crypto_bigint/uint/
div.rs

//! [`UInt`] division operations.

use super::UInt;
use crate::limb::Word;
use crate::{Integer, Limb, NonZero, Wrapping};
use core::ops::{Div, DivAssign, Rem, RemAssign};
use subtle::{Choice, CtOption};

impl<const LIMBS: usize> UInt<LIMBS> {
    /// Computes `self` / `rhs`, returns the quotient (q), remainder (r)
    /// and 1 for is_some or 0 for is_none. The results can be wrapped in [`CtOption`].
    /// NOTE: Use only if you need to access const fn. Otherwise use `div_rem` because
    /// the value for is_some needs to be checked before using `q` and `r`.
    ///
    /// This is variable only with respect to `rhs`.
    ///
    /// When used with a fixed `rhs`, this function is constant-time with respect
    /// to `self`.
    pub(crate) const fn ct_div_rem(&self, rhs: &Self) -> (Self, Self, u8) {
        let mb = rhs.bits_vartime();
        let mut bd = (LIMBS * Limb::BIT_SIZE) - mb;
        let mut rem = *self;
        let mut quo = Self::ZERO;
        let mut c = rhs.shl_vartime(bd);

        loop {
            let (mut r, borrow) = rem.sbb(&c, Limb::ZERO);
            rem = Self::ct_select(r, rem, borrow.0);
            r = quo.bitor(&Self::ONE);
            quo = Self::ct_select(r, quo, borrow.0);
            if bd == 0 {
                break;
            }
            bd -= 1;
            c = c.shr_vartime(1);
            quo = quo.shl_vartime(1);
        }

        let is_some = Limb(mb as Word).is_nonzero();
        quo = Self::ct_select(Self::ZERO, quo, is_some);
        (quo, rem, (is_some & 1) as u8)
    }

    /// Computes `self` % `rhs`, returns the remainder and
    /// and 1 for is_some or 0 for is_none. The results can be wrapped in [`CtOption`].
    /// NOTE: Use only if you need to access const fn. Otherwise use `reduce`
    /// This is variable only with respect to `rhs`.
    ///
    /// When used with a fixed `rhs`, this function is constant-time with respect
    /// to `self`.
    pub(crate) const fn ct_reduce(&self, rhs: &Self) -> (Self, u8) {
        let mb = rhs.bits_vartime();
        let mut bd = (LIMBS * Limb::BIT_SIZE) - mb;
        let mut rem = *self;
        let mut c = rhs.shl_vartime(bd);

        loop {
            let (r, borrow) = rem.sbb(&c, Limb::ZERO);
            rem = Self::ct_select(r, rem, borrow.0);
            if bd == 0 {
                break;
            }
            bd -= 1;
            c = c.shr_vartime(1);
        }

        let is_some = Limb(mb as Word).is_nonzero();
        (rem, (is_some & 1) as u8)
    }

    /// Computes `self` % 2^k. Faster than reduce since its a power of 2.
    /// Limited to 2^16-1 since UInt doesn't support higher.
    pub const fn reduce2k(&self, k: usize) -> Self {
        let highest = (LIMBS - 1) as u32;
        let index = k as u32 / (Limb::BIT_SIZE as u32);
        let res = Limb::ct_cmp(Limb::from_u32(index), Limb::from_u32(highest)) - 1;
        let le = Limb::is_nonzero(Limb(res as Word));
        let word = Limb::ct_select(Limb::from_u32(highest), Limb::from_u32(index), le).0 as usize;

        let base = k % Limb::BIT_SIZE;
        let mask = (1 << base) - 1;
        let mut out = *self;

        let outmask = Limb(out.limbs[word].0 & mask);

        out.limbs[word] = Limb::ct_select(out.limbs[word], outmask, le);

        let mut i = word + 1;
        while i < LIMBS {
            out.limbs[i] = Limb::ZERO;
            i += 1;
        }

        out
    }

    /// Computes self / rhs, returns the quotient, remainder
    /// if rhs != 0
    pub fn div_rem(&self, rhs: &Self) -> CtOption<(Self, Self)> {
        let (q, r, c) = self.ct_div_rem(rhs);
        CtOption::new((q, r), Choice::from(c))
    }

    /// Computes self % rhs, returns the remainder
    /// if rhs != 0
    pub fn reduce(&self, rhs: &Self) -> CtOption<Self> {
        let (r, c) = self.ct_reduce(rhs);
        CtOption::new(r, Choice::from(c))
    }

    /// Wrapped division is just normal division i.e. `self` / `rhs`
    /// There’s no way wrapping could ever happen.
    /// This function exists, so that all operations are accounted for in the wrapping operations.
    pub const fn wrapping_div(&self, rhs: &Self) -> Self {
        let (q, _, c) = self.ct_div_rem(rhs);
        assert!(c == 1, "divide by zero");
        q
    }

    /// Perform checked division, returning a [`CtOption`] which `is_some`
    /// only if the rhs != 0
    pub fn checked_div(&self, rhs: &Self) -> CtOption<Self> {
        let (q, _, c) = self.ct_div_rem(rhs);
        CtOption::new(q, Choice::from(c))
    }

