Chapter 5.5. Interval Analysis in Rust (TO ADD)

Overview

Interval analysis is a type of static analysis used to track the range (interval) of possible values that a variable can take during the execution of a program. By maintaining an upper and lower bound for each variable, the analysis helps optimize code by narrowing the values that a program may handle. In Rust, interval analysis is particularly important in verifying safety properties, such as ensuring that an array access is always within bounds or that certain calculations do not result in overflows.

Goals of Interval Analysis

Range detection: Identify the intervals of values a variable may assume at different points in the program.
Error prevention: Ensure safe memory accesses (e.g., avoiding out-of-bound accesses in arrays).
Optimization: Provide opportunities for compiler optimizations by deducing more precise value ranges.

Flow Sensitivity

Interval analysis in Rust can be flow-sensitive, meaning that it accounts for the different execution paths a program might take. This allows the analysis to track how intervals change as variables are assigned or modified during the execution flow, improving the precision of analysis.

Lattice-based Approach

In this approach, values of variables are represented in a lattice, where each element represents an interval. A lattice ensures that each combination of intervals has a defined result, and merging different paths of a program is done by taking the least upper bound (LUB) of intervals from each path.

For example, if a variable x can have an interval [0, 10] on one path and [5, 15] on another path, the merged interval would be [0, 15] because that represents the union of both possible value ranges.

Meet-over-all-paths (MOP) Approach

In the meet-over-all-paths (MOP) approach, the analysis is performed by considering every possible path through a program and merging the results into a final interval. This approach is path-sensitive but may be less scalable on large programs because it needs to account for all paths explicitly.

Example: Lattice-based Interval Analysis

Consider the following Rust function that updates the value of a variable x based on certain conditions:

#![allow(unused)]
fn main() {
fn example(x: i32, y: i32) -> i32 {
    if x > 0 {
        x + 5
    } else {
        y + 2
    }
}

}

The variable x can either increase by 5 if it’s positive or remain unchanged (using y) if it’s not. An interval analysis would consider two scenarios for x:

On the path where x > 0, x will take values from [x+5, ∞] if x is positive.
On the other path, y will determine the result, and the interval of y is tracked separately.

Thus, the final result interval merges these possibilities.

MIR Representation

Rust’s intermediate representation (MIR) is key to performing interval analysis effectively. Analyzing MIR allows the compiler to track variable assignments and conditions at a low level, increasing the precision of the analysis.

#![allow(unused)]
fn main() {
fn example(_1: i32, _2: i32) -> i32 {
    bb0: {
        switchInt(_1) -> [0: bb1, otherwise: bb2];
    }

    bb1: {
        _0 = _2 + const 2;
        return;
    }

    bb2: {
        _0 = _1 + const 5;
        return;
    }
}

}

In this MIR code, the interval analysis would track how _0 is assigned based on the conditions in different basic blocks, allowing for optimizations and safety checks.

Case Study: Array Bound Checking

Consider the case where interval analysis can be used to check array bounds. Rust guarantees memory safety through strict bounds checking, but interval analysis can help eliminate redundant checks or prevent unsafe accesses during compile-time.

#![allow(unused)]
fn main() {
fn get_element(arr: &[i32], index: usize) -> Option<i32> {
    if index < arr.len() {
        Some(arr[index])
    } else {
        None
    }
}

}

Using interval analysis, the compiler can infer the interval for index and ensure that it remains within bounds ([0, arr.len())). If an interval of index is known to always be within this range, the compiler could potentially eliminate the bounds check, optimizing the code.

Quick Usage Guide

Developers interested in interval analysis can explore tools or experimental Rust compiler flags for static analysis. To integrate interval analysis into a Rust project, the following steps are typical:

Define intervals for each variable.
Propagate intervals throughout the control flow of the function.
Merge intervals at control flow joins using a lattice or MOP-based approach.
Check safety properties, such as bounds checking, based on the computed intervals.

Key Steps of Interval Analysis Algorithm

Graph Construction: Build the control-flow graph (CFG) for the function.
Interval Propagation: Traverse the CFG and propagate intervals for variables through each basic block.
Merge Intervals: At each control-flow merge point, take the least upper bound of intervals.
Validation: Verify if the intervals meet safety properties like array bounds and valid arithmetic operations.

Rust Analysis Platform