filter_pushdown_audit {
                            // NB: The tag added by this scope is used for alerting. The panic
                            // message may be changed arbitrarily, but the tag key and val must
                            // stay the same.
                            sentry::with_scope(
                                |scope| {
                                    scope.set_tag("alert_id", "persist_pushdown_audit_violation")
                                },
                                || {
                                    error!(
                                        ?stats,
                                        name,
                                        mfp = ?redact(&mfp),
                                        result = ?redact(&result),
                                        "persist filter pushdown correctness violation!"
                                    );
                                    if panic_on_audit_failure {
                                        panic!(
                                            "persist filter pushdown correctness violation! {}",
                                            name
                                        );
                                    }
                                },
                            );
                        }
                        match result {
                            Ok((row, time, diff)) => {
                                // Additional `until` filtering due to temporal filters.
                                if !until.less_equal(&time) {
                                    let mut emit_time = cap_time;
                                    emit_time.0 = time;
                                    give(Ok(Cow::Owned(row)), emit_time, diff);
                                    *work += 1;
                                }
                            }
                            Err((err, time, diff)) => {
                                // Additional `until` filtering due to temporal filters.
                                if !until.less_equal(&time) {
                                    let mut emit_time = cap_time;
                                    emit_time.0 = time;
                                    give(Err(err), emit_time, diff);
                                    *work += 1;
                                }
                            }
                        }
                    }
                    // The MFP built its output into `row_builder`, so the decoded row's
                    // allocation is free to go back to `row_buf`.
                    drop(datums_local);
                    row_buf.replace(SourceData(Ok(row)));
                } else {
                    let mut emit_time = cap_time;
                    emit_time.0 = time;
                    // The output copies the row out, so the allocation stays with `row_buf`.
                    give(Ok(Cow::Borrowed(&row)), emit_time, diff.into());
                    row_buf.replace(SourceData(Ok(row)));
                    *work += 1;
                }
            }
            (SourceData(Err(err)), ()) => {
                // A discarded part that turns out to hold an error row is
                // as much a pushdown violation as one whose MFP yields
                // output: errors must surface regardless of any filter.
                // Without this arm the audit was blind to exactly the
                // undercounted-err-stats violation class.
                if let Some(stats) = &is_filter_pushdown_audit {
                    sentry::with_scope(
                        |scope| scope.set_tag("alert_id", "persist_pushdown_audit_violation"),
                        || {
                            // `err` is redacted for the same reason the
                            // `Ok`-row arm redacts its MFP output: these
                            // events go to Sentry, and a `DecodeError`
                            // carries the raw source record bytes while
                            // several `EvalError`s embed user input.
                            error!(
                                ?stats,
                                name,
                                err = ?redact(&err),
                                "persist filter pushdown correctness violation!"
                            );
                            if panic_on_audit_failure {
                                panic!("persist filter pushdown correctness violation! {}", name);
                            }
                        },
                    );
                }
                let mut emit_time = cap_time;
                emit_time.0 = time;
                give(Err(E::from(err)), emit_time, diff.into());
                *work += 1;
            }
        }
        if *work >= yield_fuel {
            return false;
        }
    }
    true
}

/// A trait representing a type that can be used in `backpressure`.
pub trait Backpressureable: Clone + 'static {
    /// Return the weight of the object, in bytes.
    fn byte_size(&self) -> usize;
}

impl<T: Clone + 'static> Backpressureable for (usize, ExchangeableBatchPart<T>) {
    fn byte_size(&self) -> usize {
        self.1.encoded_size_bytes()
    }
}

/// Flow control configuration.
#[derive(Debug)]
pub struct FlowControl<'scope, T: timely::progress::Timestamp> {
    /// Stream providing in-flight frontier updates.
    ///
    /// As implied by its type, this stream never emits data, only progress updates.
    ///
    /// TODO: Replace `Infallible` with `!` once the latter is stabilized.
    pub progress_stream: StreamVec<'scope, T, Infallible>,
    /// Maximum number of in-flight bytes.
    pub max_inflight_bytes: usize,
    /// The minimum range of timestamps (be they granular or not) that must be emitted,
    /// ignoring `max_inflight_bytes` to ensure forward progress is made.
    pub summary: T::Summary,

    /// Optional metrics for the `backpressure` operator to keep up-to-date.
    pub metrics: Option<BackpressureOperatorMetrics>,
}

/// Apply flow control to the `data` input, based on the given `FlowControl`.
///
/// The `FlowControl` should have a `progress_stream` that is the pristine, unaltered
/// frontier of the downstream operator we want to backpressure from, a `max_inflight_bytes`,
/// and a `summary`. Note that the `data` input expects all the second part of the tuple
/// timestamp to be 0, and all data to be on the `chosen_worker` worker.
///
/// The `summary` represents the _minimum_ range of timestamps that needs to be emitted before
/// reasoning about `max_inflight_bytes`. In practice this means that we may overshoot
/// `max_inflight_bytes`.
///
/// The implementation of this operator is very subtle. Many inline comments have been added.
pub fn backpressure<'scope, T, O>(
    scope: Scope<'scope, (T, Subtime)>,
    name: &str,
    data: StreamVec<'scope, (T, Subtime), O>,
    flow_control: FlowControl<'scope, (T, Subtime)>,
    chosen_worker: usize,
    // A probe used to inspect this operator during unit-testing
    probe: Option<UnboundedSender<(Antichain<(T, Subtime)>, usize, usize)>>,
) -> (StreamVec<'scope, (T, Subtime), O>, PressOnDropButton)
where
    T: TimelyTimestamp + Lattice + Codec64 + TotalOrder,
    O: Backpressureable + std::fmt::Debug,
{
    let worker_index = scope.index();

    let (flow_control_stream, flow_control_max_bytes, metrics) = (
        flow_control.progress_stream,
        flow_control.max_inflight_bytes,
        flow_control.metrics,
    );

    // Both the `flow_control` input and the data input are disconnected from the output. We manually
    // manage the output's frontier using a `CapabilitySet`. Note that we also adjust the
    // `flow_control` progress stream using the `summary` here, using a `feedback` operator in a
    // non-circular fashion.
    let (handle, summaried_flow) = scope.feedback(flow_control.summary.clone());
    flow_control_stream.connect_loop(handle);

    let mut builder = AsyncOperatorBuilder::new(
        format!("persist_source_backpressure({})", name),
        scope.clone(),
    );
    let (data_output, data_stream) = builder.new_output::<CapacityContainerBuilder<Vec<_>>>();

    let mut data_input = builder.new_disconnected_input(data, Pipeline);
    let mut flow_control_input = builder.new_disconnected_input(summaried_flow, Pipeline);

    // Helper method used to synthesize current and next frontier for ordered times.
    fn synthesize_frontiers<T: PartialOrder + Clone>(
        mut frontier: Antichain<(T, Subtime)>,
        mut time: (T, Subtime),
        part_number: &mut u64,
    ) -> (
        (T, Subtime),
        Antichain<(T, Subtime)>,
        Antichain<(T, Subtime)>,
    ) {
        let mut next_frontier = frontier.clone();
        time.1 = Subtime(*part_number);
        frontier.insert(time.clone());
        *part_number += 1;
        let mut next_time = time.clone();
        next_time.1 = Subtime(*part_number);
        next_frontier.insert(next_time);
        (time, frontier, next_frontier)
    }

    // _Refine_ the data stream by amending the second input with the part number. This also
    // ensures that we order the parts by time.
    let data_input = async_stream::stream!({
        let mut part_number = 0;
        let mut parts: Vec<((T, Subtime), O)> = Vec::new();
        loop {
            match data_input.next().await {
                None => {
                    let empty = Antichain::new();
                    parts.sort_by_key(|val| val.0.clone());
                    for (part_time, d) in parts.drain(..) {
                        let (part_time, frontier, next_frontier) = synthesize_frontiers(
                            empty.clone(),
                            part_time.clone(),
                            &mut part_number,
                        );
                        yield Either::Right((part_time, d, frontier, next_frontier))
                    }
                    break;
                }
                Some(Event::Data(stamp, data)) => {
                    // Backpressure accounts a part against the time at which it can first cause
                    // downstream work, which is the least time the message is stamped with.
                    let time = stamp.least().expect("message stamped with no capabilities");
                    for d in data {
                        parts.push((time.clone(), d));
                    }
                }
                Some(Event::Progress(prog)) => {
                    parts.sort_by_key(|val| val.0.clone());
                    for (part_time, d) in parts.extract_if(.., |p| !prog.less_equal(&p.0)) {
                        let (part_time, frontier, next_frontier) =
                            synthesize_frontiers(prog.clone(), part_time.clone(), &mut part_number);
                        yield Either::Right((part_time, d, frontier, next_frontier))
                    }
                    yield Either::Left(prog)
                }
            }
        }
    });
    let shutdown_button = builder.build(move |caps| async move {
        // The output capability.
        let mut cap_set = CapabilitySet::from_elem(caps.into_element());

