datafusion_physical_expr/intervals/cp_solver.rs
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// Licensed to the Apache Software Foundation (ASF) under one
// or more contributor license agreements. See the NOTICE file
// distributed with this work for additional information
// regarding copyright ownership. The ASF licenses this file
// to you under the Apache License, Version 2.0 (the
// "License"); you may not use this file except in compliance
// with the License. You may obtain a copy of the License at
//
//http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing,
// software distributed under the License is distributed on an
// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied. See the License for the
// specific language governing permissions and limitations
// under the License.
//! Constraint propagator/solver for custom PhysicalExpr graphs.
use std::collections::HashSet;
use std::fmt::{Display, Formatter};
use std::mem::{size_of, size_of_val};
use std::sync::Arc;
use super::utils::{
convert_duration_type_to_interval, convert_interval_type_to_duration, get_inverse_op,
};
use crate::expressions::Literal;
use crate::utils::{build_dag, ExprTreeNode};
use crate::PhysicalExpr;
use arrow_schema::{DataType, Schema};
use datafusion_common::{internal_err, Result};
use datafusion_expr::interval_arithmetic::{apply_operator, satisfy_greater, Interval};
use datafusion_expr::Operator;
use petgraph::graph::NodeIndex;
use petgraph::stable_graph::{DefaultIx, StableGraph};
use petgraph::visit::{Bfs, Dfs, DfsPostOrder, EdgeRef};
use petgraph::Outgoing;
// Interval arithmetic provides a way to perform mathematical operations on
// intervals, which represent a range of possible values rather than a single
// point value. This allows for the propagation of ranges through mathematical
// operations, and can be used to compute bounds for a complicated expression.
// The key idea is that by breaking down a complicated expression into simpler
// terms, and then combining the bounds for those simpler terms, one can
// obtain bounds for the overall expression.
//
// For example, consider a mathematical expression such as x^2 + y = 4. Since
// it would be a binary tree in [PhysicalExpr] notation, this type of an
// hierarchical computation is well-suited for a graph based implementation.
// In such an implementation, an equation system f(x) = 0 is represented by a
// directed acyclic expression graph (DAEG).
//
// In order to use interval arithmetic to compute bounds for this expression,
// one would first determine intervals that represent the possible values of x
// and y. Let's say that the interval for x is [1, 2] and the interval for y
// is [-3, 1]. In the chart below, you can see how the computation takes place.
//
// This way of using interval arithmetic to compute bounds for a complex
// expression by combining the bounds for the constituent terms within the
// original expression allows us to reason about the range of possible values
// of the expression. This information later can be used in range pruning of
// the provably unnecessary parts of `RecordBatch`es.
//
// References
// 1 - Kabak, Mehmet Ozan. Analog Circuit Start-Up Behavior Analysis: An Interval
// Arithmetic Based Approach, Chapter 4. Stanford University, 2015.
// 2 - Moore, Ramon E. Interval analysis. Vol. 4. Englewood Cliffs: Prentice-Hall, 1966.
// 3 - F. Messine, "Deterministic global optimization using interval constraint
// propagation techniques," RAIRO-Operations Research, vol. 38, no. 04,
// pp. 277{293, 2004.
//
// ``` text
// Computing bounds for an expression using interval arithmetic. Constraint propagation through a top-down evaluation of the expression
// graph using inverse semantics.
//
// [-2, 5] ∩ [4, 4] = [4, 4] [4, 4]
// +-----+ +-----+ +-----+ +-----+
// +----| + |----+ +----| + |----+ +----| + |----+ +----| + |----+
// | | | | | | | | | | | | | | | |
// | +-----+ | | +-----+ | | +-----+ | | +-----+ |
// | | | | | | | |
// +-----+ +-----+ +-----+ +-----+ +-----+ +-----+ +-----+ +-----+
// | 2 | | y | | 2 | [1, 4] | y | | 2 | [1, 4] | y | | 2 | [1, 4] | y | [0, 1]*
// |[.] | | | |[.] | | | |[.] | | | |[.] | | |
// +-----+ +-----+ +-----+ +-----+ +-----+ +-----+ +-----+ +-----+
// | | | [-3, 1] |
// | | | |
// +---+ +---+ +---+ +---+
// | x | [1, 2] | x | [1, 2] | x | [1, 2] | x | [1, 2]
// +---+ +---+ +---+ +---+
//
// (a) Bottom-up evaluation: Step1 (b) Bottom up evaluation: Step2 (a) Top-down propagation: Step1 (b) Top-down propagation: Step2
//
// [1 - 3, 4 + 1] = [-2, 5] [1 - 3, 4 + 1] = [-2, 5]
// +-----+ +-----+ +-----+ +-----+
// +----| + |----+ +----| + |----+ +----| + |----+ +----| + |----+
// | | | | | | | | | | | | | | | |
// | +-----+ | | +-----+ | | +-----+ | | +-----+ |
// | | | | | | | |
// +-----+ +-----+ +-----+ +-----+ +-----+ +-----+ +-----+ +-----+
// | 2 |[1, 4] | y | | 2 |[1, 4] | y | | 2 |[3, 4]** | y | | 2 |[1, 4] | y |
// |[.] | | | |[.] | | | |[.] | | | |[.] | | |
// +-----+ +-----+ +-----+ +-----+ +-----+ +-----+ +-----+ +-----+
// | [-3, 1] | [-3, 1] | [0, 1] | [-3, 1]
// | | | |
// +---+ +---+ +---+ +---+
// | x | [1, 2] | x | [1, 2] | x | [1, 2] | x | [sqrt(3), 2]***
// +---+ +---+ +---+ +---+
//
// (c) Bottom-up evaluation: Step3 (d) Bottom-up evaluation: Step4 (c) Top-down propagation: Step3 (d) Top-down propagation: Step4
//
// * [-3, 1] ∩ ([4, 4] - [1, 4]) = [0, 1]
// ** [1, 4] ∩ ([4, 4] - [0, 1]) = [3, 4]
// *** [1, 2] ∩ [sqrt(3), sqrt(4)] = [sqrt(3), 2]
// ```
/// This object implements a directed acyclic expression graph (DAEG) that
/// is used to compute ranges for expressions through interval arithmetic.
#[derive(Clone, Debug)]
pub struct ExprIntervalGraph {
graph: StableGraph<ExprIntervalGraphNode, usize>,
root: NodeIndex,
}
impl ExprIntervalGraph {
/// Estimate size of bytes including `Self`.
pub fn size(&self) -> usize {
let node_memory_usage = self.graph.node_count()
* (size_of::<ExprIntervalGraphNode>() + size_of::<NodeIndex>());
let edge_memory_usage =
self.graph.edge_count() * (size_of::<usize>() + size_of::<NodeIndex>() * 2);
size_of_val(self) + node_memory_usage + edge_memory_usage
}
}
/// This object encapsulates all possible constraint propagation results.
#[derive(PartialEq, Debug)]
pub enum PropagationResult {
CannotPropagate,
Infeasible,
Success,
}
/// This is a node in the DAEG; it encapsulates a reference to the actual
/// [`PhysicalExpr`] as well as an interval containing expression bounds.
