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::ops::*;

mod helper_macros;

#[test]
fn test_sqrt() {
    // some fixed cases
    let a = ubig!(10000);
    assert_eq!(a.sqrt(), ubig!(100));
    assert_eq!(a.sqrt_rem(), (ubig!(100), ubig!(0)));
    let a = ubig!(100000);
    assert_eq!(a.sqrt(), ubig!(316));
    assert_eq!(a.sqrt_rem(), (ubig!(316), ubig!(144)));
    let a = ubig!(1234567890123456789);
    assert_eq!(a.sqrt(), ubig!(1111111106));
    assert_eq!(a.sqrt_rem(), (ubig!(1111111106), ubig!(246913553)));
    let a = ubig!(12345679012345678987654320987654321);
    assert_eq!(a.sqrt(), ubig!(111111111111111111));
    assert_eq!(a.sqrt_rem(), (ubig!(111111111111111111), ubig!(0)));
    let a = ubig!(100788288067706660892852085821456193179743392153874910688885216801600345870807);
    assert_eq!(a.sqrt(), ubig!(317471712232297416216550966658362741242));
    assert_eq!(
        a.sqrt_rem(),
        (
            ubig!(317471712232297416216550966658362741242),
            ubig!(547939222817117722717438201919698168243)
        )
    );

    assert_eq!(ibig!(10000).sqrt(), ubig!(100));
    assert_eq!(ibig!(100000).sqrt(), ubig!(316));

    // sqrt on 2^i - 1
    for i in [10, 20, 50, 64, 100, 128, 200, 256, 512, 400, 512] {
        let a = (ubig!(1) << i) - ubig!(1);
        let s = (ubig!(1) << (i / 2)) - ubig!(1);
        assert_eq!(a.sqrt(), s);
        assert_eq!(a.sqrt_rem(), (s.clone(), s * 2u8), "failed when i = {}", i);
    }

    // sqrt on 3^(3+12*i)
    let sqrt3_cases = [
        (ubig!(5), ubig!(2)),             // sqrt(3^3)
        (ubig!(3787), ubig!(7538)),       // sqrt(3^15)
        (ubig!(2761448), ubig!(2428283)), // sqrt(3^27)
        (ubig!(2013095912), ubig!(2107864523)),
        (ubig!(1467546920229), ubig!(1934876898306)),
        (ubig!(1069841704847421), ubig!(1224877059345186)),
        (ubig!(779914602833770326), ubig!(501110532100715031)),
        (ubig!(568557745465818567888), ubig!(225657412133007072843)),
        (ubig!(414478596444581735990496), ubig!(553764985337871833514651)),
        (ubig!(302154896808100085537072070), ubig!(598857875470661932825826247)),
        (ubig!(220270919773104962356525539752), ubig!(186420045640482600067047651323)),
        (
            ubig!(160577500514593517557907118479516),
            ubig!(155515158234106646561085883459451),
        ),
        (
            ubig!(117060997875138674299714289371567517),
            ubig!(2066707243966299471754695247556498),
        ),
        (
            ubig!(85337467450976093564491716951872719899),
            ubig!(74283355028981034794886393634200214866),
        ),
        (
            ubig!(62211013771761572208514461657915212806688),
            ubig!(35437748659873332231051228234751469262203),
        ),
        (
            ubig!(45351829039614186140007042548620190136075759),
            ubig!(57415363151470492239180169175796859839103146),
        ),
        (
            ubig!(33061483369878741696065134017944118609199228772),
            ubig!(30190341552430022310094722410181632071126298123),
        ),
    ];
    for (i, (s, r)) in sqrt3_cases.into_iter().enumerate() {
        let e = 3 + 12 * i;
        let pow = ubig!(3).pow(e);
        assert_eq!(pow.sqrt(), s);
        assert_eq!(pow.sqrt_rem(), (s, r));
    }
}

#[test]
#[should_panic]
fn test_sqrt_negative_panic() {
    let _ = ibig!(-1).sqrt();
}

#[test]
fn test_sqrt_rem_perfect_square_trailing_zeros() {
    // Regression: a perfect square whose estimate has many trailing zero bits. `sqrt_rem` squares
    // the estimate's all-zero low half to verify the remainder, routing through the NTT sqr path
    // which previously panicked on the zero input (`la_bits == 0`). The shift is large enough that
    // the low half exceeds THRESHOLD_NTT (4000 words), forcing the NTT path. This is the
    // `dashu-float` `hypot(3,4)` crash, reached directly through the integer sqrt.
    let shift = 560_000usize;
    let s = ubig!(1) << shift;
    let n = &s * &s;
    assert_eq!(n.sqrt_rem(), (s, ubig!(0)));
}

#[test]
fn test_nth_root() {
    // the nth root of 0 is 0 (regression: it used to return 1 via the `bits <= n` shortcut)
    assert_eq!(ubig!(0).nth_root(1), ubig!(0));
    assert_eq!(ubig!(0).nth_root(3), ubig!(0));
    assert_eq!(ubig!(0).nth_root(5), ubig!(0));
    assert_eq!(ibig!(0).nth_root(3), ibig!(0));
    assert_eq!(ubig!(2).nth_root(1), ubig!(2));
    assert_eq!(ubig!(2).nth_root(2), ubig!(1));
    assert_eq!(ubig!(2).nth_root(3), ubig!(1));
    assert_eq!(ibig!(-2).nth_root(1), ibig!(-2));
    assert_eq!(ibig!(2).nth_root(2), ibig!(1));
    assert_eq!(ibig!(-2).nth_root(3), ibig!(-1));
    assert_eq!(ibig!(-32).nth_root(5), ibig!(-2));

    let test_cases = [
        (
            ubig!(123456789),
            [
                ubig!(11111),
                ubig!(497),
                ubig!(105),
                ubig!(41),
                ubig!(22),
                ubig!(14),
            ],
        ),
        (
            (ubig!(1) << 512) + ubig!(1),
            [
                ubig!(
                    115792089237316195423570985008687907853269984665640564039457584007913129639936
                ),
                ubig!(2375668978229576954621987151322942598255746237355560),
                ubig!(340282366920938463463374607431768211456),
                ubig!(6690699980388625489511488543534),
                ubig!(48740834812604276470692694),
                ubig!(10427830626922116451064),
            ],
        ),
    ];

    for (n, roots) in test_cases {
        for (i, root) in roots.into_iter().enumerate() {
            assert_eq!(n.nth_root(i + 2), root);
        }
    }

    // large order roots
    assert_eq!(ubig!(123456789).nth_root(26), ubig!(2));
    assert_eq!(ubig!(123456789).nth_root(27), ubig!(1));
    let n128 = (ubig!(1) << 128) + ubig!(1);
    assert_eq!(n128.nth_root(128), ubig!(2));
    assert_eq!(n128.nth_root(129), ubig!(1));
}

#[test]
#[should_panic]
fn test_zeroth_root_panic() {
    let _ = ubig!(2).nth_root(0);
}

#[test]
#[should_panic]
fn test_even_root_negative_panic() {
    let _ = ibig!(-1).nth_root(4);
}