    /// Wrapped (modular) remainder calculation is just `self` % `rhs`.
    /// There’s no way wrapping could ever happen.
    /// This function exists, so that all operations are accounted for in the wrapping operations.
    pub const fn wrapping_rem(&self, rhs: &Self) -> Self {
        let (r, c) = self.ct_reduce(rhs);
        assert!(c == 1, "modulo zero");
        r
    }

    /// Perform checked reduction, returning a [`CtOption`] which `is_some`
    /// only if the rhs != 0
    pub fn checked_rem(&self, rhs: &Self) -> CtOption<Self> {
        let (r, c) = self.ct_reduce(rhs);
        CtOption::new(r, Choice::from(c))
    }
}

impl<const LIMBS: usize> Div<&NonZero<UInt<LIMBS>>> for &UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    type Output = UInt<LIMBS>;

    fn div(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
        *self / *rhs
    }
}

impl<const LIMBS: usize> Div<&NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    type Output = UInt<LIMBS>;

    fn div(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
        self / *rhs
    }
}

impl<const LIMBS: usize> Div<NonZero<UInt<LIMBS>>> for &UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    type Output = UInt<LIMBS>;

    fn div(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
        *self / rhs
    }
}

impl<const LIMBS: usize> Div<NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    type Output = UInt<LIMBS>;

    fn div(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
        let (q, _, _) = self.ct_div_rem(&rhs);
        q
    }
}

impl<const LIMBS: usize> DivAssign<&NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    fn div_assign(&mut self, rhs: &NonZero<UInt<LIMBS>>) {
        let (q, _, _) = self.ct_div_rem(rhs);
        *self = q
    }
}

impl<const LIMBS: usize> DivAssign<NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    fn div_assign(&mut self, rhs: NonZero<UInt<LIMBS>>) {
        *self /= &rhs;
    }
}

impl<const LIMBS: usize> Div<NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn div(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
        Wrapping(self.0.wrapping_div(rhs.as_ref()))
    }
}

impl<const LIMBS: usize> Div<NonZero<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn div(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
        *self / rhs
    }
}

impl<const LIMBS: usize> Div<&NonZero<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn div(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
        *self / *rhs
    }
}

impl<const LIMBS: usize> Div<&NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn div(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
        self / *rhs
    }
}

impl<const LIMBS: usize> DivAssign<&NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    fn div_assign(&mut self, rhs: &NonZero<UInt<LIMBS>>) {
        *self = Wrapping(self.0.wrapping_div(rhs.as_ref()))
    }
}

impl<const LIMBS: usize> DivAssign<NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    fn div_assign(&mut self, rhs: NonZero<UInt<LIMBS>>) {
        *self /= &rhs;
    }
}

impl<const LIMBS: usize> Rem<&NonZero<UInt<LIMBS>>> for &UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    type Output = UInt<LIMBS>;

    fn rem(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
        *self % *rhs
    }
}

impl<const LIMBS: usize> Rem<&NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    type Output = UInt<LIMBS>;

    fn rem(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
        self % *rhs
    }
}

impl<const LIMBS: usize> Rem<NonZero<UInt<LIMBS>>> for &UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    type Output = UInt<LIMBS>;

    fn rem(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
        *self % rhs
    }
}

impl<const LIMBS: usize> Rem<NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    type Output = UInt<LIMBS>;

    fn rem(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
        let (r, _) = self.ct_reduce(&rhs);
        r
    }
}

impl<const LIMBS: usize> RemAssign<&NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    fn rem_assign(&mut self, rhs: &NonZero<UInt<LIMBS>>) {
        let (r, _) = self.ct_reduce(rhs);
        *self = r
    }
}

impl<const LIMBS: usize> RemAssign<NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
    UInt<LIMBS>: Integer,
{
    fn rem_assign(&mut self, rhs: NonZero<UInt<LIMBS>>) {
        *self %= &rhs;
    }
}

impl<const LIMBS: usize> Rem<NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn rem(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
        Wrapping(self.0.wrapping_rem(rhs.as_ref()))
    }
}

impl<const LIMBS: usize> Rem<NonZero<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn rem(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
        *self % rhs
    }
}

impl<const LIMBS: usize> Rem<&NonZero<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn rem(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
        *self % *rhs
    }
}

impl<const LIMBS: usize> Rem<&NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn rem(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
        self % *rhs
    }
}

impl<const LIMBS: usize> RemAssign<NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    fn rem_assign(&mut self, rhs: NonZero<UInt<LIMBS>>) {
        *self %= &rhs;
    }
}

impl<const LIMBS: usize> RemAssign<&NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    fn rem_assign(&mut self, rhs: &NonZero<UInt<LIMBS>>) {
        *self = Wrapping(self.0.wrapping_rem(rhs.as_ref()))
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::{limb::HI_BIT, Limb, U256};

