dashu-int 0.4.1

A big integer library with good performance
Documentation 
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use dashu_int::{
    fast_div::ConstDivisor,
    ops::{DivRem, ExtendedGcd, Gcd},
    rand::UniformBits,
    IBig, UBig,
};
use rand_v08::{distributions::uniform::Uniform, prelude::*};

mod helper_macros;

#[test]
fn test_uniform_bits() {
    let mut rng = StdRng::seed_from_u64(1);

    let distr = UniformBits::new(0);
    let x: UBig = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert!(x.is_zero());
    let x: IBig = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert!(x.is_zero());

    let distr = UniformBits::new(2);
    let x: UBig = (&mut rng).sample_iter(&distr).take(1000).min().unwrap();
    assert_eq!(x, UBig::ZERO);
    let x: UBig = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert_eq!(x, UBig::from(3u8));
    let x: IBig = (&mut rng).sample_iter(&distr).take(1000).min().unwrap();
    assert_eq!(x, IBig::from(-3));
    let x: IBig = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert_eq!(x, IBig::from(3));

    let distr = UniformBits::new(200);
    let x: UBig = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert!(x < UBig::ONE << 200);
    let x: IBig = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert!(x < IBig::ONE << 200);
    let x: IBig = (&mut rng).sample_iter(&distr).take(1000).min().unwrap();
    assert!(x > IBig::NEG_ONE << 200);
}

#[test]
fn test_uniform_ubig() {
    let mut rng = StdRng::seed_from_u64(1);

    let distr = Uniform::from(ubig!(3)..ubig!(7));
    let x = (&mut rng).sample_iter(&distr).take(1000).min().unwrap();
    assert_eq!(x, ubig!(3));
    let x = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert_eq!(x, ubig!(6));

    let distr = Uniform::from(ubig!(3)..=ubig!(7));
    let x = (&mut rng).sample_iter(&distr).take(1000).min().unwrap();
    assert_eq!(x, ubig!(3));
    let x = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert_eq!(x, ubig!(7));

    let distr = Uniform::from(ubig!(0b100) << 128..ubig!(0b1000) << 128);
    let x = (&mut rng).sample_iter(&distr).take(1000).min().unwrap();
    assert!(x >= ubig!(0b100) << 128 && x < ubig!(0b101) << 128);
    let x = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert!(x >= ubig!(0b111) << 128 && x < ubig!(0b1000) << 128);
}

#[test]
fn test_uniform_ibig() {
    let mut rng = StdRng::seed_from_u64(1);

    let distr = Uniform::from(ibig!(-7)..ibig!(3));
    let x = (&mut rng).sample_iter(&distr).take(1000).min().unwrap();
    assert_eq!(x, ibig!(-7));
    let x = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert_eq!(x, ibig!(2));

    let distr = Uniform::from(ibig!(-7)..=ibig!(3));
    let x = (&mut rng).sample_iter(&distr).take(1000).min().unwrap();
    assert_eq!(x, ibig!(-7));
    let x = (&mut rng).sample_iter(&distr).take(1000).max().unwrap();
    assert_eq!(x, ibig!(3));
}

#[test]
fn test_random_arithmetic() {
    let mut rng = StdRng::seed_from_u64(3);
    let p = ubig!(1000000007);

    // 10^2 bits: 10^5 cases
    // ..to..
    // 10^6 bits: 10 cases
    for log_num_bits in 2..=6 {
        let num_bits = match 10usize.checked_pow(log_num_bits) {
            None => continue,
            Some(x) => x,
        };
        let num_cases = 10u32.pow(7 - log_num_bits);
        for i in 0..num_cases {
            let len_a = rng.gen_range(10..num_bits);
            let len_b = rng.gen_range(10..num_bits);
            let a = rng.gen_range(ubig!(100)..ubig!(1) << len_a);
            let b = rng.gen_range(ubig!(100)..ubig!(1) << len_b);
            let c = rng.sample(Uniform::new(ubig!(0), &a));

            let radix = rng.gen_range(2..=36);
            assert_eq!(UBig::from_str_radix(&a.in_radix(radix).to_string(), radix).unwrap(), a);

            assert_eq!((&a + &b) % &p, ((&a % &p) + (&b % &p)) % &p);
            assert_eq!(&a + &b - &a, b);
            assert_eq!((&a * &b) % &p, ((&a % &p) * (&b % &p)) % &p);
            assert_eq!((&a * &b + &c).div_rem(&a), (b.clone(), c.clone()));
            assert_eq!((&a + ubig!(1)) * (&a - ubig!(1)), a.sqr() - ubig!(1));

            // pow can be very slow when exponent is too large, test with lower frequency
            if log_num_bits <= 5 && i % 8 == 0 {
                assert_eq!((ubig!(5).pow(num_bits) + 1u8).ilog(&ubig!(25)), num_bits / 2);
            }

            // gcd is much slower than primitive operations, test with even lower frequency
            if i % 32 == 0 {
                let (g, ca, cb) = (&a).gcd_ext(&b);
                assert_eq!(g, (&a).gcd(&b));
                assert_eq!(&a % &g, ubig!(0));
                assert_eq!(&b % &g, ubig!(0));
                assert_eq!(a * ca + b * cb, g.into());
            }
        }
    }
}

#[test]
fn test_random_modular_arithmetic() {
    let mut rng = StdRng::seed_from_u64(3);
    let p = ConstDivisor::new(ubig!(1000000007));
    let one = p.reduce(ubig!(1));

    // 10^2 bits: 10^5 cases
    // ..to..
    // 10^6 bits: 10 cases
    for log_num_bits in 2..=6 {
        let num_bits = match 10usize.checked_pow(log_num_bits) {
            None => continue,
            Some(x) => x,
        };
        let num_cases = 10u32.pow(7 - log_num_bits);
        for _ in 0..num_cases {
            let len_a = rng.gen_range(10..num_bits);
            let len_b = rng.gen_range(10..num_bits);
            let a = p.reduce(rng.gen_range(ubig!(100)..ubig!(1) << len_a));
            let b = p.reduce(rng.gen_range(ubig!(100)..ubig!(1) << len_b));

            assert_eq!(&a + &b - &a, b);
            assert_eq!(&a * &b / &a, b);
            assert_eq!((&a + &one) * (&a - &one), a.sqr() - &one);
        }
    }
}