feat: add SliceExec (#379)

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# Please go through the following checklist
- [x] The PR title and commit messages adhere to guidelines here:
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In particular `!` is used if and only if at least one breaking change
has been introduced.
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scripts/run_ci_checks.sh`.
- The following upstream PRs have been merged:
  - [x] #381
  - [x] #401
  - [x] #404

# Rationale for this change
This PR replaces #121 and is designed to test whether our `ProofPlan`s
are truly composable now.
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your changes and offer better suggestions for fixes.

 Example:
 Add `NestedLoopJoinExec`.
 Closes #345.

Since we added `HashJoinExec` in #323 it has been possible to do
provable inner joins. However performance is not satisfactory in some
cases. Hence we need to fix the problem by implement
`NestedLoopJoinExec` and speed up the code
 for `HashJoinExec`.
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# What changes are included in this PR?
- add `SliceExec`.
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- Add `NestedLoopJoinExec`.
- Speed up `HashJoinExec`.
- Route joins to `NestedLoopJoinExec` if the outer input is sufficiently
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# Are these changes tested?
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Yes.

crates/proof-of-sql/src/base/proof/error.rs

@@ -6,4 +6,7 @@ pub enum ProofError {
     #[snafu(display("Verification error: {error}"))]
     /// This error occurs when a proof failed to verify.
     VerificationError { error: &'static str },
+    /// This error occurs when a query plan is not supported.
+    #[snafu(display("Unsupported query plan: {error}"))]
+    UnsupportedQueryPlan { error: &'static str },
 }

crates/proof-of-sql/src/sql/proof_plans/dyn_proof_plan.rs

@@ -1,4 +1,4 @@
-use super::{EmptyExec, FilterExec, GroupByExec, ProjectionExec, TableExec};
+use super::{EmptyExec, FilterExec, GroupByExec, ProjectionExec, SliceExec, TableExec};
 use crate::{
     base::{
         database::{ColumnField, ColumnRef, OwnedTable, Table, TableEvaluation, TableRef},
@@ -43,4 +43,9 @@ pub enum DynProofPlan {
     ///     SELECT <result_expr1>, ..., <result_exprN> FROM <table> WHERE <where_clause>
     /// ```
     Filter(FilterExec),
+    /// `ProofPlan` for queries of the form
+    /// ```ignore
+    ///     <ProofPlan> LIMIT <fetch> [OFFSET <skip>]
+    /// ```
+    Slice(SliceExec),
 }

crates/proof-of-sql/src/sql/proof_plans/filter_exec.rs

@@ -249,7 +249,7 @@ impl ProverEvaluate for FilterExec {
 }
 
 #[allow(clippy::unnecessary_wraps, clippy::too_many_arguments)]
-fn verify_filter<S: Scalar>(
+pub(super) fn verify_filter<S: Scalar>(
     builder: &mut VerificationBuilder<S>,
     alpha: S,
     beta: S,

crates/proof-of-sql/src/sql/proof_plans/mod.rs

@@ -35,5 +35,11 @@ pub(crate) use group_by_exec::GroupByExec;
 #[cfg(all(test, feature = "blitzar"))]
 mod group_by_exec_test;
 
+mod slice_exec;
+#[allow(unused_imports)]
+pub(crate) use slice_exec::SliceExec;
+#[cfg(all(test, feature = "blitzar"))]
+mod slice_exec_test;
+
 mod dyn_proof_plan;
 pub use dyn_proof_plan::DynProofPlan;

