Best Practices for Testing Floating-Point Calculations in Rust

Testing floating-point calculations can be quite challenging due to the imprecise nature of floating-point arithmetic. In Rust, a language that emphasizes safety and performance, understanding how to effectively test your floating-point code is crucial to ensure the reliability of your applications. This article explores some best practices for testing floating-point calculations in Rust.

Understanding Floating-Point Precision

Floating-point numbers are represented in a way that cannot perfectly represent all real numbers. This makes them susceptible to rounding errors. For example, repeated arithmetic operations on floating-point numbers can accumulate small errors, leading to significant discrepancies in expected outcomes.

Using the approx Crate

A common technique to handle precision issues in Rust is using the approx crate, which provides several functions for comparing floating-point numbers within a tolerance:

use approx::assert_relative_eq;

fn main() {
    let a = 1.0_f32 / 3.0;
    let b = (0.1_f32 + 0.1 + 0.1) / 3.0;
    assert_relative_eq!(a, b, epsilon = 1.0e-6);
}

Choosing the Right Tolerance

When comparing floating-point numbers, choosing the correct tolerance is vital. The tolerance should be tight enough to ensure accuracy but not so tight that minor arithmetic differences due to machine precision cause false negatives. A typical approach is to use a relative comparison which scales with the magnitude of the values being compared.

Testing Computational Functions

Functions that execute complex calculations can produce results sensitive to floating-point errors. Consider the following example where we compute a square root:

fn compute_sqrt(val: f64) -> f64 {
    val.sqrt()
}

#[cfg(test)]
mod tests {
    use super::*;
    use approx::assert_relative_eq;

    #[test]
    fn test_compute_sqrt() {
        let result = compute_sqrt(2.0);
        assert_relative_eq!(result, 1.4142135, epsilon = 1e-5);
    }
}

Edge Cases in Floating-Point Testing

Testing should cover edge cases such as NaN (Not a Number) and infinity. Rust provides methods to check these conditions:

fn handle_special_cases(val: f64) -> &'static str {
    if val.is_nan() {
        "Input is NaN"
    } else if val.is_infinite() {
        "Input is infinite"
    } else {
        "Input is finite"
    }
}

Your tests should verify that your functions appropriately handle these special cases:

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_nan() {
        assert_eq!(handle_special_cases(f64::NAN), "Input is NaN");
    }

    #[test]
    fn test_infinity() {
        assert_eq!(handle_special_cases(f64::INFINITY), "Input is infinite");
    }
}

Separation of Concerns in Tests

It’s good practice to divide your tests into small, manageable sections focusing on different aspects of the calculations being tested. By focusing on different components, you ensure that no part of your floating-point arithmetic is left unchecked.

Using Property-Based Testing

Property-based testing can be a powerful tool for testing floating-point arithmetic. Crates like proptest allow you to describe the properties your floating-point calculations should fulfill, and it will automatically generate test cases:

use proptest::prelude::*;

proptest! {
    #[test]
    fn test_sqrt_of_square(val in 0.0..100.0) {
        let square = val * val;
        prop_assert!(compute_sqrt(square).abs() - val < 1.0e-6);
    }
}

Conclusion

Testing floating-point calculations effectively in Rust requires understanding the underlying precision issues and rigorously applying methods suited to address these quirks. By using libraries, thoughtfully choosing tolerances, and covering edge cases, developers can assure the reliability of software that depends heavily on floating-point arithmetic.