#[derive(Clone, Debug)]
pub struct ExprIntervalGraphNode {
expr: Arc<dyn PhysicalExpr>,
interval: Interval,
}
impl Display for ExprIntervalGraphNode {
fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", self.expr)
}
}
impl ExprIntervalGraphNode {
/// Constructs a new DAEG node with an [-∞, ∞] range.
pub fn new_unbounded(expr: Arc<dyn PhysicalExpr>, dt: &DataType) -> Result<Self> {
Interval::make_unbounded(dt)
.map(|interval| ExprIntervalGraphNode { expr, interval })
}
/// Constructs a new DAEG node with the given range.
pub fn new_with_interval(expr: Arc<dyn PhysicalExpr>, interval: Interval) -> Self {
ExprIntervalGraphNode { expr, interval }
}
/// Get the interval object representing the range of the expression.
pub fn interval(&self) -> &Interval {
&self.interval
}
/// This function creates a DAEG node from DataFusion's [`ExprTreeNode`]
/// object. Literals are created with definite, singleton intervals while
/// any other expression starts with an indefinite interval ([-∞, ∞]).
pub fn make_node(node: &ExprTreeNode<NodeIndex>, schema: &Schema) -> Result<Self> {
let expr = Arc::clone(&node.expr);
if let Some(literal) = expr.as_any().downcast_ref::<Literal>() {
let value = literal.value();
Interval::try_new(value.clone(), value.clone())
.map(|interval| Self::new_with_interval(expr, interval))
} else {
expr.data_type(schema)
.and_then(|dt| Self::new_unbounded(expr, &dt))
}
}
}
impl PartialEq for ExprIntervalGraphNode {
fn eq(&self, other: &Self) -> bool {
self.expr.eq(&other.expr)
}
}
/// This function refines intervals `left_child` and `right_child` by applying
/// constraint propagation through `parent` via operation. The main idea is
/// that we can shrink ranges of variables x and y using parent interval p.
///
/// Assuming that x,y and p has ranges [xL, xU], [yL, yU], and [pL, pU], we
/// apply the following operations:
/// - For plus operation, specifically, we would first do
/// - [xL, xU] <- ([pL, pU] - [yL, yU]) ∩ [xL, xU], and then
/// - [yL, yU] <- ([pL, pU] - [xL, xU]) ∩ [yL, yU].
/// - For minus operation, specifically, we would first do
/// - [xL, xU] <- ([yL, yU] + [pL, pU]) ∩ [xL, xU], and then
/// - [yL, yU] <- ([xL, xU] - [pL, pU]) ∩ [yL, yU].
/// - For multiplication operation, specifically, we would first do
/// - [xL, xU] <- ([pL, pU] / [yL, yU]) ∩ [xL, xU], and then
/// - [yL, yU] <- ([pL, pU] / [xL, xU]) ∩ [yL, yU].
/// - For division operation, specifically, we would first do
/// - [xL, xU] <- ([yL, yU] * [pL, pU]) ∩ [xL, xU], and then
/// - [yL, yU] <- ([xL, xU] / [pL, pU]) ∩ [yL, yU].
pub fn propagate_arithmetic(
op: &Operator,
parent: &Interval,
left_child: &Interval,
right_child: &Interval,
) -> Result<Option<(Interval, Interval)>> {
let inverse_op = get_inverse_op(*op)?;
match (left_child.data_type(), right_child.data_type()) {
// If we have a child whose type is a time interval (i.e. DataType::Interval),
// we need special handling since timestamp differencing results in a
// Duration type.
(DataType::Timestamp(..), DataType::Interval(_)) => {
propagate_time_interval_at_right(
left_child,
right_child,
parent,
op,
&inverse_op,
)
}
(DataType::Interval(_), DataType::Timestamp(..)) => {
propagate_time_interval_at_left(
left_child,
right_child,
parent,
op,
&inverse_op,
)
}
_ => {
// First, propagate to the left:
match apply_operator(&inverse_op, parent, right_child)?
.intersect(left_child)?
{
// Left is feasible:
Some(value) => Ok(
// Propagate to the right using the new left.
propagate_right(&value, parent, right_child, op, &inverse_op)?
.map(|right| (value, right)),
),
// If the left child is infeasible, short-circuit.
None => Ok(None),
}
}
}
}
/// This function refines intervals `left_child` and `right_child` by applying
/// comparison propagation through `parent` via operation. The main idea is
/// that we can shrink ranges of variables x and y using parent interval p.
/// Two intervals can be ordered in 6 ways for a Gt `>` operator:
/// ```text
/// (1): Infeasible, short-circuit
/// left: | ================ |
/// right: | ======================== |
///
/// (2): Update both interval
/// left: | ====================== |
/// right: | ====================== |
/// |
/// V
/// left: | ======= |
/// right: | ======= |
///
/// (3): Update left interval
/// left: | ============================== |
/// right: | ========== |
/// |
/// V
/// left: | ===================== |
/// right: | ========== |
///
/// (4): Update right interval
/// left: | ========== |
/// right: | =========================== |
/// |
/// V
/// left: | ========== |
/// right | ================== |
///
/// (5): No change
/// left: | ============================ |
/// right: | =================== |
///
/// (6): No change
/// left: | ==================== |
/// right: | =============== |
///
/// -inf --------------------------------------------------------------- +inf
/// ```
pub fn propagate_comparison(
op: &Operator,
parent: &Interval,
left_child: &Interval,
right_child: &Interval,
) -> Result<Option<(Interval, Interval)>> {
if parent == &Interval::CERTAINLY_TRUE {
match op {
Operator::Eq => left_child.intersect(right_child).map(|result| {
result.map(|intersection| (intersection.clone(), intersection))
}),
Operator::Gt => satisfy_greater(left_child, right_child, true),
Operator::GtEq => satisfy_greater(left_child, right_child, false),
Operator::Lt => satisfy_greater(right_child, left_child, true)
.map(|t| t.map(reverse_tuple)),
Operator::LtEq => satisfy_greater(right_child, left_child, false)
.map(|t| t.map(reverse_tuple)),
_ => internal_err!(
"The operator must be a comparison operator to propagate intervals"
),
}
} else if parent == &Interval::CERTAINLY_FALSE {
match op {
Operator::Eq => {
// TODO: Propagation is not possible until we support interval sets.
Ok(None)
}
Operator::Gt => satisfy_greater(right_child, left_child, false),
Operator::GtEq => satisfy_greater(right_child, left_child, true),
Operator::Lt => satisfy_greater(left_child, right_child, false)
.map(|t| t.map(reverse_tuple)),
Operator::LtEq => satisfy_greater(left_child, right_child, true)
.map(|t| t.map(reverse_tuple)),
_ => internal_err!(
"The operator must be a comparison operator to propagate intervals"
),
}
} else {
// Uncertainty cannot change any end-point of the intervals.
Ok(None)
}
}
impl ExprIntervalGraph {
pub fn try_new(expr: Arc<dyn PhysicalExpr>, schema: &Schema) -> Result<Self> {
// Build the full graph:
let (root, graph) =
build_dag(expr, &|node| ExprIntervalGraphNode::make_node(node, schema))?;
Ok(Self { graph, root })
}
pub fn node_count(&self) -> usize {
self.graph.node_count()
}
// Sometimes, we do not want to calculate and/or propagate intervals all
// way down to leaf expressions. For example, assume that we have a
// `SymmetricHashJoin` which has a child with an output ordering like:
//
// PhysicalSortExpr {
// expr: BinaryExpr('a', +, 'b'),
// sort_option: ..
// }
//
// i.e. its output order comes from a clause like "ORDER BY a + b". In such
// a case, we must calculate the interval for the BinaryExpr('a', +, 'b')
// instead of the columns inside this BinaryExpr, because this interval
// decides whether we prune or not. Therefore, children `PhysicalExpr`s of
// this `BinaryExpr` may be pruned for performance. The figure below
// explains this example visually.
//
// Note that we just remove the nodes from the DAEG, do not make any change
// to the plan itself.