crates/proof-of-sql/src/sql/proof_plans/slice_exec.rs

@@ -0,0 +1,212 @@
+use super::{
+    filter_exec::{prove_filter, verify_filter},
+    DynProofPlan,
+};
+use crate::{
+    base::{
+        database::{
+            filter_util::filter_columns, ColumnField, ColumnRef, OwnedTable, Table,
+            TableEvaluation, TableOptions, TableRef,
+        },
+        map::{IndexMap, IndexSet},
+        proof::ProofError,
+        scalar::Scalar,
+    },
+    sql::proof::{
+        CountBuilder, FinalRoundBuilder, FirstRoundBuilder, ProofPlan, ProverEvaluate,
+        VerificationBuilder,
+    },
+};
+use alloc::{boxed::Box, vec, vec::Vec};
+use bumpalo::Bump;
+use core::iter::{repeat, repeat_with};
+use itertools::repeat_n;
+use serde::{Deserialize, Serialize};
+
+/// `ProofPlan` for queries of the form
+/// ```ignore
+///     <ProofPlan> LIMIT <fetch> [OFFSET <skip>]
+/// ```
+#[derive(Debug, PartialEq, Serialize, Deserialize)]
+pub struct SliceExec {
+    pub(super) input: Box<DynProofPlan>,
+    pub(super) skip: usize,
+    pub(super) fetch: Option<usize>,
+}
+
+/// Get the boolean slice selection from the number of rows, skip and fetch
+fn get_slice_select(num_rows: usize, skip: usize, fetch: Option<usize>) -> Vec<bool> {
+    repeat_n(false, skip)
+        .chain(repeat_n(true, fetch.unwrap_or(num_rows)))
+        .chain(repeat(false))
+        .take(num_rows)
+        .collect()
+}
+
+impl SliceExec {
+    /// Creates a new slice execution plan.
+    #[allow(dead_code)]
+    pub fn new(input: Box<DynProofPlan>, skip: usize, fetch: Option<usize>) -> Self {
+        Self { input, skip, fetch }
+    }
+}
+
+impl ProofPlan for SliceExec
+where
+    SliceExec: ProverEvaluate,
+{
+    fn count(&self, builder: &mut CountBuilder) -> Result<(), ProofError> {
+        self.input.count(builder)?;
+        builder.count_intermediate_mles(self.input.get_column_result_fields().len());
+        builder.count_intermediate_mles(2);
+        builder.count_subpolynomials(3);
+        builder.count_degree(3);
+        builder.count_post_result_challenges(2);
+        Ok(())
+    }
+
+    #[allow(unused_variables)]
+    fn verifier_evaluate<S: Scalar>(
+        &self,
+        builder: &mut VerificationBuilder<S>,
+        accessor: &IndexMap<ColumnRef, S>,
+        _result: Option<&OwnedTable<S>>,
+        one_eval_map: &IndexMap<TableRef, S>,
+    ) -> Result<TableEvaluation<S>, ProofError> {
+        // 1. columns
+        // We do not support `GroupByExec` as input for now
+        if matches!(*self.input, DynProofPlan::GroupBy(_)) {
+            return Err(ProofError::UnsupportedQueryPlan {
+                error: "GroupByExec as input for another plan is not supported",
+            });
+        }
+        let input_table_eval =
+            self.input
+                .verifier_evaluate(builder, accessor, None, one_eval_map)?;
+        let output_one_eval = builder.consume_one_evaluation();
+        let columns_evals = input_table_eval.column_evals();
+        // 2. selection
+        // The selected range is (offset_index, max_index]
+        let offset_one_eval = builder.consume_one_evaluation();
+        let max_one_eval = builder.consume_one_evaluation();
+        let selection_eval = max_one_eval - offset_one_eval;
+        // 3. filtered_columns
+        let filtered_columns_evals: Vec<_> = repeat_with(|| builder.consume_intermediate_mle())
+            .take(columns_evals.len())
+            .collect();
+        let alpha = builder.consume_post_result_challenge();
+        let beta = builder.consume_post_result_challenge();
+
+        verify_filter(
+            builder,
+            alpha,
+            beta,
+            *input_table_eval.one_eval(),
+            output_one_eval,
+            columns_evals,
+            selection_eval,
+            &filtered_columns_evals,
+        )?;
+        Ok(TableEvaluation::new(
+            filtered_columns_evals,