        // The frontier of our output. This matches the `CapabilitySet` above.
        let mut output_frontier = Antichain::from_elem(TimelyTimestamp::minimum());
        // The frontier of the `flow_control` input.
        let mut flow_control_frontier = Antichain::from_elem(TimelyTimestamp::minimum());

        // Parts we have emitted, but have not yet retired (based on the `flow_control` edge).
        let mut inflight_parts = Vec::new();
        // Parts we have not yet emitted, but do participate in the `input_frontier`.
        let mut pending_parts = std::collections::VecDeque::new();

        // Only one worker is responsible for distributing parts
        if worker_index != chosen_worker {
            trace!(
                "We are not the chosen worker ({}), exiting...",
                chosen_worker
            );
            return;
        }
        tokio::pin!(data_input);
        'emitting_parts: loop {
            // At the beginning of our main loop, we determine the total size of
            // inflight parts.
            let inflight_bytes: usize = inflight_parts.iter().map(|(_, size)| size).sum();

            // There are 2 main cases where we can continue to emit parts:
            // - The total emitted bytes is less than `flow_control_max_bytes`.
            // - The output frontier is not beyond the `flow_control_frontier`
            //
            // SUBTLE: in the latter case, we may arbitrarily go into the backpressure `else`
            // block, as we wait for progress tracking to keep the `flow_control` frontier
            // up-to-date. This is tested in unit-tests.
            if inflight_bytes < flow_control_max_bytes
                || !PartialOrder::less_equal(&flow_control_frontier, &output_frontier)
            {
                let (time, part, next_frontier) =
                    if let Some((time, part, next_frontier)) = pending_parts.pop_front() {
                        (time, part, next_frontier)
                    } else {
                        match data_input.next().await {
                            Some(Either::Right((time, part, frontier, next_frontier))) => {
                                // Downgrade the output frontier to this part's time. This is useful
                                // "close" timestamp's from previous parts, even if we don't yet
                                // emit this part. Note that this is safe because `data_input` ensures
                                // time-ordering.
                                output_frontier = frontier;
                                cap_set.downgrade(output_frontier.iter());

                                // If the most recent value's time is _beyond_ the
                                // `flow_control` frontier (which takes into account the `summary`), we
                                // have emitted an entire `summary` worth of data, and can store this
                                // value for later.
                                if inflight_bytes >= flow_control_max_bytes
                                    && !PartialOrder::less_than(
                                        &output_frontier,
                                        &flow_control_frontier,
                                    )
                                {
                                    pending_parts.push_back((time, part, next_frontier));
                                    continue 'emitting_parts;
                                }
                                (time, part, next_frontier)
                            }
                            Some(Either::Left(prog)) => {
                                output_frontier = prog;
                                cap_set.downgrade(output_frontier.iter());
                                continue 'emitting_parts;
                            }
                            None => {
                                if pending_parts.is_empty() {
                                    break 'emitting_parts;
                                } else {
                                    continue 'emitting_parts;
                                }
                            }
                        }
                    };

                let byte_size = part.byte_size();
                // Store the value with the _frontier_ the `flow_control_input` must reach
                // to retire it. Note that if this `results_in` is `None`, then we
                // are at `T::MAX`, and give up on flow_control entirely.
                //
                // SUBTLE: If we stop storing these parts, we will likely never check the
                // `flow_control_input` ever again. This won't pile up data as that input
                // only has frontier updates. There may be spurious activations from it though.
                //
                // Also note that we don't attempt to handle overflowing the `u64` part counter.
                if let Some(emission_ts) = flow_control.summary.results_in(&time) {
                    inflight_parts.push((emission_ts, byte_size));
                }

                // Emit the data at the given time, and update the frontier and capabilities
                // to just beyond the part.
                data_output.give(&cap_set.delayed(&time), part);

                if let Some(metrics) = &metrics {
                    metrics.emitted_bytes.inc_by(u64::cast_from(byte_size))
                }

                output_frontier = next_frontier;
                cap_set.downgrade(output_frontier.iter())
            } else {
                if let Some(metrics) = &metrics {
                    metrics
                        .last_backpressured_bytes
                        .set(u64::cast_from(inflight_bytes))
                }
                let parts_count = inflight_parts.len();
                // We've exhausted our budget, listen for updates to the flow_control
                // input's frontier until we free up new budget. If we don't interact with
                // with this side of the if statement, because the stream has no data, we
                // don't cause unbounded buffering in timely.
                let new_flow_control_frontier = match flow_control_input.next().await {
                    Some(Event::Progress(frontier)) => frontier,
                    Some(Event::Data(_, _)) => {
                        unreachable!("flow_control_input should not contain data")
                    }
                    None => Antichain::new(),
                };

                // Update the `flow_control_frontier` if its advanced.
                flow_control_frontier.clone_from(&new_flow_control_frontier);

                // Retire parts that are processed downstream.
                let retired_parts = inflight_parts
                    .extract_if(.., |(ts, _size)| !flow_control_frontier.less_equal(ts));
                let (retired_size, retired_count): (usize, usize) = retired_parts
                    .fold((0, 0), |(accum_size, accum_count), (_ts, size)| {
                        (accum_size + size, accum_count + 1)
                    });
                trace!(
                    "returning {} parts with {} bytes, frontier: {:?}",
                    retired_count, retired_size, flow_control_frontier,
                );

                if let Some(metrics) = &metrics {
                    metrics.retired_bytes.inc_by(u64::cast_from(retired_size))
                }

                // Optionally emit some information for tests to examine.
                if let Some(probe) = probe.as_ref() {
                    let _ = probe.send((new_flow_control_frontier, parts_count, retired_count));
                }
            }
        }
    });
    (data_stream, shutdown_button.press_on_drop())
}

#[cfg(test)]
mod tests {
    use timely::container::CapacityContainerBuilder;
    use timely::dataflow::operators::{Enter, Probe};
    use tokio::sync::mpsc::unbounded_channel;
    use tokio::sync::oneshot;

    use super::*;

    #[mz_ore::test]
    fn test_backpressure_non_granular() {
        use Step::*;
        backpressure_runner(
            vec![(50, Part(101)), (50, Part(102)), (100, Part(1))],
            100,
            (1, Subtime(0)),
            vec![
                // Assert we backpressure only after we have emitted
                // the entire timestamp.
                AssertOutputFrontier((50, Subtime(2))),
                AssertBackpressured {
                    frontier: (1, Subtime(0)),
                    inflight_parts: 1,
                    retired_parts: 0,
                },
                AssertBackpressured {
                    frontier: (51, Subtime(0)),
                    inflight_parts: 1,
                    retired_parts: 0,
                },
                ProcessXParts(2),
                AssertBackpressured {
                    frontier: (101, Subtime(0)),
                    inflight_parts: 2,
                    retired_parts: 2,
                },
                // Assert we make later progress once processing
                // the parts.
                AssertOutputFrontier((100, Subtime(3))),
            ],
            true,
        );

        backpressure_runner(
            vec![
                (50, Part(10)),
                (50, Part(10)),
                (51, Part(100)),
                (52, Part(1000)),
            ],
            50,
            (1, Subtime(0)),
            vec![
                // Assert we backpressure only after we emitted enough bytes
                AssertOutputFrontier((51, Subtime(3))),
                AssertBackpressured {
                    frontier: (1, Subtime(0)),
                    inflight_parts: 3,
                    retired_parts: 0,
                },
                ProcessXParts(3),
                AssertBackpressured {
                    frontier: (52, Subtime(0)),
                    inflight_parts: 3,
                    retired_parts: 2,
                },
                AssertBackpressured {
                    frontier: (53, Subtime(0)),
                    inflight_parts: 1,
                    retired_parts: 1,
                },
                // Assert we make later progress once processing
                // the parts.
                AssertOutputFrontier((52, Subtime(4))),
            ],
            true,
        );