//
// ```text
//
// +-----+ +-----+
// | GT | | GT |
// +--------| |-------+ +--------| |-------+
// | +-----+ | | +-----+ |
// | | | |
// +-----+ | +-----+ |
// |Cast | | |Cast | |
// | | | --\ | | |
// +-----+ | ---------- +-----+ |
// | | --/ | |
// | | | |
// +-----+ +-----+ +-----+ +-----+
// +--|Plus |--+ +--|Plus |--+ |Plus | +--|Plus |--+
// | | | | | | | | | | | | | |
// Prune from here | +-----+ | | +-----+ | +-----+ | +-----+ |
// ------------------------------------ | | | |
// | | | | | |
// +-----+ +-----+ +-----+ +-----+ +-----+ +-----+
// | a | | b | | c | | 2 | | c | | 2 |
// | | | | | | | | | | | |
// +-----+ +-----+ +-----+ +-----+ +-----+ +-----+
//
// ```
/// This function associates stable node indices with [`PhysicalExpr`]s so
/// that we can match `Arc<dyn PhysicalExpr>` and NodeIndex objects during
/// membership tests.
pub fn gather_node_indices(
&mut self,
exprs: &[Arc<dyn PhysicalExpr>],
) -> Vec<(Arc<dyn PhysicalExpr>, usize)> {
let graph = &self.graph;
let mut bfs = Bfs::new(graph, self.root);
// We collect the node indices (usize) of [PhysicalExpr]s in the order
// given by argument `exprs`. To preserve this order, we initialize each
// expression's node index with usize::MAX, and then find the corresponding
// node indices by traversing the graph.
let mut removals = vec![];
let mut expr_node_indices = exprs
.iter()
.map(|e| (Arc::clone(e), usize::MAX))
.collect::<Vec<_>>();
while let Some(node) = bfs.next(graph) {
// Get the plan corresponding to this node:
let expr = &graph[node].expr;
// If the current expression is among `exprs`, slate its children
// for removal:
if let Some(value) = exprs.iter().position(|e| expr.eq(e)) {
// Update the node index of the associated `PhysicalExpr`:
expr_node_indices[value].1 = node.index();
for edge in graph.edges_directed(node, Outgoing) {
// Slate the child for removal, do not remove immediately.
removals.push(edge.id());
}
}
}
for edge_idx in removals {
self.graph.remove_edge(edge_idx);
}
// Get the set of node indices reachable from the root node:
let connected_nodes = self.connected_nodes();
// Remove nodes not connected to the root node:
self.graph
.retain_nodes(|_, index| connected_nodes.contains(&index));
expr_node_indices
}
/// Returns the set of node indices reachable from the root node via a
/// simple depth-first search.
fn connected_nodes(&self) -> HashSet<NodeIndex> {
let mut nodes = HashSet::new();
let mut dfs = Dfs::new(&self.graph, self.root);
while let Some(node) = dfs.next(&self.graph) {
nodes.insert(node);
}
nodes
}
/// Updates intervals for all expressions in the DAEG by successive
/// bottom-up and top-down traversals.
pub fn update_ranges(
&mut self,
leaf_bounds: &mut [(usize, Interval)],
given_range: Interval,
) -> Result<PropagationResult> {
self.assign_intervals(leaf_bounds);
let bounds = self.evaluate_bounds()?;
// There are three possible cases to consider:
// (1) given_range ⊇ bounds => Nothing to propagate
// (2) ∅ ⊂ (given_range ∩ bounds) ⊂ bounds => Can propagate
// (3) Disjoint sets => Infeasible
if given_range.contains(bounds)? == Interval::CERTAINLY_TRUE {
// First case:
Ok(PropagationResult::CannotPropagate)
} else if bounds.contains(&given_range)? != Interval::CERTAINLY_FALSE {
// Second case:
let result = self.propagate_constraints(given_range);
self.update_intervals(leaf_bounds);
result
} else {
// Third case:
Ok(PropagationResult::Infeasible)
}
}
/// This function assigns given ranges to expressions in the DAEG.
/// The argument `assignments` associates indices of sought expressions
/// with their corresponding new ranges.
pub fn assign_intervals(&mut self, assignments: &[(usize, Interval)]) {
for (index, interval) in assignments {
let node_index = NodeIndex::from(*index as DefaultIx);
self.graph[node_index].interval = interval.clone();
}
}
/// This function fetches ranges of expressions from the DAEG. The argument
/// `assignments` associates indices of sought expressions with their ranges,
/// which this function modifies to reflect the intervals in the DAEG.
pub fn update_intervals(&self, assignments: &mut [(usize, Interval)]) {
for (index, interval) in assignments.iter_mut() {
let node_index = NodeIndex::from(*index as DefaultIx);
*interval = self.graph[node_index].interval.clone();
}
}
/// Computes bounds for an expression using interval arithmetic via a
/// bottom-up traversal.
///
/// # Arguments
/// * `leaf_bounds` - &[(usize, Interval)]. Provide NodeIndex, Interval tuples for leaf variables.
///
/// # Examples
///
/// ```
/// use arrow::datatypes::DataType;
/// use arrow::datatypes::Field;
/// use arrow::datatypes::Schema;
/// use datafusion_common::ScalarValue;
/// use datafusion_expr::interval_arithmetic::Interval;
/// use datafusion_expr::Operator;
/// use datafusion_physical_expr::expressions::{BinaryExpr, Column, Literal};
/// use datafusion_physical_expr::intervals::cp_solver::ExprIntervalGraph;
/// use datafusion_physical_expr::PhysicalExpr;
/// use std::sync::Arc;
///
/// let expr = Arc::new(BinaryExpr::new(
/// Arc::new(Column::new("gnz", 0)),
/// Operator::Plus,
/// Arc::new(Literal::new(ScalarValue::Int32(Some(10)))),
/// ));
///
/// let schema = Schema::new(vec![Field::new("gnz".to_string(), DataType::Int32, true)]);
///
/// let mut graph = ExprIntervalGraph::try_new(expr, &schema).unwrap();
/// // Do it once, while constructing.
/// let node_indices = graph
/// .gather_node_indices(&[Arc::new(Column::new("gnz", 0))]);
/// let left_index = node_indices.get(0).unwrap().1;
///
/// // Provide intervals for leaf variables (here, there is only one).
/// let intervals = vec![(
/// left_index,
/// Interval::make(Some(10), Some(20)).unwrap(),
/// )];
///
/// // Evaluate bounds for the composite expression:
/// graph.assign_intervals(&intervals);
/// assert_eq!(
/// graph.evaluate_bounds().unwrap(),
/// &Interval::make(Some(20), Some(30)).unwrap(),
/// )
/// ```
pub fn evaluate_bounds(&mut self) -> Result<&Interval> {
let mut dfs = DfsPostOrder::new(&self.graph, self.root);
while let Some(node) = dfs.next(&self.graph) {
let neighbors = self.graph.neighbors_directed(node, Outgoing);
let mut children_intervals = neighbors
.map(|child| self.graph[child].interval())
.collect::<Vec<_>>();
// If the current expression is a leaf, its interval should already
// be set externally, just continue with the evaluation procedure:
if !children_intervals.is_empty() {
// Reverse to align with `PhysicalExpr`'s children:
children_intervals.reverse();
self.graph[node].interval =
self.graph[node].expr.evaluate_bounds(&children_intervals)?;
}
}
Ok(&self.graph[self.root].interval)
}
/// Updates/shrinks bounds for leaf expressions using interval arithmetic
/// via a top-down traversal.
fn propagate_constraints(
&mut self,
given_range: Interval,
) -> Result<PropagationResult> {
let mut bfs = Bfs::new(&self.graph, self.root);
// Adjust the root node with the given range:
if let Some(interval) = self.graph[self.root].interval.intersect(given_range)? {
self.graph[self.root].interval = interval;
} else {
return Ok(PropagationResult::Infeasible);
}
while let Some(node) = bfs.next(&self.graph) {
let neighbors = self.graph.neighbors_directed(node, Outgoing);
let mut children = neighbors.collect::<Vec<_>>();
// If the current expression is a leaf, its range is now final.