+            output_one_eval,
+        ))
+    }
+
+    fn get_column_result_fields(&self) -> Vec<ColumnField> {
+        self.input.get_column_result_fields()
+    }
+
+    fn get_column_references(&self) -> IndexSet<ColumnRef> {
+        self.input.get_column_references()
+    }
+
+    fn get_table_references(&self) -> IndexSet<TableRef> {
+        self.input.get_table_references()
+    }
+}
+
+impl ProverEvaluate for SliceExec {
+    #[tracing::instrument(name = "SliceExec::first_round_evaluate", level = "debug", skip_all)]
+    fn first_round_evaluate<'a, S: Scalar>(
+        &self,
+        builder: &mut FirstRoundBuilder,
+        alloc: &'a Bump,
+        table_map: &IndexMap<TableRef, Table<'a, S>>,
+    ) -> (Table<'a, S>, Vec<usize>) {
+        // 1. columns
+        let (input, input_one_eval_lengths) =
+            self.input.first_round_evaluate(builder, alloc, table_map);
+        let input_length = input.num_rows();
+        let columns = input.columns().copied().collect::<Vec<_>>();
+        // 2. select
+        let select = get_slice_select(input_length, self.skip, self.fetch);
+        // The selected range is (offset_index, max_index]
+        let offset_index = self.skip.min(input_length);
+        let max_index = if let Some(fetch) = self.fetch {
+            (self.skip + fetch).min(input_length)
+        } else {
+            input_length
+        };
+        let output_length = max_index - offset_index;
+        // Compute filtered_columns
+        let (filtered_columns, _) = filter_columns(alloc, &columns, &select);
+        let res = Table::<'a, S>::try_from_iter_with_options(
+            self.get_column_result_fields()
+                .into_iter()
+                .map(|expr| expr.name())
+                .zip(filtered_columns),
+            TableOptions::new(Some(output_length)),
+        )
+        .expect("Failed to create table from iterator");
+        let mut one_eval_lengths = input_one_eval_lengths;
+        one_eval_lengths.extend(vec![output_length, offset_index, max_index]);
+        builder.request_post_result_challenges(2);
+        (res, one_eval_lengths)
+    }
+
+    #[tracing::instrument(name = "SliceExec::prover_evaluate", level = "debug", skip_all)]
+    #[allow(unused_variables)]
+    fn final_round_evaluate<'a, S: Scalar>(
+        &self,
+        builder: &mut FinalRoundBuilder<'a, S>,
+        alloc: &'a Bump,
+        table_map: &IndexMap<TableRef, Table<'a, S>>,
+    ) -> Table<'a, S> {
+        // 1. columns
+        let input = self.input.final_round_evaluate(builder, alloc, table_map);
+        let columns = input.columns().copied().collect::<Vec<_>>();
+        // 2. select
+        let select = get_slice_select(input.num_rows(), self.skip, self.fetch);
+        let select_ref: &'a [_] = alloc.alloc_slice_copy(&select);
+        let output_length = select.iter().filter(|b| **b).count();
+        // Compute filtered_columns and indexes
+        let (filtered_columns, result_len) = filter_columns(alloc, &columns, &select);
+        // 3. Produce MLEs
+        filtered_columns.iter().copied().for_each(|column| {
+            builder.produce_intermediate_mle(column);
+        });
+        let alpha = builder.consume_post_result_challenge();
+        let beta = builder.consume_post_result_challenge();
+
+        prove_filter::<S>(
+            builder,
+            alloc,
+            alpha,
+            beta,
+            &columns,
+            select_ref,
+            &filtered_columns,
+            input.num_rows(),
+            result_len,
+        );
+        Table::<'a, S>::try_from_iter_with_options(
+            self.get_column_result_fields()
+                .into_iter()
+                .map(|expr| expr.name())
+                .zip(filtered_columns),
+            TableOptions::new(Some(output_length)),
+        )
+        .expect("Failed to create table from iterator")
+    }
+}