datafusion_physical_expr::intervals::cp_solver

Function propagate_arithmetic

Source 
pub fn propagate_arithmetic(
    op: &Operator,
    parent: &Interval,
    left_child: &Interval,
    right_child: &Interval,
) -> Result<Option<(Interval, Interval)>>
Expand description

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].