// So, just continue with the propagation procedure:
if children.is_empty() {
continue;
}
// Reverse to align with `PhysicalExpr`'s children:
children.reverse();
let children_intervals = children
.iter()
.map(|child| self.graph[*child].interval())
.collect::<Vec<_>>();
let node_interval = self.graph[node].interval();
let propagated_intervals = self.graph[node]
.expr
.propagate_constraints(node_interval, &children_intervals)?;
if let Some(propagated_intervals) = propagated_intervals {
for (child, interval) in children.into_iter().zip(propagated_intervals) {
self.graph[child].interval = interval;
}
} else {
// The constraint is infeasible, report:
return Ok(PropagationResult::Infeasible);
}
}
Ok(PropagationResult::Success)
}
/// Returns the interval associated with the node at the given `index`.
pub fn get_interval(&self, index: usize) -> Interval {
self.graph[NodeIndex::new(index)].interval.clone()
}
}
/// This is a subfunction of the `propagate_arithmetic` function that propagates to the right child.
fn propagate_right(
left: &Interval,
parent: &Interval,
right: &Interval,
op: &Operator,
inverse_op: &Operator,
) -> Result<Option<Interval>> {
match op {
Operator::Minus => apply_operator(op, left, parent),
Operator::Plus => apply_operator(inverse_op, parent, left),
Operator::Divide => apply_operator(op, left, parent),
Operator::Multiply => apply_operator(inverse_op, parent, left),
_ => internal_err!("Interval arithmetic does not support the operator {}", op),
}?
.intersect(right)
}
/// During the propagation of [`Interval`] values on an [`ExprIntervalGraph`],
/// if there exists a `timestamp - timestamp` operation, the result would be
/// of type `Duration`. However, we may encounter a situation where a time interval
/// is involved in an arithmetic operation with a `Duration` type. This function
/// offers special handling for such cases, where the time interval resides on
/// the left side of the operation.
fn propagate_time_interval_at_left(
left_child: &Interval,
right_child: &Interval,
parent: &Interval,
op: &Operator,
inverse_op: &Operator,
) -> Result<Option<(Interval, Interval)>> {
// We check if the child's time interval(s) has a non-zero month or day field(s).
// If so, we return it as is without propagating. Otherwise, we first convert
// the time intervals to the `Duration` type, then propagate, and then convert
// the bounds to time intervals again.
let result = if let Some(duration) = convert_interval_type_to_duration(left_child) {
match apply_operator(inverse_op, parent, right_child)?.intersect(duration)? {
Some(value) => {
let left = convert_duration_type_to_interval(&value);
let right = propagate_right(&value, parent, right_child, op, inverse_op)?;
match (left, right) {
(Some(left), Some(right)) => Some((left, right)),
_ => None,
}
}
None => None,
}
} else {
propagate_right(left_child, parent, right_child, op, inverse_op)?
.map(|right| (left_child.clone(), right))
};
Ok(result)
}
/// During the propagation of [`Interval`] values on an [`ExprIntervalGraph`],
/// if there exists a `timestamp - timestamp` operation, the result would be
/// of type `Duration`. However, we may encounter a situation where a time interval
/// is involved in an arithmetic operation with a `Duration` type. This function
/// offers special handling for such cases, where the time interval resides on
/// the right side of the operation.
fn propagate_time_interval_at_right(
left_child: &Interval,
right_child: &Interval,
parent: &Interval,
op: &Operator,
inverse_op: &Operator,
) -> Result<Option<(Interval, Interval)>> {
// We check if the child's time interval(s) has a non-zero month or day field(s).
// If so, we return it as is without propagating. Otherwise, we first convert
// the time intervals to the `Duration` type, then propagate, and then convert
// the bounds to time intervals again.
let result = if let Some(duration) = convert_interval_type_to_duration(right_child) {
match apply_operator(inverse_op, parent, &duration)?.intersect(left_child)? {
Some(value) => {
propagate_right(left_child, parent, &duration, op, inverse_op)?
.and_then(|right| convert_duration_type_to_interval(&right))
.map(|right| (value, right))
}
None => None,
}
} else {
apply_operator(inverse_op, parent, right_child)?
.intersect(left_child)?
.map(|value| (value, right_child.clone()))
};
Ok(result)
}
fn reverse_tuple<T, U>((first, second): (T, U)) -> (U, T) {
(second, first)
}
#[cfg(test)]
mod tests {
use super::*;
use crate::expressions::{BinaryExpr, Column};
use crate::intervals::test_utils::gen_conjunctive_numerical_expr;
use arrow::datatypes::TimeUnit;
use arrow_buffer::{IntervalDayTime, IntervalMonthDayNano};
use arrow_schema::Field;
use datafusion_common::ScalarValue;
use itertools::Itertools;
use rand::rngs::StdRng;
use rand::{Rng, SeedableRng};
use rstest::*;
#[allow(clippy::too_many_arguments)]
fn experiment(
expr: Arc<dyn PhysicalExpr>,
exprs_with_interval: (Arc<dyn PhysicalExpr>, Arc<dyn PhysicalExpr>),
left_interval: Interval,
right_interval: Interval,
left_expected: Interval,
right_expected: Interval,
result: PropagationResult,
schema: &Schema,
) -> Result<()> {
let col_stats = vec![
(Arc::clone(&exprs_with_interval.0), left_interval),
(Arc::clone(&exprs_with_interval.1), right_interval),
];
let expected = vec![
(Arc::clone(&exprs_with_interval.0), left_expected),
(Arc::clone(&exprs_with_interval.1), right_expected),
];
let mut graph = ExprIntervalGraph::try_new(expr, schema)?;
let expr_indexes = graph.gather_node_indices(
&col_stats.iter().map(|(e, _)| Arc::clone(e)).collect_vec(),
);
let mut col_stat_nodes = col_stats
.iter()
.zip(expr_indexes.iter())
.map(|((_, interval), (_, index))| (*index, interval.clone()))
.collect_vec();
let expected_nodes = expected
.iter()
.zip(expr_indexes.iter())
.map(|((_, interval), (_, index))| (*index, interval.clone()))
.collect_vec();
let exp_result =
graph.update_ranges(&mut col_stat_nodes[..], Interval::CERTAINLY_TRUE)?;
assert_eq!(exp_result, result);
col_stat_nodes.iter().zip(expected_nodes.iter()).for_each(
|((_, calculated_interval_node), (_, expected))| {
// NOTE: These randomized tests only check for conservative containment,
// not openness/closedness of endpoints.
