pi_viete.rs

pi_viete.rs

fn calculate_pi_vieta(iterations: u32) -> f64 {
    if iterations == 0 {
        return 0.0; // Or handle as an error/special case
    }

    let mut current_sqrt_term = 0.0f64; // Represents the nested sqrt part (e.g., sqrt(2), sqrt(2+sqrt(2)))
    let mut pi_approximation = 2.0f64; // Initialize with the leading '2' in the formula

    for i in 0..iterations {
        if i == 0 {
            // First term: 2 / sqrt(2)
            current_sqrt_term = 2.0f64.sqrt();
        } else {
            // Subsequent terms: 2 / sqrt(2 + previous_sqrt_term)
            current_sqrt_term = (2.0f64 + current_sqrt_term).sqrt();
        }

        // Multiply the approximation by 2 / current_sqrt_term
        pi_approximation *= 2.0 / current_sqrt_term;
    }

    pi_approximation
}

fn main() {
    println!("std::f64::consts::PI\n{:.11}", std::f64::consts::PI);

    let iterations = 17; // Number of terms to calculate for the approximation
    let pi_approx = calculate_pi_vieta(iterations);

    println!(
        "Viète's formula with {} iterations:\n{:.11}",
        iterations, pi_approx
    );

    let iterations_high = 18;
    let pi_approx_high = calculate_pi_vieta(iterations_high);
    println!(
        "Viète's formula with {} iterations:\n{:.11}",
        iterations_high, pi_approx_high
    );

    let iterations_very_high = 19; // Beyond this, f64 precision limits might show
    let pi_approx_very_high = calculate_pi_vieta(iterations_very_high);
    println!(
        "Viète's formula with {} iterations:\n{:.11}",
        iterations_very_high, pi_approx_very_high
    );
}