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#![no_std]
#![feature(asm)]
pub mod reference {
    #[inline]
    /// calculate `a * b % m`
    ///
    /// ```
    /// use fast_modulo::reference::mulmod_u64;
    /// assert_eq!(mulmod_u64(3, 4, 5), 2);
    /// assert_eq!(mulmod_u64((1 << 63) - 1, (1 << 63) - 3, (1 << 63) + 1), 8);
    /// ```
    pub fn mulmod_u64(a: u64, b: u64, m: u64) -> u64 {
        let aa = a as u128;
        let bb = b as u128;
        let mm = m as u128;
        let rr = aa * bb % mm;
        rr as _
    }

    #[inline]
    /// calcurate `a % m`
    ///
    /// ```
    /// use fast_modulo::reference::mod_u128u64;
    /// assert_eq!(mod_u128u64(17, 3), 2);
    /// assert_eq!(mod_u128u64((1 << 127) - 1, (1 << 61) - 1), 31);
    /// ```
    pub fn mod_u128u64(a: u128, m: u64) -> u64 {
        let mm = m as u128;
        let rr = a % mm;
        rr as _
    }
}

#[inline]
/// calculate `a * b % m`
///
/// required `a < m && b < m`.
/// ```
/// use fast_modulo::mulmod_u64;
/// assert_eq!(mulmod_u64(3, 4, 5), 2);
/// assert_eq!(mulmod_u64((1 << 63) - 1, (1 << 63) - 3, (1 << 63) + 1), 8);
/// ```
pub fn mulmod_u64(a: u64, mut b: u64, m: u64) -> u64 {
    unsafe {
        asm!(
            "mul rdx",
            "div {}",
            in(reg) m,
            in("rax") a,
            inout("rdx") b,
        );
    }
    b
}

#[inline]
/// calcurate `a % m`
///
/// ```
/// use fast_modulo::mod_u128u64;
/// assert_eq!(mod_u128u64(17, 3), 2);
/// assert_eq!(mod_u128u64((1 << 127) - 1, (1 << 61) - 1), 31);
/// ```
pub fn mod_u128u64(a: u128, m: u64) -> u64 {
    let qb = 65 + m.leading_zeros() - a.leading_zeros();
    if qb > 64 {
        let s = qb - 64;
        let mask = (1 << s) - 1;
        let r = mod_u128u64_unchecked(a >> s, m) as u128;
        let na = (r << s) + (a & mask);
        mod_u128u64_unchecked(na, m)
    } else {
        mod_u128u64_unchecked(a, m)
    }
}

#[inline]
/// calcurate `a % m`
///
/// This function doesn't check quotient less than $`2^{64}`$.
/// required $`a < 2^{64}m`$
/// ```
/// use fast_modulo::mod_u128u64_unchecked;
/// assert_eq!(mod_u128u64_unchecked(17, 3), 2);
/// assert_eq!(mod_u128u64_unchecked((1 << 107) - 1, (1 << 61) - 1), 70368744177663);
/// ```
pub fn mod_u128u64_unchecked(a: u128, m: u64) -> u64 {
    let hi = (a >> 64) as u64;
    let lo = (a & 0xFFFFFFFFFFFFFFFF) as u64;
    let r;
    unsafe {
        asm!(
            "div {}",
            in(reg) m,
            in("rax") lo,
            inout("rdx") hi => r,
        );
    }
    r
}

#[cfg(test)]
mod tests {
    use crate::*;
    #[test]
    fn it_works() {
        assert_eq!(2 + 2, 4);
    }
    #[test]
    fn modulo_u64() {
        use rand::prelude::*;
        let mut rng = rand::thread_rng();
        for _ in 0..1_000_000 {
            let m = rng.gen();
            let a = rng.gen::<u64>() % m;
            let b = rng.gen::<u64>() % m;
            assert_eq!(reference::mulmod_u64(a, b, m), mulmod_u64(a, b, m));
        }
    }
    #[test]
    fn modulo_u128u64() {
        use rand::prelude::*;
        let mut rng = rand::thread_rng();
        for _ in 0..1_000_000 {
            let m = rng.gen();
            let a = rng.gen();
            assert_eq!(reference::mod_u128u64(a, m), mod_u128u64(a, m));
        }
    }
    #[test]
    fn modulo_u128u64_small_divisor() {
        use rand::prelude::*;
        let mut rng = rand::thread_rng();
        for _ in 0..1_000_000 {
            let m = rng.gen::<u32>().into();
            let a = rng.gen();
            assert_eq!(reference::mod_u128u64(a, m), mod_u128u64(a, m));
        }
    }
}