// Calculated bounds are relaxed by 1 to cover all strict and
// and non-strict comparison cases since we have only closed bounds.
let one = ScalarValue::new_one(&expected.data_type()).unwrap();
assert!(
calculated_interval_node.lower()
<= &expected.lower().add(&one).unwrap(),
"{}",
format!(
"Calculated {} must be less than or equal {}",
calculated_interval_node.lower(),
expected.lower()
)
);
assert!(
calculated_interval_node.upper()
>= &expected.upper().sub(&one).unwrap(),
"{}",
format!(
"Calculated {} must be greater than or equal {}",
calculated_interval_node.upper(),
expected.upper()
)
);
},
);
Ok(())
}
macro_rules! generate_cases {
($FUNC_NAME:ident, $TYPE:ty, $SCALAR:ident) => {
fn $FUNC_NAME<const ASC: bool>(
expr: Arc<dyn PhysicalExpr>,
left_col: Arc<dyn PhysicalExpr>,
right_col: Arc<dyn PhysicalExpr>,
seed: u64,
expr_left: $TYPE,
expr_right: $TYPE,
) -> Result<()> {
let mut r = StdRng::seed_from_u64(seed);
let (left_given, right_given, left_expected, right_expected) = if ASC {
let left = r.gen_range((0 as $TYPE)..(1000 as $TYPE));
let right = r.gen_range((0 as $TYPE)..(1000 as $TYPE));
(
(Some(left), None),
(Some(right), None),
(Some(<$TYPE>::max(left, right + expr_left)), None),
(Some(<$TYPE>::max(right, left + expr_right)), None),
)
} else {
let left = r.gen_range((0 as $TYPE)..(1000 as $TYPE));
let right = r.gen_range((0 as $TYPE)..(1000 as $TYPE));
(
(None, Some(left)),
(None, Some(right)),
(None, Some(<$TYPE>::min(left, right + expr_left))),
(None, Some(<$TYPE>::min(right, left + expr_right))),
)
};
experiment(
expr,
(left_col.clone(), right_col.clone()),
Interval::make(left_given.0, left_given.1).unwrap(),
Interval::make(right_given.0, right_given.1).unwrap(),
Interval::make(left_expected.0, left_expected.1).unwrap(),
Interval::make(right_expected.0, right_expected.1).unwrap(),
PropagationResult::Success,
&Schema::new(vec![
Field::new(
left_col.as_any().downcast_ref::<Column>().unwrap().name(),
DataType::$SCALAR,
true,
),
Field::new(
right_col.as_any().downcast_ref::<Column>().unwrap().name(),
DataType::$SCALAR,
true,
),
]),
)
}
};
}
generate_cases!(generate_case_i32, i32, Int32);
generate_cases!(generate_case_i64, i64, Int64);
generate_cases!(generate_case_f32, f32, Float32);
generate_cases!(generate_case_f64, f64, Float64);
#[test]
fn testing_not_possible() -> Result<()> {
let left_col = Arc::new(Column::new("left_watermark", 0));
let right_col = Arc::new(Column::new("right_watermark", 0));
// left_watermark > right_watermark + 5
let left_and_1 = Arc::new(BinaryExpr::new(
Arc::clone(&left_col) as Arc<dyn PhysicalExpr>,
Operator::Plus,
Arc::new(Literal::new(ScalarValue::Int32(Some(5)))),
));
let expr = Arc::new(BinaryExpr::new(
left_and_1,
Operator::Gt,
Arc::clone(&right_col) as Arc<dyn PhysicalExpr>,
));
experiment(
expr,
(
Arc::clone(&left_col) as Arc<dyn PhysicalExpr>,
Arc::clone(&right_col) as Arc<dyn PhysicalExpr>,
),
Interval::make(Some(10_i32), Some(20_i32))?,
Interval::make(Some(100), None)?,
Interval::make(Some(10), Some(20))?,
Interval::make(Some(100), None)?,
PropagationResult::Infeasible,
&Schema::new(vec![
Field::new(
left_col.as_any().downcast_ref::<Column>().unwrap().name(),
DataType::Int32,
true,
),
Field::new(
right_col.as_any().downcast_ref::<Column>().unwrap().name(),
DataType::Int32,
true,
),
]),
)
}
macro_rules! integer_float_case_1 {
($TEST_FUNC_NAME:ident, $GENERATE_CASE_FUNC_NAME:ident, $TYPE:ty, $SCALAR:ident) => {
#[rstest]
#[test]
fn $TEST_FUNC_NAME(
#[values(0, 1, 2, 3, 4, 12, 32, 314, 3124, 123, 125, 211, 215, 4123)]
seed: u64,
#[values(Operator::Gt, Operator::GtEq)] greater_op: Operator,
#[values(Operator::Lt, Operator::LtEq)] less_op: Operator,
) -> Result<()> {
let left_col = Arc::new(Column::new("left_watermark", 0));
let right_col = Arc::new(Column::new("right_watermark", 0));
// left_watermark + 1 > right_watermark + 11 AND left_watermark + 3 < right_watermark + 33
let expr = gen_conjunctive_numerical_expr(
left_col.clone(),
right_col.clone(),
(
Operator::Plus,
Operator::Plus,
Operator::Plus,
Operator::Plus,
),
ScalarValue::$SCALAR(Some(1 as $TYPE)),
ScalarValue::$SCALAR(Some(11 as $TYPE)),
ScalarValue::$SCALAR(Some(3 as $TYPE)),
ScalarValue::$SCALAR(Some(33 as $TYPE)),
(greater_op, less_op),
);
// l > r + 10 AND r > l - 30
let l_gt_r = 10 as $TYPE;
let r_gt_l = -30 as $TYPE;
$GENERATE_CASE_FUNC_NAME::<true>(
expr.clone(),
left_col.clone(),
right_col.clone(),
seed,
l_gt_r,
r_gt_l,
)?;
// Descending tests
// r < l - 10 AND l < r + 30
let r_lt_l = -l_gt_r;
let l_lt_r = -r_gt_l;
$GENERATE_CASE_FUNC_NAME::<false>(
expr, left_col, right_col, seed, l_lt_r, r_lt_l,
)
}
};
}
integer_float_case_1!(case_1_i32, generate_case_i32, i32, Int32);
integer_float_case_1!(case_1_i64, generate_case_i64, i64, Int64);
integer_float_case_1!(case_1_f64, generate_case_f64, f64, Float64);
integer_float_case_1!(case_1_f32, generate_case_f32, f32, Float32);
macro_rules! integer_float_case_2 {
($TEST_FUNC_NAME:ident, $GENERATE_CASE_FUNC_NAME:ident, $TYPE:ty, $SCALAR:ident) => {
#[rstest]
#[test]
fn $TEST_FUNC_NAME(
#[values(0, 1, 2, 3, 4, 12, 32, 314, 3124, 123, 125, 211, 215, 4123)]
seed: u64,
#[values(Operator::Gt, Operator::GtEq)] greater_op: Operator,
#[values(Operator::Lt, Operator::LtEq)] less_op: Operator,
) -> Result<()> {
let left_col = Arc::new(Column::new("left_watermark", 0));
let right_col = Arc::new(Column::new("right_watermark", 0));
// left_watermark - 1 > right_watermark + 5 AND left_watermark + 3 < right_watermark + 10
let expr = gen_conjunctive_numerical_expr(
left_col.clone(),
right_col.clone(),
(
Operator::Minus,
Operator::Plus,
Operator::Plus,
Operator::Plus,
),
ScalarValue::$SCALAR(Some(1 as $TYPE)),