        backpressure_runner(
            vec![
                (50, Part(98)),
                (50, Part(1)),
                (51, Part(10)),
                (52, Part(100)),
                // Additional parts at the same timestamp
                (52, Part(10)),
                (52, Part(10)),
                (52, Part(10)),
                (52, Part(100)),
                // A later part with a later ts.
                (100, Part(100)),
            ],
            100,
            (1, Subtime(0)),
            vec![
                AssertOutputFrontier((51, Subtime(3))),
                // Assert we backpressure after we have emitted enough bytes.
                // We assert twice here because we get updates as
                // `flow_control` progresses from `(0, 0)`->`(0, 1)`-> a real frontier.
                AssertBackpressured {
                    frontier: (1, Subtime(0)),
                    inflight_parts: 3,
                    retired_parts: 0,
                },
                AssertBackpressured {
                    frontier: (51, Subtime(0)),
                    inflight_parts: 3,
                    retired_parts: 0,
                },
                ProcessXParts(1),
                // Our output frontier doesn't move, as the downstream frontier hasn't moved past
                // 50.
                AssertOutputFrontier((51, Subtime(3))),
                // After we process all of `50`, we can start emitting data at `52`, but only until
                // we exhaust out budget. We don't need to emit all of `52` because we have emitted
                // all of `51`.
                ProcessXParts(1),
                AssertOutputFrontier((52, Subtime(4))),
                AssertBackpressured {
                    frontier: (52, Subtime(0)),
                    inflight_parts: 3,
                    retired_parts: 2,
                },
                // After processing `50` and `51`, the minimum time is `52`, so we ensure that,
                // regardless of byte count, we emit the entire time (but do NOT emit the part at
                // time `100`.
                ProcessXParts(1),
                // Clear the previous `51` part, and start filling up `inflight_parts` with other
                // parts at `52`
                // This is an intermediate state.
                AssertBackpressured {
                    frontier: (53, Subtime(0)),
                    inflight_parts: 2,
                    retired_parts: 1,
                },
                // After we process all of `52`, we can continue to the next time.
                ProcessXParts(5),
                AssertBackpressured {
                    frontier: (101, Subtime(0)),
                    inflight_parts: 5,
                    retired_parts: 5,
                },
                AssertOutputFrontier((100, Subtime(9))),
            ],
            true,
        );
    }

    #[mz_ore::test]
    fn test_backpressure_granular() {
        use Step::*;
        backpressure_runner(
            vec![(50, Part(101)), (50, Part(101))],
            100,
            (0, Subtime(1)),
            vec![
                // Advance our frontier to outputting a single part.
                AssertOutputFrontier((50, Subtime(1))),
                // Receive backpressure updates until our frontier is up-to-date but
                // not beyond the parts (while considering the summary).
                AssertBackpressured {
                    frontier: (0, Subtime(1)),
                    inflight_parts: 1,
                    retired_parts: 0,
                },
                AssertBackpressured {
                    frontier: (50, Subtime(1)),
                    inflight_parts: 1,
                    retired_parts: 0,
                },
                // Process that part.
                ProcessXParts(1),
                // Assert that we clear the backpressure status
                AssertBackpressured {
                    frontier: (50, Subtime(2)),
                    inflight_parts: 1,
                    retired_parts: 1,
                },
                // Ensure we make progress to the next part.
                AssertOutputFrontier((50, Subtime(2))),
            ],
            false,
        );

        backpressure_runner(
            vec![
                (50, Part(10)),
                (50, Part(10)),
                (51, Part(35)),
                (52, Part(100)),
            ],
            50,
            (0, Subtime(1)),
            vec![
                // we can emit 3 parts before we hit the backpressure limit
                AssertOutputFrontier((51, Subtime(3))),
                AssertBackpressured {
                    frontier: (0, Subtime(1)),
                    inflight_parts: 3,
                    retired_parts: 0,
                },
                AssertBackpressured {
                    frontier: (50, Subtime(1)),
                    inflight_parts: 3,
                    retired_parts: 0,
                },
                // Retire the single part.
                ProcessXParts(1),
                AssertBackpressured {
                    frontier: (50, Subtime(2)),
                    inflight_parts: 3,
                    retired_parts: 1,
                },
                // Ensure we make progress, and then
                // can retire the next 2 parts.
                AssertOutputFrontier((52, Subtime(4))),
                ProcessXParts(2),
                AssertBackpressured {
                    frontier: (52, Subtime(4)),
                    inflight_parts: 3,
                    retired_parts: 2,
                },
            ],
            false,
        );
    }

    type Time = (u64, Subtime);
    #[derive(Clone, Debug)]
    struct Part(usize);
    impl Backpressureable for Part {
        fn byte_size(&self) -> usize {
            self.0
        }
    }

    /// Actions taken by `backpressure_runner`.
    enum Step {
        /// Assert that the output frontier of the `backpressure` operator has AT LEAST made it
        /// this far. This is a single time because we assume
        AssertOutputFrontier(Time),
        /// Assert that we have entered the backpressure flow in the `backpressure` operator. This
        /// allows us to assert what feedback frontier we got to, and how many inflight parts we
        /// retired.
        AssertBackpressured {
            frontier: Time,
            inflight_parts: usize,
            retired_parts: usize,
        },
        /// Process X parts in the downstream operator. This affects the feedback frontier.
        ProcessXParts(usize),
    }

    /// A function that runs the `steps` to ensure that `backpressure` works as expected.
    fn backpressure_runner(
        // The input data to the `backpressure` operator
        input: Vec<(u64, Part)>,
        // The maximum inflight bytes the `backpressure` operator allows through.
        max_inflight_bytes: usize,
        // The feedback summary used by the `backpressure` operator.
        summary: Time,
        // List of steps to run through.
        steps: Vec<Step>,
        // Whether or not to consume records in the non-granular scope. This is useful when the
        // `summary` is something like `(1, 0)`.
        non_granular_consumer: bool,
    ) {
        timely::execute::execute_directly(move |worker| {
            let (
                backpressure_probe,
                consumer_tx,
                mut backpressure_status_rx,
                finalizer_tx,
                _token,
            ) =
                // Set up the top-level non-granular scope.
                worker.dataflow::<u64, _, _>(|outer_scope| {
                    let (non_granular_feedback_handle, non_granular_feedback) =
                        if non_granular_consumer {
                            let (h, f) = outer_scope.feedback(Default::default());
                            (Some(h), Some(f))
                        } else {
                            (None, None)
                        };
                    let (
                        backpressure_probe,
                        consumer_tx,
                        backpressure_status_rx,
                        token,
                        backpressured,
                        finalizer_tx,
                    ) = outer_scope.scoped::<(u64, Subtime), _, _>("hybrid", |scope| {
                        let (input, finalizer_tx) =
                            iterator_operator(scope.clone(), input.into_iter());

                        let (flow_control, granular_feedback_handle) = if non_granular_consumer {
                            (
                                FlowControl {
                                    progress_stream: non_granular_feedback.unwrap().enter(scope),
                                    max_inflight_bytes,
                                    summary,
                                    metrics: None
                                },
                                None,
                            )
                        } else {
                            let (granular_feedback_handle, granular_feedback) =
                                scope.feedback(Default::default());
                            (
                                FlowControl {
                                    progress_stream: granular_feedback,
                                    max_inflight_bytes,
                                    summary,
                                    metrics: None,
                                },
                                Some(granular_feedback_handle),
                            )
                        };

                        let (backpressure_status_tx, backpressure_status_rx) = unbounded_channel();

                        let (backpressured, token) = backpressure(
                            scope,
                            "test",
                            input,
                            flow_control,
                            0,
                            Some(backpressure_status_tx),
                        );

                        // If we want to granularly consume the output, we setup the consumer here.
                        let tx = if !non_granular_consumer {
                            Some(consumer_operator(
                                scope.clone(),
                                backpressured.clone(),
                                granular_feedback_handle.unwrap(),
                            ))
                        } else {
                            None
                        };

                        let (probe_handle, backpressured) = backpressured.probe();
                        (
                            probe_handle,
                            tx,
                            backpressure_status_rx,
                            token,
                            backpressured.leave(outer_scope),
                            finalizer_tx,
                        )
                    });

                    // If we want to non-granularly consume the output, we setup the consumer here.
                    let consumer_tx = if non_granular_consumer {
                        consumer_operator(
                            outer_scope.clone(),
                            backpressured,
                            non_granular_feedback_handle.unwrap(),
                        )
                    } else {
                        consumer_tx.unwrap()
                    };

