dashu-int 0.6.0

Arbitrary-precision integer math library for Rust, balancing ergonomics and efficiency. Provides UBig and IBig (unsigned and signed), with small values inlined on the stack. Efficient arithmetic, modular arithmetic, and number theory (pow, ilog, gcd, gcd_ext); two's-complement bit operations; parsing and formatting in base 2-36; optional serde, rand, num-traits, rkyv, and zeroize.
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 as u32).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);
        }
    }
}