ScalarValue::$SCALAR(Some(5 as $TYPE)),
ScalarValue::$SCALAR(Some(3 as $TYPE)),
ScalarValue::$SCALAR(Some(10 as $TYPE)),
(greater_op, less_op),
);
// l > r + 6 AND r > l - 7
let l_gt_r = 6 as $TYPE;
let r_gt_l = -7 as $TYPE;
$GENERATE_CASE_FUNC_NAME::<true>(
expr.clone(),
left_col.clone(),
right_col.clone(),
seed,
l_gt_r,
r_gt_l,
)?;
// Descending tests
// r < l - 6 AND l < r + 7
let r_lt_l = -l_gt_r;
let l_lt_r = -r_gt_l;
$GENERATE_CASE_FUNC_NAME::<false>(
expr, left_col, right_col, seed, l_lt_r, r_lt_l,
)
}
};
}
integer_float_case_2!(case_2_i32, generate_case_i32, i32, Int32);
integer_float_case_2!(case_2_i64, generate_case_i64, i64, Int64);
integer_float_case_2!(case_2_f64, generate_case_f64, f64, Float64);
integer_float_case_2!(case_2_f32, generate_case_f32, f32, Float32);
macro_rules! integer_float_case_3 {
($TEST_FUNC_NAME:ident, $GENERATE_CASE_FUNC_NAME:ident, $TYPE:ty, $SCALAR:ident) => {
#[rstest]
#[test]
fn $TEST_FUNC_NAME(
#[values(0, 1, 2, 3, 4, 12, 32, 314, 3124, 123, 125, 211, 215, 4123)]
seed: u64,
#[values(Operator::Gt, Operator::GtEq)] greater_op: Operator,
#[values(Operator::Lt, Operator::LtEq)] less_op: Operator,
) -> Result<()> {
let left_col = Arc::new(Column::new("left_watermark", 0));
let right_col = Arc::new(Column::new("right_watermark", 0));
// left_watermark - 1 > right_watermark + 5 AND left_watermark - 3 < right_watermark + 10
let expr = gen_conjunctive_numerical_expr(
left_col.clone(),
right_col.clone(),
(
Operator::Minus,
Operator::Plus,
Operator::Minus,
Operator::Plus,
),
ScalarValue::$SCALAR(Some(1 as $TYPE)),
ScalarValue::$SCALAR(Some(5 as $TYPE)),
ScalarValue::$SCALAR(Some(3 as $TYPE)),
ScalarValue::$SCALAR(Some(10 as $TYPE)),
(greater_op, less_op),
);
// l > r + 6 AND r > l - 13
let l_gt_r = 6 as $TYPE;
let r_gt_l = -13 as $TYPE;
$GENERATE_CASE_FUNC_NAME::<true>(
expr.clone(),
left_col.clone(),
right_col.clone(),
seed,
l_gt_r,
r_gt_l,
)?;
// Descending tests
// r < l - 6 AND l < r + 13
let r_lt_l = -l_gt_r;
let l_lt_r = -r_gt_l;
$GENERATE_CASE_FUNC_NAME::<false>(
expr, left_col, right_col, seed, l_lt_r, r_lt_l,
)
}
};
}
integer_float_case_3!(case_3_i32, generate_case_i32, i32, Int32);
integer_float_case_3!(case_3_i64, generate_case_i64, i64, Int64);
integer_float_case_3!(case_3_f64, generate_case_f64, f64, Float64);
integer_float_case_3!(case_3_f32, generate_case_f32, f32, Float32);
macro_rules! integer_float_case_4 {
($TEST_FUNC_NAME:ident, $GENERATE_CASE_FUNC_NAME:ident, $TYPE:ty, $SCALAR:ident) => {
#[rstest]
#[test]
fn $TEST_FUNC_NAME(
#[values(0, 1, 2, 3, 4, 12, 32, 314, 3124, 123, 125, 211, 215, 4123)]
seed: u64,
#[values(Operator::Gt, Operator::GtEq)] greater_op: Operator,
#[values(Operator::Lt, Operator::LtEq)] less_op: Operator,
) -> Result<()> {
let left_col = Arc::new(Column::new("left_watermark", 0));
let right_col = Arc::new(Column::new("right_watermark", 0));
// left_watermark - 10 > right_watermark - 5 AND left_watermark - 30 < right_watermark - 3
let expr = gen_conjunctive_numerical_expr(
left_col.clone(),
right_col.clone(),
(
Operator::Minus,
Operator::Minus,
Operator::Minus,
Operator::Plus,
),
ScalarValue::$SCALAR(Some(10 as $TYPE)),
ScalarValue::$SCALAR(Some(5 as $TYPE)),
ScalarValue::$SCALAR(Some(3 as $TYPE)),
ScalarValue::$SCALAR(Some(10 as $TYPE)),
(greater_op, less_op),
);
// l > r + 5 AND r > l - 13
let l_gt_r = 5 as $TYPE;
let r_gt_l = -13 as $TYPE;
$GENERATE_CASE_FUNC_NAME::<true>(
expr.clone(),
left_col.clone(),
right_col.clone(),
seed,
l_gt_r,
r_gt_l,
)?;
// Descending tests
// r < l - 5 AND l < r + 13
let r_lt_l = -l_gt_r;
let l_lt_r = -r_gt_l;
$GENERATE_CASE_FUNC_NAME::<false>(
expr, left_col, right_col, seed, l_lt_r, r_lt_l,
)
}
};
}
integer_float_case_4!(case_4_i32, generate_case_i32, i32, Int32);
integer_float_case_4!(case_4_i64, generate_case_i64, i64, Int64);
integer_float_case_4!(case_4_f64, generate_case_f64, f64, Float64);
integer_float_case_4!(case_4_f32, generate_case_f32, f32, Float32);
macro_rules! integer_float_case_5 {
($TEST_FUNC_NAME:ident, $GENERATE_CASE_FUNC_NAME:ident, $TYPE:ty, $SCALAR:ident) => {
#[rstest]
#[test]
fn $TEST_FUNC_NAME(
#[values(0, 1, 2, 3, 4, 12, 32, 314, 3124, 123, 125, 211, 215, 4123)]
seed: u64,
#[values(Operator::Gt, Operator::GtEq)] greater_op: Operator,
#[values(Operator::Lt, Operator::LtEq)] less_op: Operator,
) -> Result<()> {
let left_col = Arc::new(Column::new("left_watermark", 0));
let right_col = Arc::new(Column::new("right_watermark", 0));
// left_watermark - 10 > right_watermark - 5 AND left_watermark - 30 < right_watermark - 3
let expr = gen_conjunctive_numerical_expr(
left_col.clone(),
right_col.clone(),
(
Operator::Minus,
Operator::Minus,
Operator::Minus,
Operator::Minus,
),
ScalarValue::$SCALAR(Some(10 as $TYPE)),
ScalarValue::$SCALAR(Some(5 as $TYPE)),
ScalarValue::$SCALAR(Some(30 as $TYPE)),
ScalarValue::$SCALAR(Some(3 as $TYPE)),
(greater_op, less_op),
);
// l > r + 5 AND r > l - 27
let l_gt_r = 5 as $TYPE;
let r_gt_l = -27 as $TYPE;
$GENERATE_CASE_FUNC_NAME::<true>(
expr.clone(),
left_col.clone(),
right_col.clone(),
seed,
l_gt_r,
r_gt_l,
)?;
// Descending tests
// r < l - 5 AND l < r + 27
let r_lt_l = -l_gt_r;
let l_lt_r = -r_gt_l;
$GENERATE_CASE_FUNC_NAME::<false>(
expr, left_col, right_col, seed, l_lt_r, r_lt_l,
)
}
};
}
integer_float_case_5!(case_5_i32, generate_case_i32, i32, Int32);
integer_float_case_5!(case_5_i64, generate_case_i64, i64, Int64);
integer_float_case_5!(case_5_f64, generate_case_f64, f64, Float64);
integer_float_case_5!(case_5_f32, generate_case_f32, f32, Float32);
#[test]
fn test_gather_node_indices_dont_remove() -> Result<()> {
// Expression: a@0 + b@1 + 1 > a@0 - b@1, given a@0 + b@1.