                    (
                        backpressure_probe,
                        consumer_tx,
                        backpressure_status_rx,
                        finalizer_tx,
                        token,
                    )
                });

            use Step::*;
            for step in steps {
                match step {
                    AssertOutputFrontier(time) => {
                        eprintln!("checking advance to {time:?}");
                        backpressure_probe.with_frontier(|front| {
                            eprintln!("current backpressure output frontier: {front:?}");
                        });
                        while backpressure_probe.less_than(&time) {
                            worker.step();
                            backpressure_probe.with_frontier(|front| {
                                eprintln!("current backpressure output frontier: {front:?}");
                            });
                            std::thread::sleep(std::time::Duration::from_millis(25));
                        }
                    }
                    ProcessXParts(parts) => {
                        eprintln!("processing {parts:?} parts");
                        for _ in 0..parts {
                            consumer_tx.send(()).unwrap();
                        }
                    }
                    AssertBackpressured {
                        frontier,
                        inflight_parts,
                        retired_parts,
                    } => {
                        let frontier = Antichain::from_elem(frontier);
                        eprintln!(
                            "asserting backpressured at {frontier:?}, with {inflight_parts:?} inflight parts \
                            and {retired_parts:?} retired"
                        );
                        let (new_frontier, new_count, new_retired_count) = loop {
                            if let Ok(val) = backpressure_status_rx.try_recv() {
                                break val;
                            }
                            worker.step();
                            std::thread::sleep(std::time::Duration::from_millis(25));
                        };
                        assert_eq!(
                            (frontier, inflight_parts, retired_parts),
                            (new_frontier, new_count, new_retired_count)
                        );
                    }
                }
            }
            // Send the input to the empty frontier.
            let _ = finalizer_tx.send(());
        });
    }

    /// An operator that emits `Part`'s at the specified timestamps. Does not
    /// drop its capability until it gets a signal from the `Sender` it returns.
    fn iterator_operator<'scope, I: Iterator<Item = (u64, Part)> + 'static>(
        scope: Scope<'scope, (u64, Subtime)>,
        mut input: I,
    ) -> (StreamVec<'scope, (u64, Subtime), Part>, oneshot::Sender<()>) {
        let (finalizer_tx, finalizer_rx) = oneshot::channel();
        let mut iterator = AsyncOperatorBuilder::new("iterator".to_string(), scope);
        let (output_handle, output) = iterator.new_output::<CapacityContainerBuilder<Vec<Part>>>();

        iterator.build(|mut caps| async move {
            let mut capability = Some(caps.pop().unwrap());
            let mut last = None;
            while let Some(element) = input.next() {
                let time = element.0.clone();
                let part = element.1;
                last = Some((time, Subtime(0)));
                output_handle.give(&capability.as_ref().unwrap().delayed(&last.unwrap()), part);
            }
            if let Some(last) = last {
                capability
                    .as_mut()
                    .unwrap()
                    .downgrade(&(last.0 + 1, last.1));
            }

            let _ = finalizer_rx.await;
            capability.take();
        });

        (output, finalizer_tx)
    }

    /// An operator that consumes its input ONLY when given a signal to do from
    /// the `UnboundedSender` it returns. Each `send` corresponds with 1 `Data` event
    /// being processed. Also connects the `feedback` handle to its output.
    fn consumer_operator<
        'scope,
        T: timely::progress::Timestamp,
        O: Backpressureable + std::fmt::Debug,
    >(
        scope: Scope<'scope, T>,
        input: StreamVec<'scope, T, O>,
        feedback: timely::dataflow::operators::feedback::Handle<
            'scope,
            T,
            Vec<std::convert::Infallible>,
        >,
    ) -> UnboundedSender<()> {
        let (tx, mut rx) = unbounded_channel::<()>();
        let mut consumer = AsyncOperatorBuilder::new("consumer".to_string(), scope);
        let (output_handle, output) =
            consumer.new_output::<CapacityContainerBuilder<Vec<std::convert::Infallible>>>();
        let mut input = consumer.new_input_for(input, Pipeline, &output_handle);

        consumer.build(|_caps| async move {
            while let Some(()) = rx.recv().await {
                // Consume exactly one messages (unless the input is exhausted).
                while let Some(Event::Progress(_)) = input.next().await {}
            }
        });
        output.connect_loop(feedback);

        tx
    }

    /// End-to-end persist filter-pushdown soundness checks.
    ///
    /// These mirror the real audit contract in [`PendingWork::do_work`]: build
    /// a part from actual rows, compute the *real* production column statistics
    /// from it, then run [`filter_result`] and assert it never returns
    /// [`FilterResult::Discard`] for a part whose MFP would produce output (an
    /// `Ok` row or an error row) on some actual row. A `Discard` in that case is
    /// exactly the wrongly-skipped part the runtime audit panics on.
    ///
    /// Unlike the interpreter-level proptests in `mz_expr::interpret`, this
    /// exercises the full path stats derivation -> `col_stats` -> interpreter,
    /// so it catches both interpreter bugs and stats-derivation bugs (e.g. a
    /// column stat range that fails to contain a real value). See
    /// database-issues#9656 / PER-50.
    mod filter_pushdown_audit {
        use itertools::Itertools;
        use mz_expr::func::variadic::{And, Or};
        use mz_expr::func::{
            AddFloat32, AddTimestampInterval, CastNumericToFloat32, CastNumericToMzTimestamp, Eq,
            Gt, Gte, IsNull, JsonbGetString, JsonbGetStringStringify, Lt, Lte, MulFloat32,
            MulFloat64, Not, RoundNumericBinary, TryParseMonotonicIso8601Timestamp,
        };
        use mz_expr::{BinaryFunc, MapFilterProject, MirScalarExpr, UnaryFunc};
        use mz_ore::metrics::MetricsRegistry;
        use mz_persist_types::part::PartBuilder;
        use mz_persist_types::stats::{PartStats, PartStatsMetrics};
        use mz_repr::adt::interval::Interval;
        use mz_repr::adt::numeric::Numeric;
        use mz_repr::{Diff, ReprScalarType, SqlScalarType};
        use proptest::prelude::*;
        use proptest::sample::{Index, select};
        use proptest::strategy::Union;

        use super::*;

        fn f32_lit(x: f32) -> MirScalarExpr {
            MirScalarExpr::literal_ok(Datum::from(x), ReprScalarType::Float32)
        }

        fn f64_lit(x: f64) -> MirScalarExpr {
            MirScalarExpr::literal_ok(Datum::from(x), ReprScalarType::Float64)
        }

        fn numeric_datum(x: f64) -> Datum<'static> {
            Datum::from(Numeric::from(x))
        }

        fn numeric_desc() -> RelationDesc {
            RelationDesc::builder()
                .with_column(
                    "c0",
                    SqlScalarType::Numeric { max_scale: None }.nullable(false),
                )
                .finish()
        }

        /// Compute the real production `PartStats` from a set of rows, the same
        /// way the storage read path does.
        fn build_part_stats(desc: &RelationDesc, rows: &[SourceData]) -> PartStats {
            let mut builder = PartBuilder::new(desc, &UnitSchema);
            for row in rows {
                builder.push(row, &(), 1u64, 1i64);
            }
            let part = builder.finish();
            PartStats::new::<SourceData, RelationDesc>(&part, desc).expect("stats")
        }

        /// Ground truth: does the MFP produce any output (an `Ok` row that
        /// passes the filter, or an error row) on at least one actual row? If
        /// so, the part must not be discarded.
        fn mfp_yields_output(plan: &MfpPlan, rows: &[Row]) -> bool {
            let arena = RowArena::new();
            let mut row_builder = Row::default();
            for row in rows {
                let mut datums: Vec<Datum> = row.iter().collect();
                let mut results = plan.evaluate::<DataflowError, _>(
                    &mut datums,
                    &arena,
                    Timestamp::MIN,
                    Diff::from(1),
                    |_| true,
                    &mut row_builder,
                );
                if results.next().is_some() {
                    return true;
                }
            }
            false
        }

        fn comparison_funcs() -> impl Strategy<Value = BinaryFunc> {
            select(vec![
                BinaryFunc::Lte(Lte),
                BinaryFunc::Lt(Lt),
                BinaryFunc::Gte(Gte),
                BinaryFunc::Gt(Gt),
                BinaryFunc::Eq(Eq),
            ])
        }

        fn f32_consts() -> impl Strategy<Value = f32> {
            select(vec![
                0.0f32,
                1.0,
                -1.0,
                0.0087531805,
                745213.56,
                76700000000.0,
                f32::MAX,
                1e30,
                -1e30,
            ])
        }