    #[cfg(feature = "rand")]
    use {
        crate::{CheckedMul, Random},
        rand_chacha::ChaChaRng,
        rand_core::RngCore,
        rand_core::SeedableRng,
    };

    #[test]
    fn div_word() {
        for (n, d, e, ee) in &[
            (200u64, 2u64, 100u64, 0),
            (100u64, 25u64, 4u64, 0),
            (100u64, 10u64, 10u64, 0),
            (1024u64, 8u64, 128u64, 0),
            (27u64, 13u64, 2u64, 1u64),
            (26u64, 13u64, 2u64, 0u64),
            (14u64, 13u64, 1u64, 1u64),
            (13u64, 13u64, 1u64, 0u64),
            (12u64, 13u64, 0u64, 12u64),
            (1u64, 13u64, 0u64, 1u64),
        ] {
            let lhs = U256::from(*n);
            let rhs = U256::from(*d);
            let (q, r, is_some) = lhs.ct_div_rem(&rhs);
            assert_eq!(is_some, 1);
            assert_eq!(U256::from(*e), q);
            assert_eq!(U256::from(*ee), r);
        }
    }

    #[cfg(feature = "rand")]
    #[test]
    fn div() {
        let mut rng = ChaChaRng::from_seed([7u8; 32]);
        for _ in 0..25 {
            let num = U256::random(&mut rng).shr_vartime(128);
            let den = U256::random(&mut rng).shr_vartime(128);
            let n = num.checked_mul(&den);
            if n.is_some().unwrap_u8() == 1 {
                let (q, _, is_some) = n.unwrap().ct_div_rem(&den);
                assert_eq!(is_some, 1);
                assert_eq!(q, num);
            }
        }
    }

    #[test]
    fn div_max() {
        let mut a = U256::ZERO;
        let mut b = U256::ZERO;
        b.limbs[b.limbs.len() - 1] = Limb(Word::MAX);
        let q = a.wrapping_div(&b);
        assert_eq!(q, UInt::ZERO);
        a.limbs[a.limbs.len() - 1] = Limb(1 << (HI_BIT - 7));
        b.limbs[b.limbs.len() - 1] = Limb(0x82 << (HI_BIT - 7));
        let q = a.wrapping_div(&b);
        assert_eq!(q, UInt::ZERO);
    }

    #[test]
    fn div_zero() {
        let (q, r, is_some) = U256::ONE.ct_div_rem(&U256::ZERO);
        assert_eq!(is_some, 0);
        assert_eq!(q, U256::ZERO);
        assert_eq!(r, U256::ONE);
    }

    #[test]
    fn div_one() {
        let (q, r, is_some) = U256::from(10u8).ct_div_rem(&U256::ONE);
        assert_eq!(is_some, 1);
        assert_eq!(q, U256::from(10u8));
        assert_eq!(r, U256::ZERO);
    }

    #[test]
    fn reduce_one() {
        let (r, is_some) = U256::from(10u8).ct_reduce(&U256::ONE);
        assert_eq!(is_some, 1);
        assert_eq!(r, U256::ZERO);
    }

    #[test]
    fn reduce_zero() {
        let u = U256::from(10u8);
        let (r, is_some) = u.ct_reduce(&U256::ZERO);
        assert_eq!(is_some, 0);
        assert_eq!(r, u);
    }

    #[test]
    fn reduce_tests() {
        let (r, is_some) = U256::from(10u8).ct_reduce(&U256::from(2u8));
        assert_eq!(is_some, 1);
        assert_eq!(r, U256::ZERO);
        let (r, is_some) = U256::from(10u8).ct_reduce(&U256::from(3u8));
        assert_eq!(is_some, 1);
        assert_eq!(r, U256::ONE);
        let (r, is_some) = U256::from(10u8).ct_reduce(&U256::from(7u8));
        assert_eq!(is_some, 1);
        assert_eq!(r, U256::from(3u8));
    }

    #[test]
    fn reduce_max() {
        let mut a = U256::ZERO;
        let mut b = U256::ZERO;
        b.limbs[b.limbs.len() - 1] = Limb(Word::MAX);
        let r = a.wrapping_rem(&b);
        assert_eq!(r, UInt::ZERO);
        a.limbs[a.limbs.len() - 1] = Limb(1 << (HI_BIT - 7));
        b.limbs[b.limbs.len() - 1] = Limb(0x82 << (HI_BIT - 7));
        let r = a.wrapping_rem(&b);
        assert_eq!(r, a);
    }

    #[cfg(feature = "rand")]
    #[test]
    fn reduce2krand() {
        let mut rng = ChaChaRng::from_seed([7u8; 32]);
        for _ in 0..25 {
            let num = U256::random(&mut rng);
            let k = (rng.next_u32() % 256) as usize;
            let den = U256::ONE.shl_vartime(k);

            let a = num.reduce2k(k);
            let e = num.wrapping_rem(&den);
            assert_eq!(a, e);
        }
    }
}
crypto_bigint/uint/div.rs

crypto_bigint/uint/
div.rs