// Do not remove a@0 or b@1, only remove edges since a@0 - b@1 also
// depends on leaf nodes a@0 and b@1.
let left_expr = Arc::new(BinaryExpr::new(
Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Plus,
Arc::new(Column::new("b", 1)),
)),
Operator::Plus,
Arc::new(Literal::new(ScalarValue::Int32(Some(1)))),
));
let right_expr = Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Minus,
Arc::new(Column::new("b", 1)),
));
let expr = Arc::new(BinaryExpr::new(left_expr, Operator::Gt, right_expr));
let mut graph = ExprIntervalGraph::try_new(
expr,
&Schema::new(vec![
Field::new("a", DataType::Int32, true),
Field::new("b", DataType::Int32, true),
]),
)
.unwrap();
// Define a test leaf node.
let leaf_node = Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Plus,
Arc::new(Column::new("b", 1)),
));
// Store the current node count.
let prev_node_count = graph.node_count();
// Gather the index of node in the expression graph that match the test leaf node.
graph.gather_node_indices(&[leaf_node]);
// Store the final node count.
let final_node_count = graph.node_count();
// Assert that the final node count is equal the previous node count.
// This means we did not remove any node.
assert_eq!(prev_node_count, final_node_count);
Ok(())
}
#[test]
fn test_gather_node_indices_remove() -> Result<()> {
// Expression: a@0 + b@1 + 1 > y@0 - z@1, given a@0 + b@1.
// We expect to remove two nodes since we do not need a@ and b@.
let left_expr = Arc::new(BinaryExpr::new(
Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Plus,
Arc::new(Column::new("b", 1)),
)),
Operator::Plus,
Arc::new(Literal::new(ScalarValue::Int32(Some(1)))),
));
let right_expr = Arc::new(BinaryExpr::new(
Arc::new(Column::new("y", 0)),
Operator::Minus,
Arc::new(Column::new("z", 1)),
));
let expr = Arc::new(BinaryExpr::new(left_expr, Operator::Gt, right_expr));
let mut graph = ExprIntervalGraph::try_new(
expr,
&Schema::new(vec![
Field::new("a", DataType::Int32, true),
Field::new("b", DataType::Int32, true),
Field::new("y", DataType::Int32, true),
Field::new("z", DataType::Int32, true),
]),
)
.unwrap();
// Define a test leaf node.
let leaf_node = Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Plus,
Arc::new(Column::new("b", 1)),
));
// Store the current node count.
let prev_node_count = graph.node_count();
// Gather the index of node in the expression graph that match the test leaf node.
graph.gather_node_indices(&[leaf_node]);
// Store the final node count.
let final_node_count = graph.node_count();
// Assert that the final node count is two less than the previous node
// count; i.e. that we did remove two nodes.
assert_eq!(prev_node_count, final_node_count + 2);
Ok(())
}
#[test]
fn test_gather_node_indices_remove_one() -> Result<()> {
// Expression: a@0 + b@1 + 1 > a@0 - z@1, given a@0 + b@1.
// We expect to remove one nodesince we still need a@ but not b@.
let left_expr = Arc::new(BinaryExpr::new(
Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Plus,
Arc::new(Column::new("b", 1)),
)),
Operator::Plus,
Arc::new(Literal::new(ScalarValue::Int32(Some(1)))),
));
let right_expr = Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Minus,
Arc::new(Column::new("z", 1)),
));
let expr = Arc::new(BinaryExpr::new(left_expr, Operator::Gt, right_expr));
let mut graph = ExprIntervalGraph::try_new(
expr,
&Schema::new(vec![
Field::new("a", DataType::Int32, true),
Field::new("b", DataType::Int32, true),
Field::new("z", DataType::Int32, true),
]),
)
.unwrap();
// Define a test leaf node.
let leaf_node = Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Plus,
Arc::new(Column::new("b", 1)),
));
// Store the current node count.
let prev_node_count = graph.node_count();
// Gather the index of node in the expression graph that match the test leaf node.
graph.gather_node_indices(&[leaf_node]);
// Store the final node count.
let final_node_count = graph.node_count();
// Assert that the final node count is one less than the previous node
// count; i.e. that we did remove two nodes.
assert_eq!(prev_node_count, final_node_count + 1);
Ok(())
}
#[test]
fn test_gather_node_indices_cannot_provide() -> Result<()> {
// Expression: a@0 + 1 + b@1 > y@0 - z@1 -> provide a@0 + b@1
// TODO: We expect nodes a@0 and b@1 to be pruned, and intervals to be provided from the a@0 + b@1 node.
// However, we do not have an exact node for a@0 + b@1 due to the binary tree structure of the expressions.
// Pruning and interval providing for BinaryExpr expressions are more challenging without exact matches.
// Currently, we only support exact matches for BinaryExprs, but we plan to extend support beyond exact matches in the future.
let left_expr = Arc::new(BinaryExpr::new(
Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Plus,
Arc::new(Literal::new(ScalarValue::Int32(Some(1)))),
)),
Operator::Plus,
Arc::new(Column::new("b", 1)),
));
let right_expr = Arc::new(BinaryExpr::new(
Arc::new(Column::new("y", 0)),
Operator::Minus,
Arc::new(Column::new("z", 1)),
));
let expr = Arc::new(BinaryExpr::new(left_expr, Operator::Gt, right_expr));
let mut graph = ExprIntervalGraph::try_new(
expr,
&Schema::new(vec![
Field::new("a", DataType::Int32, true),
Field::new("b", DataType::Int32, true),
Field::new("y", DataType::Int32, true),
Field::new("z", DataType::Int32, true),
]),
)
.unwrap();
// Define a test leaf node.
let leaf_node = Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Plus,
Arc::new(Column::new("b", 1)),
));
// Store the current node count.
let prev_node_count = graph.node_count();
// Gather the index of node in the expression graph that match the test leaf node.
graph.gather_node_indices(&[leaf_node]);
// Store the final node count.
let final_node_count = graph.node_count();
// Assert that the final node count is equal the previous node count (i.e., no node was pruned).
assert_eq!(prev_node_count, final_node_count);
Ok(())
}
#[test]
fn test_propagate_constraints_singleton_interval_at_right() -> Result<()> {
let expression = BinaryExpr::new(
Arc::new(Column::new("ts_column", 0)),
Operator::Plus,
Arc::new(Literal::new(ScalarValue::new_interval_mdn(0, 1, 321))),
);
let parent = Interval::try_new(
// 15.10.2020 - 10:11:12.000_000_321 AM
ScalarValue::TimestampNanosecond(Some(1_602_756_672_000_000_321), None),
// 16.10.2020 - 10:11:12.000_000_321 AM
ScalarValue::TimestampNanosecond(Some(1_602_843_072_000_000_321), None),
)?;
let left_child = Interval::try_new(
// 10.10.2020 - 10:11:12 AM
ScalarValue::TimestampNanosecond(Some(1_602_324_672_000_000_000), None),
// 20.10.2020 - 10:11:12 AM
ScalarValue::TimestampNanosecond(Some(1_603_188_672_000_000_000), None),
)?;
let right_child = Interval::try_new(
// 1 day 321 ns
ScalarValue::IntervalMonthDayNano(Some(IntervalMonthDayNano {
months: 0,
days: 1,
nanoseconds: 321,
})),
// 1 day 321 ns
ScalarValue::IntervalMonthDayNano(Some(IntervalMonthDayNano {
months: 0,
days: 1,
nanoseconds: 321,
})),
)?;
let children = vec![&left_child, &right_child];
let result = expression
.propagate_constraints(&parent, &children)?
.unwrap();
assert_eq!(
vec![
Interval::try_new(
// 14.10.2020 - 10:11:12 AM
ScalarValue::TimestampNanosecond(
Some(1_602_670_272_000_000_000),
None
),
// 15.10.2020 - 10:11:12 AM
ScalarValue::TimestampNanosecond(
Some(1_602_756_672_000_000_000),
None
),
)?,
Interval::try_new(
// 1 day 321 ns in Duration type
ScalarValue::IntervalMonthDayNano(Some(IntervalMonthDayNano {
months: 0,
days: 1,
nanoseconds: 321,
})),
// 1 day 321 ns in Duration type
ScalarValue::IntervalMonthDayNano(Some(IntervalMonthDayNano {
months: 0,
days: 1,
nanoseconds: 321,
})),
)?