        /// `(a::float4 + round(c0, scale)::float4) * b::float4 <cmp> c::float4`.
        /// `round` overflows and the float arithmetic can produce an error or a
        /// NaN on interior values of `c0` that the endpoints don't reveal.
        fn float_arith_predicate(
            scale: i32,
            a: f32,
            b: f32,
            c: f32,
            cmp: BinaryFunc,
        ) -> MirScalarExpr {
            let round = MirScalarExpr::CallBinary {
                func: BinaryFunc::RoundNumeric(RoundNumericBinary),
                expr1: Box::new(MirScalarExpr::column(0)),
                expr2: Box::new(MirScalarExpr::literal_ok(
                    Datum::from(scale),
                    ReprScalarType::Int32,
                )),
            };
            let cast = MirScalarExpr::CallUnary {
                func: UnaryFunc::CastNumericToFloat32(CastNumericToFloat32),
                expr: Box::new(round),
            };
            let add = MirScalarExpr::CallBinary {
                func: BinaryFunc::AddFloat32(AddFloat32),
                expr1: Box::new(f32_lit(a)),
                expr2: Box::new(cast),
            };
            let mul = MirScalarExpr::CallBinary {
                func: BinaryFunc::MulFloat32(MulFloat32),
                expr1: Box::new(add),
                expr2: Box::new(f32_lit(b)),
            };
            MirScalarExpr::CallBinary {
                func: cmp,
                expr1: Box::new(mul),
                expr2: Box::new(f32_lit(c)),
            }
        }

        /// `c0::mz_timestamp <cmp> <ts>`. The cast errors on fractional or
        /// out-of-range `c0`, an interior-error condition the interpreter's
        /// endpoint sampling can miss.
        fn cast_mz_timestamp_predicate(ts: u64, cmp: BinaryFunc) -> MirScalarExpr {
            let cast = MirScalarExpr::CallUnary {
                func: UnaryFunc::CastNumericToMzTimestamp(CastNumericToMzTimestamp),
                expr: Box::new(MirScalarExpr::column(0)),
            };
            MirScalarExpr::CallBinary {
                func: cmp,
                expr1: Box::new(cast),
                expr2: Box::new(MirScalarExpr::literal_ok(
                    Datum::MzTimestamp(Timestamp::from(ts)),
                    ReprScalarType::MzTimestamp,
                )),
            }
        }

        fn arb_numeric_rows() -> impl Strategy<Value = Vec<Row>> {
            let magnitudes = vec![
                0.0f64, 1.0, 2.0, 1.5, 2.5, 0.25, -1.0, 10.0, 100.0, 1e10, -1e10, 3.0e38, 3.4e38,
                3.5e38, 1e40, -1e40, 1e300,
            ];
            prop::collection::vec(
                select(magnitudes).prop_map(|x| Row::pack_slice(&[numeric_datum(x)])),
                1..8,
            )
        }

        fn arb_predicate() -> impl Strategy<Value = MirScalarExpr> {
            let float_arith = (
                select(vec![0i32, 2, -5, 24699]),
                f32_consts(),
                f32_consts(),
                f32_consts(),
                comparison_funcs(),
            )
                .prop_map(|(scale, a, b, c, cmp)| float_arith_predicate(scale, a, b, c, cmp));
            let cast_ts = (select(vec![0u64, 1, 2, 100, u64::MAX]), comparison_funcs())
                .prop_map(|(ts, cmp)| cast_mz_timestamp_predicate(ts, cmp));
            proptest::strategy::Union::new(vec![float_arith.boxed(), cast_ts.boxed()])
        }

        #[mz_ore::test]
        #[cfg_attr(miri, ignore)] // error: unsupported operation: can't call foreign function `decContextDefault`
        fn filter_result_never_discards_matching_part() {
            fn check(rows: Vec<Row>, predicate: MirScalarExpr) -> Result<(), TestCaseError> {
                let desc = numeric_desc();
                let plan = MapFilterProject::new(1)
                    .filter(std::iter::once(predicate))
                    .into_plan()
                    .expect("into_plan");

                let source_rows: Vec<_> = rows.iter().map(|r| SourceData(Ok(r.clone()))).collect();
                let part_stats = build_part_stats(&desc, &source_rows);
                let metrics = PartStatsMetrics::new(&MetricsRegistry::new());
                let stats = RelationPartStats::new("test", &metrics, &desc, &part_stats);

                let decision = filter_result(&desc, ResultSpec::anything(), stats, &plan);

                if mfp_yields_output(&plan, &rows) {
                    prop_assert!(
                        !matches!(decision, FilterResult::Discard),
                        "filter pushdown discarded a part whose MFP yields output on a real \
                         row (wrongly-skipped part; the runtime audit would panic).\n\
                         rows={rows:?}\nplan={plan:?}",
                    );
                }
                Ok(())
            }

            proptest!(|(rows in arb_numeric_rows(), predicate in arb_predicate())| {
                check(rows, predicate)?;
            });
        }

        /// Assert that `filter_result` keeps a part it must keep, and that the
        /// case is not vacuous: the MFP has to yield output on a real row for
        /// "must keep" to mean anything.
        fn assert_part_kept(desc: &RelationDesc, rows: &[Row], predicate: MirScalarExpr) {
            let plan = MapFilterProject::new(1)
                .filter(std::iter::once(predicate))
                .into_plan()
                .expect("into_plan");
            assert!(
                mfp_yields_output(&plan, rows),
                "nothing to keep: the MFP yields no output on any of these rows.\n\
                 rows={rows:?}\nplan={plan:?}",
            );

            let source_rows: Vec<_> = rows.iter().map(|r| SourceData(Ok(r.clone()))).collect();
            let part_stats = build_part_stats(desc, &source_rows);
            let metrics = PartStatsMetrics::new(&MetricsRegistry::new());
            let stats = RelationPartStats::new("test", &metrics, desc, &part_stats);
            let decision = filter_result(desc, ResultSpec::anything(), stats, &plan);
            assert!(
                !matches!(decision, FilterResult::Discard),
                "filter pushdown discarded a part whose MFP yields output on a real row.\n\
                 rows={rows:?}\nplan={plan:?}",
            );
        }

        /// A part holding `-NaN` must not hide the rest of its rows from a
        /// filter on that column.
        ///
        /// `PrimitiveStats` takes a float column's bounds in arrow's *total*
        /// order, where `-NaN` sorts below `-Infinity`, so such a part records
        /// `lower = -NaN` against a finite `upper`. `OrderedFloat`, the `Datum`
        /// order the interpreter compares in, ranks every NaN *above* every
        /// finite value, so those bounds arrive unordered. Reading them as an
        /// empty range discarded the part, which lost every other row in it
        /// (PER-53). Both float widths take the same path.
        #[mz_ore::test]
        #[cfg_attr(miri, ignore)] // unsupported operation: can't call foreign function
        fn negative_nan_does_not_discard_matching_part() {
            // Both rows have to land in the same part. Split across parts each
            // one gets ordered bounds of its own and nothing is discarded.
            let desc = RelationDesc::builder()
                .with_column("c0", SqlScalarType::Float32.nullable(false))
                .finish();
            let rows = [
                Row::pack_slice(&[Datum::from(-f32::NAN)]),
                Row::pack_slice(&[Datum::from(0.0f32)]),
            ];
            assert_part_kept(
                &desc,
                &rows,
                MirScalarExpr::CallBinary {
                    func: BinaryFunc::Lt(Lt),
                    expr1: Box::new(MirScalarExpr::column(0)),
                    expr2: Box::new(f32_lit(1.0)),
                },
            );

            let desc = RelationDesc::builder()
                .with_column("c0", SqlScalarType::Float64.nullable(false))
                .finish();
            let rows = [
                Row::pack_slice(&[Datum::from(-f64::NAN)]),
                Row::pack_slice(&[Datum::from(0.0f64)]),
            ];
            assert_part_kept(
                &desc,
                &rows,
                MirScalarExpr::CallBinary {
                    func: BinaryFunc::Lt(Lt),
                    expr1: Box::new(MirScalarExpr::column(0)),
                    expr2: Box::new(f64_lit(1.0)),
                },
            );
        }

        /// A part holding NaNs of both signs must not hide its other rows.
        ///
        /// Arrow's total order puts `-NaN` below and `+NaN` above everything,
        /// so such a part records the bounds `(-NaN, +NaN)`. Under
        /// `OrderedFloat` those decode to `NaN == NaN`: not an inverted range
        /// but a seemingly valid one claiming the part holds nothing but NaN,
        /// so widening unordered bounds does not catch it. A filter that a
        /// finite row matches but NaN does not then discarded the part. Only
        /// the stats decode still sees the NaN signs, so the guard lives in
        /// `mz_repr::stats::col_values`.
        #[mz_ore::test]
        #[cfg_attr(miri, ignore)] // unsupported operation: can't call foreign function
        fn mixed_sign_nans_do_not_discard_matching_part() {
            let desc = RelationDesc::builder()
                .with_column("c0", SqlScalarType::Float32.nullable(false))
                .finish();
            let rows = [
                Row::pack_slice(&[Datum::from(-f32::NAN)]),
                Row::pack_slice(&[Datum::from(f32::NAN)]),
                Row::pack_slice(&[Datum::from(0.0f32)]),
            ];
            assert_part_kept(
                &desc,
                &rows,
                MirScalarExpr::CallBinary {
                    func: BinaryFunc::Eq(Eq),
                    expr1: Box::new(MirScalarExpr::column(0)),
                    expr2: Box::new(f32_lit(0.0)),
                },
            );

            let desc = RelationDesc::builder()
                .with_column("c0", SqlScalarType::Float64.nullable(false))
                .finish();
            let rows = [
                Row::pack_slice(&[Datum::from(-f64::NAN)]),
                Row::pack_slice(&[Datum::from(f64::NAN)]),
                Row::pack_slice(&[Datum::from(0.0f64)]),
            ];
            assert_part_kept(
                &desc,
                &rows,
                MirScalarExpr::CallBinary {
                    func: BinaryFunc::Eq(Eq),
                    expr1: Box::new(MirScalarExpr::column(0)),
                    expr2: Box::new(f64_lit(0.0)),
                },
            );
        }

