feat: add compare_single_row_of_tables (#391)

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# Rationale for this change
We need to add this function in order to perform sort-merge joins.
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 Example:
 Add `NestedLoopJoinExec`.
 Closes #345.

Since we added `HashJoinExec` in #323 it has been possible to do
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 for `HashJoinExec`.
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# What changes are included in this PR?
See title.
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# Are these changes tested?
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Yes.

crates/proof-of-sql/src/base/database/order_by_util.rs

@@ -1,6 +1,6 @@
 //! Contains the utility functions for ordering.
 use crate::base::{
-    database::{Column, OwnedColumn},
+    database::{Column, OwnedColumn, TableOperationError, TableOperationResult},
     scalar::{Scalar, ScalarExt},
 };
 use alloc::vec::Vec;
@@ -31,6 +31,74 @@ pub(crate) fn compare_indexes_by_columns<S: Scalar>(
         .unwrap_or(Ordering::Equal)
 }
 
+/// Compares the tuples `(left[0][i], left[1][i], ...)` and
+/// `(right[0][j], right[1][j], ...)` in lexicographic order.
+///
+/// Requires that columns in `left` and `right` have the same column types for now
+///
+/// # Panics
+/// Panics if `left` and `right` have different number of columns
+/// which should never happen since this function should only be called
+/// for joins.
+#[allow(dead_code)]
+pub(crate) fn compare_single_row_of_tables<S: Scalar>(
+    left: &[Column<S>],
+    right: &[Column<S>],
+    left_row_index: usize,
+    right_row_index: usize,
+) -> TableOperationResult<Ordering> {
+    // Should never happen
+    assert_eq!(left.len(), right.len());
+    left.iter()
+        .zip(right.iter())
+        .try_for_each(|(left_col, right_col)| {
+            if left_col.column_type() != right_col.column_type() {
+                return Err(TableOperationError::JoinIncompatibleTypes {
+                    left_type: left_col.column_type(),
+                    right_type: right_col.column_type(),
+                });
+            }
+            Ok(())
+        })?;
+    Ok(left
+        .iter()
+        .zip(right.iter())
+        .map(|(left_col, right_col)| match (left_col, right_col) {
+            (Column::Boolean(left_col), Column::Boolean(right_col)) => {
+                left_col[left_row_index].cmp(&right_col[right_row_index])
+            }
+            (Column::TinyInt(left_col), Column::TinyInt(right_col)) => {
+                left_col[left_row_index].cmp(&right_col[right_row_index])
+            }
+            (Column::SmallInt(left_col), Column::SmallInt(right_col)) => {
+                left_col[left_row_index].cmp(&right_col[right_row_index])
+            }
+            (Column::Int(left_col), Column::Int(right_col)) => {
+                left_col[left_row_index].cmp(&right_col[right_row_index])
+            }
+            (Column::BigInt(left_col), Column::BigInt(right_col))
+            | (Column::TimestampTZ(_, _, left_col), Column::TimestampTZ(_, _, right_col)) => {
+                left_col[left_row_index].cmp(&right_col[right_row_index])
+            }
+            (Column::Int128(left_col), Column::Int128(right_col)) => {
+                left_col[left_row_index].cmp(&right_col[right_row_index])
+            }
+            (Column::Decimal75(_, _, left_col), Column::Decimal75(_, _, right_col)) => {
+                left_col[left_row_index].signed_cmp(&right_col[right_row_index])
+            }
+            (Column::Scalar(left_col), Column::Scalar(right_col)) => {
+                left_col[left_row_index].cmp(&right_col[right_row_index])
+            }
+            (Column::VarChar((left_col, _)), Column::VarChar((right_col, _))) => {
+                left_col[left_row_index].cmp(right_col[right_row_index])
+            }
+            // Should never happen since we checked the column types
+            _ => unreachable!(),
+        })
+        .find(|&ord| ord != Ordering::Equal)
+        .unwrap_or(Ordering::Equal))
+}
+
 /// Compares the tuples `(order_by[0][i], order_by[1][i], ...)` and
 /// `(order_by[0][j], order_by[1][j], ...)` in lexicographic order.
 ///

crates/proof-of-sql/src/base/database/order_by_util_test.rs

@@ -1,6 +1,6 @@
 use crate::{
     base::{
-        database::{order_by_util::*, Column, OwnedColumn},
+        database::{order_by_util::*, Column, ColumnType, OwnedColumn, TableOperationError},
         math::decimal::Precision,
         scalar::test_scalar::TestScalar,
     },
@@ -78,6 +78,65 @@ fn we_can_compare_indexes_by_columns_for_mixed_columns() {
     assert_eq!(compare_indexes_by_columns(columns, 6, 9), Ordering::Equal);
 }
 