],
result
);
Ok(())
}
#[test]
fn test_propagate_constraints_column_interval_at_left() -> Result<()> {
let expression = BinaryExpr::new(
Arc::new(Column::new("interval_column", 1)),
Operator::Plus,
Arc::new(Column::new("ts_column", 0)),
);
let parent = Interval::try_new(
// 15.10.2020 - 10:11:12 AM
ScalarValue::TimestampMillisecond(Some(1_602_756_672_000), None),
// 16.10.2020 - 10:11:12 AM
ScalarValue::TimestampMillisecond(Some(1_602_843_072_000), None),
)?;
let right_child = Interval::try_new(
// 10.10.2020 - 10:11:12 AM
ScalarValue::TimestampMillisecond(Some(1_602_324_672_000), None),
// 20.10.2020 - 10:11:12 AM
ScalarValue::TimestampMillisecond(Some(1_603_188_672_000), None),
)?;
let left_child = Interval::try_new(
// 2 days in millisecond
ScalarValue::IntervalDayTime(Some(IntervalDayTime {
days: 0,
milliseconds: 172_800_000,
})),
// 10 days in millisecond
ScalarValue::IntervalDayTime(Some(IntervalDayTime {
days: 0,
milliseconds: 864_000_000,
})),
)?;
let children = vec![&left_child, &right_child];
let result = expression
.propagate_constraints(&parent, &children)?
.unwrap();
assert_eq!(
vec![
Interval::try_new(
// 2 days in millisecond
ScalarValue::IntervalDayTime(Some(IntervalDayTime {
days: 0,
milliseconds: 172_800_000,
})),
// 6 days
ScalarValue::IntervalDayTime(Some(IntervalDayTime {
days: 0,
milliseconds: 518_400_000,
})),
)?,
Interval::try_new(
// 10.10.2020 - 10:11:12 AM
ScalarValue::TimestampMillisecond(Some(1_602_324_672_000), None),
// 14.10.2020 - 10:11:12 AM
ScalarValue::TimestampMillisecond(Some(1_602_670_272_000), None),
)?
],
result
);
Ok(())
}
#[test]
fn test_propagate_comparison() -> Result<()> {
// In the examples below:
// `left` is unbounded: [?, ?],
// `right` is known to be [1000,1000]
// so `left` < `right` results in no new knowledge of `right` but knowing that `left` is now < 1000:` [?, 999]
let left = Interval::make_unbounded(&DataType::Int64)?;
let right = Interval::make(Some(1000_i64), Some(1000_i64))?;
assert_eq!(
(Some((
Interval::make(None, Some(999_i64))?,
Interval::make(Some(1000_i64), Some(1000_i64))?,
))),
propagate_comparison(
&Operator::Lt,
&Interval::CERTAINLY_TRUE,
&left,
&right
)?
);
let left =
Interval::make_unbounded(&DataType::Timestamp(TimeUnit::Nanosecond, None))?;
let right = Interval::try_new(
ScalarValue::TimestampNanosecond(Some(1000), None),
ScalarValue::TimestampNanosecond(Some(1000), None),
)?;
assert_eq!(
(Some((
Interval::try_new(
ScalarValue::try_from(&DataType::Timestamp(
TimeUnit::Nanosecond,
None
))
.unwrap(),
ScalarValue::TimestampNanosecond(Some(999), None),
)?,
Interval::try_new(
ScalarValue::TimestampNanosecond(Some(1000), None),
ScalarValue::TimestampNanosecond(Some(1000), None),
)?
))),
propagate_comparison(
&Operator::Lt,
&Interval::CERTAINLY_TRUE,
&left,
&right
)?
);
let left = Interval::make_unbounded(&DataType::Timestamp(
TimeUnit::Nanosecond,
Some("+05:00".into()),
))?;
let right = Interval::try_new(
ScalarValue::TimestampNanosecond(Some(1000), Some("+05:00".into())),
ScalarValue::TimestampNanosecond(Some(1000), Some("+05:00".into())),
)?;
assert_eq!(
(Some((
Interval::try_new(
ScalarValue::try_from(&DataType::Timestamp(
TimeUnit::Nanosecond,
Some("+05:00".into()),
))
.unwrap(),
ScalarValue::TimestampNanosecond(Some(999), Some("+05:00".into())),
)?,
Interval::try_new(
ScalarValue::TimestampNanosecond(Some(1000), Some("+05:00".into())),
ScalarValue::TimestampNanosecond(Some(1000), Some("+05:00".into())),
)?
))),
propagate_comparison(
&Operator::Lt,
&Interval::CERTAINLY_TRUE,
&left,
&right
)?
);
Ok(())
}
#[test]
fn test_propagate_or() -> Result<()> {
let expr = Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::Or,
Arc::new(Column::new("b", 1)),
));
let parent = Interval::CERTAINLY_FALSE;
let children_set = vec![
vec![&Interval::CERTAINLY_FALSE, &Interval::UNCERTAIN],
vec![&Interval::UNCERTAIN, &Interval::CERTAINLY_FALSE],
vec![&Interval::CERTAINLY_FALSE, &Interval::CERTAINLY_FALSE],
vec![&Interval::UNCERTAIN, &Interval::UNCERTAIN],
];
for children in children_set {
assert_eq!(
expr.propagate_constraints(&parent, &children)?.unwrap(),
vec![Interval::CERTAINLY_FALSE, Interval::CERTAINLY_FALSE],
);
}
let parent = Interval::CERTAINLY_FALSE;
let children_set = vec![
vec![&Interval::CERTAINLY_TRUE, &Interval::UNCERTAIN],
vec![&Interval::UNCERTAIN, &Interval::CERTAINLY_TRUE],
];
for children in children_set {
assert_eq!(expr.propagate_constraints(&parent, &children)?, None,);
}
let parent = Interval::CERTAINLY_TRUE;
let children = vec![&Interval::CERTAINLY_FALSE, &Interval::UNCERTAIN];
assert_eq!(
expr.propagate_constraints(&parent, &children)?.unwrap(),
vec![Interval::CERTAINLY_FALSE, Interval::CERTAINLY_TRUE]
);
let parent = Interval::CERTAINLY_TRUE;
let children = vec![&Interval::UNCERTAIN, &Interval::UNCERTAIN];
assert_eq!(
expr.propagate_constraints(&parent, &children)?.unwrap(),
// Empty means unchanged intervals.
vec![]
);
Ok(())
}
#[test]
fn test_propagate_certainly_false_and() -> Result<()> {
let expr = Arc::new(BinaryExpr::new(
Arc::new(Column::new("a", 0)),
Operator::And,
Arc::new(Column::new("b", 1)),
));
let parent = Interval::CERTAINLY_FALSE;
let children_and_results_set = vec![
(
vec![&Interval::CERTAINLY_TRUE, &Interval::UNCERTAIN],
vec![Interval::CERTAINLY_TRUE, Interval::CERTAINLY_FALSE],
),
(
vec![&Interval::UNCERTAIN, &Interval::CERTAINLY_TRUE],
vec![Interval::CERTAINLY_FALSE, Interval::CERTAINLY_TRUE],
),
(
vec![&Interval::UNCERTAIN, &Interval::UNCERTAIN],
// Empty means unchanged intervals.
vec![],
),
(
vec![&Interval::CERTAINLY_FALSE, &Interval::UNCERTAIN],
vec![],
),
];
for (children, result) in children_and_results_set {
assert_eq!(
expr.propagate_constraints(&parent, &children)?.unwrap(),
result
);
}
Ok(())
}
}