        // Wide-schema variant: multiple column types populated from
        // `interesting_datums`, a predicate vocabulary that reaches the
        // interpreter's special cases (jsonb map specs and their unions,
        // `TryParseMonotonicIso8601Timestamp`, dynamically-monotone
        // timestamp+interval, the infinity guard on float multiplication),
        // Err rows, and real mz_now bounds instead of an unconstrained time
        // range.

        const NUM: usize = 0;
        const F32: usize = 1;
        const F64: usize = 2;
        const STR: usize = 3;
        const J1: usize = 4;
        const J2: usize = 5;
        const BOOL: usize = 6;
        const TS: usize = 7;
        const MZTS: usize = 8;
        const WIDE_ARITY: usize = 9;

        fn wide_scalar_type(col: usize) -> SqlScalarType {
            match col {
                NUM => SqlScalarType::Numeric { max_scale: None },
                F32 => SqlScalarType::Float32,
                F64 => SqlScalarType::Float64,
                STR => SqlScalarType::String,
                J1 | J2 => SqlScalarType::Jsonb,
                BOOL => SqlScalarType::Bool,
                TS => SqlScalarType::Timestamp { precision: None },
                MZTS => SqlScalarType::MzTimestamp,
                _ => unreachable!("no such column"),
            }
        }

        fn wide_repr_type(col: usize) -> ReprScalarType {
            match col {
                NUM => ReprScalarType::Numeric,
                F32 => ReprScalarType::Float32,
                F64 => ReprScalarType::Float64,
                STR => ReprScalarType::String,
                J1 | J2 => ReprScalarType::Jsonb,
                BOOL => ReprScalarType::Bool,
                TS => ReprScalarType::Timestamp,
                MZTS => ReprScalarType::MzTimestamp,
                _ => unreachable!("no such column"),
            }
        }

        fn wide_desc() -> RelationDesc {
            let mut builder = RelationDesc::builder();
            for col in 0..WIDE_ARITY {
                // The bool column stays non-nullable so an all-Err part
                // exercises the fabricated default bounds a non-nullable
                // column gets when no Ok row provides a value.
                let nullable = col != BOOL;
                builder = builder
                    .with_column(format!("c{col}"), wide_scalar_type(col).nullable(nullable));
            }
            builder.finish()
        }

        fn wide_pool(col: usize) -> Vec<Datum<'static>> {
            let mut pool: Vec<_> = wide_scalar_type(col).interesting_datums().collect();
            if col != BOOL {
                pool.push(Datum::Null);
            }
            pool
        }

        fn arb_wide_rows() -> impl Strategy<Value = Vec<SourceData>> {
            let pools: Vec<Vec<Datum<'static>>> = (0..WIDE_ARITY).map(wide_pool).collect();
            let ok_row = prop::collection::vec(any::<Index>(), WIDE_ARITY).prop_map(move |picks| {
                let datums = picks
                    .iter()
                    .zip_eq(&pools)
                    .map(|(pick, pool)| pool[pick.index(pool.len())]);
                SourceData(Ok(Row::pack(datums)))
            });
            let err_row = Just(SourceData(Err(DataflowError::from(
                EvalError::DivisionByZero,
            ))));
            let row = Union::new_weighted(vec![(9, ok_row.boxed()), (1, err_row.boxed())]);
            prop::collection::vec(row, 2..8)
        }

        fn lit(datum: Datum<'static>, typ: ReprScalarType) -> MirScalarExpr {
            if datum.is_null() {
                MirScalarExpr::literal_null(typ)
            } else {
                MirScalarExpr::literal_ok(datum, typ)
            }
        }

        fn is_null(expr: MirScalarExpr) -> MirScalarExpr {
            MirScalarExpr::CallUnary {
                func: UnaryFunc::IsNull(IsNull),
                expr: Box::new(expr),
            }
        }

        fn not(expr: MirScalarExpr) -> MirScalarExpr {
            MirScalarExpr::CallUnary {
                func: UnaryFunc::Not(Not),
                expr: Box::new(expr),
            }
        }

        fn binary(func: BinaryFunc, a: MirScalarExpr, b: MirScalarExpr) -> MirScalarExpr {
            MirScalarExpr::CallBinary {
                func,
                expr1: Box::new(a),
                expr2: Box::new(b),
            }
        }

        /// `col <cmp> lit`, with the literal drawn from the same interesting
        /// pool as the row values, so poison values show up on both sides.
        fn arb_cmp_col_lit() -> impl Strategy<Value = MirScalarExpr> {
            (0..WIDE_ARITY, any::<Index>(), comparison_funcs()).prop_map(|(col, pick, cmp)| {
                let pool = wide_pool(col);
                let datum = pool[pick.index(pool.len())];
                binary(
                    cmp,
                    MirScalarExpr::column(col),
                    lit(datum, wide_repr_type(col)),
                )
            })
        }

        fn arb_is_null_pred() -> impl Strategy<Value = MirScalarExpr> {
            (0..WIDE_ARITY, any::<bool>()).prop_map(|(col, negate)| {
                let expr = is_null(MirScalarExpr::column(col));
                if negate { not(expr) } else { expr }
            })
        }

        fn jsonb_keys() -> impl Strategy<Value = &'static str> {
            select(vec!["x", "y", "nested", "absent"])
        }

        fn jsonb_get(expr: MirScalarExpr, key: &'static str, stringify: bool) -> MirScalarExpr {
            let func = if stringify {
                BinaryFunc::JsonbGetStringStringify(JsonbGetStringStringify)
            } else {
                BinaryFunc::JsonbGetString(JsonbGetString)
            };
            binary(
                func,
                expr,
                MirScalarExpr::literal_ok(Datum::String(key), ReprScalarType::String),
            )
        }

        /// `(jN -> 'key') IS NULL` or `(jN ->> 'key') = 'a'`, the shapes that
        /// consume the Nested specs built from real jsonb map stats.
        fn arb_jsonb_pred() -> impl Strategy<Value = MirScalarExpr> {
            (
                select(vec![J1, J2]),
                jsonb_keys(),
                any::<bool>(),
                any::<bool>(),
            )
                .prop_map(|(col, key, stringify, wrap_eq)| {
                    let get = jsonb_get(MirScalarExpr::column(col), key, stringify);
                    if wrap_eq {
                        let typ = if stringify {
                            ReprScalarType::String
                        } else {
                            ReprScalarType::Jsonb
                        };
                        binary(BinaryFunc::Eq(Eq), get, lit(Datum::String("a"), typ))
                    } else {
                        is_null(get)
                    }
                })
        }

        /// `((CASE WHEN <cond> THEN j1 ELSE j2 END) ->> 'key') IS NULL`, the
        /// PER-6 shape: unioning the two columns' Nested specs.
        fn arb_case_jsonb_pred() -> impl Strategy<Value = MirScalarExpr> {
            (any::<bool>(), jsonb_keys(), any::<bool>()).prop_map(
                |(cond_is_col, key, stringify)| {
                    let cond = if cond_is_col {
                        MirScalarExpr::column(BOOL)
                    } else {
                        is_null(MirScalarExpr::column(STR))
                    };
                    let case = MirScalarExpr::If {
                        cond: Box::new(cond),
                        then: Box::new(MirScalarExpr::column(J1)),
                        els: Box::new(MirScalarExpr::column(J2)),
                    };
                    is_null(jsonb_get(case, key, stringify))
                },
            )
        }

