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///! Calculate the value of PI using the Chudnovsky_algorithm.
///!  cargo run --example calc_pi --release

type FP = arpfloat::FP256;

fn main() {
    // https://en.wikipedia.org/wiki/Chudnovsky_algorithm
    let iterations = 5;

    // Constants:
    let c1 = FP::from_u64(10005).sqrt();
    let c2 = FP::from_u64(545140134);
    let c3 = FP::from_i64(-262537412640768000);
    let c16 = FP::from_u64(16);
    let c12 = FP::from_u64(12);

    // Initial state.
    let mut kc = FP::from_u64(6);
    let mut m = FP::from_u64(1);
    let mut l = FP::from_u64(13591409);
    let mut x = FP::from_u64(1);
    let mut s = FP::from_u64(13591409);

    for q in 1..iterations + 1 {
        let q3 = FP::from_u64(q * q * q);
        let k3 = kc * kc * kc;
        m = (k3 - (kc * c16)) * m / q3;
        l = l + c2;
        x = x * c3;
        s = s + (m * l / x);
        kc = kc + c12;
    }
    let pi = FP::from_u64(426880) * (c1 / s);
    println!("pi = {}", pi);
    assert_eq!(pi.as_f64(), std::f64::consts::PI);
}