+#[test]
+fn we_can_compare_single_row_of_tables() {
+    let left_slice_a = &[55, 44, 44, 66, 66, 77, 66, 66, 66, 66];
+    let left_slice_b = &[22, 44, 55, 44, 33, 22, 22, 11, 22, 22];
+    let left_slice_c = &[11, 55, 11, 44, 77, 11, 22, 55, 11, 22];
+    let left_column_a = Column::BigInt::<TestScalar>(left_slice_a);
+    let left_column_b = Column::BigInt::<TestScalar>(left_slice_b);
+    let left_column_c = Column::BigInt::<TestScalar>(left_slice_c);
+    let left = &[left_column_a, left_column_b, left_column_c];
+
+    let right_slice_a = &[77, 44, 66, 44, 77, 77, 66, 66, 55, 66];
+    let right_slice_b = &[22, 55, 11, 77, 33, 33, 22, 22, 22, 11];
+    let right_slice_c = &[11, 55, 22, 0, 77, 11, 33, 55, 11, 22];
+    let right_column_a = Column::BigInt::<TestScalar>(right_slice_a);
+    let right_column_b = Column::BigInt::<TestScalar>(right_slice_b);
+    let right_column_c = Column::BigInt::<TestScalar>(right_slice_c);
+    let right = &[right_column_a, right_column_b, right_column_c];
+
+    assert_eq!(
+        compare_single_row_of_tables(left, right, 0, 1).unwrap(),
+        Ordering::Greater
+    );
+    assert_eq!(
+        compare_single_row_of_tables(left, right, 1, 2).unwrap(),
+        Ordering::Less
+    );
+    assert_eq!(
+        compare_single_row_of_tables(left, right, 2, 3).unwrap(),
+        Ordering::Less
+    );
+    assert_eq!(
+        compare_single_row_of_tables(left, right, 2, 1).unwrap(),
+        Ordering::Less
+    );
+    assert_eq!(
+        compare_single_row_of_tables(left, right, 5, 0).unwrap(),
+        Ordering::Equal
+    );
+}
+
+#[test]
+fn we_cannot_compare_single_row_of_tables_if_type_mismatch() {
+    let left_slice = &[55, 44, 66, 66, 66, 77, 66, 66, 66, 66];
+    let right_slice = &[
+        true, false, true, true, false, true, false, true, false, true,
+    ];
+    let left_column = Column::BigInt::<TestScalar>(left_slice);
+    let right_column = Column::Boolean::<TestScalar>(right_slice);
+    let left = &[left_column];
+    let right = &[right_column];
+    assert_eq!(
+        compare_single_row_of_tables(left, right, 0, 1),
+        Err(TableOperationError::JoinIncompatibleTypes {
+            left_type: ColumnType::BigInt,
+            right_type: ColumnType::Boolean
+        })
+    );
+}
+
 #[test]
 fn we_can_compare_indexes_by_owned_columns_for_mixed_columns() {
     let slice_a = ["55", "44", "66", "66", "66", "77", "66", "66", "66", "66"]

crates/proof-of-sql/src/base/database/table_operation_error.rs

@@ -1,4 +1,4 @@
-use crate::base::database::ColumnField;
+use crate::base::database::{ColumnField, ColumnType};
 use alloc::vec::Vec;
 use core::result::Result;
 use snafu::Snafu;
@@ -16,6 +16,16 @@ pub enum TableOperationError {
         /// The schema of the table that caused the error
         actual_schema: Vec<ColumnField>,
     },
+    /// Errors related to joining tables on columns with incompatible types.
+    #[snafu(display(
+        "Cannot join tables on columns with incompatible types: {left_type:?} and {right_type:?}"
+    ))]
+    JoinIncompatibleTypes {
+        /// The left-hand side data type
+        left_type: ColumnType,
+        /// The right-hand side data type
+        right_type: ColumnType,
+    },
 }
 
 /// Result type for table operations