        /// `try_parse_monotonic_iso8601_timestamp(c_str) <cmp> <ts>`, the one
        /// SpecialUnary implementation in the interpreter.
        fn arb_iso_parse_pred() -> impl Strategy<Value = MirScalarExpr> {
            (comparison_funcs(), any::<Index>(), any::<bool>()).prop_map(
                |(cmp, pick, wrap_null)| {
                    let parse = MirScalarExpr::CallUnary {
                        func: UnaryFunc::TryParseMonotonicIso8601Timestamp(
                            TryParseMonotonicIso8601Timestamp,
                        ),
                        expr: Box::new(MirScalarExpr::column(STR)),
                    };
                    if wrap_null {
                        is_null(parse)
                    } else {
                        let pool: Vec<_> = SqlScalarType::Timestamp { precision: None }
                            .interesting_datums()
                            .collect();
                        let datum = pool[pick.index(pool.len())];
                        binary(cmp, parse, lit(datum, ReprScalarType::Timestamp))
                    }
                },
            )
        }

        /// `(c_ts + <interval>) <cmp> <ts>`, the DynamicMonotone handler:
        /// day-only intervals are treated as monotone, month-bearing ones must
        /// stay conservative.
        fn arb_ts_interval_pred() -> impl Strategy<Value = MirScalarExpr> {
            let intervals = select(vec![
                Interval::new(0, 2, 0),
                Interval::new(0, 0, 3_600_000_000),
                Interval::new(1, 0, 0),
                Interval::new(-1, 0, 0),
            ]);
            (comparison_funcs(), intervals, any::<Index>()).prop_map(|(cmp, iv, pick)| {
                let add = binary(
                    BinaryFunc::AddTimestampInterval(AddTimestampInterval),
                    MirScalarExpr::column(TS),
                    lit(Datum::Interval(iv), ReprScalarType::Interval),
                );
                let pool: Vec<_> = SqlScalarType::Timestamp { precision: None }
                    .interesting_datums()
                    .collect();
                let datum = pool[pick.index(pool.len())];
                binary(cmp, add, lit(datum, ReprScalarType::Timestamp))
            })
        }

        /// `(c_f64 * <const>) <cmp> <const>`, aimed at the interpreter's
        /// infinity guard: multiplication is monotone but not
        /// infinity-monotone.
        fn arb_float_mul_pred() -> impl Strategy<Value = MirScalarExpr> {
            let consts = || select(vec![0.0f64, 1.0, -1.0, 1e300, -1e300, f64::INFINITY]);
            (comparison_funcs(), consts(), consts()).prop_map(|(cmp, a, c)| {
                let mul = binary(
                    BinaryFunc::MulFloat64(MulFloat64),
                    MirScalarExpr::column(F64),
                    lit(Datum::from(a), ReprScalarType::Float64),
                );
                binary(cmp, mul, lit(Datum::from(c), ReprScalarType::Float64))
            })
        }

        /// `mz_now() <cmp> <mz_timestamp expr>`, compiled by `into_plan` into
        /// the temporal lower/upper bounds that `filter_result` checks against
        /// the part's time range.
        fn arb_temporal_pred() -> impl Strategy<Value = MirScalarExpr> {
            let cmps = select(vec![
                BinaryFunc::Lte(Lte),
                BinaryFunc::Lt(Lt),
                BinaryFunc::Gte(Gte),
                BinaryFunc::Gt(Gt),
            ]);
            (cmps, any::<bool>(), any::<Index>()).prop_map(|(cmp, use_col, pick)| {
                let mz_now = MirScalarExpr::CallUnmaterializable(UnmaterializableFunc::MzNow);
                let rhs = if use_col {
                    MirScalarExpr::column(MZTS)
                } else {
                    let pool = wide_pool(MZTS);
                    lit(pool[pick.index(pool.len())], ReprScalarType::MzTimestamp)
                };
                binary(cmp, mz_now, rhs)
            })
        }

        fn arb_wide_predicate() -> impl Strategy<Value = MirScalarExpr> {
            let leaf = Union::new(vec![
                arb_cmp_col_lit().boxed(),
                arb_is_null_pred().boxed(),
                arb_jsonb_pred().boxed(),
                arb_case_jsonb_pred().boxed(),
                arb_iso_parse_pred().boxed(),
                arb_ts_interval_pred().boxed(),
                arb_float_mul_pred().boxed(),
                arb_temporal_pred().boxed(),
                // The numeric shapes from the narrow test, aimed at the
                // fallible-interior mechanisms; both reference column 0.
                (
                    select(vec![0i32, 2, -5, 24699]),
                    f32_consts(),
                    f32_consts(),
                    f32_consts(),
                    comparison_funcs(),
                )
                    .prop_map(|(s, a, b, c, cmp)| float_arith_predicate(s, a, b, c, cmp))
                    .boxed(),
                (select(vec![0u64, 1, 2, 100, u64::MAX]), comparison_funcs())
                    .prop_map(|(ts, cmp)| cast_mz_timestamp_predicate(ts, cmp))
                    .boxed(),
            ])
            .boxed();
            Union::new_weighted(vec![
                (3, leaf.clone()),
                (
                    1,
                    (leaf.clone(), leaf.clone(), any::<bool>())
                        .prop_map(|(a, b, is_and)| {
                            let func = if is_and { And.into() } else { Or.into() };
                            MirScalarExpr::CallVariadic {
                                func,
                                exprs: vec![a, b],
                            }
                        })
                        .boxed(),
                ),
                (1, leaf.prop_map(not).boxed()),
            ])
        }

        /// The zero-column count(*) path: when the read desc projects away
        /// every column and each row is known to pass, `filter_result`
        /// replaces the part with a synthesized single-row KV instead of
        /// keeping or discarding it. Errors and filters that can skip rows
        /// must suppress the substitution.
        #[mz_ore::test]
        #[cfg_attr(miri, ignore)] // too slow
        fn zero_column_relation_replace_with() {
            let desc = RelationDesc::empty();
            let metrics = PartStatsMetrics::new(&MetricsRegistry::new());
            let ok_rows = vec![
                SourceData(Ok(Row::default())),
                SourceData(Ok(Row::default())),
            ];

            // No predicates, no errors: every row passes, so the part is
            // replaced with the synthesized KV.
            let plan = MapFilterProject::<MirScalarExpr>::new(0)
                .into_plan()
                .expect("into_plan");
            let part_stats = build_part_stats(&desc, &ok_rows);
            let stats = RelationPartStats::new("test", &metrics, &desc, &part_stats);
            let decision = filter_result(&desc, ResultSpec::anything(), stats, &plan);
            assert!(
                matches!(decision, FilterResult::ReplaceWith { .. }),
                "expected ReplaceWith, got {decision:?}",
            );

            // An error row must disable the substitution: the part has to be
            // fetched so the error surfaces.
            let mixed_rows = vec![
                SourceData(Ok(Row::default())),
                SourceData(Err(DataflowError::from(EvalError::DivisionByZero))),
            ];
            let part_stats = build_part_stats(&desc, &mixed_rows);
            let stats = RelationPartStats::new("test", &metrics, &desc, &part_stats);
            let decision = filter_result(&desc, ResultSpec::anything(), stats, &plan);
            assert!(
                matches!(decision, FilterResult::Keep),
                "expected Keep, got {decision:?}",
            );

            // A constant-false filter never keeps anything: plain Discard.
            let plan = MapFilterProject::new(0)
                .filter(std::iter::once(MirScalarExpr::literal_ok(
                    Datum::False,
                    ReprScalarType::Bool,
                )))
                .into_plan()
                .expect("into_plan");
            let part_stats = build_part_stats(&desc, &ok_rows);
            let stats = RelationPartStats::new("test", &metrics, &desc, &part_stats);
            let decision = filter_result(&desc, ResultSpec::anything(), stats, &plan);
            assert!(
                matches!(decision, FilterResult::Discard),
                "expected Discard, got {decision:?}",
            );
        }

        /// Schema drift between the stats and the read desc must degrade to
        /// "no stats", never to a narrower spec.
        ///
        /// Two real shapes: a column appended by `ALTER TABLE ... ADD COLUMN`
        /// after the part was written (present in the read desc, absent from
        /// the stats), and demand pushdown projecting the read desc down to a
        /// subset of the written columns (stats carry extra columns).
        #[mz_ore::test]
        #[cfg_attr(miri, ignore)] // too slow
        fn schema_drift_degrades_to_no_stats() {
            let metrics = PartStatsMetrics::new(&MetricsRegistry::new());

            // Part written before ALTER TABLE ... ADD COLUMN b.
            let write_desc = RelationDesc::builder()
                .with_column("a", SqlScalarType::Int32.nullable(false))
                .finish();
            let rows = vec![SourceData(Ok(Row::pack_slice(&[Datum::Int32(1)])))];
            let part_stats = build_part_stats(&write_desc, &rows);

            let read_desc = RelationDesc::builder()
                .with_column("a", SqlScalarType::Int32.nullable(false))
                .with_column("b", SqlScalarType::Float64.nullable(true))
                .finish();
            let stats = RelationPartStats::new("test", &metrics, &read_desc, &part_stats);
            // Old rows read the new column as null, so `b IS NULL` matches
            // them and the part must be kept.
            let plan = MapFilterProject::new(2)
                .filter(std::iter::once(is_null(MirScalarExpr::column(1))))
                .into_plan()
                .expect("into_plan");
            let decision = filter_result(&read_desc, ResultSpec::anything(), stats, &plan);
            assert!(
                !matches!(decision, FilterResult::Discard),
                "part written before ADD COLUMN was discarded: {decision:?}",
            );

            // Demand pushdown: the read desc is a projection of the written
            // schema. The surviving column's stats must still line up with it
            // by name, so a matching filter keeps the part.
            let write_desc = RelationDesc::builder()
                .with_column("a", SqlScalarType::Int32.nullable(false))
                .with_column("b", SqlScalarType::Float64.nullable(true))
                .finish();
            let rows = vec![SourceData(Ok(Row::pack_slice(&[
                Datum::Int32(1),
                Datum::from(5.0f64),
            ])))];
            let part_stats = build_part_stats(&write_desc, &rows);

            let read_desc = RelationDesc::builder()
                .with_column("b", SqlScalarType::Float64.nullable(true))
                .finish();
            let stats = RelationPartStats::new("test", &metrics, &read_desc, &part_stats);
            let plan = MapFilterProject::new(1)
                .filter(std::iter::once(binary(
                    BinaryFunc::Eq(Eq),
                    MirScalarExpr::column(0),
                    lit(Datum::from(5.0f64), ReprScalarType::Float64),
                )))
                .into_plan()
                .expect("into_plan");
            let decision = filter_result(&read_desc, ResultSpec::anything(), stats, &plan);
            assert!(
                !matches!(decision, FilterResult::Discard),
                "projected read desc discarded a matching part: {decision:?}",
            );
        }

        /// Ground truth, mirroring [`PendingWork::do_work`]: a part yields
        /// output if any Err row survives `until`, or if the MFP applied to
        /// any Ok row at its effective time produces anything at all. The
        /// runtime audit fires on any result from `evaluate`, before the
        /// additional `until` filtering of the produced rows, so this must
        /// not post-filter either.
        fn part_yields_output(
            plan: &MfpPlan,
            rows: &[SourceData],
            eval_time: Timestamp,
            until: &Antichain<Timestamp>,
        ) -> bool {
            if until.less_equal(&eval_time) {
                return false;
            }
            let arena = RowArena::new();
            let mut row_builder = Row::default();
            for source_data in rows {
                match &source_data.0 {
                    Err(_) => return true,
                    Ok(row) => {
                        let mut datums: Vec<Datum> = row.iter().collect();
                        let mut results = plan.evaluate::<DataflowError, _>(
                            &mut datums,
                            &arena,
                            eval_time,
                            Diff::from(1),
                            |time| !until.less_equal(time),
                            &mut row_builder,
                        );
                        if results.next().is_some() {
                            return true;
                        }
                    }
                }
            }
            false
        }

        #[mz_ore::test]
        #[cfg_attr(miri, ignore)] // too slow, and decNumber FFI is unsupported
        fn wide_filter_result_never_discards_matching_part() {
            fn check(
                rows: Vec<SourceData>,
                predicate: MirScalarExpr,
                eval_time: u64,
                until: Option<u64>,
            ) -> Result<(), TestCaseError> {
                let desc = wide_desc();
                // Predicate shapes that use mz_now in a way the temporal
                // filter machinery does not support fail to plan; there is
                // nothing to check for those.
                let Ok(plan) = MapFilterProject::new(desc.arity())
                    .filter(std::iter::once(predicate))
                    .into_plan()
                else {
                    return Ok(());
                };
                let eval_time = Timestamp::from(eval_time);
                let until =
                    until.map_or_else(Antichain::new, |t| Antichain::from_elem(Timestamp::from(t)));

                let part_stats = build_part_stats(&desc, &rows);
                let metrics = PartStatsMetrics::new(&MetricsRegistry::new());
                let stats = RelationPartStats::new("test", &metrics, &desc, &part_stats);

                // Mirror the read path: mz_now is bounded by the part's
                // frontier and the dataflow's until, both inclusive, with an
                // empty until standing in for MAX. A frontier past the until
                // is discarded before stats are consulted.
                let upper = until.as_option().copied().unwrap_or(Timestamp::MAX);
                if eval_time > upper {
                    return Ok(());
                }
                let time_range = ResultSpec::value_between(
                    Datum::MzTimestamp(eval_time),
                    Datum::MzTimestamp(upper),
                );
                let decision = filter_result(&desc, time_range, stats, &plan);

                if part_yields_output(&plan, &rows, eval_time, &until) {
                    prop_assert!(
                        !matches!(decision, FilterResult::Discard),
                        "filter pushdown discarded a part whose MFP yields output on a real \
                         row (wrongly-skipped part; the runtime audit would panic).\n\
                         rows={rows:?}\nplan={plan:?}\neval_time={eval_time}\nuntil={until:?}",
                    );
                }
                Ok(())
            }

            // The vocabulary is wide (9 columns, 10 predicate shapes), so a
            // specific poison-value-plus-predicate coincidence is rare per
            // case. The default 256 cases demonstrably miss known bugs; 4096
            // still runs in a couple of seconds because each case is cheap.
            // An explicit PROPTEST_CASES (already parsed into the default
            // config) wins, for long local or nightly runs.
            let default = ProptestConfig::default();
            let cases = if std::env::var_os("PROPTEST_CASES").is_some() {
                default.cases
            } else {
                4096
            };
            let config = ProptestConfig { cases, ..default };
            proptest!(config, |(
                rows in arb_wide_rows(),
                predicate in arb_wide_predicate(),
                eval_time in select(vec![1u64, 5]),
                until in select(vec![None, Some(1u64), Some(5), Some(8), Some(100)]),
            )| {
                check(rows, predicate, eval_time, until)?;
            });
        }

        /// Filter decisions are made per part: rows split across several
        /// parts get an independent decision per part, and a part whose own
        /// rows yield output must never be discarded, regardless of what the
        /// sibling parts contain (e.g. a poison value in one part must not
        /// affect another part's decision, and vice versa).
        #[mz_ore::test]
        #[cfg_attr(miri, ignore)] // too slow, and decNumber FFI is unsupported
        fn multi_part_decisions_are_independent() {
            fn check(
                parts: Vec<Vec<SourceData>>,
                predicate: MirScalarExpr,
                eval_time: u64,
                until: Option<u64>,
            ) -> Result<(), TestCaseError> {
                let desc = wide_desc();
                let Ok(plan) = MapFilterProject::new(desc.arity())
                    .filter(std::iter::once(predicate))
                    .into_plan()
                else {
                    return Ok(());
                };
                let eval_time = Timestamp::from(eval_time);
                let until =
                    until.map_or_else(Antichain::new, |t| Antichain::from_elem(Timestamp::from(t)));
                let upper = until.as_option().copied().unwrap_or(Timestamp::MAX);
                if eval_time > upper {
                    return Ok(());
                }
                let metrics = PartStatsMetrics::new(&MetricsRegistry::new());

                for rows in &parts {
                    let part_stats = build_part_stats(&desc, rows);
                    let stats = RelationPartStats::new("test", &metrics, &desc, &part_stats);
                    let time_range = ResultSpec::value_between(
                        Datum::MzTimestamp(eval_time),
                        Datum::MzTimestamp(upper),
                    );
                    let decision = filter_result(&desc, time_range, stats, &plan);
                    if part_yields_output(&plan, rows, eval_time, &until) {
                        prop_assert!(
                            !matches!(decision, FilterResult::Discard),
                            "filter pushdown discarded a part whose MFP yields output on a \
                             real row.\nrows={rows:?}\nplan={plan:?}\neval_time={eval_time}\n\
                             until={until:?}",
                        );
                    }
                }
                Ok(())
            }

            let default = ProptestConfig::default();
            let cases = if std::env::var_os("PROPTEST_CASES").is_some() {
                default.cases
            } else {
                1024
            };
            let config = ProptestConfig { cases, ..default };
            proptest!(config, |(
                parts in prop::collection::vec(arb_wide_rows(), 2..4),
                predicate in arb_wide_predicate(),
                eval_time in select(vec![1u64, 5]),
                until in select(vec![None, Some(5u64), Some(100)]),
            )| {
                check(parts, predicate, eval_time, until)?;
            });
        }
    }
}